Problem 525

Rolling Ellipse — C(1,4)+C(3,4) via adaptive Simpson.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 525
# Rolling Ellipse — C(1,4)+C(3,4) via adaptive Simpson.

extern {
    function sin(x: f64) -> f64
    function cos(x: f64) -> f64
    function atan2(y: f64, x: f64) -> f64
    function sqrt(x: f64) -> f64
    function hypot(x: f64, y: f64) -> f64
    function fabs(x: f64) -> f64
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
}

const PI: f64 = 3.14159265358979323846

function speed(t: f64, a: f64, b: f64) -> f64 {
    let s: f64 = sin(t)
    let c: f64 = cos(t)
    let denom: f64 = a * a * s * s + b * b * c * c
    let d: f64 = sqrt(denom)
    let theta: f64 = atan2(b * c, a * s) - PI
    let thetap: f64 = -a * b / denom
    let px: f64 = a * c
    let py: f64 = b * s
    let jx: f64 = -py
    let jy: f64 = px
    let ppx: f64 = -a * s
    let ppy: f64 = b * c
    let wx: f64 = thetap * jx + ppx
    let wy: f64 = thetap * jy + ppy
    let ct: f64 = cos(theta)
    let st: f64 = sin(theta)
    let rwx: f64 = wx * ct - wy * st
    let rwy: f64 = wx * st + wy * ct
    let dx: f64 = d - rwx
    let dy: f64 = -rwy
    return hypot(dx, dy)
}

function simpson(a0: f64, b0: f64, fa: f64, fm: f64, fb: f64) -> f64 {
    return (b0 - a0) * (fa + 4.0 * fm + fb) / 6.0
}

function adaptive_simpson(a: f64, b: f64, ea: f64, eb: f64, eps: f64) -> f64 {
    # iterative stack: a,b,fa,fm,fb,s,eps  (7 doubles per frame)
    let stack: ptr<f64> = calloc(7 * 10000, 8)
    if stack == null { return 0.0 }
    let fa: f64 = speed(a, ea, eb)
    let fb: f64 = speed(b, ea, eb)
    let m: f64 = (a + b) / 2.0
    let fm: f64 = speed(m, ea, eb)
    let whole: f64 = simpson(a, b, fa, fm, fb)
    let mut sp: i64 = 0
    stack[0] = a; stack[1] = b; stack[2] = fa; stack[3] = fm
    stack[4] = fb; stack[5] = whole; stack[6] = eps
    sp = 1
    let mut total: f64 = 0.0
    while sp > 0 {
        sp = sp - 1
        let base: i64 = sp * 7
        let a1: f64 = stack[base]
        let b1: f64 = stack[base + 1]
        let fa1: f64 = stack[base + 2]
        let fm1: f64 = stack[base + 3]
        let fb1: f64 = stack[base + 4]
        let s1: f64 = stack[base + 5]
        let eps1: f64 = stack[base + 6]
        let m1: f64 = (a1 + b1) / 2.0
        let lm: f64 = (a1 + m1) / 2.0
        let rm: f64 = (m1 + b1) / 2.0
        let flm: f64 = speed(lm, ea, eb)
        let frm: f64 = speed(rm, ea, eb)
        let left: f64 = simpson(a1, m1, fa1, flm, fm1)
        let right: f64 = simpson(m1, b1, fm1, frm, fb1)
        if fabs((left + right) - s1) <= 15.0 * eps1 {
            total = total + left + right + ((left + right) - s1) / 15.0
        } else {
            let e2: f64 = eps1 / 2.0
            let b2: i64 = sp * 7
            stack[b2] = m1; stack[b2 + 1] = b1; stack[b2 + 2] = fm1
            stack[b2 + 3] = frm; stack[b2 + 4] = fb1; stack[b2 + 5] = right; stack[b2 + 6] = e2
            sp = sp + 1
            let b3: i64 = sp * 7
            stack[b3] = a1; stack[b3 + 1] = m1; stack[b3 + 2] = fa1
            stack[b3 + 3] = flm; stack[b3 + 4] = fm1; stack[b3 + 5] = left; stack[b3 + 6] = e2
            sp = sp + 1
        }
    }
    free(stack)
    return total
}

function center_curve_length(a: f64, b: f64) -> f64 {
    let t0: f64 = -PI / 2.0
    let t1: f64 = t0 + 2.0 * PI
    return adaptive_simpson(t0, t1, a, b, 1.0e-12)
}

function main() -> i32 {
    let ans: f64 = center_curve_length(1.0, 4.0) + center_curve_length(3.0, 4.0)
    printf("%.8f\n", ans)
    return 0
}

Generated C

#include <stdint.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* Flow runtime helpers */
typedef struct flow_temp_node { struct flow_temp_node* next; } flow_temp_node;
static flow_temp_node* flow_temp_head = NULL;
static int flow_temp_atexit_set = 0;
__attribute__((unused)) static void flow_temp_free_all(void) {
    while (flow_temp_head) {
        flow_temp_node* n = flow_temp_head;
        flow_temp_head = n->next;
        free(n);
    }
}
__attribute__((unused)) static void* flow_temp_alloc(size_t nbytes) {
    flow_temp_node* node = (flow_temp_node*)malloc(sizeof(flow_temp_node) + nbytes);
    if (!node) return NULL;
    node->next = flow_temp_head;
    flow_temp_head = node;
    if (!flow_temp_atexit_set) {
        flow_temp_atexit_set = 1;
        atexit(flow_temp_free_all);
    }
    return (void*)(node + 1);
}
#ifndef FLOW_DIAG
#define FLOW_DIAG(msg) fprintf(stderr, "%s", (msg))
#endif
#ifndef FLOW_LOG
#define FLOW_LOG(fmt, ...) printf(fmt, __VA_ARGS__)
#endif
#ifndef FLOW_LOG_EMPTY
#define FLOW_LOG_EMPTY(fmt) printf(fmt)
#endif
static char* flow_strcat(const char* a, const char* b) {
    size_t la = strlen(a ? a : ""), lb = strlen(b ? b : "");
    char* r = (char*)flow_temp_alloc(la + lb + 1);
    if (!r) return NULL;
    if (la) memcpy(r, a, la);
    if (lb) memcpy(r + la, b, lb);
    r[la + lb] = '\0';
    return r;
}

#define __flow_in_arr(arr, val) __extension__ ({ \
    int _found = 0; \
    size_t _n = sizeof(arr)/sizeof((arr)[0]); \
    for (size_t _i = 0; _i < _n; _i++) { \
        if ((arr)[_i] == (val)) { _found = 1; break; } \
    } _found; })

/* Unified fault handler (MISRA #279) — override with -DFLOW_FAULT_HANDLER=fn */
#ifndef FLOW_FAULT_HANDLER
__attribute__((unused)) static inline void flow_fault_handler(const char* msg) {
    fprintf(stderr, "flow: %s\n", msg ? msg : "fault");
    abort();
#if defined(__GNUC__) || defined(__clang__)
    __builtin_unreachable();
#endif
}
#else
#define flow_fault_handler FLOW_FAULT_HANDLER
#endif
#define flow_div_by_zero_handler() flow_fault_handler("division by zero")
#define flow_shift_ub_handler() flow_fault_handler("invalid shift (amount out of range or left-shift of negative)")

#ifndef FLOW_CHECKED_DIV
#define FLOW_CHECKED_DIV(L, R) (((R) != 0) ? ((L) / (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_MOD
#define FLOW_CHECKED_MOD(L, R) (((R) != 0) ? ((L) % (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHL
#define FLOW_CHECKED_SHL(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull)) && ((L) >= 0)) ? ((L) << (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHR
#define FLOW_CHECKED_SHR(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull))) ? ((L) >> (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif

#include <math.h>

void* _ui_state = NULL;

static inline float i32_to_f32(int32_t v) { return (float)v; }

/* Host stub for @gpu kernels (device codegen replaces this). */
static inline int32_t gpu_thread_id(void) { return 0; }

double atan2(double y, double x);
double hypot(double x, double y);
double speed_f64_f64_f64(double t, double a, double b);
double simpson_f64_f64_f64_f64_f64(double a0, double b0, double fa, double fm, double fb);
double adaptive_simpson_f64_f64_f64_f64_f64(double a, double b, double ea, double eb, double eps);
double center_curve_length_f64_f64(double a, double b);
int32_t main(void);

static const double PI = 3.14159265358979323846;









double speed_f64_f64_f64(double t, double a, double b) {
    double s = sin(t);
    double c = cos(t);
    double denom = ((((a * a) * s) * s) + (((b * b) * c) * c));
    double d = sqrt(denom);
    double theta = (atan2((b * c), (a * s)) - PI);
    double thetap = (((-a) * b) / denom);
    double px = (a * c);
    double py = (b * s);
    double jx = (-py);
    double jy = px;
    double ppx = ((-a) * s);
    double ppy = (b * c);
    double wx = ((thetap * jx) + ppx);
    double wy = ((thetap * jy) + ppy);
    double ct = cos(theta);
    double st = sin(theta);
    double rwx = ((wx * ct) - (wy * st));
    double rwy = ((wx * st) + (wy * ct));
    double dx = (d - rwx);
    double dy = (-rwy);
    return hypot(dx, dy);
}

double simpson_f64_f64_f64_f64_f64(double a0, double b0, double fa, double fm, double fb) {
    return (((b0 - a0) * ((fa + (4.0 * fm)) + fb)) / 6.0);
}

double adaptive_simpson_f64_f64_f64_f64_f64(double a, double b, double ea, double eb, double eps) {
    double* stack = (double*)(calloc((7 * 10000), 8));
    if (stack == NULL) {
        return 0.0;
    }
    double fa = speed_f64_f64_f64(a, ea, eb);
    double fb = speed_f64_f64_f64(b, ea, eb);
    double m = ((a + b) / 2.0);
    double fm = speed_f64_f64_f64(m, ea, eb);
    double whole = simpson_f64_f64_f64_f64_f64(a, b, fa, fm, fb);
    int64_t sp = 0;
    stack[0] = a;
    stack[1] = b;
    stack[2] = fa;
    stack[3] = fm;
    stack[4] = fb;
    stack[5] = whole;
    stack[6] = eps;
    sp = 1;
    double total = 0.0;
    while (sp > 0) {
        sp = (sp - 1);
        int64_t base = (sp * 7);
        double a1 = stack[base];
        double b1 = stack[(base + 1)];
        double fa1 = stack[(base + 2)];
        double fm1 = stack[(base + 3)];
        double fb1 = stack[(base + 4)];
        double s1 = stack[(base + 5)];
        double eps1 = stack[(base + 6)];
        double m1 = ((a1 + b1) / 2.0);
        double lm = ((a1 + m1) / 2.0);
        double rm = ((m1 + b1) / 2.0);
        double flm = speed_f64_f64_f64(lm, ea, eb);
        double frm = speed_f64_f64_f64(rm, ea, eb);
        double left = simpson_f64_f64_f64_f64_f64(a1, m1, fa1, flm, fm1);
        double right = simpson_f64_f64_f64_f64_f64(m1, b1, fm1, frm, fb1);
        if (fabs(((left + right) - s1)) <= (15.0 * eps1)) {
            total = (((total + left) + right) + (((left + right) - s1) / 15.0));
        } else {
            double e2 = (eps1 / 2.0);
            int64_t b2 = (sp * 7);
            stack[b2] = m1;
            stack[(b2 + 1)] = b1;
            stack[(b2 + 2)] = fm1;
            stack[(b2 + 3)] = frm;
            stack[(b2 + 4)] = fb1;
            stack[(b2 + 5)] = right;
            stack[(b2 + 6)] = e2;
            sp = (sp + 1);
            int64_t b3 = (sp * 7);
            stack[b3] = a1;
            stack[(b3 + 1)] = m1;
            stack[(b3 + 2)] = fa1;
            stack[(b3 + 3)] = flm;
            stack[(b3 + 4)] = fm1;
            stack[(b3 + 5)] = left;
            stack[(b3 + 6)] = e2;
            sp = (sp + 1);
        }
    }
    free(stack);
    return total;
}

double center_curve_length_f64_f64(double a, double b) {
    double t0 = ((-PI) / 2.0);
    double t1 = (t0 + (2.0 * PI));
    return adaptive_simpson_f64_f64_f64_f64_f64(t0, t1, a, b, 1.0e-12);
}

int32_t main(void) {
    double ans = (center_curve_length_f64_f64(1.0, 4.0) + center_curve_length_f64_f64(3.0, 4.0));
    printf("%.8f\n", ans);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%.8f\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
  func.func private @sin(f64) -> f64
  func.func private @cos(f64) -> f64
  func.func private @atan2(f64, f64) -> f64
  func.func private @sqrt(f64) -> f64
  func.func private @hypot(f64, f64) -> f64
  func.func private @fabs(f64) -> f64
  func.func private @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  // Constant: PI
  llvm.mlir.global internal constant @PI(3.14159265358979323846 : f64) : f64
  func.func @speed(%arg0: f64, %arg1: f64, %arg2: f64) -> f64 {
    %0 = math.sin %arg0 : f64
    %1 = math.cos %arg0 : f64
    %2 = arith.mulf %arg1, %arg1 : f64
    %3 = arith.mulf %2, %0 : f64
    %4 = arith.mulf %3, %0 : f64
    %5 = arith.mulf %arg2, %arg2 : f64
    %6 = arith.mulf %5, %1 : f64
    %7 = arith.mulf %6, %1 : f64
    %8 = arith.addf %4, %7 : f64
    %9 = math.sqrt %8 : f64
    %11 = arith.mulf %arg2, %1 : f64
    %12 = arith.mulf %arg1, %0 : f64
    %10 = func.call @atan2(%11, %12) : (f64, f64) -> f64
    %13 = llvm.mlir.addressof @PI : !llvm.ptr
    %14 = llvm.load %13 : !llvm.ptr -> f64
    %15 = arith.subf %10, %14 : f64
    %16 = arith.negf %arg1 : f64
    %17 = arith.mulf %16, %arg2 : f64
    %18 = arith.divf %17, %8 : f64
    %19 = arith.mulf %arg1, %1 : f64
    %20 = arith.mulf %arg2, %0 : f64
    %21 = arith.negf %20 : f64
    %22 = arith.negf %arg1 : f64
    %23 = arith.mulf %22, %0 : f64
    %24 = arith.mulf %arg2, %1 : f64
    %25 = arith.mulf %18, %21 : f64
    %26 = arith.addf %25, %23 : f64
    %27 = arith.mulf %18, %19 : f64
    %28 = arith.addf %27, %24 : f64
    %29 = math.cos %15 : f64
    %30 = math.sin %15 : f64
    %31 = arith.mulf %26, %29 : f64
    %32 = arith.mulf %28, %30 : f64
    %33 = arith.subf %31, %32 : f64
    %34 = arith.mulf %26, %30 : f64
    %35 = arith.mulf %28, %29 : f64
    %36 = arith.addf %34, %35 : f64
    %37 = arith.subf %9, %33 : f64
    %38 = arith.negf %36 : f64
    %39 = func.call @hypot(%37, %38) : (f64, f64) -> f64
    func.return %39 : f64
  }
  func.func @simpson(%arg0: f64, %arg1: f64, %arg2: f64, %arg3: f64, %arg4: f64) -> f64 {
    %40 = arith.subf %arg1, %arg0 : f64
    %41 = arith.constant 4.0 : f32
    %43 = arith.extf %41 : f32 to f64
    %42 = arith.mulf %43, %arg3 : f64
    %44 = arith.addf %arg2, %42 : f64
    %45 = arith.addf %44, %arg4 : f64
    %46 = arith.mulf %40, %45 : f64
    %47 = arith.constant 6.0 : f32
    %49 = arith.extf %47 : f32 to f64
    %48 = arith.divf %46, %49 : f64
    func.return %48 : f64
  }
  func.func @adaptive_simpson(%arg0: f64, %arg1: f64, %arg2: f64, %arg3: f64, %arg4: f64) -> f64 {
    %51 = arith.constant 7 : i32
    %52 = arith.constant 10000 : i32
    %53 = arith.muli %51, %52 : i32
    %54 = arith.constant 8 : i32
    %55 = arith.extsi %53 : i32 to i64
    %56 = arith.extsi %54 : i32 to i64
    %50 = func.call @calloc(%55, %56) : (i64, i64) -> !llvm.ptr
    %57 = llvm.mlir.zero : !llvm.ptr
    %58 = llvm.icmp "eq" %50, %57 : !llvm.ptr
    cf.cond_br %58, ^bb0, ^bb1
    ^bb0:
      %59 = arith.constant 0.0 : f32
      %60 = arith.extf %59 : f32 to f64
      func.return %60 : f64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %61 = func.call @speed(%arg0, %arg2, %arg3) : (f64, f64, f64) -> f64
    %62 = func.call @speed(%arg1, %arg2, %arg3) : (f64, f64, f64) -> f64
    %63 = arith.addf %arg0, %arg1 : f64
    %64 = arith.constant 2.0 : f32
    %66 = arith.extf %64 : f32 to f64
    %65 = arith.divf %63, %66 : f64
    %67 = func.call @speed(%65, %arg2, %arg3) : (f64, f64, f64) -> f64
    %68 = func.call @simpson(%arg0, %arg1, %61, %67, %62) : (f64, f64, f64, f64, f64) -> f64
    %69 = arith.constant 0 : i32
    %70 = arith.extsi %69 : i32 to i64
    %71 = llvm.mlir.constant(1 : i64) : i64
    %72 = llvm.alloca %71 x i64 : (i64) -> !llvm.ptr
    llvm.store %70, %72 : i64, !llvm.ptr
    %73 = arith.constant 0 : i32
    %74 = arith.extsi %73 : i32 to i64
    %75 = llvm.getelementptr %50[%74] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %arg0, %75 : f64, !llvm.ptr
    %76 = arith.constant 1 : i32
    %77 = arith.extsi %76 : i32 to i64
    %78 = llvm.getelementptr %50[%77] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %arg1, %78 : f64, !llvm.ptr
    %79 = arith.constant 2 : i32
    %80 = arith.extsi %79 : i32 to i64
    %81 = llvm.getelementptr %50[%80] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %61, %81 : f64, !llvm.ptr
    %82 = arith.constant 3 : i32
    %83 = arith.extsi %82 : i32 to i64
    %84 = llvm.getelementptr %50[%83] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %67, %84 : f64, !llvm.ptr
    %85 = arith.constant 4 : i32
    %86 = arith.extsi %85 : i32 to i64
    %87 = llvm.getelementptr %50[%86] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %62, %87 : f64, !llvm.ptr
    %88 = arith.constant 5 : i32
    %89 = arith.extsi %88 : i32 to i64
    %90 = llvm.getelementptr %50[%89] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %68, %90 : f64, !llvm.ptr
    %91 = arith.constant 6 : i32
    %92 = arith.extsi %91 : i32 to i64
    %93 = llvm.getelementptr %50[%92] : (!llvm.ptr, i64) -> !llvm.ptr, f64
    llvm.store %arg4, %93 : f64, !llvm.ptr
    %94 = arith.constant 1 : i32
    %95 = arith.extsi %94 : i32 to i64
    llvm.store %95, %72 : i64, !llvm.ptr
    %96 = arith.constant 0.0 : f32
    %97 = arith.extf %96 : f32 to f64
    %98 = llvm.mlir.constant(1 : i64) : i64
    %99 = llvm.alloca %98 x f64 : (i64) -> !llvm.ptr
    llvm.store %97, %99 : f64, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %100 = llvm.load %72 : !llvm.ptr -> i64
    %101 = arith.constant 0 : i32
    %103 = arith.extsi %101 : i32 to i64
    %102 = arith.cmpi sgt, %100, %103 : i64
    cf.cond_br %102, ^bb4, ^bb5
    ^bb4:
      %104 = llvm.load %72 : !llvm.ptr -> i64
      %105 = arith.constant 1 : i32
      %107 = arith.extsi %105 : i32 to i64
      %106 = arith.subi %104, %107 : i64
      llvm.store %106, %72 : i64, !llvm.ptr
      %108 = llvm.load %72 : !llvm.ptr -> i64
      %109 = arith.constant 7 : i32
      %111 = arith.extsi %109 : i32 to i64
      %110 = arith.muli %108, %111 : i64
      %113 = llvm.getelementptr %50[%110] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %112 = llvm.load %113 : !llvm.ptr -> f64
      %115 = arith.constant 1 : i32
      %117 = arith.extsi %115 : i32 to i64
      %116 = arith.addi %110, %117 : i64
      %118 = llvm.getelementptr %50[%116] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %114 = llvm.load %118 : !llvm.ptr -> f64
      %120 = arith.constant 2 : i32
      %122 = arith.extsi %120 : i32 to i64
      %121 = arith.addi %110, %122 : i64
      %123 = llvm.getelementptr %50[%121] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %119 = llvm.load %123 : !llvm.ptr -> f64
      %125 = arith.constant 3 : i32
      %127 = arith.extsi %125 : i32 to i64
      %126 = arith.addi %110, %127 : i64
      %128 = llvm.getelementptr %50[%126] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %124 = llvm.load %128 : !llvm.ptr -> f64
      %130 = arith.constant 4 : i32
      %132 = arith.extsi %130 : i32 to i64
      %131 = arith.addi %110, %132 : i64
      %133 = llvm.getelementptr %50[%131] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %129 = llvm.load %133 : !llvm.ptr -> f64
      %135 = arith.constant 5 : i32
      %137 = arith.extsi %135 : i32 to i64
      %136 = arith.addi %110, %137 : i64
      %138 = llvm.getelementptr %50[%136] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %134 = llvm.load %138 : !llvm.ptr -> f64
      %140 = arith.constant 6 : i32
      %142 = arith.extsi %140 : i32 to i64
      %141 = arith.addi %110, %142 : i64
      %143 = llvm.getelementptr %50[%141] : (!llvm.ptr, i64) -> !llvm.ptr, f64
      %139 = llvm.load %143 : !llvm.ptr -> f64
      %144 = arith.addf %112, %114 : f64
      %145 = arith.constant 2.0 : f32
      %147 = arith.extf %145 : f32 to f64
      %146 = arith.divf %144, %147 : f64
      %148 = arith.addf %112, %146 : f64
      %149 = arith.constant 2.0 : f32
      %151 = arith.extf %149 : f32 to f64
      %150 = arith.divf %148, %151 : f64
      %152 = arith.addf %146, %114 : f64
      %153 = arith.constant 2.0 : f32
      %155 = arith.extf %153 : f32 to f64
      %154 = arith.divf %152, %155 : f64
      %156 = func.call @speed(%150, %arg2, %arg3) : (f64, f64, f64) -> f64
      %157 = func.call @speed(%154, %arg2, %arg3) : (f64, f64, f64) -> f64
      %158 = func.call @simpson(%112, %146, %119, %156, %124) : (f64, f64, f64, f64, f64) -> f64
      %159 = func.call @simpson(%146, %114, %124, %157, %129) : (f64, f64, f64, f64, f64) -> f64
      %160 = arith.addf %158, %159 : f64
      %161 = arith.subf %160, %134 : f64
      %162 = math.absf %161 : f64
      %163 = arith.constant 15.0 : f32
      %165 = arith.extf %163 : f32 to f64
      %164 = arith.mulf %165, %139 : f64
      %166 = arith.cmpf ole, %162, %164 : f64
      cf.cond_br %166, ^bb6, ^bb7
      ^bb6:
        %167 = llvm.load %99 : !llvm.ptr -> f64
        %168 = arith.addf %167, %158 : f64
        %169 = arith.addf %168, %159 : f64
        %170 = arith.addf %158, %159 : f64
        %171 = arith.subf %170, %134 : f64
        %172 = arith.constant 15.0 : f32
        %174 = arith.extf %172 : f32 to f64
        %173 = arith.divf %171, %174 : f64
        %175 = arith.addf %169, %173 : f64
        llvm.store %175, %99 : f64, !llvm.ptr
        cf.br ^bb8
      ^bb7:
        %176 = arith.constant 2.0 : f32
        %178 = arith.extf %176 : f32 to f64
        %177 = arith.divf %139, %178 : f64
        %179 = llvm.load %72 : !llvm.ptr -> i64
        %180 = arith.constant 7 : i32
        %182 = arith.extsi %180 : i32 to i64
        %181 = arith.muli %179, %182 : i64
        %183 = llvm.getelementptr %50[%181] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %146, %183 : f64, !llvm.ptr
        %184 = arith.constant 1 : i32
        %186 = arith.extsi %184 : i32 to i64
        %185 = arith.addi %181, %186 : i64
        %187 = llvm.getelementptr %50[%185] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %114, %187 : f64, !llvm.ptr
        %188 = arith.constant 2 : i32
        %190 = arith.extsi %188 : i32 to i64
        %189 = arith.addi %181, %190 : i64
        %191 = llvm.getelementptr %50[%189] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %124, %191 : f64, !llvm.ptr
        %192 = arith.constant 3 : i32
        %194 = arith.extsi %192 : i32 to i64
        %193 = arith.addi %181, %194 : i64
        %195 = llvm.getelementptr %50[%193] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %157, %195 : f64, !llvm.ptr
        %196 = arith.constant 4 : i32
        %198 = arith.extsi %196 : i32 to i64
        %197 = arith.addi %181, %198 : i64
        %199 = llvm.getelementptr %50[%197] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %129, %199 : f64, !llvm.ptr
        %200 = arith.constant 5 : i32
        %202 = arith.extsi %200 : i32 to i64
        %201 = arith.addi %181, %202 : i64
        %203 = llvm.getelementptr %50[%201] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %159, %203 : f64, !llvm.ptr
        %204 = arith.constant 6 : i32
        %206 = arith.extsi %204 : i32 to i64
        %205 = arith.addi %181, %206 : i64
        %207 = llvm.getelementptr %50[%205] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %177, %207 : f64, !llvm.ptr
        %208 = llvm.load %72 : !llvm.ptr -> i64
        %209 = arith.constant 1 : i32
        %211 = arith.extsi %209 : i32 to i64
        %210 = arith.addi %208, %211 : i64
        llvm.store %210, %72 : i64, !llvm.ptr
        %212 = llvm.load %72 : !llvm.ptr -> i64
        %213 = arith.constant 7 : i32
        %215 = arith.extsi %213 : i32 to i64
        %214 = arith.muli %212, %215 : i64
        %216 = llvm.getelementptr %50[%214] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %112, %216 : f64, !llvm.ptr
        %217 = arith.constant 1 : i32
        %219 = arith.extsi %217 : i32 to i64
        %218 = arith.addi %214, %219 : i64
        %220 = llvm.getelementptr %50[%218] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %146, %220 : f64, !llvm.ptr
        %221 = arith.constant 2 : i32
        %223 = arith.extsi %221 : i32 to i64
        %222 = arith.addi %214, %223 : i64
        %224 = llvm.getelementptr %50[%222] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %119, %224 : f64, !llvm.ptr
        %225 = arith.constant 3 : i32
        %227 = arith.extsi %225 : i32 to i64
        %226 = arith.addi %214, %227 : i64
        %228 = llvm.getelementptr %50[%226] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %156, %228 : f64, !llvm.ptr
        %229 = arith.constant 4 : i32
        %231 = arith.extsi %229 : i32 to i64
        %230 = arith.addi %214, %231 : i64
        %232 = llvm.getelementptr %50[%230] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %124, %232 : f64, !llvm.ptr
        %233 = arith.constant 5 : i32
        %235 = arith.extsi %233 : i32 to i64
        %234 = arith.addi %214, %235 : i64
        %236 = llvm.getelementptr %50[%234] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %158, %236 : f64, !llvm.ptr
        %237 = arith.constant 6 : i32
        %239 = arith.extsi %237 : i32 to i64
        %238 = arith.addi %214, %239 : i64
        %240 = llvm.getelementptr %50[%238] : (!llvm.ptr, i64) -> !llvm.ptr, f64
        llvm.store %177, %240 : f64, !llvm.ptr
        %241 = llvm.load %72 : !llvm.ptr -> i64
        %242 = arith.constant 1 : i32
        %244 = arith.extsi %242 : i32 to i64
        %243 = arith.addi %241, %244 : i64
        llvm.store %243, %72 : i64, !llvm.ptr
        cf.br ^bb8
      ^bb8:
      cf.br ^bb3
    ^bb5:
    func.call @free(%50) : (!llvm.ptr) -> ()
    %246 = llvm.load %99 : !llvm.ptr -> f64
    func.return %246 : f64
  }
  func.func @center_curve_length(%arg0: f64, %arg1: f64) -> f64 {
    %247 = llvm.mlir.addressof @PI : !llvm.ptr
    %248 = llvm.load %247 : !llvm.ptr -> f64
    %249 = arith.negf %248 : f64
    %250 = arith.constant 2.0 : f32
    %252 = arith.extf %250 : f32 to f64
    %251 = arith.divf %249, %252 : f64
    %253 = arith.constant 2.0 : f32
    %254 = llvm.mlir.addressof @PI : !llvm.ptr
    %255 = llvm.load %254 : !llvm.ptr -> f64
    %257 = arith.extf %253 : f32 to f64
    %256 = arith.mulf %257, %255 : f64
    %258 = arith.addf %251, %256 : f64
    %260 = arith.constant 0 : f32
    %261 = arith.extf %260 : f32 to f64
    %259 = func.call @adaptive_simpson(%251, %258, %arg0, %arg1, %261) : (f64, f64, f64, f64, f64) -> f64
    func.return %259 : f64
  }
  func.func @main() -> i32 {
    %263 = arith.constant 1.0 : f32
    %264 = arith.constant 4.0 : f32
    %265 = arith.extf %263 : f32 to f64
    %266 = arith.extf %264 : f32 to f64
    %262 = func.call @center_curve_length(%265, %266) : (f64, f64) -> f64
    %268 = arith.constant 3.0 : f32
    %269 = arith.constant 4.0 : f32
    %270 = arith.extf %268 : f32 to f64
    %271 = arith.extf %269 : f32 to f64
    %267 = func.call @center_curve_length(%270, %271) : (f64, f64) -> f64
    %272 = arith.addf %262, %267 : f64
    %273 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %274 = llvm.call @printf(%273, %272) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, f64) -> i32
    %275 = arith.constant 0 : i32
    func.return %275 : i32
  }
}