Forward-over-reverse Hessian is NaN at `-O2`, correct at `-O0`/`-O1`/`-O3` and with `-fno-slp-vectorize`

[shadow-orange41]

Enzyme produces NaN at -O2 at the forward-over-reverse hessian, while the other flags -O0, -O1, -O3 produce the correct Hessian results. However, with -O2 -fno-slp-vectorize, it produces the correct results.

Minimal reproducible example:

#include <cmath>
#include <cstdio>
using namespace std;

void f(float *x, float *out) {
  float t3[5] = {0.6f, 0.6f, 0.6f, 0.6f, 0.6f};
  float s0 = exp(atan2(acos(exp(x[0])) - atan2(sin(x[0]), x[0]),
                       atan2(x[0], -2.0f) + x[0]));
  for (int i = 0; i < 5; i++) {
    float t0 = s0 + x[i];
    float t2 = s0 + cos(asinh(sqrt(s0) / x[i])) + t0;
    t3[i] = t3[i] * log(pow(s0, atan2(pow(s0, s0), pow(s0, t3[i])))) + t2;
    out[i] = acosh(t0) * t2 + t3[i];
  }
}

extern int enzyme_dup;
extern int enzyme_const;
template <typename RT, typename... T> RT __enzyme_autodiff(void *, T...);
template <typename RT, typename... T> RT __enzyme_fwddiff(void *, T...);

void grad(float *x, float *dx, float *y, float *dy) {
  __enzyme_autodiff<void>((void *)f, enzyme_dup, x, dx, enzyme_dup, y, dy);
}

int main() {
  float x[5] = {-0.9383832812309265f, -0.45288288593292236f,
                -0.24080416560173035f, -0.6241748332977295f,
                -0.4739071726799011f};
  float dx[5] = {1, 0, 0, 0, 0};             
  float y[5] = {0}, dy[5] = {1, 0, 0, 0, 0}; 
  float g[5] = {0}, h[5] = {0};

  __enzyme_fwddiff<void>((void *)grad, enzyme_dup, x, dx, enzyme_dup, g, h,
                         enzyme_const, y, enzyme_const, dy);

  for (int i = 0; i < 5; i++)
    printf("%.9g ", h[i]);
  printf("\n");
}

Build and run:

clang++ -std=c++17 -O2 repro.cpp -I $ENZYME_INC -fplugin=$ENZYME -o repro
./repro

Output:

-O0                      3.91245604 0 0 0 0
-O1                      3.91245651 0 0 0 0
-O2                      -nan       0 0 0 0     <-- wrong
-O3                      3.91245627 0 0 0 0
-O2 -fno-slp-vectorize   3.91245651 0 0 0 0

Environment: clang 16.0.6, Enzyme main at a9975371, x86-64 (AMD EPYC 9654, AVX-512).