Average Error: 33.5 → 33.5
Time: 56.4s
Precision: 64
\[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]
↓
\[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\sqrt[3]{\mathsf{expm1}\left(a\right)} \cdot \left(\sqrt[3]{\mathsf{expm1}\left(a\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(a\right)}\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]
\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|
↓
\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\sqrt[3]{\mathsf{expm1}\left(a\right)} \cdot \left(\sqrt[3]{\mathsf{expm1}\left(a\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(a\right)}\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|
double f(double a) {
        double r908481 = a;
        double r908482 = expm1(r908481);
        double r908483 = sin(r908482);
        double r908484 = expm1(r908483);
        double r908485 = atan(r908481);
        double r908486 = atan2(r908484, r908485);
        double r908487 = fmod(r908486, r908481);
        double r908488 = fabs(r908487);
        return r908488;
}
↓
double f(double a) {
        double r908489 = a;
        double r908490 = expm1(r908489);
        double r908491 = cbrt(r908490);
        double r908492 = r908491 * r908491;
        double r908493 = r908491 * r908492;
        double r908494 = sin(r908493);
        double r908495 = expm1(r908494);
        double r908496 = atan(r908489);
        double r908497 = atan2(r908495, r908496);
        double r908498 = fmod(r908497, r908489);
        double r908499 = fabs(r908498);
        return r908499;
}

Error

Bits error versus a

Derivation

  1. Initial program 33.5

    \[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]
  2. Using strategy rm

  3. Applied add-cube-cbrt33.5

    \[\leadsto \left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \color{blue}{\left(\left(\sqrt[3]{\mathsf{expm1}\left(a\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(a\right)}\right) \cdot \sqrt[3]{\mathsf{expm1}\left(a\right)}\right)}\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]

  4. Final simplification33.5

    \[\leadsto \left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\sqrt[3]{\mathsf{expm1}\left(a\right)} \cdot \left(\sqrt[3]{\mathsf{expm1}\left(a\right)} \cdot \sqrt[3]{\mathsf{expm1}\left(a\right)}\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]

Reproduce

herbie shell --seed 2019151 
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))