Random Jason Timeout Test 006

Average Error: 33.5 → 33.6

Time: 41.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 7.953652505345186e+78

Math

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

↓

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

C

double f(double a) {
        double r24484 = a;
        double r24485 = expm1(r24484);
        double r24486 = sin(r24485);
        double r24487 = expm1(r24486);
        double r24488 = atan(r24484);
        double r24489 = atan2(r24487, r24488);
        double r24490 = fmod(r24489, r24484);
        double r24491 = fabs(r24490);
        return r24491;
}

↓

double f(double a) {
        double r24492 = a;
        double r24493 = expm1(r24492);
        double r24494 = sin(r24493);
        double r24495 = expm1(r24494);
        double r24496 = cbrt(r24495);
        double r24497 = r24496 * r24496;
        double r24498 = cbrt(r24496);
        double r24499 = r24498 * r24498;
        double r24500 = r24499 * r24498;
        double r24501 = r24497 * r24500;
        double r24502 = atan(r24492);
        double r24503 = atan2(r24501, r24502);
        double r24504 = fmod(r24503, r24492);
        double r24505 = fabs(r24504);
        return r24505;
}

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-cbrt 33.5

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

5. Applied add-cube-cbrt 33.6

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

6. Final simplification 33.6

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

Reproduce

herbie shell --seed 2019326 
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  :precision binary64
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))