Random Jason Timeout Test 006

Average Error: 33.6 → 33.6

Time: 19.2s

Precision: 64

• could not determine a ground truth for program body

  1. a = 9.095231353254208e+232

Math

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

↓

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

C

double f(double a) {
        double r19393 = a;
        double r19394 = expm1(r19393);
        double r19395 = sin(r19394);
        double r19396 = expm1(r19395);
        double r19397 = atan(r19393);
        double r19398 = atan2(r19396, r19397);
        double r19399 = fmod(r19398, r19393);
        double r19400 = fabs(r19399);
        return r19400;
}

↓

double f(double a) {
        double r19401 = a;
        double r19402 = expm1(r19401);
        double r19403 = cbrt(r19402);
        double r19404 = r19403 * r19403;
        double r19405 = r19404 * r19403;
        double r19406 = sin(r19405);
        double r19407 = expm1(r19406);
        double r19408 = atan(r19401);
        double r19409 = atan2(r19407, r19408);
        double r19410 = fmod(r19409, r19401);
        double r19411 = cbrt(r19410);
        double r19412 = r19411 * r19411;
        double r19413 = cbrt(r19404);
        double r19414 = cbrt(r19403);
        double r19415 = r19413 * r19414;
        double r19416 = r19404 * r19415;
        double r19417 = sin(r19416);
        double r19418 = expm1(r19417);
        double r19419 = atan2(r19418, r19408);
        double r19420 = fmod(r19419, r19401);
        double r19421 = cbrt(r19420);
        double r19422 = r19412 * r19421;
        double r19423 = fabs(r19422);
        return r19423;
}

Error

Bits error versus a

Derivation

1. Initial program 33.6

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

3. Applied add-cube-cbrt 33.6

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

5. Applied add-cube-cbrt 33.6

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

7. Applied add-cube-cbrt 33.6

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

8. Applied cbrt-prod 33.6

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

9. Final simplification 33.6

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

Reproduce

herbie shell --seed 2020001 
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  :precision binary64
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))