Random Jason Timeout Test 006

Average Error: 33.6 → 33.6

Time: 19.5s

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 r19426 = a;
        double r19427 = expm1(r19426);
        double r19428 = sin(r19427);
        double r19429 = expm1(r19428);
        double r19430 = atan(r19426);
        double r19431 = atan2(r19429, r19430);
        double r19432 = fmod(r19431, r19426);
        double r19433 = fabs(r19432);
        return r19433;
}

↓

double f(double a) {
        double r19434 = a;
        double r19435 = expm1(r19434);
        double r19436 = cbrt(r19435);
        double r19437 = r19436 * r19436;
        double r19438 = r19437 * r19436;
        double r19439 = sin(r19438);
        double r19440 = expm1(r19439);
        double r19441 = atan(r19434);
        double r19442 = atan2(r19440, r19441);
        double r19443 = fmod(r19442, r19434);
        double r19444 = cbrt(r19443);
        double r19445 = r19444 * r19444;
        double r19446 = cbrt(r19437);
        double r19447 = cbrt(r19436);
        double r19448 = r19446 * r19447;
        double r19449 = r19437 * r19448;
        double r19450 = sin(r19449);
        double r19451 = expm1(r19450);
        double r19452 = atan2(r19451, r19441);
        double r19453 = fmod(r19452, r19434);
        double r19454 = cbrt(r19453);
        double r19455 = r19445 * r19454;
        double r19456 = fabs(r19455);
        return r19456;
}

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)))