Random Jason Timeout Test 006

Average Error: 33.9 → 34.0

Time: 26.0s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. a = 1.3481840315279074e+121

Math

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

↓

\[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\left({\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}^{\left(4 + 1\right)} \cdot \sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right) \cdot \left({\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]

C

double f(double a) {
        double r21373 = a;
        double r21374 = expm1(r21373);
        double r21375 = sin(r21374);
        double r21376 = expm1(r21375);
        double r21377 = atan(r21373);
        double r21378 = atan2(r21376, r21377);
        double r21379 = fmod(r21378, r21373);
        double r21380 = fabs(r21379);
        return r21380;
}

↓

double f(double a) {
        double r21381 = a;
        double r21382 = expm1(r21381);
        double r21383 = sin(r21382);
        double r21384 = cbrt(r21383);
        double r21385 = cbrt(r21384);
        double r21386 = 4.0;
        double r21387 = 1.0;
        double r21388 = r21386 + r21387;
        double r21389 = pow(r21385, r21388);
        double r21390 = r21389 * r21385;
        double r21391 = 2.0;
        double r21392 = pow(r21385, r21391);
        double r21393 = r21392 * r21385;
        double r21394 = r21390 * r21393;
        double r21395 = expm1(r21394);
        double r21396 = atan(r21381);
        double r21397 = atan2(r21395, r21396);
        double r21398 = fmod(r21397, r21381);
        double r21399 = fabs(r21398);
        return r21399;
}

Error

Bits error versus a

Derivation

1. Initial program 33.9

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

3. Applied add-cube-cbrt 33.9

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

5. Applied add-cube-cbrt 33.9

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

6. Applied associate-*r* 33.9

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

7. Simplified 34.0

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

9. Applied add-cube-cbrt 34.0

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

10. Simplified 34.0

    \[\leadsto \left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\left({\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}^{\left(4 + 1\right)} \cdot \sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right) \cdot \left(\color{blue}{{\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}^{2}} \cdot \sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]

11. Final simplification 34.0

    \[\leadsto \left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\left({\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}^{\left(4 + 1\right)} \cdot \sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right) \cdot \left({\left(\sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{\sin \left(\mathsf{expm1}\left(a\right)\right)}}\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  :precision binary64
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))