Random Jason Timeout Test 006

Average Error: 33.7 → 33.7

Time: 18.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = 2.182169612233222e+173

Math

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

↓

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

C

double f(double a) {
        double r8714 = a;
        double r8715 = expm1(r8714);
        double r8716 = sin(r8715);
        double r8717 = expm1(r8716);
        double r8718 = atan(r8714);
        double r8719 = atan2(r8717, r8718);
        double r8720 = fmod(r8719, r8714);
        double r8721 = fabs(r8720);
        return r8721;
}

↓

double f(double a) {
        double r8722 = a;
        double r8723 = expm1(r8722);
        double r8724 = sin(r8723);
        double r8725 = expm1(r8724);
        double r8726 = atan(r8722);
        double r8727 = atan2(r8725, r8726);
        double r8728 = 3.0;
        double r8729 = pow(r8727, r8728);
        double r8730 = cbrt(r8729);
        double r8731 = fmod(r8730, r8722);
        double r8732 = cbrt(r8731);
        double r8733 = r8732 * r8732;
        double r8734 = pow(r8729, r8728);
        double r8735 = cbrt(r8734);
        double r8736 = cbrt(r8735);
        double r8737 = fmod(r8736, r8722);
        double r8738 = cbrt(r8737);
        double r8739 = r8733 * r8738;
        double r8740 = fabs(r8739);
        return r8740;
}

Error

Bits error versus a

Derivation

1. Initial program 33.7

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

3. Applied add-cbrt-cube 33.8

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

4. Simplified 33.8

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

6. Applied add-cube-cbrt 33.8

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

8. Applied add-cbrt-cube 33.7

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

9. Simplified 33.7

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

10. Final simplification 33.7

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

Reproduce

herbie shell --seed 2019352 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  :precision binary64
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))