Random Jason Timeout Test 006

Average Error: 33.4 → 33.4

Time: 49.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.461159083214139e+105

Math

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

↓

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

C

double f(double a) {
        double r993850 = a;
        double r993851 = expm1(r993850);
        double r993852 = sin(r993851);
        double r993853 = expm1(r993852);
        double r993854 = atan(r993850);
        double r993855 = atan2(r993853, r993854);
        double r993856 = fmod(r993855, r993850);
        double r993857 = fabs(r993856);
        return r993857;
}

↓

double f(double a) {
        double r993858 = a;
        double r993859 = expm1(r993858);
        double r993860 = sin(r993859);
        double r993861 = expm1(r993860);
        double r993862 = atan(r993858);
        double r993863 = atan2(r993861, r993862);
        double r993864 = fmod(r993863, r993858);
        double r993865 = cbrt(r993864);
        double r993866 = r993865 * r993865;
        double r993867 = cbrt(r993860);
        double r993868 = r993867 * r993867;
        double r993869 = cbrt(r993868);
        double r993870 = cbrt(r993867);
        double r993871 = r993867 * r993870;
        double r993872 = r993869 * r993871;
        double r993873 = r993872 * r993867;
        double r993874 = expm1(r993873);
        double r993875 = atan2(r993874, r993862);
        double r993876 = fmod(r993875, r993858);
        double r993877 = cbrt(r993876);
        double r993878 = r993877 * r993877;
        double r993879 = r993877 * r993878;
        double r993880 = cbrt(r993879);
        double r993881 = r993866 * r993880;
        double r993882 = fabs(r993881);
        return r993882;
}

Error

Bits error versus a

Derivation

1. Initial program 33.4

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

3. Applied add-cube-cbrt 33.4

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

5. Applied add-cube-cbrt 33.3

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

7. Applied add-cube-cbrt 33.4

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

8. Applied cbrt-prod 33.3

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

9. Applied associate-*l* 33.4

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

11. Applied add-cube-cbrt 33.4

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

12. Final simplification 33.4

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

Reproduce

herbie shell --seed 2019162 
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))