Random Jason Timeout Test 004

Average Error: 33.7 → 33.4

Time: 37.3s

Precision: 64

• could not determine a ground truth for program body

  1. a = 8.127274774152907e-69
  2. c = -8.077195036329744e+39

Math

\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

↓

\[e^{\log \left(\left(\cosh c\right) \bmod \left(\left(\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)}} \cdot \sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}}}\right) \cdot \sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)\right)}\]

C

double f(double a, double c) {
        double r21765 = c;
        double r21766 = cosh(r21765);
        double r21767 = a;
        double r21768 = log1p(r21767);
        double r21769 = fmod(r21766, r21768);
        return r21769;
}

↓

double f(double a, double c) {
        double r21770 = c;
        double r21771 = cosh(r21770);
        double r21772 = a;
        double r21773 = log1p(r21772);
        double r21774 = cbrt(r21773);
        double r21775 = cbrt(r21774);
        double r21776 = r21774 * r21774;
        double r21777 = cbrt(r21776);
        double r21778 = r21775 * r21777;
        double r21779 = cbrt(r21778);
        double r21780 = r21774 * r21779;
        double r21781 = r21780 * r21777;
        double r21782 = r21781 * r21774;
        double r21783 = fmod(r21771, r21782);
        double r21784 = log(r21783);
        double r21785 = exp(r21784);
        return r21785;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.7

   \[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
2. Using strategy rm

3. Applied add-cube-cbrt 33.4

   \[\leadsto \left(\left(\cosh c\right) \bmod \color{blue}{\left(\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)}\right)\]
4. Using strategy rm

5. Applied add-cube-cbrt 33.4

   \[\leadsto \left(\left(\cosh c\right) \bmod \left(\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}}}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)\right)\]

6. Applied cbrt-prod 33.4

   \[\leadsto \left(\left(\cosh c\right) \bmod \left(\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}} \cdot \sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)}}\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)\right)\]
7. Using strategy rm

8. Applied add-cube-cbrt 33.4

   \[\leadsto \left(\left(\cosh c\right) \bmod \left(\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \left(\sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}} \cdot \sqrt[3]{\sqrt[3]{\color{blue}{\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}}}}\right)\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)\right)\]

9. Applied cbrt-prod 33.4

   \[\leadsto \left(\left(\cosh c\right) \bmod \left(\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \left(\sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}} \cdot \sqrt[3]{\color{blue}{\sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}} \cdot \sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)}}}}\right)\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)\right)\]
10. Using strategy rm

11. Applied add-exp-log 33.4

    \[\leadsto \color{blue}{e^{\log \left(\left(\cosh c\right) \bmod \left(\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \left(\sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}} \cdot \sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)}}}\right)\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)\right)}}\]

12. Simplified 33.4

    \[\leadsto e^{\color{blue}{\log \left(\left(\cosh c\right) \bmod \left(\left(\sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}} \cdot \left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)}} \cdot \sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}}}\right)\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)\right)}}\]

13. Final simplification 33.4

    \[\leadsto e^{\log \left(\left(\cosh c\right) \bmod \left(\left(\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)}} \cdot \sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}}}\right) \cdot \sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)\right)}\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))