Random Jason Timeout Test 004

Average Error: 34.6 → 34.6

Time: 14.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.5176730339456097e-221
  2. c = 6.3839812888094375e+72

Math

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

↓

\[e^{\sqrt[3]{{\left(2 \cdot \sqrt[3]{{\left(\log \left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{1}{3}}\right)\right)}^{3}} + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}^{3}}}\]

C

double f(double a, double c) {
        double r9320 = c;
        double r9321 = cosh(r9320);
        double r9322 = a;
        double r9323 = log1p(r9322);
        double r9324 = fmod(r9321, r9323);
        return r9324;
}

↓

double f(double a, double c) {
        double r9325 = 2.0;
        double r9326 = c;
        double r9327 = cosh(r9326);
        double r9328 = a;
        double r9329 = log1p(r9328);
        double r9330 = fmod(r9327, r9329);
        double r9331 = 0.3333333333333333;
        double r9332 = pow(r9330, r9331);
        double r9333 = log(r9332);
        double r9334 = 3.0;
        double r9335 = pow(r9333, r9334);
        double r9336 = cbrt(r9335);
        double r9337 = r9325 * r9336;
        double r9338 = cbrt(r9330);
        double r9339 = log(r9338);
        double r9340 = r9337 + r9339;
        double r9341 = pow(r9340, r9334);
        double r9342 = cbrt(r9341);
        double r9343 = exp(r9342);
        return r9343;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.6

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

3. Applied add-exp-log 34.6

   \[\leadsto \color{blue}{e^{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]
4. Using strategy rm

5. Applied add-cbrt-cube 34.6

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

6. Simplified 34.6

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

8. Applied add-cube-cbrt 34.6

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

9. Applied log-prod 34.6

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

10. Simplified 34.6

    \[\leadsto e^{\sqrt[3]{{\left(\color{blue}{2 \cdot \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)} + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}^{3}}}\]
11. Using strategy rm

12. Applied add-cbrt-cube 34.6

    \[\leadsto e^{\sqrt[3]{{\left(2 \cdot \color{blue}{\sqrt[3]{\left(\log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right) \cdot \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}} + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}^{3}}}\]

13. Simplified 34.6

    \[\leadsto e^{\sqrt[3]{{\left(2 \cdot \sqrt[3]{\color{blue}{{\left(\log \left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{1}{3}}\right)\right)}^{3}}} + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}^{3}}}\]

14. Final simplification 34.6

    \[\leadsto e^{\sqrt[3]{{\left(2 \cdot \sqrt[3]{{\left(\log \left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{1}{3}}\right)\right)}^{3}} + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}^{3}}}\]

Reproduce

herbie shell --seed 2020089 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))