Random Jason Timeout Test 004

Average Error: 34.8 → 34.8

Time: 35.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = -4.499027040135842e-161
  2. c = 6.80656641367954e+59

Math

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

↓

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

C

double f(double a, double c) {
        double r16482 = c;
        double r16483 = cosh(r16482);
        double r16484 = a;
        double r16485 = log1p(r16484);
        double r16486 = fmod(r16483, r16485);
        return r16486;
}

↓

double f(double a, double c) {
        double r16487 = c;
        double r16488 = cosh(r16487);
        double r16489 = a;
        double r16490 = log1p(r16489);
        double r16491 = fmod(r16488, r16490);
        double r16492 = log(r16491);
        double r16493 = 2.0;
        double r16494 = pow(r16492, r16493);
        double r16495 = cbrt(r16494);
        double r16496 = cbrt(r16492);
        double r16497 = r16496 * r16496;
        double r16498 = r16497 * r16496;
        double r16499 = cbrt(r16498);
        double r16500 = r16495 * r16499;
        double r16501 = 3.0;
        double r16502 = pow(r16500, r16501);
        double r16503 = cbrt(r16502);
        double r16504 = exp(r16503);
        return r16504;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.8

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

3. Applied add-exp-log 34.8

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

5. Applied add-cbrt-cube 34.8

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

6. Simplified 34.8

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

8. Applied add-cube-cbrt 34.8

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

9. Simplified 34.8

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

11. Applied add-cube-cbrt 34.8

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

12. Final simplification 34.8

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

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))