Random Jason Timeout Test 004

Average Error: 33.8 → 33.8

Time: 14.4s

Precision: 64

• could not determine a ground truth for program body

  1. a = -4.643259684384098e-199
  2. c = 217359335082.17374

Math

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

↓

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

C

double f(double a, double c) {
        double r10946 = c;
        double r10947 = cosh(r10946);
        double r10948 = a;
        double r10949 = log1p(r10948);
        double r10950 = fmod(r10947, r10949);
        return r10950;
}

↓

double f(double a, double c) {
        double r10951 = c;
        double r10952 = cosh(r10951);
        double r10953 = a;
        double r10954 = log1p(r10953);
        double r10955 = fmod(r10952, r10954);
        double r10956 = log(r10955);
        double r10957 = cbrt(r10956);
        double r10958 = exp(r10957);
        double r10959 = pow(r10958, r10957);
        double r10960 = pow(r10959, r10957);
        return r10960;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.8

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

3. Applied add-exp-log 33.8

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

5. Applied add-cube-cbrt 33.8

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

6. Applied exp-prod 33.8

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

8. Applied add-log-exp 33.8

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

9. Applied exp-to-pow 33.8

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

10. Applied pow-pow 33.8

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

12. Applied pow-unpow 33.8

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

13. Final simplification 33.8

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

Reproduce

herbie shell --seed 2020027 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))