Random Jason Timeout Test 004

Average Error: 34.1 → 34.1

Time: 13.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = 3.043105375567236e+91
  2. c = -5.968297493912559e+121

Math

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

↓

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

C

double f(double a, double c) {
        double r11836 = c;
        double r11837 = cosh(r11836);
        double r11838 = a;
        double r11839 = log1p(r11838);
        double r11840 = fmod(r11837, r11839);
        return r11840;
}

↓

double f(double a, double c) {
        double r11841 = c;
        double r11842 = cosh(r11841);
        double r11843 = a;
        double r11844 = log1p(r11843);
        double r11845 = fmod(r11842, r11844);
        return r11845;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.1

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

3. Applied add-exp-log 34.1

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

5. Applied pow1 34.1

   \[\leadsto e^{\log \color{blue}{\left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{1}\right)}}\]

6. Applied log-pow 34.1

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

7. Applied exp-prod 34.1

   \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}}\]

8. Simplified 34.1

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

10. Applied add-cbrt-cube 34.1

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

11. Simplified 34.1

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

13. Applied *-un-lft-identity 34.1

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

14. Applied unpow-prod-down 34.1

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

15. Simplified 34.1

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

16. Simplified 34.1

    \[\leadsto 1 \cdot \color{blue}{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

17. Final simplification 34.1

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

Reproduce

herbie shell --seed 2020039 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))