Random Jason Timeout Test 004

Average Error: 34.2 → 33.9

Time: 49.1s

Precision: 64

• could not determine a ground truth for program body

  1. a = 5.0362447883134526e+148
  2. c = 1.0422426701817188e+213

Math

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

↓

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

C

double f(double a, double c) {
        double r968013 = c;
        double r968014 = cosh(r968013);
        double r968015 = a;
        double r968016 = log1p(r968015);
        double r968017 = fmod(r968014, r968016);
        return r968017;
}

↓

double f(double a, double c) {
        double r968018 = c;
        double r968019 = cosh(r968018);
        double r968020 = a;
        double r968021 = log1p(r968020);
        double r968022 = cbrt(r968021);
        double r968023 = r968022 * r968022;
        double r968024 = cbrt(r968022);
        double r968025 = cbrt(r968023);
        double r968026 = log(r968025);
        double r968027 = exp(r968026);
        double r968028 = r968024 * r968027;
        double r968029 = cbrt(r968028);
        double r968030 = r968029 * r968024;
        double r968031 = r968024 * r968030;
        double r968032 = r968023 * r968031;
        double r968033 = fmod(r968019, r968032);
        return r968033;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.2

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

3. Applied add-cube-cbrt 33.9

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

5. Applied add-cube-cbrt 33.9

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

7. Applied add-cube-cbrt 33.9

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

8. Applied cbrt-prod 33.9

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

10. Applied add-exp-log 33.9

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

11. Final simplification 33.9

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

Reproduce

herbie shell --seed 2019152 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))