Random Jason Timeout Test 004

Average Error: 34.1 → 33.8

Time: 50.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = -7.071243489957898e-233
  2. c = -2.62121008631225e+105

Math

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

↓

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

C

double f(double a, double c) {
        double r885087 = c;
        double r885088 = cosh(r885087);
        double r885089 = a;
        double r885090 = log1p(r885089);
        double r885091 = fmod(r885088, r885090);
        return r885091;
}

↓

double f(double a, double c) {
        double r885092 = c;
        double r885093 = cosh(r885092);
        double r885094 = a;
        double r885095 = log1p(r885094);
        double r885096 = cbrt(r885095);
        double r885097 = r885096 * r885096;
        double r885098 = cbrt(r885097);
        double r885099 = cbrt(r885096);
        double r885100 = r885098 * r885099;
        double r885101 = cbrt(r885100);
        double r885102 = r885101 * r885099;
        double r885103 = r885102 * r885099;
        double r885104 = r885097 * r885103;
        double r885105 = fmod(r885093, r885104);
        double r885106 = log(r885105);
        double r885107 = exp(r885106);
        return r885107;
}

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-cube-cbrt 33.8

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

5. Applied add-cube-cbrt 33.8

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

7. Applied add-cube-cbrt 33.8

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

8. Applied cbrt-prod 33.8

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

10. Applied add-exp-log 33.8

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

11. Final simplification 33.8

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

Reproduce

herbie shell --seed 2019143 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))