Random Jason Timeout Test 004

Average Error: 34.2 → 34.2

Time: 20.0s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. a = 1.3858168798121923e-23
  2. c = 1.3481840315279074e+121

Math

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

↓

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

C

double f(double a, double c) {
        double r10129 = c;
        double r10130 = cosh(r10129);
        double r10131 = a;
        double r10132 = log1p(r10131);
        double r10133 = fmod(r10130, r10132);
        return r10133;
}

↓

double f(double a, double c) {
        double r10134 = c;
        double r10135 = cosh(r10134);
        double r10136 = a;
        double r10137 = log1p(r10136);
        double r10138 = fmod(r10135, r10137);
        double r10139 = cbrt(r10138);
        double r10140 = r10139 * r10139;
        double r10141 = r10140 * r10139;
        double r10142 = log(r10141);
        double r10143 = cbrt(r10142);
        double r10144 = log(r10138);
        double r10145 = cbrt(r10144);
        double r10146 = r10143 * r10145;
        double r10147 = r10146 * r10145;
        double r10148 = exp(r10147);
        return r10148;
}

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-exp-log 34.2

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

5. Applied add-cube-cbrt 34.2

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

7. Applied add-cube-cbrt 34.2

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

8. Final simplification 34.2

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))