Random Jason Timeout Test 004

Average Error: 33.9 → 33.9

Time: 36.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 2.8867912426112395e-62
  2. c = 1439059428709982.0

Math

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

↓

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

C

double f(double a, double c) {
        double r15576 = c;
        double r15577 = cosh(r15576);
        double r15578 = a;
        double r15579 = log1p(r15578);
        double r15580 = fmod(r15577, r15579);
        return r15580;
}

↓

double f(double a, double c) {
        double r15581 = c;
        double r15582 = cosh(r15581);
        double r15583 = a;
        double r15584 = log1p(r15583);
        double r15585 = fmod(r15582, r15584);
        double r15586 = log(r15585);
        double r15587 = cbrt(r15586);
        double r15588 = r15587 * r15587;
        double r15589 = r15588 * r15587;
        double r15590 = exp(r15589);
        return r15590;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.9

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

3. Applied add-exp-log 33.9

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

5. Applied add-cube-cbrt 33.9

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

6. Final simplification 33.9

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

Reproduce

herbie shell --seed 2019322 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))