Random Jason Timeout Test 004

Average Error: 33.9 → 33.9

Time: 1.0m

Precision: 64

• could not determine a ground truth for program body

  1. a = -1.3952531104493216e-235
  2. c = 1.242935524573972e+38

Math

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

↓

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

C

double f(double a, double c) {
        double r1241641 = c;
        double r1241642 = cosh(r1241641);
        double r1241643 = a;
        double r1241644 = log1p(r1241643);
        double r1241645 = fmod(r1241642, r1241644);
        return r1241645;
}

↓

double f(double a, double c) {
        double r1241646 = c;
        double r1241647 = cosh(r1241646);
        double r1241648 = a;
        double r1241649 = log1p(r1241648);
        double r1241650 = fmod(r1241647, r1241649);
        double r1241651 = log(r1241650);
        double r1241652 = exp(r1241651);
        double r1241653 = sqrt(r1241652);
        double r1241654 = r1241651 * r1241651;
        double r1241655 = r1241651 * r1241654;
        double r1241656 = cbrt(r1241655);
        double r1241657 = exp(r1241656);
        double r1241658 = sqrt(r1241657);
        double r1241659 = r1241653 * r1241658;
        return r1241659;
}

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-sqr-sqrt 33.9

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

7. Applied add-cbrt-cube 33.9

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

8. Final simplification 33.9

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

Reproduce

herbie shell --seed 2019165 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))