Random Jason Timeout Test 004

Average Error: 34.5 → 34.2

Time: 49.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = 7.203729442536309e-206
  2. c = 1.6495200433389913e+108

Math

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

↓

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

C

double f(double a, double c) {
        double r944445 = c;
        double r944446 = cosh(r944445);
        double r944447 = a;
        double r944448 = log1p(r944447);
        double r944449 = fmod(r944446, r944448);
        return r944449;
}

↓

double f(double a, double c) {
        double r944450 = c;
        double r944451 = cosh(r944450);
        double r944452 = a;
        double r944453 = log1p(r944452);
        double r944454 = cbrt(r944453);
        double r944455 = r944454 * r944454;
        double r944456 = cbrt(r944454);
        double r944457 = cbrt(r944456);
        double r944458 = r944457 * r944457;
        double r944459 = r944458 * r944457;
        double r944460 = cbrt(r944459);
        double r944461 = r944460 * r944458;
        double r944462 = r944456 * r944456;
        double r944463 = r944461 * r944462;
        double r944464 = r944455 * r944463;
        double r944465 = fmod(r944451, r944464);
        return r944465;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.5

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

3. Applied add-cube-cbrt 34.2

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

5. Applied add-cube-cbrt 34.2

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

7. Applied add-cube-cbrt 34.2

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

9. Applied add-cube-cbrt 34.2

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

10. Final simplification 34.2

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

Reproduce

herbie shell --seed 2019158 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))