Random Jason Timeout Test 004

Average Error: 34.8 → 34.5

Time: 18.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = -2.840126302710892e-249
  2. c = -5.1406143375706616e+203

Math

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

↓

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

C

double f(double a, double c) {
        double r13724 = c;
        double r13725 = cosh(r13724);
        double r13726 = a;
        double r13727 = log1p(r13726);
        double r13728 = fmod(r13725, r13727);
        return r13728;
}

↓

double f(double a, double c) {
        double r13729 = c;
        double r13730 = cosh(r13729);
        double r13731 = a;
        double r13732 = log1p(r13731);
        double r13733 = cbrt(r13732);
        double r13734 = r13733 * r13733;
        double r13735 = cbrt(r13734);
        double r13736 = cbrt(r13733);
        double r13737 = r13735 * r13736;
        double r13738 = r13734 * r13737;
        double r13739 = fmod(r13730, r13738);
        double r13740 = sqrt(r13739);
        double r13741 = r13740 * r13740;
        return r13741;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.8

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

3. Applied add-cube-cbrt 34.5

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

5. Applied add-cube-cbrt 34.5

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

6. Applied cbrt-prod 34.5

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

8. Applied add-sqr-sqrt 34.5

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

9. Final simplification 34.5

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))