Random Jason Timeout Test 004

Average Error: 34.3 → 33.8

Time: 34.9s

Precision: 64

• could not determine a ground truth for program body

  1. a = -8.084874607089052e-106
  2. c = -2.0501759922108544e+40

Math

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

↓

\[\left(\sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{8}} \cdot \left(e^{-c} + e^{c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{8}} \cdot \left(e^{-c} + e^{c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{8}} \cdot \left(e^{-c} + e^{c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

C

double f(double a, double c) {
        double r15719 = c;
        double r15720 = cosh(r15719);
        double r15721 = a;
        double r15722 = log1p(r15721);
        double r15723 = fmod(r15720, r15722);
        return r15723;
}

↓

double f(double a, double c) {
        double r15724 = 0.125;
        double r15725 = cbrt(r15724);
        double r15726 = c;
        double r15727 = -r15726;
        double r15728 = exp(r15727);
        double r15729 = exp(r15726);
        double r15730 = r15728 + r15729;
        double r15731 = r15725 * r15730;
        double r15732 = a;
        double r15733 = log1p(r15732);
        double r15734 = fmod(r15731, r15733);
        double r15735 = cbrt(r15734);
        double r15736 = r15735 * r15735;
        double r15737 = r15736 * r15735;
        return r15737;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.3

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

3. Applied add-cbrt-cube 34.3

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

4. Simplified 34.3

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

5. Taylor expanded around inf 34.3

   \[\leadsto \left(\left(\sqrt[3]{\color{blue}{\frac{1}{8} \cdot {\left(e^{c} + e^{-c}\right)}^{3}}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
6. Using strategy rm

7. Applied cbrt-prod 34.1

   \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\frac{1}{8}} \cdot \sqrt[3]{{\left(e^{c} + e^{-c}\right)}^{3}}\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

8. Simplified 34.1

   \[\leadsto \left(\left(\sqrt[3]{\frac{1}{8}} \cdot \color{blue}{\left(e^{-c} + e^{c}\right)}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
9. Using strategy rm

10. Applied add-cube-cbrt 33.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{8}} \cdot \left(e^{-c} + e^{c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{8}} \cdot \left(e^{-c} + e^{c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{8}} \cdot \left(e^{-c} + e^{c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

11. Final simplification 33.8

    \[\leadsto \left(\sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{8}} \cdot \left(e^{-c} + e^{c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{8}} \cdot \left(e^{-c} + e^{c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{8}} \cdot \left(e^{-c} + e^{c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))