Random Jason Timeout Test 004

Average Error: 34.8 → 34.8

Time: 34.3s

Precision: 64

• could not determine a ground truth for program body

  1. a = -4.499027040135842e-161
  2. c = 6.80656641367954e+59

Math

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

↓

\[e^{\sqrt[3]{{\left(\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{2}} \cdot \sqrt[3]{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{3}}}\]

C

double f(double a, double c) {
        double r16116 = c;
        double r16117 = cosh(r16116);
        double r16118 = a;
        double r16119 = log1p(r16118);
        double r16120 = fmod(r16117, r16119);
        return r16120;
}

↓

double f(double a, double c) {
        double r16121 = c;
        double r16122 = cosh(r16121);
        double r16123 = a;
        double r16124 = log1p(r16123);
        double r16125 = fmod(r16122, r16124);
        double r16126 = log(r16125);
        double r16127 = 2.0;
        double r16128 = pow(r16126, r16127);
        double r16129 = cbrt(r16128);
        double r16130 = cbrt(r16126);
        double r16131 = r16130 * r16130;
        double r16132 = r16131 * r16130;
        double r16133 = cbrt(r16132);
        double r16134 = r16129 * r16133;
        double r16135 = 3.0;
        double r16136 = pow(r16134, r16135);
        double r16137 = cbrt(r16136);
        double r16138 = exp(r16137);
        return r16138;
}

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-exp-log 34.8

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

5. Applied add-cbrt-cube 34.8

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

6. Simplified 34.8

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

8. Applied add-cube-cbrt 34.8

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

9. Simplified 34.8

   \[\leadsto e^{\sqrt[3]{{\left(\color{blue}{\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{2}}} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{3}}}\]
10. Using strategy rm

11. Applied add-cube-cbrt 34.8

    \[\leadsto e^{\sqrt[3]{{\left(\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{2}} \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{3}}}\]

12. Final simplification 34.8

    \[\leadsto e^{\sqrt[3]{{\left(\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{2}} \cdot \sqrt[3]{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{3}}}\]

Reproduce

herbie shell --seed 2019198 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))