Random Jason Timeout Test 012

Average Error: 61.1 → 60.2

Time: 26.3s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.0551194375545526e+290

Math

\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

↓

\[e^{\left(\sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}}\]

C

double f(double a) {
        double r4872 = a;
        double r4873 = cosh(r4872);
        double r4874 = r4872 * r4872;
        double r4875 = fmod(r4873, r4874);
        double r4876 = log1p(r4872);
        double r4877 = pow(r4875, r4876);
        double r4878 = acos(r4877);
        return r4878;
}

↓

double f(double a) {
        double r4879 = a;
        double r4880 = cosh(r4879);
        double r4881 = r4879 * r4879;
        double r4882 = fmod(r4880, r4881);
        double r4883 = exp(r4882);
        double r4884 = log(r4883);
        double r4885 = log1p(r4879);
        double r4886 = pow(r4884, r4885);
        double r4887 = acos(r4886);
        double r4888 = log(r4887);
        double r4889 = expm1(r4888);
        double r4890 = log1p(r4889);
        double r4891 = cbrt(r4890);
        double r4892 = r4891 * r4891;
        double r4893 = r4892 * r4891;
        double r4894 = exp(r4893);
        return r4894;
}

Error

Bits error versus a

Derivation

1. Initial program 61.1

   \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
2. Using strategy rm

3. Applied add-log-exp 60.2

   \[\leadsto \cos^{-1} \left({\color{blue}{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
4. Using strategy rm

5. Applied add-exp-log 60.2

   \[\leadsto \color{blue}{e^{\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}}\]
6. Using strategy rm

7. Applied log1p-expm1-u 60.2

   \[\leadsto e^{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}}\]
8. Using strategy rm

9. Applied add-cube-cbrt 60.2

   \[\leadsto e^{\color{blue}{\left(\sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}}}\]

10. Final simplification 60.2

    \[\leadsto e^{\left(\sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))