Random Jason Timeout Test 012

Average Error: 61.2 → 60.2

Time: 38.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 3.0260304830237114e+184

Math

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

↓

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

C

double f(double a) {
        double r14710 = a;
        double r14711 = cosh(r14710);
        double r14712 = r14710 * r14710;
        double r14713 = fmod(r14711, r14712);
        double r14714 = log1p(r14710);
        double r14715 = pow(r14713, r14714);
        double r14716 = acos(r14715);
        return r14716;
}

↓

double f(double a) {
        double r14717 = a;
        double r14718 = cosh(r14717);
        double r14719 = r14717 * r14717;
        double r14720 = fmod(r14718, r14719);
        double r14721 = cbrt(r14720);
        double r14722 = r14721 * r14721;
        double r14723 = exp(r14722);
        double r14724 = log(r14723);
        double r14725 = log1p(r14717);
        double r14726 = pow(r14724, r14725);
        double r14727 = pow(r14721, r14725);
        double r14728 = r14726 * r14727;
        double r14729 = acos(r14728);
        return r14729;
}

Error

Bits error versus a

Derivation

1. Initial program 61.2

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

3. Applied add-log-exp 60.3

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

5. Applied add-cube-cbrt 60.3

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

6. Applied unpow-prod-down 60.3

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

7. Simplified 60.3

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

8. Simplified 60.2

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

9. Final simplification 60.2

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

Reproduce

herbie shell --seed 2019304 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))