Random Jason Timeout Test 012

Average Error: 61.0 → 60.1

Time: 29.4s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.2797145410448457e+152

Math

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

↓

\[\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) + \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)\right)\right)\]

C

double f(double a) {
        double r3892 = a;
        double r3893 = cosh(r3892);
        double r3894 = r3892 * r3892;
        double r3895 = fmod(r3893, r3894);
        double r3896 = log1p(r3892);
        double r3897 = pow(r3895, r3896);
        double r3898 = acos(r3897);
        return r3898;
}

↓

double f(double a) {
        double r3899 = 2.0;
        double r3900 = a;
        double r3901 = cosh(r3900);
        double r3902 = r3900 * r3900;
        double r3903 = fmod(r3901, r3902);
        double r3904 = exp(r3903);
        double r3905 = log(r3904);
        double r3906 = log1p(r3900);
        double r3907 = pow(r3905, r3906);
        double r3908 = acos(r3907);
        double r3909 = exp(r3908);
        double r3910 = cbrt(r3909);
        double r3911 = log(r3910);
        double r3912 = r3899 * r3911;
        double r3913 = r3912 + r3911;
        double r3914 = log1p(r3913);
        double r3915 = expm1(r3914);
        return r3915;
}

Error

Bits error versus a

Derivation

1. Initial program 61.0

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

3. Applied add-log-exp 60.1

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

5. Applied expm1-log1p-u 60.1

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

7. Applied add-log-exp 60.1

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

9. Applied add-cube-cbrt 60.1

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

10. Applied log-prod 60.1

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

11. Simplified 60.1

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{2 \cdot \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)} + \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)\right)\right)\]

12. Final simplification 60.1

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) + \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))