Random Jason Timeout Test 012

Average Error: 61.2 → 60.3

Time: 56.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = 7.953652505345186e+78

Math

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

↓

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

C

double f(double a) {
        double r13963 = a;
        double r13964 = cosh(r13963);
        double r13965 = r13963 * r13963;
        double r13966 = fmod(r13964, r13965);
        double r13967 = log1p(r13963);
        double r13968 = pow(r13966, r13967);
        double r13969 = acos(r13968);
        return r13969;
}

↓

double f(double a) {
        double r13970 = a;
        double r13971 = cosh(r13970);
        double r13972 = r13970 * r13970;
        double r13973 = fmod(r13971, r13972);
        double r13974 = exp(r13973);
        double r13975 = sqrt(r13974);
        double r13976 = log(r13975);
        double r13977 = r13976 + r13976;
        double r13978 = log1p(r13970);
        double r13979 = pow(r13977, r13978);
        double r13980 = acos(r13979);
        return r13980;
}

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-sqr-sqrt 60.3

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

6. Applied log-prod 60.3

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

7. Final simplification 60.3

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

Reproduce

herbie shell --seed 2019326 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))