Random Jason Timeout Test 012

Average Error: 60.5 → 59.6

Time: 1.3m

Precision: 64

• could not determine a ground truth for program body

  1. a = 3.517832587491486e+241

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 r1605850 = a;
        double r1605851 = cosh(r1605850);
        double r1605852 = r1605850 * r1605850;
        double r1605853 = fmod(r1605851, r1605852);
        double r1605854 = log1p(r1605850);
        double r1605855 = pow(r1605853, r1605854);
        double r1605856 = acos(r1605855);
        return r1605856;
}

↓

double f(double a) {
        double r1605857 = a;
        double r1605858 = cosh(r1605857);
        double r1605859 = r1605857 * r1605857;
        double r1605860 = fmod(r1605858, r1605859);
        double r1605861 = exp(r1605860);
        double r1605862 = sqrt(r1605861);
        double r1605863 = log(r1605862);
        double r1605864 = r1605863 + r1605863;
        double r1605865 = log1p(r1605857);
        double r1605866 = pow(r1605864, r1605865);
        double r1605867 = acos(r1605866);
        return r1605867;
}

Error

Bits error versus a

Derivation

1. Initial program 60.5

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

3. Applied add-log-exp 59.6

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

5. Applied add-sqr-sqrt 59.6

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

6. Applied log-prod 59.6

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

7. Final simplification 59.6

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

Reproduce

herbie shell --seed 2019149 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))