Random Jason Timeout Test 012

Average Error: 60.4 → 59.6

Time: 1.1m

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.6495200433389913e+108

Math

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

↓

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

C

double f(double a) {
        double r930791 = a;
        double r930792 = cosh(r930791);
        double r930793 = r930791 * r930791;
        double r930794 = fmod(r930792, r930793);
        double r930795 = log1p(r930791);
        double r930796 = pow(r930794, r930795);
        double r930797 = acos(r930796);
        return r930797;
}

↓

double f(double a) {
        double r930798 = a;
        double r930799 = cosh(r930798);
        double r930800 = r930798 * r930798;
        double r930801 = fmod(r930799, r930800);
        double r930802 = r930801 * r930801;
        double r930803 = r930801 * r930802;
        double r930804 = cbrt(r930803);
        double r930805 = log1p(r930798);
        double r930806 = pow(r930804, r930805);
        double r930807 = acos(r930806);
        return r930807;
}

Error

Bits error versus a

Derivation

1. Initial program 60.4

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

3. Applied add-log-exp 59.5

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

5. Applied add-cbrt-cube 59.5

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

6. Simplified 59.6

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

7. Final simplification 59.6

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))