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 r1304696 = a;
        double r1304697 = cosh(r1304696);
        double r1304698 = r1304696 * r1304696;
        double r1304699 = fmod(r1304697, r1304698);
        double r1304700 = log1p(r1304696);
        double r1304701 = pow(r1304699, r1304700);
        double r1304702 = acos(r1304701);
        return r1304702;
}

↓

double f(double a) {
        double r1304703 = a;
        double r1304704 = cosh(r1304703);
        double r1304705 = r1304703 * r1304703;
        double r1304706 = fmod(r1304704, r1304705);
        double r1304707 = r1304706 * r1304706;
        double r1304708 = r1304706 * r1304707;
        double r1304709 = cbrt(r1304708);
        double r1304710 = log1p(r1304703);
        double r1304711 = pow(r1304709, r1304710);
        double r1304712 = acos(r1304711);
        return r1304712;
}

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

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

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 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))