Random Jason Timeout Test 012

Average Error: 60.3 → 59.4

Time: 52.3s

Precision: 64

• could not determine a ground truth for program body

  1. a = 4.608700736709935e+77

Math

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

↓

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

C

double f(double a) {
        double r489619 = a;
        double r489620 = cosh(r489619);
        double r489621 = r489619 * r489619;
        double r489622 = fmod(r489620, r489621);
        double r489623 = log1p(r489619);
        double r489624 = pow(r489622, r489623);
        double r489625 = acos(r489624);
        return r489625;
}

↓

double f(double a) {
        double r489626 = a;
        double r489627 = cosh(r489626);
        double r489628 = r489626 * r489626;
        double r489629 = fmod(r489627, r489628);
        double r489630 = exp(r489629);
        double r489631 = log(r489630);
        double r489632 = log1p(r489626);
        double r489633 = pow(r489631, r489632);
        double r489634 = acos(r489633);
        double r489635 = cbrt(r489634);
        double r489636 = r489635 * r489635;
        double r489637 = r489635 * r489636;
        return r489637;
}

Error

Bits error versus a

Derivation

1. Initial program 60.3

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

3. Applied add-log-exp 59.4

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

5. Applied add-cube-cbrt 59.4

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

6. Final simplification 59.4

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

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))