Average Error: 31.1 → 31.1
Time: 7.6s
Precision: 64
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}
↓
{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}
double f(double a) {
        double r81647 = a;
        double r81648 = asin(r81647);
        double r81649 = fmod(r81647, r81648);
        double r81650 = atan(r81649);
        double r81651 = r81647 * r81647;
        double r81652 = pow(r81650, r81651);
        return r81652;
}
↓
double f(double a) {
        double r81653 = a;
        double r81654 = asin(r81653);
        double r81655 = fmod(r81653, r81654);
        double r81656 = atan(r81655);
        double r81657 = r81653 * r81653;
        double r81658 = pow(r81656, r81657);
        return r81658;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.1

    \[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]

  2. Final simplification31.1

    \[\leadsto {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))