Average Error: 30.9 → 30.9
Time: 6.8s
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 r610 = a;
        double r611 = asin(r610);
        double r612 = fmod(r610, r611);
        double r613 = atan(r612);
        double r614 = r610 * r610;
        double r615 = pow(r613, r614);
        return r615;
}
↓
double f(double a) {
        double r616 = a;
        double r617 = asin(r616);
        double r618 = fmod(r616, r617);
        double r619 = atan(r618);
        double r620 = r616 * r616;
        double r621 = pow(r619, r620);
        return r621;
}

Error

Bits error versus a

Derivation

  1. Initial program 30.9

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

  2. Final simplification30.9

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))