Average Error: 31.1 → 31.1
Time: 5.5s
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 r136651 = a;
        double r136652 = asin(r136651);
        double r136653 = fmod(r136651, r136652);
        double r136654 = atan(r136653);
        double r136655 = r136651 * r136651;
        double r136656 = pow(r136654, r136655);
        return r136656;
}
↓
double f(double a) {
        double r136657 = a;
        double r136658 = asin(r136657);
        double r136659 = fmod(r136657, r136658);
        double r136660 = atan(r136659);
        double r136661 = r136657 * r136657;
        double r136662 = pow(r136660, r136661);
        return r136662;
}

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 2020049 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))