Average Error: 31.0 → 31.0
Time: 11.1s
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 r127537 = a;
        double r127538 = asin(r127537);
        double r127539 = fmod(r127537, r127538);
        double r127540 = atan(r127539);
        double r127541 = r127537 * r127537;
        double r127542 = pow(r127540, r127541);
        return r127542;
}
↓
double f(double a) {
        double r127543 = a;
        double r127544 = asin(r127543);
        double r127545 = fmod(r127543, r127544);
        double r127546 = atan(r127545);
        double r127547 = r127543 * r127543;
        double r127548 = pow(r127546, r127547);
        return r127548;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.0

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

  2. Final simplification31.0

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))