Average Error: 31.0 → 31.0
Time: 20.2s
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 r72327 = a;
        double r72328 = asin(r72327);
        double r72329 = fmod(r72327, r72328);
        double r72330 = atan(r72329);
        double r72331 = r72327 * r72327;
        double r72332 = pow(r72330, r72331);
        return r72332;
}
↓
double f(double a) {
        double r72333 = a;
        double r72334 = asin(r72333);
        double r72335 = fmod(r72333, r72334);
        double r72336 = atan(r72335);
        double r72337 = r72333 * r72333;
        double r72338 = pow(r72336, r72337);
        return r72338;
}

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 2019325 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))