Average Error: 31.0 → 31.0
Time: 5.2s
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 r83389 = a;
        double r83390 = asin(r83389);
        double r83391 = fmod(r83389, r83390);
        double r83392 = atan(r83391);
        double r83393 = r83389 * r83389;
        double r83394 = pow(r83392, r83393);
        return r83394;
}
↓
double f(double a) {
        double r83395 = a;
        double r83396 = asin(r83395);
        double r83397 = fmod(r83395, r83396);
        double r83398 = atan(r83397);
        double r83399 = r83395 * r83395;
        double r83400 = pow(r83398, r83399);
        return r83400;
}

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 2020060 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))