Average Error: 31.3 → 31.3
Time: 16.1s
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 r88968 = a;
        double r88969 = asin(r88968);
        double r88970 = fmod(r88968, r88969);
        double r88971 = atan(r88970);
        double r88972 = r88968 * r88968;
        double r88973 = pow(r88971, r88972);
        return r88973;
}
↓
double f(double a) {
        double r88974 = a;
        double r88975 = asin(r88974);
        double r88976 = fmod(r88974, r88975);
        double r88977 = atan(r88976);
        double r88978 = r88974 * r88974;
        double r88979 = pow(r88977, r88978);
        return r88979;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.3

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

  2. Final simplification31.3

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))