Average Error: 31.0 → 31.0
Time: 20.4s
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 r78155 = a;
        double r78156 = asin(r78155);
        double r78157 = fmod(r78155, r78156);
        double r78158 = atan(r78157);
        double r78159 = r78155 * r78155;
        double r78160 = pow(r78158, r78159);
        return r78160;
}
↓
double f(double a) {
        double r78161 = a;
        double r78162 = asin(r78161);
        double r78163 = fmod(r78161, r78162);
        double r78164 = atan(r78163);
        double r78165 = r78161 * r78161;
        double r78166 = pow(r78164, r78165);
        return r78166;
}

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)))