Average Error: 30.9 → 30.9
Time: 14.5s
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 r116163 = a;
        double r116164 = asin(r116163);
        double r116165 = fmod(r116163, r116164);
        double r116166 = atan(r116165);
        double r116167 = r116163 * r116163;
        double r116168 = pow(r116166, r116167);
        return r116168;
}
↓
double f(double a) {
        double r116169 = a;
        double r116170 = asin(r116169);
        double r116171 = fmod(r116169, r116170);
        double r116172 = atan(r116171);
        double r116173 = r116169 * r116169;
        double r116174 = pow(r116172, r116173);
        return r116174;
}

Error

Bits error versus a

Derivation

  1. Initial program 30.9

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

  2. Final simplification30.9

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))