Average Error: 31.4 → 31.4
Time: 16.2s
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 r78180 = a;
        double r78181 = asin(r78180);
        double r78182 = fmod(r78180, r78181);
        double r78183 = atan(r78182);
        double r78184 = r78180 * r78180;
        double r78185 = pow(r78183, r78184);
        return r78185;
}
↓
double f(double a) {
        double r78186 = a;
        double r78187 = asin(r78186);
        double r78188 = fmod(r78186, r78187);
        double r78189 = atan(r78188);
        double r78190 = r78186 * r78186;
        double r78191 = pow(r78189, r78190);
        return r78191;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.4

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

  2. Final simplification31.4

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))