Average Error: 30.9 → 30.9
Time: 5.4s
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 r122207 = a;
        double r122208 = asin(r122207);
        double r122209 = fmod(r122207, r122208);
        double r122210 = atan(r122209);
        double r122211 = r122207 * r122207;
        double r122212 = pow(r122210, r122211);
        return r122212;
}
↓
double f(double a) {
        double r122213 = a;
        double r122214 = asin(r122213);
        double r122215 = fmod(r122213, r122214);
        double r122216 = atan(r122215);
        double r122217 = r122213 * r122213;
        double r122218 = pow(r122216, r122217);
        return r122218;
}

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 2020025 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))