Average Error: 31.3 → 31.3
Time: 6.8s
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 r114315 = a;
        double r114316 = asin(r114315);
        double r114317 = fmod(r114315, r114316);
        double r114318 = atan(r114317);
        double r114319 = r114315 * r114315;
        double r114320 = pow(r114318, r114319);
        return r114320;
}
↓
double f(double a) {
        double r114321 = a;
        double r114322 = asin(r114321);
        double r114323 = fmod(r114321, r114322);
        double r114324 = atan(r114323);
        double r114325 = r114321 * r114321;
        double r114326 = pow(r114324, r114325);
        return r114326;
}

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 2020081 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))