Average Error: 31.0 → 31.0
Time: 20.3s
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 r67866 = a;
        double r67867 = asin(r67866);
        double r67868 = fmod(r67866, r67867);
        double r67869 = atan(r67868);
        double r67870 = r67866 * r67866;
        double r67871 = pow(r67869, r67870);
        return r67871;
}
↓
double f(double a) {
        double r67872 = a;
        double r67873 = asin(r67872);
        double r67874 = fmod(r67872, r67873);
        double r67875 = atan(r67874);
        double r67876 = r67872 * r67872;
        double r67877 = pow(r67875, r67876);
        return r67877;
}

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 2019196 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))