Average Error: 31.6 → 31.6
Time: 5.6s
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 r96811 = a;
        double r96812 = asin(r96811);
        double r96813 = fmod(r96811, r96812);
        double r96814 = atan(r96813);
        double r96815 = r96811 * r96811;
        double r96816 = pow(r96814, r96815);
        return r96816;
}
↓
double f(double a) {
        double r96817 = a;
        double r96818 = asin(r96817);
        double r96819 = fmod(r96817, r96818);
        double r96820 = atan(r96819);
        double r96821 = r96817 * r96817;
        double r96822 = pow(r96820, r96821);
        return r96822;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.6

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

  2. Final simplification31.6

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))