Average Error: 31.2 → 31.2
Time: 17.2s
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 r2121873 = a;
        double r2121874 = asin(r2121873);
        double r2121875 = fmod(r2121873, r2121874);
        double r2121876 = atan(r2121875);
        double r2121877 = r2121873 * r2121873;
        double r2121878 = pow(r2121876, r2121877);
        return r2121878;
}
↓
double f(double a) {
        double r2121879 = a;
        double r2121880 = asin(r2121879);
        double r2121881 = fmod(r2121879, r2121880);
        double r2121882 = atan(r2121881);
        double r2121883 = r2121879 * r2121879;
        double r2121884 = pow(r2121882, r2121883);
        return r2121884;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.2

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

  2. Final simplification31.2

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))