Average Error: 31.4 → 31.4
Time: 5.1s
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 r64958 = a;
        double r64959 = asin(r64958);
        double r64960 = fmod(r64958, r64959);
        double r64961 = atan(r64960);
        double r64962 = r64958 * r64958;
        double r64963 = pow(r64961, r64962);
        return r64963;
}
↓
double f(double a) {
        double r64964 = a;
        double r64965 = asin(r64964);
        double r64966 = fmod(r64964, r64965);
        double r64967 = atan(r64966);
        double r64968 = r64964 * r64964;
        double r64969 = pow(r64967, r64968);
        return r64969;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.4

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

  2. Final simplification31.4

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

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))