Average Error: 30.5 → 30.5
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 r93868 = a;
        double r93869 = asin(r93868);
        double r93870 = fmod(r93868, r93869);
        double r93871 = atan(r93870);
        double r93872 = r93868 * r93868;
        double r93873 = pow(r93871, r93872);
        return r93873;
}
↓
double f(double a) {
        double r93874 = a;
        double r93875 = asin(r93874);
        double r93876 = fmod(r93874, r93875);
        double r93877 = atan(r93876);
        double r93878 = r93874 * r93874;
        double r93879 = pow(r93877, r93878);
        return r93879;
}

Error

Bits error versus a

Derivation

  1. Initial program 30.5

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

  2. Final simplification30.5

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))