Average Error: 31.4 → 31.4
Time: 5.2s
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 r96083 = a;
        double r96084 = asin(r96083);
        double r96085 = fmod(r96083, r96084);
        double r96086 = atan(r96085);
        double r96087 = r96083 * r96083;
        double r96088 = pow(r96086, r96087);
        return r96088;
}
↓
double f(double a) {
        double r96089 = a;
        double r96090 = asin(r96089);
        double r96091 = fmod(r96089, r96090);
        double r96092 = atan(r96091);
        double r96093 = r96089 * r96089;
        double r96094 = pow(r96092, r96093);
        return r96094;
}

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 2020001 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))