Average Error: 31.0 → 31.0
Time: 7.2s
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 r116219 = a;
        double r116220 = asin(r116219);
        double r116221 = fmod(r116219, r116220);
        double r116222 = atan(r116221);
        double r116223 = r116219 * r116219;
        double r116224 = pow(r116222, r116223);
        return r116224;
}
↓
double f(double a) {
        double r116225 = a;
        double r116226 = asin(r116225);
        double r116227 = fmod(r116225, r116226);
        double r116228 = atan(r116227);
        double r116229 = r116225 * r116225;
        double r116230 = pow(r116228, r116229);
        return r116230;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.0

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

  2. Final simplification31.0

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))