Average Error: 31.0 → 31.0
Time: 15.0s
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 r138264 = a;
        double r138265 = asin(r138264);
        double r138266 = fmod(r138264, r138265);
        double r138267 = atan(r138266);
        double r138268 = r138264 * r138264;
        double r138269 = pow(r138267, r138268);
        return r138269;
}
↓
double f(double a) {
        double r138270 = a;
        double r138271 = asin(r138270);
        double r138272 = fmod(r138270, r138271);
        double r138273 = atan(r138272);
        double r138274 = r138270 * r138270;
        double r138275 = pow(r138273, r138274);
        return r138275;
}

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 2020046 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))