Average Error: 30.4 → 30.4
Time: 6.4s
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 r100285 = a;
        double r100286 = asin(r100285);
        double r100287 = fmod(r100285, r100286);
        double r100288 = atan(r100287);
        double r100289 = r100285 * r100285;
        double r100290 = pow(r100288, r100289);
        return r100290;
}
↓
double f(double a) {
        double r100291 = a;
        double r100292 = asin(r100291);
        double r100293 = fmod(r100291, r100292);
        double r100294 = atan(r100293);
        double r100295 = r100291 * r100291;
        double r100296 = pow(r100294, r100295);
        return r100296;
}

Error

Bits error versus a

Derivation

  1. Initial program 30.4

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

  2. Final simplification30.4

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))