Average Error: 31.1 → 31.1
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 r67564 = a;
        double r67565 = asin(r67564);
        double r67566 = fmod(r67564, r67565);
        double r67567 = atan(r67566);
        double r67568 = r67564 * r67564;
        double r67569 = pow(r67567, r67568);
        return r67569;
}
↓
double f(double a) {
        double r67570 = a;
        double r67571 = asin(r67570);
        double r67572 = fmod(r67570, r67571);
        double r67573 = atan(r67572);
        double r67574 = r67570 * r67570;
        double r67575 = pow(r67573, r67574);
        return r67575;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.1

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

  2. Final simplification31.1

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))