Average Error: 30.8 → 30.8
Time: 7.1s
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 r90767 = a;
        double r90768 = asin(r90767);
        double r90769 = fmod(r90767, r90768);
        double r90770 = atan(r90769);
        double r90771 = r90767 * r90767;
        double r90772 = pow(r90770, r90771);
        return r90772;
}
↓
double f(double a) {
        double r90773 = a;
        double r90774 = asin(r90773);
        double r90775 = fmod(r90773, r90774);
        double r90776 = atan(r90775);
        double r90777 = r90773 * r90773;
        double r90778 = pow(r90776, r90777);
        return r90778;
}

Error

Bits error versus a

Derivation

  1. Initial program 30.8

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

  2. Final simplification30.8

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))