Average Error: 31.2 → 31.2
Time: 16.7s
Precision: 64
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
double f(double a) {
        double r11281628 = a;
        double r11281629 = asin(r11281628);
        double r11281630 = fmod(r11281628, r11281629);
        double r11281631 = atan(r11281630);
        double r11281632 = r11281628 * r11281628;
        double r11281633 = pow(r11281631, r11281632);
        return r11281633;
}
↓
double f(double a) {
        double r11281634 = a;
        double r11281635 = asin(r11281634);
        double r11281636 = fmod(r11281634, r11281635);
        double r11281637 = atan(r11281636);
        double r11281638 = r11281634 * r11281634;
        double r11281639 = pow(r11281637, r11281638);
        return r11281639;
}


{\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)}

Error

Bits error versus a

Derivation

  1. Initial program 31.2

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

  2. Final simplification31.2

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

Reproduce

herbie shell --seed 2019101 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))