Average Error: 31.2 → 31.2
Time: 19.1s
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 r86743 = a;
        double r86744 = asin(r86743);
        double r86745 = fmod(r86743, r86744);
        double r86746 = atan(r86745);
        double r86747 = r86743 * r86743;
        double r86748 = pow(r86746, r86747);
        return r86748;
}
↓
double f(double a) {
        double r86749 = a;
        double r86750 = asin(r86749);
        double r86751 = fmod(r86749, r86750);
        double r86752 = atan(r86751);
        double r86753 = r86749 * r86749;
        double r86754 = pow(r86752, r86753);
        return r86754;
}

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 2019179 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))