Average Error: 30.9 → 30.9
Time: 5.4s
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 r144741 = a;
        double r144742 = asin(r144741);
        double r144743 = fmod(r144741, r144742);
        double r144744 = atan(r144743);
        double r144745 = r144741 * r144741;
        double r144746 = pow(r144744, r144745);
        return r144746;
}
↓
double f(double a) {
        double r144747 = a;
        double r144748 = asin(r144747);
        double r144749 = fmod(r144747, r144748);
        double r144750 = atan(r144749);
        double r144751 = r144747 * r144747;
        double r144752 = pow(r144750, r144751);
        return r144752;
}

Error

Bits error versus a

Derivation

  1. Initial program 30.9

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

  2. Final simplification30.9

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

Reproduce

herbie shell --seed 2020003 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))