Average Error: 30.9 → 30.9
Time: 10.9s
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 r29655 = a;
        double r29656 = asin(r29655);
        double r29657 = fmod(r29655, r29656);
        double r29658 = atan(r29657);
        double r29659 = r29655 * r29655;
        double r29660 = pow(r29658, r29659);
        return r29660;
}
↓
double f(double a) {
        double r29661 = a;
        double r29662 = asin(r29661);
        double r29663 = fmod(r29661, r29662);
        double r29664 = atan(r29663);
        double r29665 = r29661 * r29661;
        double r29666 = pow(r29664, r29665);
        return r29666;
}

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 2020045 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))