Average Error: 30.8 → 30.8
Time: 18.8s
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 r6625671 = a;
        double r6625672 = asin(r6625671);
        double r6625673 = fmod(r6625671, r6625672);
        double r6625674 = atan(r6625673);
        double r6625675 = r6625671 * r6625671;
        double r6625676 = pow(r6625674, r6625675);
        return r6625676;
}
↓
double f(double a) {
        double r6625677 = a;
        double r6625678 = asin(r6625677);
        double r6625679 = fmod(r6625677, r6625678);
        double r6625680 = atan(r6625679);
        double r6625681 = r6625677 * r6625677;
        double r6625682 = pow(r6625680, r6625681);
        return r6625682;
}

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 2019173 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))