Average Error: 31.1 → 31.1
Time: 5.3s
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 r102656 = a;
        double r102657 = asin(r102656);
        double r102658 = fmod(r102656, r102657);
        double r102659 = atan(r102658);
        double r102660 = r102656 * r102656;
        double r102661 = pow(r102659, r102660);
        return r102661;
}
↓
double f(double a) {
        double r102662 = a;
        double r102663 = asin(r102662);
        double r102664 = fmod(r102662, r102663);
        double r102665 = atan(r102664);
        double r102666 = r102662 * r102662;
        double r102667 = pow(r102665, r102666);
        return r102667;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.1

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

  2. Final simplification31.1

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

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))