Average Error: 31.0 → 31.0
Time: 11.4s
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 r123665 = a;
        double r123666 = asin(r123665);
        double r123667 = fmod(r123665, r123666);
        double r123668 = atan(r123667);
        double r123669 = r123665 * r123665;
        double r123670 = pow(r123668, r123669);
        return r123670;
}
↓
double f(double a) {
        double r123671 = a;
        double r123672 = asin(r123671);
        double r123673 = fmod(r123671, r123672);
        double r123674 = atan(r123673);
        double r123675 = r123671 * r123671;
        double r123676 = pow(r123674, r123675);
        return r123676;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.0

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

  2. Final simplification31.0

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))