Average Error: 31.2 → 31.2
Time: 7.4s
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 r95544 = a;
        double r95545 = asin(r95544);
        double r95546 = fmod(r95544, r95545);
        double r95547 = atan(r95546);
        double r95548 = r95544 * r95544;
        double r95549 = pow(r95547, r95548);
        return r95549;
}
↓
double f(double a) {
        double r95550 = a;
        double r95551 = asin(r95550);
        double r95552 = fmod(r95550, r95551);
        double r95553 = atan(r95552);
        double r95554 = r95550 * r95550;
        double r95555 = pow(r95553, r95554);
        return r95555;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.2

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

  2. Final simplification31.2

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))