Average Error: 30.9 → 30.9
Time: 11.3s
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 r16366 = a;
        double r16367 = asin(r16366);
        double r16368 = fmod(r16366, r16367);
        double r16369 = atan(r16368);
        double r16370 = r16366 * r16366;
        double r16371 = pow(r16369, r16370);
        return r16371;
}
↓
double f(double a) {
        double r16372 = a;
        double r16373 = asin(r16372);
        double r16374 = fmod(r16372, r16373);
        double r16375 = atan(r16374);
        double r16376 = r16372 * r16372;
        double r16377 = pow(r16375, r16376);
        return r16377;
}

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)))