Average Error: 30.5 → 30.5
Time: 11.5s
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 r109412 = a;
        double r109413 = asin(r109412);
        double r109414 = fmod(r109412, r109413);
        double r109415 = atan(r109414);
        double r109416 = r109412 * r109412;
        double r109417 = pow(r109415, r109416);
        return r109417;
}
↓
double f(double a) {
        double r109418 = a;
        double r109419 = asin(r109418);
        double r109420 = fmod(r109418, r109419);
        double r109421 = atan(r109420);
        double r109422 = r109418 * r109418;
        double r109423 = pow(r109421, r109422);
        return r109423;
}

Error

Bits error versus a

Derivation

  1. Initial program 30.5

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

  2. Final simplification30.5

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))