Average Error: 31.5 → 31.5
Time: 5.7s
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 r108524 = a;
        double r108525 = asin(r108524);
        double r108526 = fmod(r108524, r108525);
        double r108527 = atan(r108526);
        double r108528 = r108524 * r108524;
        double r108529 = pow(r108527, r108528);
        return r108529;
}
↓
double f(double a) {
        double r108530 = a;
        double r108531 = asin(r108530);
        double r108532 = fmod(r108530, r108531);
        double r108533 = atan(r108532);
        double r108534 = r108530 * r108530;
        double r108535 = pow(r108533, r108534);
        return r108535;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.5

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

  2. Final simplification31.5

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))