Average Error: 30.5 → 30.5
Time: 10.2s
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 r163333 = a;
        double r163334 = asin(r163333);
        double r163335 = fmod(r163333, r163334);
        double r163336 = atan(r163335);
        double r163337 = r163333 * r163333;
        double r163338 = pow(r163336, r163337);
        return r163338;
}
↓
double f(double a) {
        double r163339 = a;
        double r163340 = asin(r163339);
        double r163341 = fmod(r163339, r163340);
        double r163342 = atan(r163341);
        double r163343 = r163339 * r163339;
        double r163344 = pow(r163342, r163343);
        return r163344;
}

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)))