Average Error: 30.4 → 30.4
Time: 6.3s
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 r97401 = a;
        double r97402 = asin(r97401);
        double r97403 = fmod(r97401, r97402);
        double r97404 = atan(r97403);
        double r97405 = r97401 * r97401;
        double r97406 = pow(r97404, r97405);
        return r97406;
}
↓
double f(double a) {
        double r97407 = a;
        double r97408 = asin(r97407);
        double r97409 = fmod(r97407, r97408);
        double r97410 = atan(r97409);
        double r97411 = r97407 * r97407;
        double r97412 = pow(r97410, r97411);
        return r97412;
}

Error

Bits error versus a

Derivation

  1. Initial program 30.4

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

  2. Final simplification30.4

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))