Average Error: 30.9 → 30.9
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 r128345 = a;
        double r128346 = asin(r128345);
        double r128347 = fmod(r128345, r128346);
        double r128348 = atan(r128347);
        double r128349 = r128345 * r128345;
        double r128350 = pow(r128348, r128349);
        return r128350;
}
↓
double f(double a) {
        double r128351 = a;
        double r128352 = asin(r128351);
        double r128353 = fmod(r128351, r128352);
        double r128354 = atan(r128353);
        double r128355 = r128351 * r128351;
        double r128356 = pow(r128354, r128355);
        return r128356;
}

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 2019352 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))