Average Error: 30.9 → 30.9
Time: 21.0s
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 r94177 = a;
        double r94178 = asin(r94177);
        double r94179 = fmod(r94177, r94178);
        double r94180 = atan(r94179);
        double r94181 = r94177 * r94177;
        double r94182 = pow(r94180, r94181);
        return r94182;
}
↓
double f(double a) {
        double r94183 = a;
        double r94184 = asin(r94183);
        double r94185 = fmod(r94183, r94184);
        double r94186 = atan(r94185);
        double r94187 = r94183 * r94183;
        double r94188 = pow(r94186, r94187);
        return r94188;
}

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 2019304 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))