Average Error: 31.2 → 31.2
Time: 21.4s
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 r71943 = a;
        double r71944 = asin(r71943);
        double r71945 = fmod(r71943, r71944);
        double r71946 = atan(r71945);
        double r71947 = r71943 * r71943;
        double r71948 = pow(r71946, r71947);
        return r71948;
}
↓
double f(double a) {
        double r71949 = a;
        double r71950 = asin(r71949);
        double r71951 = fmod(r71949, r71950);
        double r71952 = atan(r71951);
        double r71953 = r71949 * r71949;
        double r71954 = pow(r71952, r71953);
        return r71954;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.2

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

  2. Final simplification31.2

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))