Average Error: 31.6 → 31.6
Time: 5.4s
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 r152616 = a;
        double r152617 = asin(r152616);
        double r152618 = fmod(r152616, r152617);
        double r152619 = atan(r152618);
        double r152620 = r152616 * r152616;
        double r152621 = pow(r152619, r152620);
        return r152621;
}
↓
double f(double a) {
        double r152622 = a;
        double r152623 = asin(r152622);
        double r152624 = fmod(r152622, r152623);
        double r152625 = atan(r152624);
        double r152626 = r152622 * r152622;
        double r152627 = pow(r152625, r152626);
        return r152627;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.6

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

  2. Final simplification31.6

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))