Average Error: 31.4 → 31.4
Time: 5.2s
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 r131796 = a;
        double r131797 = asin(r131796);
        double r131798 = fmod(r131796, r131797);
        double r131799 = atan(r131798);
        double r131800 = r131796 * r131796;
        double r131801 = pow(r131799, r131800);
        return r131801;
}
↓
double f(double a) {
        double r131802 = a;
        double r131803 = asin(r131802);
        double r131804 = fmod(r131802, r131803);
        double r131805 = atan(r131804);
        double r131806 = r131802 * r131802;
        double r131807 = pow(r131805, r131806);
        return r131807;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.4

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

  2. Final simplification31.4

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))