Average Error: 31.3 → 31.3
Time: 5.5s
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 r82648 = a;
        double r82649 = asin(r82648);
        double r82650 = fmod(r82648, r82649);
        double r82651 = atan(r82650);
        double r82652 = r82648 * r82648;
        double r82653 = pow(r82651, r82652);
        return r82653;
}
↓
double f(double a) {
        double r82654 = a;
        double r82655 = asin(r82654);
        double r82656 = fmod(r82654, r82655);
        double r82657 = atan(r82656);
        double r82658 = r82654 * r82654;
        double r82659 = pow(r82657, r82658);
        return r82659;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.3

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

  2. Final simplification31.3

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

Reproduce

herbie shell --seed 2019356 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))