Average Error: 30.7 → 30.7
Time: 17.9s
Precision: 64
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
double f(double a) {
        double r13361578 = a;
        double r13361579 = asin(r13361578);
        double r13361580 = fmod(r13361578, r13361579);
        double r13361581 = atan(r13361580);
        double r13361582 = r13361578 * r13361578;
        double r13361583 = pow(r13361581, r13361582);
        return r13361583;
}
↓
double f(double a) {
        double r13361584 = a;
        double r13361585 = asin(r13361584);
        double r13361586 = fmod(r13361584, r13361585);
        double r13361587 = atan(r13361586);
        double r13361588 = r13361584 * r13361584;
        double r13361589 = pow(r13361587, r13361588);
        return r13361589;
}


{\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)}

Error

Bits error versus a

Derivation

  1. Initial program 30.7

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

  2. Final simplification30.7

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))