Average Error: 31.1 → 31.1
Time: 20.9s
Precision: 64
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
{\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 r55602 = a;
        double r55603 = asin(r55602);
        double r55604 = fmod(r55602, r55603);
        double r55605 = atan(r55604);
        double r55606 = r55602 * r55602;
        double r55607 = pow(r55605, r55606);
        return r55607;
}
↓
double f(double a) {
        double r55608 = a;
        double r55609 = asin(r55608);
        double r55610 = fmod(r55608, r55609);
        double r55611 = atan(r55610);
        double r55612 = r55608 * r55608;
        double r55613 = pow(r55611, r55612);
        return r55613;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.1

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

  2. Final simplification31.1

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))