Average Error: 31.1 → 31.1
Time: 20.0s
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 r55637 = a;
        double r55638 = asin(r55637);
        double r55639 = fmod(r55637, r55638);
        double r55640 = atan(r55639);
        double r55641 = r55637 * r55637;
        double r55642 = pow(r55640, r55641);
        return r55642;
}
↓
double f(double a) {
        double r55643 = a;
        double r55644 = asin(r55643);
        double r55645 = fmod(r55643, r55644);
        double r55646 = atan(r55645);
        double r55647 = r55643 * r55643;
        double r55648 = pow(r55646, r55647);
        return r55648;
}

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)))