Average Error: 30.7 → 30.7
Time: 13.5s
Precision: 64
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}\]
{\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(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}
double f(double a) {
        double r116002 = a;
        double r116003 = asin(r116002);
        double r116004 = fmod(r116002, r116003);
        double r116005 = atan(r116004);
        double r116006 = r116002 * r116002;
        double r116007 = pow(r116005, r116006);
        return r116007;
}
↓
double f(double a) {
        double r116008 = a;
        double r116009 = asin(r116008);
        double r116010 = fmod(r116008, r116009);
        double r116011 = atan(r116010);
        double r116012 = r116008 * r116008;
        double r116013 = 2.0;
        double r116014 = r116012 / r116013;
        double r116015 = pow(r116011, r116014);
        double r116016 = r116015 * r116015;
        return r116016;
}

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. Using strategy rm

  3. Applied sqr-pow30.7

    \[\leadsto \color{blue}{{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}}\]

  4. Final simplification30.7

    \[\leadsto {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))