Average Error: 31.0 → 30.9
Time: 5.6s
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 r100433 = a;
        double r100434 = asin(r100433);
        double r100435 = fmod(r100433, r100434);
        double r100436 = atan(r100435);
        double r100437 = r100433 * r100433;
        double r100438 = pow(r100436, r100437);
        return r100438;
}
↓
double f(double a) {
        double r100439 = a;
        double r100440 = asin(r100439);
        double r100441 = fmod(r100439, r100440);
        double r100442 = atan(r100441);
        double r100443 = r100439 * r100439;
        double r100444 = 2.0;
        double r100445 = r100443 / r100444;
        double r100446 = pow(r100442, r100445);
        double r100447 = r100446 * r100446;
        return r100447;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.0

    \[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
  2. Using strategy rm

  3. Applied sqr-pow30.9

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

  4. Final simplification30.9

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

Reproduce

herbie shell --seed 2019362 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))