Fuzzer 002

Average Error: 31.3 → 31.2

Time: 23.8s

Precision: 64

Math

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

↓

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

C

double f(double a) {
        double r112439 = a;
        double r112440 = asin(r112439);
        double r112441 = fmod(r112439, r112440);
        double r112442 = atan(r112441);
        double r112443 = r112439 * r112439;
        double r112444 = pow(r112442, r112443);
        return r112444;
}

↓

double f(double a) {
        double r112445 = a;
        double r112446 = asin(r112445);
        double r112447 = fmod(r112445, r112446);
        double r112448 = atan(r112447);
        double r112449 = r112445 * r112445;
        double r112450 = 2.0;
        double r112451 = r112449 / r112450;
        double r112452 = pow(r112448, r112451);
        double r112453 = r112452 * r112452;
        return r112453;
}

Error

Bits error versus a

Derivation

1. Initial program 31.3

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

3. Applied sqr-pow 31.2

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

4. Final simplification 31.2

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

Reproduce

herbie shell --seed 2019303 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))