Fuzzer 002

Average Error: 31.5 → 31.5

Time: 27.8s

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 r74860 = a;
        double r74861 = asin(r74860);
        double r74862 = fmod(r74860, r74861);
        double r74863 = atan(r74862);
        double r74864 = r74860 * r74860;
        double r74865 = pow(r74863, r74864);
        return r74865;
}

↓

double f(double a) {
        double r74866 = a;
        double r74867 = asin(r74866);
        double r74868 = fmod(r74866, r74867);
        double r74869 = atan(r74868);
        double r74870 = r74866 * r74866;
        double r74871 = 2.0;
        double r74872 = r74870 / r74871;
        double r74873 = pow(r74869, r74872);
        double r74874 = r74873 * r74873;
        return r74874;
}

Error

Bits error versus a

Derivation

1. Initial program 31.5

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

3. Applied sqr-pow 31.5

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

4. Final simplification 31.5

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

Reproduce

herbie shell --seed 2019199 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))