Fuzzer 002

Average Error: 31.3 → 31.3

Time: 18.2s

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 r5132965 = a;
        double r5132966 = asin(r5132965);
        double r5132967 = fmod(r5132965, r5132966);
        double r5132968 = atan(r5132967);
        double r5132969 = r5132965 * r5132965;
        double r5132970 = pow(r5132968, r5132969);
        return r5132970;
}

↓

double f(double a) {
        double r5132971 = a;
        double r5132972 = asin(r5132971);
        double r5132973 = fmod(r5132971, r5132972);
        double r5132974 = atan(r5132973);
        double r5132975 = r5132971 * r5132971;
        double r5132976 = 2.0;
        double r5132977 = r5132975 / r5132976;
        double r5132978 = pow(r5132974, r5132977);
        double r5132979 = r5132978 * r5132978;
        return r5132979;
}

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 31.3

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

4. Final simplification 31.3

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

Reproduce

herbie shell --seed 2019169 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))