Fuzzer 002

Average Error: 30.6 → 30.6

Time: 22.1s

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 r3702869 = a;
        double r3702870 = asin(r3702869);
        double r3702871 = fmod(r3702869, r3702870);
        double r3702872 = atan(r3702871);
        double r3702873 = r3702869 * r3702869;
        double r3702874 = pow(r3702872, r3702873);
        return r3702874;
}

↓

double f(double a) {
        double r3702875 = a;
        double r3702876 = asin(r3702875);
        double r3702877 = fmod(r3702875, r3702876);
        double r3702878 = atan(r3702877);
        double r3702879 = r3702875 * r3702875;
        double r3702880 = 2.0;
        double r3702881 = r3702879 / r3702880;
        double r3702882 = pow(r3702878, r3702881);
        double r3702883 = r3702882 * r3702882;
        return r3702883;
}

Error

Bits error versus a

Derivation

1. Initial program 30.6

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

3. Applied sqr-pow 30.6

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

4. Final simplification 30.6

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))