Fuzzer 002

Average Error: 31.0 → 30.9

Time: 27.4s

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 r56866 = a;
        double r56867 = asin(r56866);
        double r56868 = fmod(r56866, r56867);
        double r56869 = atan(r56868);
        double r56870 = r56866 * r56866;
        double r56871 = pow(r56869, r56870);
        return r56871;
}

↓

double f(double a) {
        double r56872 = a;
        double r56873 = asin(r56872);
        double r56874 = fmod(r56872, r56873);
        double r56875 = atan(r56874);
        double r56876 = r56872 * r56872;
        double r56877 = 2.0;
        double r56878 = r56876 / r56877;
        double r56879 = pow(r56875, r56878);
        double r56880 = r56879 * r56879;
        return r56880;
}

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-pow 30.9

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

4. Final simplification 30.9

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))