Fuzzer 002

Average Error: 31.2 → 31.2

Time: 25.6s

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 r65933 = a;
        double r65934 = asin(r65933);
        double r65935 = fmod(r65933, r65934);
        double r65936 = atan(r65935);
        double r65937 = r65933 * r65933;
        double r65938 = pow(r65936, r65937);
        return r65938;
}

↓

double f(double a) {
        double r65939 = a;
        double r65940 = asin(r65939);
        double r65941 = fmod(r65939, r65940);
        double r65942 = atan(r65941);
        double r65943 = r65939 * r65939;
        double r65944 = 2.0;
        double r65945 = r65943 / r65944;
        double r65946 = pow(r65942, r65945);
        double r65947 = r65946 * r65946;
        return r65947;
}

Error

Bits error versus a

Derivation

1. Initial program 31.2

   \[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
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 2019323 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))