Fuzzer 002

Average Error: 31.5 → 31.4

Time: 5.7s

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 r148177 = a;
        double r148178 = asin(r148177);
        double r148179 = fmod(r148177, r148178);
        double r148180 = atan(r148179);
        double r148181 = r148177 * r148177;
        double r148182 = pow(r148180, r148181);
        return r148182;
}

↓

double f(double a) {
        double r148183 = a;
        double r148184 = asin(r148183);
        double r148185 = fmod(r148183, r148184);
        double r148186 = atan(r148185);
        double r148187 = r148183 * r148183;
        double r148188 = 2.0;
        double r148189 = r148187 / r148188;
        double r148190 = pow(r148186, r148189);
        double r148191 = r148190 * r148190;
        return r148191;
}

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 31.4

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

4. Final simplification 31.4

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

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))