Fuzzer 002

Average Error: 31.0 → 30.9

Time: 6.1s

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 r119515 = a;
        double r119516 = asin(r119515);
        double r119517 = fmod(r119515, r119516);
        double r119518 = atan(r119517);
        double r119519 = r119515 * r119515;
        double r119520 = pow(r119518, r119519);
        return r119520;
}

↓

double f(double a) {
        double r119521 = a;
        double r119522 = asin(r119521);
        double r119523 = fmod(r119521, r119522);
        double r119524 = atan(r119523);
        double r119525 = r119521 * r119521;
        double r119526 = 2.0;
        double r119527 = r119525 / r119526;
        double r119528 = pow(r119524, r119527);
        double r119529 = r119528 * r119528;
        return r119529;
}

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 2019362 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))