Fuzzer 002

Average Error: 31.3 → 31.2

Time: 25.9s

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 r71263 = a;
        double r71264 = asin(r71263);
        double r71265 = fmod(r71263, r71264);
        double r71266 = atan(r71265);
        double r71267 = r71263 * r71263;
        double r71268 = pow(r71266, r71267);
        return r71268;
}

↓

double f(double a) {
        double r71269 = a;
        double r71270 = asin(r71269);
        double r71271 = fmod(r71269, r71270);
        double r71272 = atan(r71271);
        double r71273 = r71269 * r71269;
        double r71274 = 2.0;
        double r71275 = r71273 / r71274;
        double r71276 = pow(r71272, r71275);
        double r71277 = r71276 * r71276;
        return r71277;
}

Error

Bits error versus a

Derivation

1. Initial program 31.3

   \[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
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 2019303 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))