Fuzzer 002

Average Error: 30.8 → 30.8

Time: 26.5s

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 r4427291 = a;
        double r4427292 = asin(r4427291);
        double r4427293 = fmod(r4427291, r4427292);
        double r4427294 = atan(r4427293);
        double r4427295 = r4427291 * r4427291;
        double r4427296 = pow(r4427294, r4427295);
        return r4427296;
}

↓

double f(double a) {
        double r4427297 = a;
        double r4427298 = asin(r4427297);
        double r4427299 = fmod(r4427297, r4427298);
        double r4427300 = atan(r4427299);
        double r4427301 = r4427297 * r4427297;
        double r4427302 = 2.0;
        double r4427303 = r4427301 / r4427302;
        double r4427304 = pow(r4427300, r4427303);
        double r4427305 = r4427304 * r4427304;
        return r4427305;
}

Error

Bits error versus a

Derivation

1. Initial program 30.8

   \[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
2. Using strategy rm

3. Applied sqr-pow 30.8

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

4. Final simplification 30.8

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

Reproduce

herbie shell --seed 2019141 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))