Fuzzer 002

Average Error: 31.3 → 31.3

Time: 21.5s

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 r3904994 = a;
        double r3904995 = asin(r3904994);
        double r3904996 = fmod(r3904994, r3904995);
        double r3904997 = atan(r3904996);
        double r3904998 = r3904994 * r3904994;
        double r3904999 = pow(r3904997, r3904998);
        return r3904999;
}

↓

double f(double a) {
        double r3905000 = a;
        double r3905001 = asin(r3905000);
        double r3905002 = fmod(r3905000, r3905001);
        double r3905003 = atan(r3905002);
        double r3905004 = r3905000 * r3905000;
        double r3905005 = 2.0;
        double r3905006 = r3905004 / r3905005;
        double r3905007 = pow(r3905003, r3905006);
        double r3905008 = r3905007 * r3905007;
        return r3905008;
}

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 31.3

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

4. Final simplification 31.3

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))