Fuzzer 002

Average Error: 31.4 → 31.4

Time: 20.7s

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 r70423 = a;
        double r70424 = asin(r70423);
        double r70425 = fmod(r70423, r70424);
        double r70426 = atan(r70425);
        double r70427 = r70423 * r70423;
        double r70428 = pow(r70426, r70427);
        return r70428;
}

↓

double f(double a) {
        double r70429 = a;
        double r70430 = asin(r70429);
        double r70431 = fmod(r70429, r70430);
        double r70432 = atan(r70431);
        double r70433 = r70429 * r70429;
        double r70434 = 2.0;
        double r70435 = r70433 / r70434;
        double r70436 = pow(r70432, r70435);
        double r70437 = r70436 * r70436;
        return r70437;
}

Error

Bits error versus a

Derivation

1. Initial program 31.4

   \[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
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 2019208 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))