Fuzzer 002

Average Error: 30.6 → 30.6

Time: 18.2s

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 r5220054 = a;
        double r5220055 = asin(r5220054);
        double r5220056 = fmod(r5220054, r5220055);
        double r5220057 = atan(r5220056);
        double r5220058 = r5220054 * r5220054;
        double r5220059 = pow(r5220057, r5220058);
        return r5220059;
}

↓

double f(double a) {
        double r5220060 = a;
        double r5220061 = asin(r5220060);
        double r5220062 = fmod(r5220060, r5220061);
        double r5220063 = atan(r5220062);
        double r5220064 = r5220060 * r5220060;
        double r5220065 = 2.0;
        double r5220066 = r5220064 / r5220065;
        double r5220067 = pow(r5220063, r5220066);
        double r5220068 = r5220067 * r5220067;
        return r5220068;
}

Error

Bits error versus a

Derivation

1. Initial program 30.6

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

3. Applied sqr-pow 30.6

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

4. Final simplification 30.6

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

Reproduce

herbie shell --seed 2019162 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))