Fuzzer 002

Average Error: 31.0 → 30.9

Time: 24.0s

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 r80172 = a;
        double r80173 = asin(r80172);
        double r80174 = fmod(r80172, r80173);
        double r80175 = atan(r80174);
        double r80176 = r80172 * r80172;
        double r80177 = pow(r80175, r80176);
        return r80177;
}

↓

double f(double a) {
        double r80178 = a;
        double r80179 = asin(r80178);
        double r80180 = fmod(r80178, r80179);
        double r80181 = atan(r80180);
        double r80182 = r80178 * r80178;
        double r80183 = 2.0;
        double r80184 = r80182 / r80183;
        double r80185 = pow(r80181, r80184);
        double r80186 = r80185 * r80185;
        return r80186;
}

Error

Bits error versus a

Derivation

1. Initial program 31.0

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

3. Applied sqr-pow 30.9

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

4. Final simplification 30.9

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

Reproduce

herbie shell --seed 2019306 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))