Fuzzer 002

Average Error: 31.5 → 31.5

Time: 24.2s

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 r65991 = a;
        double r65992 = asin(r65991);
        double r65993 = fmod(r65991, r65992);
        double r65994 = atan(r65993);
        double r65995 = r65991 * r65991;
        double r65996 = pow(r65994, r65995);
        return r65996;
}

↓

double f(double a) {
        double r65997 = a;
        double r65998 = asin(r65997);
        double r65999 = fmod(r65997, r65998);
        double r66000 = atan(r65999);
        double r66001 = r65997 * r65997;
        double r66002 = 2.0;
        double r66003 = r66001 / r66002;
        double r66004 = pow(r66000, r66003);
        double r66005 = r66004 * r66004;
        return r66005;
}

Error

Bits error versus a

Derivation

1. Initial program 31.5

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

3. Applied sqr-pow 31.5

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

4. Final simplification 31.5

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))