Fuzzer 002

Average Error: 31.3 → 31.3

Time: 27.1s

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 r2935415 = a;
        double r2935416 = asin(r2935415);
        double r2935417 = fmod(r2935415, r2935416);
        double r2935418 = atan(r2935417);
        double r2935419 = r2935415 * r2935415;
        double r2935420 = pow(r2935418, r2935419);
        return r2935420;
}

↓

double f(double a) {
        double r2935421 = a;
        double r2935422 = asin(r2935421);
        double r2935423 = fmod(r2935421, r2935422);
        double r2935424 = atan(r2935423);
        double r2935425 = r2935421 * r2935421;
        double r2935426 = 2.0;
        double r2935427 = r2935425 / r2935426;
        double r2935428 = pow(r2935424, r2935427);
        double r2935429 = r2935428 * r2935428;
        return r2935429;
}

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 2019152 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))