Fuzzer 002

Average Error: 31.4 → 31.4

Time: 20.4s

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 r120403 = a;
        double r120404 = asin(r120403);
        double r120405 = fmod(r120403, r120404);
        double r120406 = atan(r120405);
        double r120407 = r120403 * r120403;
        double r120408 = pow(r120406, r120407);
        return r120408;
}

↓

double f(double a) {
        double r120409 = a;
        double r120410 = asin(r120409);
        double r120411 = fmod(r120409, r120410);
        double r120412 = atan(r120411);
        double r120413 = r120409 * r120409;
        double r120414 = 2.0;
        double r120415 = r120413 / r120414;
        double r120416 = pow(r120412, r120415);
        double r120417 = r120416 * r120416;
        return r120417;
}

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 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))