Fuzzer 002

Average Error: 30.6 → 30.6

Time: 25.6s

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 r4601338 = a;
        double r4601339 = asin(r4601338);
        double r4601340 = fmod(r4601338, r4601339);
        double r4601341 = atan(r4601340);
        double r4601342 = r4601338 * r4601338;
        double r4601343 = pow(r4601341, r4601342);
        return r4601343;
}

↓

double f(double a) {
        double r4601344 = a;
        double r4601345 = asin(r4601344);
        double r4601346 = fmod(r4601344, r4601345);
        double r4601347 = atan(r4601346);
        double r4601348 = r4601344 * r4601344;
        double r4601349 = 2.0;
        double r4601350 = r4601348 / r4601349;
        double r4601351 = pow(r4601347, r4601350);
        double r4601352 = r4601351 * r4601351;
        return r4601352;
}

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