Fuzzer 002

Average Error: 30.6 → 30.6

Time: 5.6s

Precision: 64

Math

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

↓

\[{\left(\tan^{-1} \left(\left(\sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)} \cdot \sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)}\right) \cdot \sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)}\right)\right)}^{\left(a \cdot a\right)}\]

C

double f(double a) {
        double r133352 = a;
        double r133353 = asin(r133352);
        double r133354 = fmod(r133352, r133353);
        double r133355 = atan(r133354);
        double r133356 = r133352 * r133352;
        double r133357 = pow(r133355, r133356);
        return r133357;
}

↓

double f(double a) {
        double r133358 = a;
        double r133359 = asin(r133358);
        double r133360 = fmod(r133358, r133359);
        double r133361 = cbrt(r133360);
        double r133362 = r133361 * r133361;
        double r133363 = r133362 * r133361;
        double r133364 = atan(r133363);
        double r133365 = r133358 * r133358;
        double r133366 = pow(r133364, r133365);
        return r133366;
}

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 add-cube-cbrt 30.6

   \[\leadsto {\left(\tan^{-1} \color{blue}{\left(\left(\sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)} \cdot \sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)}\right) \cdot \sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)}\right)}\right)}^{\left(a \cdot a\right)}\]

4. Final simplification 30.6

   \[\leadsto {\left(\tan^{-1} \left(\left(\sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)} \cdot \sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)}\right) \cdot \sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)}\right)\right)}^{\left(a \cdot a\right)}\]

Reproduce

herbie shell --seed 2020036 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))