Fuzzer 002

Average Error: 31.3 → 31.3

Time: 19.2s

Precision: 64

Math

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

↓

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

C

double f(double a) {
        double r1818369 = a;
        double r1818370 = asin(r1818369);
        double r1818371 = fmod(r1818369, r1818370);
        double r1818372 = atan(r1818371);
        double r1818373 = r1818369 * r1818369;
        double r1818374 = pow(r1818372, r1818373);
        return r1818374;
}

↓

double f(double a) {
        double r1818375 = a;
        double r1818376 = asin(r1818375);
        double r1818377 = fmod(r1818375, r1818376);
        double r1818378 = cbrt(r1818377);
        double r1818379 = r1818378 * r1818378;
        double r1818380 = r1818378 * r1818379;
        double r1818381 = atan(r1818380);
        double r1818382 = r1818375 * r1818375;
        double r1818383 = pow(r1818381, r1818382);
        return r1818383;
}

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 add-cube-cbrt 31.3

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

4. Final simplification 31.3

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))