Fuzzer 002

Average Error: 30.6 → 30.6

Time: 5.9s

Precision: 64

Math

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

↓

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

C

double f(double a) {
        double r88452 = a;
        double r88453 = asin(r88452);
        double r88454 = fmod(r88452, r88453);
        double r88455 = atan(r88454);
        double r88456 = r88452 * r88452;
        double r88457 = pow(r88455, r88456);
        return r88457;
}

↓

double f(double a) {
        double r88458 = a;
        double r88459 = asin(r88458);
        double r88460 = fmod(r88458, r88459);
        double r88461 = sqrt(r88460);
        double r88462 = r88461 * r88461;
        double r88463 = atan(r88462);
        double r88464 = r88458 * r88458;
        double r88465 = pow(r88463, r88464);
        return r88465;
}

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-sqr-sqrt 30.6

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

4. Final simplification 30.6

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

Reproduce

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