Fuzzer 002

Average Error: 31.2 → 31.2

Time: 26.2s

Precision: 64

Math

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

↓

\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}\]

C

double f(double a) {
        double r66472 = a;
        double r66473 = asin(r66472);
        double r66474 = fmod(r66472, r66473);
        double r66475 = atan(r66474);
        double r66476 = r66472 * r66472;
        double r66477 = pow(r66475, r66476);
        return r66477;
}

↓

double f(double a) {
        double r66478 = a;
        double r66479 = asin(r66478);
        double r66480 = fmod(r66478, r66479);
        double r66481 = atan(r66480);
        double r66482 = r66478 * r66478;
        double r66483 = 2.0;
        double r66484 = r66482 / r66483;
        double r66485 = pow(r66481, r66484);
        double r66486 = r66485 * r66485;
        return r66486;
}

Error

Bits error versus a

Derivation

1. Initial program 31.2

   \[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
2. Using strategy rm

3. Applied sqr-pow 31.2

   \[\leadsto \color{blue}{{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}}\]

4. Final simplification 31.2

   \[\leadsto {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))