Fuzzer 002

Average Error: 31.5 → 31.4

Time: 5.7s

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 r97375 = a;
        double r97376 = asin(r97375);
        double r97377 = fmod(r97375, r97376);
        double r97378 = atan(r97377);
        double r97379 = r97375 * r97375;
        double r97380 = pow(r97378, r97379);
        return r97380;
}

↓

double f(double a) {
        double r97381 = a;
        double r97382 = asin(r97381);
        double r97383 = fmod(r97381, r97382);
        double r97384 = atan(r97383);
        double r97385 = r97381 * r97381;
        double r97386 = 2.0;
        double r97387 = r97385 / r97386;
        double r97388 = pow(r97384, r97387);
        double r97389 = r97388 * r97388;
        return r97389;
}

Error

Bits error versus a

Derivation

1. Initial program 31.5

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

3. Applied sqr-pow 31.4

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

4. Final simplification 31.4

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

Reproduce

herbie shell --seed 2020002 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))