Fuzzer 002

Average Error: 30.4 → 30.3

Time: 6.4s

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 r80367 = a;
        double r80368 = asin(r80367);
        double r80369 = fmod(r80367, r80368);
        double r80370 = atan(r80369);
        double r80371 = r80367 * r80367;
        double r80372 = pow(r80370, r80371);
        return r80372;
}

↓

double f(double a) {
        double r80373 = a;
        double r80374 = asin(r80373);
        double r80375 = fmod(r80373, r80374);
        double r80376 = atan(r80375);
        double r80377 = r80373 * r80373;
        double r80378 = 2.0;
        double r80379 = r80377 / r80378;
        double r80380 = pow(r80376, r80379);
        double r80381 = r80380 * r80380;
        return r80381;
}

Error

Bits error versus a

Derivation

1. Initial program 30.4

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

3. Applied sqr-pow 30.3

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

4. Final simplification 30.3

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

Reproduce

herbie shell --seed 2020064 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))