Fuzzer 002

Average Error: 30.9 → 30.9

Time: 5.9s

Precision: 64

Math

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

↓

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

C

double f(double a) {
        double r152422 = a;
        double r152423 = asin(r152422);
        double r152424 = fmod(r152422, r152423);
        double r152425 = atan(r152424);
        double r152426 = r152422 * r152422;
        double r152427 = pow(r152425, r152426);
        return r152427;
}

↓

double f(double a) {
        double r152428 = a;
        double r152429 = asin(r152428);
        double r152430 = fmod(r152428, r152429);
        double r152431 = atan(r152430);
        double r152432 = r152428 * r152428;
        double r152433 = 2.0;
        double r152434 = r152432 / r152433;
        double r152435 = pow(r152431, r152434);
        double r152436 = r152435 * r152435;
        return r152436;
}

Error

Bits error versus a

Derivation

1. Initial program 30.9

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

3. Applied sqr-pow 30.9

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

4. Final simplification 30.9

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

Reproduce

herbie shell --seed 2019344 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))