Fuzzer 002

Average Error: 30.8 → 30.8

Time: 21.7s

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 r4156444 = a;
        double r4156445 = asin(r4156444);
        double r4156446 = fmod(r4156444, r4156445);
        double r4156447 = atan(r4156446);
        double r4156448 = r4156444 * r4156444;
        double r4156449 = pow(r4156447, r4156448);
        return r4156449;
}

↓

double f(double a) {
        double r4156450 = a;
        double r4156451 = asin(r4156450);
        double r4156452 = fmod(r4156450, r4156451);
        double r4156453 = atan(r4156452);
        double r4156454 = r4156450 * r4156450;
        double r4156455 = 2.0;
        double r4156456 = r4156454 / r4156455;
        double r4156457 = pow(r4156453, r4156456);
        double r4156458 = r4156457 * r4156457;
        return r4156458;
}

Error

Bits error versus a

Derivation

1. Initial program 30.8

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

3. Applied sqr-pow 30.8

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

4. Final simplification 30.8

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))