Fuzzer 002

Average Error: 31.2 → 31.1

Time: 24.1s

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 r3463628 = a;
        double r3463629 = asin(r3463628);
        double r3463630 = fmod(r3463628, r3463629);
        double r3463631 = atan(r3463630);
        double r3463632 = r3463628 * r3463628;
        double r3463633 = pow(r3463631, r3463632);
        return r3463633;
}

↓

double f(double a) {
        double r3463634 = a;
        double r3463635 = asin(r3463634);
        double r3463636 = fmod(r3463634, r3463635);
        double r3463637 = atan(r3463636);
        double r3463638 = r3463634 * r3463634;
        double r3463639 = 2.0;
        double r3463640 = r3463638 / r3463639;
        double r3463641 = pow(r3463637, r3463640);
        double r3463642 = r3463641 * r3463641;
        return r3463642;
}

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 31.1

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

4. Final simplification 31.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))