math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 3.5s

Precision: 64

Math

\[\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\]

↓

\[re \cdot \left(im + im\right)\]

C

double f(double re, double im) {
        double r8654 = re;
        double r8655 = im;
        double r8656 = r8654 * r8655;
        double r8657 = r8655 * r8654;
        double r8658 = r8656 + r8657;
        return r8658;
}

↓

double f(double re, double im) {
        double r8659 = re;
        double r8660 = im;
        double r8661 = r8660 + r8660;
        double r8662 = r8659 * r8661;
        return r8662;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.2

   \[\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\]

2. Simplified 0.2

   \[\leadsto \color{blue}{\frac{\left(im \cdot re\right)}{\left(im \cdot re\right)}}\]
3. Using strategy rm

4. Applied distribute-rgt-out 0.1

   \[\leadsto \color{blue}{re \cdot \left(\frac{im}{im}\right)}\]

5. Final simplification 0.1

   \[\leadsto re \cdot \left(im + im\right)\]

Reproduce

herbie shell --seed 2019119 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))