math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 3.3s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r8666 = re;
        double r8667 = im;
        double r8668 = r8666 * r8667;
        double r8669 = r8667 * r8666;
        double r8670 = r8668 + r8669;
        return r8670;
}

↓

double f(double re, double im) {
        double r8671 = im;
        double r8672 = re;
        double r8673 = r8672 + r8672;
        double r8674 = r8671 * r8673;
        return r8674;
}

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 p16-distribute-lft-out 0.1

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019104 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))