math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 1.8m

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 r17409 = re;
        double r17410 = im;
        double r17411 = r17409 * r17410;
        double r17412 = r17410 * r17409;
        double r17413 = r17411 + r17412;
        return r17413;
}

↓

double f(double re, double im) {
        double r17414 = im;
        double r17415 = re;
        double r17416 = r17415 + r17415;
        double r17417 = r17414 * r17416;
        return r17417;
}

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 0.1

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019151 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))