math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 4.9s

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 r10885 = re;
        double r10886 = im;
        double r10887 = r10885 * r10886;
        double r10888 = r10886 * r10885;
        double r10889 = r10887 + r10888;
        return r10889;
}

↓

double f(double re, double im) {
        double r10890 = im;
        double r10891 = re;
        double r10892 = r10891 + r10891;
        double r10893 = r10890 * r10892;
        return r10893;
}

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 2019138 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))