math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 4.7s

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 r10978 = re;
        double r10979 = im;
        double r10980 = r10978 * r10979;
        double r10981 = r10979 * r10978;
        double r10982 = r10980 + r10981;
        return r10982;
}

↓

double f(double re, double im) {
        double r10983 = im;
        double r10984 = re;
        double r10985 = r10984 + r10984;
        double r10986 = r10983 * r10985;
        return r10986;
}

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)))