math.square on complex, imaginary part

Average Error: 0.1 → 0.1

Time: 1.7m

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 r16943 = re;
        double r16944 = im;
        double r16945 = r16943 * r16944;
        double r16946 = r16944 * r16943;
        double r16947 = r16945 + r16946;
        return r16947;
}

↓

double f(double re, double im) {
        double r16948 = im;
        double r16949 = re;
        double r16950 = r16949 + r16949;
        double r16951 = r16948 * r16950;
        return r16951;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.1

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

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 2019153 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))