Average Error: 0.0 → 0.0

Time: 620.0ms

Precision: 64

\[re \cdot im + im \cdot re\]

↓

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

re \cdot im + im \cdot re

↓

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

double f(double re, double im) {
        double r2857 = re;
        double r2858 = im;
        double r2859 = r2857 * r2858;
        double r2860 = r2858 * r2857;
        double r2861 = r2859 + r2860;
        return r2861;
}

↓

double f(double re, double im) {
        double r2862 = im;
        double r2863 = re;
        double r2864 = r2863 + r2863;
        double r2865 = r2862 * r2864;
        return r2865;
}

Error

The X axis uses an exponential scale — Bits error versus `re`

Try it out

In
Out

Enter valid numbers for all inputs

Derivation

Initial program 0.0
\[re \cdot im + im \cdot re\]
Simplified0.0
\[\leadsto \color{blue}{im \cdot \left(re + re\right)}\]
Final simplification0.0
\[\leadsto im \cdot \left(re + re\right)\]

Reproduce

herbie shell --seed 2020083 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))