Average Error: 0.0 → 0.0

Time: 419.0ms

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 r686 = re;
        double r687 = im;
        double r688 = r686 * r687;
        double r689 = r687 * r686;
        double r690 = r688 + r689;
        return r690;
}

↓

double f(double re, double im) {
        double r691 = im;
        double r692 = re;
        double r693 = r692 + r692;
        double r694 = r691 * r693;
        return r694;
}

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 2019353 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))