Average Error: 0.0 → 0.0

Time: 726.0ms

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 r98 = re;
        double r99 = im;
        double r100 = r98 * r99;
        double r101 = r99 * r98;
        double r102 = r100 + r101;
        return r102;
}

↓

double f(double re, double im) {
        double r103 = im;
        double r104 = re;
        double r105 = r104 + r104;
        double r106 = r103 * r105;
        return r106;
}

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 2020025 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))