Average Error: 0.0 → 0.0

Time: 427.0ms

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 r1375 = re;
        double r1376 = im;
        double r1377 = r1375 * r1376;
        double r1378 = r1376 * r1375;
        double r1379 = r1377 + r1378;
        return r1379;
}

↓

double f(double re, double im) {
        double r1380 = im;
        double r1381 = re;
        double r1382 = r1381 + r1381;
        double r1383 = r1380 * r1382;
        return r1383;
}

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 2019346 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))