Average Error: 0.0 → 0.0

Time: 437.0ms

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 r1355 = re;
        double r1356 = im;
        double r1357 = r1355 * r1356;
        double r1358 = r1356 * r1355;
        double r1359 = r1357 + r1358;
        return r1359;
}

↓

double f(double re, double im) {
        double r1360 = im;
        double r1361 = re;
        double r1362 = r1361 + r1361;
        double r1363 = r1360 * r1362;
        return r1363;
}

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 2020001 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))