Average Error: 0.0 → 0.0

Time: 422.0ms

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 r281 = re;
        double r282 = im;
        double r283 = r281 * r282;
        double r284 = r282 * r281;
        double r285 = r283 + r284;
        return r285;
}

↓

double f(double re, double im) {
        double r286 = im;
        double r287 = re;
        double r288 = r287 + r287;
        double r289 = r286 * r288;
        return r289;
}

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 2019362 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))