Average Error: 0.0 → 0.0

Time: 374.0ms

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 r1364 = re;
        double r1365 = im;
        double r1366 = r1364 * r1365;
        double r1367 = r1365 * r1364;
        double r1368 = r1366 + r1367;
        return r1368;
}

↓

double f(double re, double im) {
        double r1369 = im;
        double r1370 = re;
        double r1371 = r1370 + r1370;
        double r1372 = r1369 * r1371;
        return r1372;
}

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 2020046 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))