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 r270 = re;
        double r271 = im;
        double r272 = r270 * r271;
        double r273 = r271 * r270;
        double r274 = r272 + r273;
        return r274;
}

↓

double f(double re, double im) {
        double r275 = im;
        double r276 = re;
        double r277 = r276 + r276;
        double r278 = r275 * r277;
        return r278;
}

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 2020003 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))