Average Error: 0.0 → 0.0

Time: 1.7s

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 r8290 = re;
        double r8291 = im;
        double r8292 = r8290 * r8291;
        double r8293 = r8291 * r8290;
        double r8294 = r8292 + r8293;
        return r8294;
}

↓

double f(double re, double im) {
        double r8295 = im;
        double r8296 = re;
        double r8297 = r8296 + r8296;
        double r8298 = r8295 * r8297;
        return r8298;
}

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
\[\leadsto \color{blue}{\left(re + re\right) \cdot im}\]
Final simplification0.0
\[\leadsto im \cdot \left(re + re\right)\]

Reproduce

herbie shell --seed 2019139 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))