Average Error: 0.0 → 0.0

Time: 1.3s

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 r8367 = re;
        double r8368 = im;
        double r8369 = r8367 * r8368;
        double r8370 = r8368 * r8367;
        double r8371 = r8369 + r8370;
        return r8371;
}

↓

double f(double re, double im) {
        double r8372 = im;
        double r8373 = re;
        double r8374 = r8373 + r8373;
        double r8375 = r8372 * r8374;
        return r8375;
}

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 2019137 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))