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 r675 = re;
        double r676 = im;
        double r677 = r675 * r676;
        double r678 = r676 * r675;
        double r679 = r677 + r678;
        return r679;
}

↓

double f(double re, double im) {
        double r680 = im;
        double r681 = re;
        double r682 = r681 + r681;
        double r683 = r680 * r682;
        return r683;
}

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 2020024 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))