Average Error: 0.0 → 0.0

Time: 1.1s

Precision: 64

\[re \cdot im + im \cdot re\]

↓

\[re \cdot \left(im + im\right)\]

re \cdot im + im \cdot re

↓

re \cdot \left(im + im\right)

double f(double re, double im) {
        double r8127 = re;
        double r8128 = im;
        double r8129 = r8127 * r8128;
        double r8130 = r8128 * r8127;
        double r8131 = r8129 + r8130;
        return r8131;
}

↓

double f(double re, double im) {
        double r8132 = re;
        double r8133 = im;
        double r8134 = r8133 + r8133;
        double r8135 = r8132 * r8134;
        return r8135;
}

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

Reproduce

herbie shell --seed 2019323 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))