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 r8130 = re;
        double r8131 = im;
        double r8132 = r8130 * r8131;
        double r8133 = r8131 * r8130;
        double r8134 = r8132 + r8133;
        return r8134;
}

↓

double f(double re, double im) {
        double r8135 = re;
        double r8136 = im;
        double r8137 = r8136 + r8136;
        double r8138 = r8135 * r8137;
        return r8138;
}

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 2019208 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))