Average Error: 0.0 → 0.0

Time: 967.0ms

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 r8124 = re;
        double r8125 = im;
        double r8126 = r8124 * r8125;
        double r8127 = r8125 * r8124;
        double r8128 = r8126 + r8127;
        return r8128;
}

↓

double f(double re, double im) {
        double r8129 = re;
        double r8130 = im;
        double r8131 = r8130 + r8130;
        double r8132 = r8129 * r8131;
        return r8132;
}

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 2019315 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))