Average Error: 0.0 → 0.0

Time: 2.1s

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 r8574 = re;
        double r8575 = im;
        double r8576 = r8574 * r8575;
        double r8577 = r8575 * r8574;
        double r8578 = r8576 + r8577;
        return r8578;
}

↓

double f(double re, double im) {
        double r8579 = re;
        double r8580 = im;
        double r8581 = r8580 + r8580;
        double r8582 = r8579 * r8581;
        return r8582;
}

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 2019168 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))