Average Error: 0.0 → 0.0

Time: 1.2s

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 r8400 = re;
        double r8401 = im;
        double r8402 = r8400 * r8401;
        double r8403 = r8401 * r8400;
        double r8404 = r8402 + r8403;
        return r8404;
}

↓

double f(double re, double im) {
        double r8405 = re;
        double r8406 = im;
        double r8407 = r8406 + r8406;
        double r8408 = r8405 * r8407;
        return r8408;
}

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 2019133 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))