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 r8378 = re;
        double r8379 = im;
        double r8380 = r8378 * r8379;
        double r8381 = r8379 * r8378;
        double r8382 = r8380 + r8381;
        return r8382;
}

↓

double f(double re, double im) {
        double r8383 = re;
        double r8384 = im;
        double r8385 = r8384 + r8384;
        double r8386 = r8383 * r8385;
        return r8386;
}

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 2019347 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))