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 r8255 = re;
        double r8256 = im;
        double r8257 = r8255 * r8256;
        double r8258 = r8256 * r8255;
        double r8259 = r8257 + r8258;
        return r8259;
}

↓

double f(double re, double im) {
        double r8260 = re;
        double r8261 = im;
        double r8262 = r8261 + r8261;
        double r8263 = r8260 * r8262;
        return r8263;
}

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
\[\leadsto \color{blue}{\left(im + im\right) \cdot re}\]
Final simplification0.0
\[\leadsto re \cdot \left(im + im\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))