Average Error: 0.0 → 0.0

Time: 1.6s

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 r8261 = re;
        double r8262 = im;
        double r8263 = r8261 * r8262;
        double r8264 = r8262 * r8261;
        double r8265 = r8263 + r8264;
        return r8265;
}

↓

double f(double re, double im) {
        double r8266 = re;
        double r8267 = im;
        double r8268 = r8267 + r8267;
        double r8269 = r8266 * r8268;
        return r8269;
}

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 2019172 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))