Average Error: 0.0 → 0.0
Time: 420.0ms
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 r291 = re;
        double r292 = im;
        double r293 = r291 * r292;
        double r294 = r292 * r291;
        double r295 = r293 + r294;
        return r295;
}
↓
double f(double re, double im) {
        double r296 = re;
        double r297 = im;
        double r298 = r297 + r297;
        double r299 = r296 * r298;
        return r299;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[re \cdot im + im \cdot re\]

  2. Simplified0.0

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

  3. Final simplification0.0

    \[\leadsto re \cdot \left(im + im\right)\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))