Average Error: 0.0 → 0.0
Time: 2.4s
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 r622 = re;
        double r623 = im;
        double r624 = r622 * r623;
        double r625 = r623 * r622;
        double r626 = r624 + r625;
        return r626;
}
↓
double f(double re, double im) {
        double r627 = re;
        double r628 = im;
        double r629 = r628 + r628;
        double r630 = r627 * r629;
        return r630;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{2 \cdot \left(re \cdot im\right)}\]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))