Average Error: 0.0 → 0
Time: 8.3s
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 r755 = re;
        double r756 = im;
        double r757 = r755 * r756;
        double r758 = r756 * r755;
        double r759 = r757 + r758;
        return r759;
}
↓
double f(double re, double im) {
        double r760 = re;
        double r761 = im;
        double r762 = r761 + r761;
        double r763 = r760 * r762;
        return r763;
}

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

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))