Average Error: 0.0 → 0.0
Time: 1.5s
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 r8249 = re;
        double r8250 = im;
        double r8251 = r8249 * r8250;
        double r8252 = r8250 * r8249;
        double r8253 = r8251 + r8252;
        return r8253;
}
↓
double f(double re, double im) {
        double r8254 = re;
        double r8255 = im;
        double r8256 = r8255 + r8255;
        double r8257 = r8254 * r8256;
        return r8257;
}

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