Average Error: 0.0 → 0.0
Time: 9.0s
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 r167466 = re;
        double r167467 = im;
        double r167468 = r167466 * r167467;
        double r167469 = r167467 * r167466;
        double r167470 = r167468 + r167469;
        return r167470;
}
↓
double f(double re, double im) {
        double r167471 = re;
        double r167472 = im;
        double r167473 = r167472 + r167472;
        double r167474 = r167471 * r167473;
        return r167474;
}

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

    \[\leadsto \color{blue}{re \cdot im + re \cdot im}\]
  3. Using strategy rm

  4. Applied distribute-lft-out0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))