Average Error: 0.0 → 0.0
Time: 1.8s
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 r8389 = re;
        double r8390 = im;
        double r8391 = r8389 * r8390;
        double r8392 = r8390 * r8389;
        double r8393 = r8391 + r8392;
        return r8393;
}
↓
double f(double re, double im) {
        double r8394 = re;
        double r8395 = im;
        double r8396 = r8395 + r8395;
        double r8397 = r8394 * r8396;
        return r8397;
}

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 2019130 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))