Average Error: 0.0 → 0.0
Time: 1.7s
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 r8433 = re;
        double r8434 = im;
        double r8435 = r8433 * r8434;
        double r8436 = r8434 * r8433;
        double r8437 = r8435 + r8436;
        return r8437;
}
↓
double f(double re, double im) {
        double r8438 = re;
        double r8439 = im;
        double r8440 = r8439 + r8439;
        double r8441 = r8438 * r8440;
        return r8441;
}

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 2019129 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))