Average Error: 0.0 → 0.0
Time: 1.3s
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 r8414 = re;
        double r8415 = im;
        double r8416 = r8414 * r8415;
        double r8417 = r8415 * r8414;
        double r8418 = r8416 + r8417;
        return r8418;
}
↓
double f(double re, double im) {
        double r8419 = re;
        double r8420 = im;
        double r8421 = r8420 + r8420;
        double r8422 = r8419 * r8421;
        return r8422;
}

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 2019152 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))