Average Error: 0.0 → 0
Time: 2.3s
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 r8432 = re;
        double r8433 = im;
        double r8434 = r8432 * r8433;
        double r8435 = r8433 * r8432;
        double r8436 = r8434 + r8435;
        return r8436;
}
↓
double f(double re, double im) {
        double r8437 = re;
        double r8438 = im;
        double r8439 = r8438 + r8438;
        double r8440 = r8437 * r8439;
        return r8440;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019124 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))