Average Error: 0.0 → 0.0
Time: 3.2s
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 r68205 = re;
        double r68206 = im;
        double r68207 = r68205 * r68206;
        double r68208 = r68206 * r68205;
        double r68209 = r68207 + r68208;
        return r68209;
}
↓
double f(double re, double im) {
        double r68210 = re;
        double r68211 = im;
        double r68212 = r68211 + r68211;
        double r68213 = r68210 * r68212;
        return r68213;
}

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 2019155 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))