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 r8449 = re;
        double r8450 = im;
        double r8451 = r8449 * r8450;
        double r8452 = r8450 * r8449;
        double r8453 = r8451 + r8452;
        return r8453;
}
↓
double f(double re, double im) {
        double r8454 = re;
        double r8455 = im;
        double r8456 = r8455 + r8455;
        double r8457 = r8454 * r8456;
        return r8457;
}

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 2019104 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))