Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[im \cdot \left(re + re\right)\]
re \cdot im + im \cdot re
↓
im \cdot \left(re + re\right)
double f(double re, double im) {
        double r68339 = re;
        double r68340 = im;
        double r68341 = r68339 * r68340;
        double r68342 = r68340 * r68339;
        double r68343 = r68341 + r68342;
        return r68343;
}
↓
double f(double re, double im) {
        double r68344 = im;
        double r68345 = re;
        double r68346 = r68345 + r68345;
        double r68347 = r68344 * r68346;
        return r68347;
}

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-rgt-out0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))