Average Error: 0.0 → 0.0
Time: 3.1s
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 r56390 = re;
        double r56391 = im;
        double r56392 = r56390 * r56391;
        double r56393 = r56391 * r56390;
        double r56394 = r56392 + r56393;
        return r56394;
}
↓
double f(double re, double im) {
        double r56395 = im;
        double r56396 = re;
        double r56397 = r56396 + r56396;
        double r56398 = r56395 * r56397;
        return r56398;
}

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