Average Error: 0.0 → 0.0
Time: 5.3s
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 r485593 = re;
        double r485594 = im;
        double r485595 = r485593 * r485594;
        double r485596 = r485594 * r485593;
        double r485597 = r485595 + r485596;
        return r485597;
}
↓
double f(double re, double im) {
        double r485598 = im;
        double r485599 = re;
        double r485600 = r485599 + r485599;
        double r485601 = r485598 * r485600;
        return r485601;
}

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 2019173 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))