Average Error: 0.0 → 0.0
Time: 4.5s
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 r203749 = re;
        double r203750 = im;
        double r203751 = r203749 * r203750;
        double r203752 = r203750 * r203749;
        double r203753 = r203751 + r203752;
        return r203753;
}
↓
double f(double re, double im) {
        double r203754 = im;
        double r203755 = re;
        double r203756 = r203755 + r203755;
        double r203757 = r203754 * r203756;
        return r203757;
}

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 2019158 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))