Average Error: 0.0 → 0.0
Time: 450.0ms
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[re \cdot im + im \cdot re\]
re \cdot im + im \cdot re
↓
re \cdot im + im \cdot re
double f(double re, double im) {
        double r692 = re;
        double r693 = im;
        double r694 = r692 * r693;
        double r695 = r693 * r692;
        double r696 = r694 + r695;
        return r696;
}
↓
double f(double re, double im) {
        double r697 = re;
        double r698 = im;
        double r699 = r697 * r698;
        double r700 = r698 * r697;
        double r701 = r699 + r700;
        return r701;
}

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. Final simplification0.0

    \[\leadsto re \cdot im + im \cdot re\]

Reproduce

herbie shell --seed 2019347 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))