Average Error: 0.0 → 0.0
Time: 3.7s
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 r643 = re;
        double r644 = im;
        double r645 = r643 * r644;
        double r646 = r644 * r643;
        double r647 = r645 + r646;
        return r647;
}
↓
double f(double re, double im) {
        double r648 = re;
        double r649 = im;
        double r650 = r648 * r649;
        double r651 = r649 * r648;
        double r652 = r650 + r651;
        return r652;
}

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 2020047 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))