Average Error: 0.0 → 0.0
Time: 3.6s
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 r645 = re;
        double r646 = im;
        double r647 = r645 * r646;
        double r648 = r646 * r645;
        double r649 = r647 + r648;
        return r649;
}
↓
double f(double re, double im) {
        double r650 = re;
        double r651 = im;
        double r652 = r650 * r651;
        double r653 = r651 * r650;
        double r654 = r652 + r653;
        return r654;
}

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 2020043 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))