math.square on complex, real part

Average Error: 0.0 → 0.0

Time: 12.7s

Precision: 64

Math

\[re \cdot re - im \cdot im\]

↓

\[\left(im + re\right) \cdot \left(re - im\right)\]

C

double f(double re, double im) {
        double r332992 = re;
        double r332993 = r332992 * r332992;
        double r332994 = im;
        double r332995 = r332994 * r332994;
        double r332996 = r332993 - r332995;
        return r332996;
}

↓

double f(double re, double im) {
        double r332997 = im;
        double r332998 = re;
        double r332999 = r332997 + r332998;
        double r333000 = r332998 - r332997;
        double r333001 = r332999 * r333000;
        return r333001;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.0

   \[re \cdot re - im \cdot im\]
2. Using strategy rm

3. Applied difference-of-squares 0.0

   \[\leadsto \color{blue}{\left(re + im\right) \cdot \left(re - im\right)}\]

4. Final simplification 0.0

   \[\leadsto \left(im + re\right) \cdot \left(re - im\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))