math.square on complex, real part

Average Error: 0.0 → 0.0

Time: 8.5s

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 r334405 = re;
        double r334406 = r334405 * r334405;
        double r334407 = im;
        double r334408 = r334407 * r334407;
        double r334409 = r334406 - r334408;
        return r334409;
}

↓

double f(double re, double im) {
        double r334410 = im;
        double r334411 = re;
        double r334412 = r334410 + r334411;
        double r334413 = r334411 - r334410;
        double r334414 = r334412 * r334413;
        return r334414;
}

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 2019171 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))