math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 12.1s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r800573 = re;
        double r800574 = r800573 * r800573;
        double r800575 = im;
        double r800576 = r800575 * r800575;
        double r800577 = r800574 - r800576;
        return r800577;
}

↓

double f(double re, double im) {
        double r800578 = re;
        double r800579 = im;
        double r800580 = r800578 - r800579;
        double r800581 = r800579 + r800578;
        double r800582 = r800580 * r800581;
        return r800582;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.3

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

2. Simplified 0.1

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019128 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))