_multiplyComplex, real part

Average Error: 0.0 → 0.0

Time: 2.5s

Precision: 64

Math

\[x.re \cdot y.re - x.im \cdot y.im\]

↓

\[(x.re \cdot y.re + \left(-x.im \cdot y.im\right))_*\]

C

double f(double x_re, double x_im, double y_re, double y_im) {
        double r4544424 = x_re;
        double r4544425 = y_re;
        double r4544426 = r4544424 * r4544425;
        double r4544427 = x_im;
        double r4544428 = y_im;
        double r4544429 = r4544427 * r4544428;
        double r4544430 = r4544426 - r4544429;
        return r4544430;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r4544431 = x_re;
        double r4544432 = y_re;
        double r4544433 = x_im;
        double r4544434 = y_im;
        double r4544435 = r4544433 * r4544434;
        double r4544436 = -r4544435;
        double r4544437 = fma(r4544431, r4544432, r4544436);
        return r4544437;
}

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Derivation

1. Initial program 0.0

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

3. Applied fma-neg 0.0

   \[\leadsto \color{blue}{(x.re \cdot y.re + \left(-x.im \cdot y.im\right))_*}\]

4. Final simplification 0.0

   \[\leadsto (x.re \cdot y.re + \left(-x.im \cdot y.im\right))_*\]

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))