_multiplyComplex, real part

Average Error: 0.0 → 0.0

Time: 2.2s

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 r665284 = x_re;
        double r665285 = y_re;
        double r665286 = r665284 * r665285;
        double r665287 = x_im;
        double r665288 = y_im;
        double r665289 = r665287 * r665288;
        double r665290 = r665286 - r665289;
        return r665290;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r665291 = x_re;
        double r665292 = y_re;
        double r665293 = x_im;
        double r665294 = y_im;
        double r665295 = r665293 * r665294;
        double r665296 = -r665295;
        double r665297 = fma(r665291, r665292, r665296);
        return r665297;
}

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 2019112 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))