_multiplyComplex, real part

Average Error: 0.0 → 0.0

Time: 7.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\mathsf{fma}\left(x.re, y.re, -x.im \cdot y.im\right)\]

C

double f(double x_re, double x_im, double y_re, double y_im) {
        double r61377 = x_re;
        double r61378 = y_re;
        double r61379 = r61377 * r61378;
        double r61380 = x_im;
        double r61381 = y_im;
        double r61382 = r61380 * r61381;
        double r61383 = r61379 - r61382;
        return r61383;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r61384 = x_re;
        double r61385 = y_re;
        double r61386 = x_im;
        double r61387 = y_im;
        double r61388 = r61386 * r61387;
        double r61389 = -r61388;
        double r61390 = fma(r61384, r61385, r61389);
        return r61390;
}

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

   \[\leadsto \color{blue}{\mathsf{fma}\left(x.re, y.re, -x.im \cdot y.im\right)}\]

4. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(x.re, y.re, -x.im \cdot y.im\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))