_multiplyComplex, real part

Average Error: 0.0 → 0.0

Time: 6.8s

Precision: 64

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

Math

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

↓

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

C

double f(double x_re, double x_im, double y_re, double y_im) {
        double r81745 = x_re;
        double r81746 = y_re;
        double r81747 = r81745 * r81746;
        double r81748 = x_im;
        double r81749 = y_im;
        double r81750 = r81748 * r81749;
        double r81751 = r81747 - r81750;
        return r81751;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r81752 = x_re;
        double r81753 = y_re;
        double r81754 = y_im;
        double r81755 = x_im;
        double r81756 = r81754 * r81755;
        double r81757 = -r81756;
        double r81758 = fma(r81752, r81753, r81757);
        return r81758;
}

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. Simplified 0.0

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

5. Final simplification 0.0

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

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)))