_multiplyComplex, imaginary part

Average Error: 0.0 → 0.0

Time: 1.6s

Precision: 64

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

Math

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

↓

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

C

double f(double x_re, double x_im, double y_re, double y_im) {
        double r39609 = x_re;
        double r39610 = y_im;
        double r39611 = r39609 * r39610;
        double r39612 = x_im;
        double r39613 = y_re;
        double r39614 = r39612 * r39613;
        double r39615 = r39611 + r39614;
        return r39615;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r39616 = x_re;
        double r39617 = y_im;
        double r39618 = x_im;
        double r39619 = y_re;
        double r39620 = r39618 * r39619;
        double r39621 = fma(r39616, r39617, r39620);
        return r39621;
}

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

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

2. Simplified 0.0

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

3. Final simplification 0.0

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

Reproduce

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