_multiplyComplex, imaginary part

Average Error: 0.0 → 0.0

Time: 829.0ms

Precision: 64

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 r80501 = x_re;
        double r80502 = y_im;
        double r80503 = r80501 * r80502;
        double r80504 = x_im;
        double r80505 = y_re;
        double r80506 = r80504 * r80505;
        double r80507 = r80503 + r80506;
        return r80507;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r80508 = x_re;
        double r80509 = y_im;
        double r80510 = x_im;
        double r80511 = y_re;
        double r80512 = r80510 * r80511;
        double r80513 = fma(r80508, r80509, r80512);
        return r80513;
}

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 2020083 +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)))