_multiplyComplex, real part

Average Error: 0.0 → 0.0

Time: 5.2s

Precision: 64

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 r2052135 = x_re;
        double r2052136 = y_re;
        double r2052137 = r2052135 * r2052136;
        double r2052138 = x_im;
        double r2052139 = y_im;
        double r2052140 = r2052138 * r2052139;
        double r2052141 = r2052137 - r2052140;
        return r2052141;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r2052142 = x_re;
        double r2052143 = y_re;
        double r2052144 = x_im;
        double r2052145 = y_im;
        double r2052146 = r2052144 * r2052145;
        double r2052147 = -r2052146;
        double r2052148 = fma(r2052142, r2052143, r2052147);
        return r2052148;
}

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 2019144 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))