Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[\mathsf{fma}\left(x.re, y.re, -x.im \cdot y.im\right)\]
x.re \cdot y.re - x.im \cdot y.im
↓
\mathsf{fma}\left(x.re, y.re, -x.im \cdot y.im\right)
double f(double x_re, double x_im, double y_re, double y_im) {
        double r49201 = x_re;
        double r49202 = y_re;
        double r49203 = r49201 * r49202;
        double r49204 = x_im;
        double r49205 = y_im;
        double r49206 = r49204 * r49205;
        double r49207 = r49203 - r49206;
        return r49207;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r49208 = x_re;
        double r49209 = y_re;
        double r49210 = x_im;
        double r49211 = y_im;
        double r49212 = r49210 * r49211;
        double r49213 = -r49212;
        double r49214 = fma(r49208, r49209, r49213);
        return r49214;
}

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-neg0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 +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)))