Average Error: 0.0 → 0.0
Time: 6.0s
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 r1311150 = x_re;
        double r1311151 = y_re;
        double r1311152 = r1311150 * r1311151;
        double r1311153 = x_im;
        double r1311154 = y_im;
        double r1311155 = r1311153 * r1311154;
        double r1311156 = r1311152 - r1311155;
        return r1311156;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1311157 = x_re;
        double r1311158 = y_re;
        double r1311159 = x_im;
        double r1311160 = y_im;
        double r1311161 = r1311159 * r1311160;
        double r1311162 = -r1311161;
        double r1311163 = fma(r1311157, r1311158, r1311162);
        return r1311163;
}

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 2019134 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))