Average Error: 0.0 → 0.0
Time: 2.1s
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 r93984 = x_re;
        double r93985 = y_re;
        double r93986 = r93984 * r93985;
        double r93987 = x_im;
        double r93988 = y_im;
        double r93989 = r93987 * r93988;
        double r93990 = r93986 - r93989;
        return r93990;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r93991 = x_re;
        double r93992 = y_re;
        double r93993 = x_im;
        double r93994 = y_im;
        double r93995 = r93993 * r93994;
        double r93996 = -r93995;
        double r93997 = fma(r93991, r93992, r93996);
        return r93997;
}

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 2020025 +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)))