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 r41993 = x_re;
        double r41994 = y_re;
        double r41995 = r41993 * r41994;
        double r41996 = x_im;
        double r41997 = y_im;
        double r41998 = r41996 * r41997;
        double r41999 = r41995 - r41998;
        return r41999;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r42000 = x_re;
        double r42001 = y_re;
        double r42002 = x_im;
        double r42003 = y_im;
        double r42004 = r42002 * r42003;
        double r42005 = -r42004;
        double r42006 = fma(r42000, r42001, r42005);
        return r42006;
}

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 2020034 +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)))