Average Error: 0.0 → 0.0
Time: 4.8s
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 r1467054 = x_re;
        double r1467055 = y_re;
        double r1467056 = r1467054 * r1467055;
        double r1467057 = x_im;
        double r1467058 = y_im;
        double r1467059 = r1467057 * r1467058;
        double r1467060 = r1467056 - r1467059;
        return r1467060;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1467061 = x_re;
        double r1467062 = y_re;
        double r1467063 = x_im;
        double r1467064 = y_im;
        double r1467065 = r1467063 * r1467064;
        double r1467066 = -r1467065;
        double r1467067 = fma(r1467061, r1467062, r1467066);
        return r1467067;
}

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 2019143 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))