Average Error: 0.0 → 0.0
Time: 5.2s
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 r1050071 = x_re;
        double r1050072 = y_re;
        double r1050073 = r1050071 * r1050072;
        double r1050074 = x_im;
        double r1050075 = y_im;
        double r1050076 = r1050074 * r1050075;
        double r1050077 = r1050073 - r1050076;
        return r1050077;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1050078 = x_re;
        double r1050079 = y_re;
        double r1050080 = x_im;
        double r1050081 = y_im;
        double r1050082 = r1050080 * r1050081;
        double r1050083 = -r1050082;
        double r1050084 = fma(r1050078, r1050079, r1050083);
        return r1050084;
}

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 2019139 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))