_multiplyComplex, imaginary part

Average Error: 0.0 → 0.0

Time: 3.8s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x.re \cdot y.im + x.im \cdot y.re\]

↓

\[\mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)\]

C

double f(double x_re, double x_im, double y_re, double y_im) {
        double r98972 = x_re;
        double r98973 = y_im;
        double r98974 = r98972 * r98973;
        double r98975 = x_im;
        double r98976 = y_re;
        double r98977 = r98975 * r98976;
        double r98978 = r98974 + r98977;
        return r98978;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r98979 = x_re;
        double r98980 = y_im;
        double r98981 = x_im;
        double r98982 = y_re;
        double r98983 = r98981 * r98982;
        double r98984 = fma(r98979, r98980, r98983);
        return r98984;
}

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

   \[x.re \cdot y.im + x.im \cdot y.re\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))