Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[(x.re \cdot y.im + \left(x.im \cdot y.re\right))_*\]
x.re \cdot y.im + x.im \cdot y.re
↓
(x.re \cdot y.im + \left(x.im \cdot y.re\right))_*
double f(double x_re, double x_im, double y_re, double y_im) {
        double r668088 = x_re;
        double r668089 = y_im;
        double r668090 = r668088 * r668089;
        double r668091 = x_im;
        double r668092 = y_re;
        double r668093 = r668091 * r668092;
        double r668094 = r668090 + r668093;
        return r668094;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r668095 = x_re;
        double r668096 = y_im;
        double r668097 = x_im;
        double r668098 = y_re;
        double r668099 = r668097 * r668098;
        double r668100 = fma(r668095, r668096, r668099);
        return r668100;
}

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. Simplified0.0

    \[\leadsto \color{blue}{(x.re \cdot y.im + \left(x.im \cdot y.re\right))_*}\]

  3. Final simplification0.0

    \[\leadsto (x.re \cdot y.im + \left(x.im \cdot y.re\right))_*\]

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))