Average Error: 0.0 → 0.0
Time: 2.4s
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 r5181107 = x_re;
        double r5181108 = y_im;
        double r5181109 = r5181107 * r5181108;
        double r5181110 = x_im;
        double r5181111 = y_re;
        double r5181112 = r5181110 * r5181111;
        double r5181113 = r5181109 + r5181112;
        return r5181113;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r5181114 = x_re;
        double r5181115 = y_im;
        double r5181116 = x_im;
        double r5181117 = y_re;
        double r5181118 = r5181116 * r5181117;
        double r5181119 = fma(r5181114, r5181115, r5181118);
        return r5181119;
}

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 2019104 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))