Average Error: 0.3 → 0.3
Time: 9.0s
Precision: 64
\[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]
↓
\[x.re \cdot y.re - x.im \cdot y.im\]
\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)
↓
x.re \cdot y.re - x.im \cdot y.im
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1532307 = x_re;
        double r1532308 = y_re;
        double r1532309 = r1532307 * r1532308;
        double r1532310 = x_im;
        double r1532311 = y_im;
        double r1532312 = r1532310 * r1532311;
        double r1532313 = r1532309 - r1532312;
        return r1532313;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1532314 = x_re;
        double r1532315 = y_re;
        double r1532316 = r1532314 * r1532315;
        double r1532317 = x_im;
        double r1532318 = y_im;
        double r1532319 = r1532317 * r1532318;
        double r1532320 = r1532316 - r1532319;
        return r1532320;
}

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 0.3

    \[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]

  2. Final simplification0.3

    \[\leadsto x.re \cdot y.re - x.im \cdot y.im\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))