Average Error: 0.3 → 0.3
Time: 6.8s
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 r979122 = x_re;
        double r979123 = y_re;
        double r979124 = r979122 * r979123;
        double r979125 = x_im;
        double r979126 = y_im;
        double r979127 = r979125 * r979126;
        double r979128 = r979124 - r979127;
        return r979128;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r979129 = x_re;
        double r979130 = y_re;
        double r979131 = r979129 * r979130;
        double r979132 = x_im;
        double r979133 = y_im;
        double r979134 = r979132 * r979133;
        double r979135 = r979131 - r979134;
        return r979135;
}

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 2019121 +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)))