Average Error: 0.1 → 0
Time: 14.5s
Precision: 64
\[x + \frac{x - y}{2.0}\]
↓
\[\mathsf{fma}\left(1.5, x, -0.5 \cdot y\right)\]
x + \frac{x - y}{2.0}
↓
\mathsf{fma}\left(1.5, x, -0.5 \cdot y\right)
double f(double x, double y) {
        double r32386707 = x;
        double r32386708 = y;
        double r32386709 = r32386707 - r32386708;
        double r32386710 = 2.0;
        double r32386711 = r32386709 / r32386710;
        double r32386712 = r32386707 + r32386711;
        return r32386712;
}
↓
double f(double x, double y) {
        double r32386713 = 1.5;
        double r32386714 = x;
        double r32386715 = 0.5;
        double r32386716 = y;
        double r32386717 = r32386715 * r32386716;
        double r32386718 = -r32386717;
        double r32386719 = fma(r32386713, r32386714, r32386718);
        return r32386719;
}

Error

Bits error versus x

Bits error versus y

Target

Original0.1
Target0.1
Herbie0
\[1.5 \cdot x - 0.5 \cdot y\]

Derivation

  1. Initial program 0.1

    \[x + \frac{x - y}{2.0}\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{1.5 \cdot x - 0.5 \cdot y}\]
  3. Using strategy rm

  4. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1.5, x, -0.5 \cdot y\right)}\]

  5. Final simplification0

    \[\leadsto \mathsf{fma}\left(1.5, x, -0.5 \cdot y\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"

  :herbie-target
  (- (* 1.5 x) (* 0.5 y))

  (+ x (/ (- x y) 2.0)))