Average Error: 0.1 → 0
Time: 12.4s
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 r28459294 = x;
        double r28459295 = y;
        double r28459296 = r28459294 - r28459295;
        double r28459297 = 2.0;
        double r28459298 = r28459296 / r28459297;
        double r28459299 = r28459294 + r28459298;
        return r28459299;
}
↓
double f(double x, double y) {
        double r28459300 = 1.5;
        double r28459301 = x;
        double r28459302 = 0.5;
        double r28459303 = y;
        double r28459304 = r28459302 * r28459303;
        double r28459305 = -r28459304;
        double r28459306 = fma(r28459300, r28459301, r28459305);
        return r28459306;
}

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 2019164 +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)))