Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A

Average Error: 1.4 → 1.4

Time: 11.5s

Precision: 64

Math

\[x + y \cdot \frac{z - t}{z - a}\]

↓

\[x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r657677 = x;
        double r657678 = y;
        double r657679 = z;
        double r657680 = t;
        double r657681 = r657679 - r657680;
        double r657682 = a;
        double r657683 = r657679 - r657682;
        double r657684 = r657681 / r657683;
        double r657685 = r657678 * r657684;
        double r657686 = r657677 + r657685;
        return r657686;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r657687 = x;
        double r657688 = y;
        double r657689 = z;
        double r657690 = a;
        double r657691 = r657689 - r657690;
        double r657692 = r657689 / r657691;
        double r657693 = t;
        double r657694 = r657693 / r657691;
        double r657695 = r657692 - r657694;
        double r657696 = r657688 * r657695;
        double r657697 = r657687 + r657696;
        return r657697;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.4
Target	1.3
Herbie	1.4

\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

1. Initial program 1.4

   \[x + y \cdot \frac{z - t}{z - a}\]
2. Using strategy rm

3. Applied div-sub 1.4

   \[\leadsto x + y \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{t}{z - a}\right)}\]

4. Final simplification 1.4

   \[\leadsto x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))