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

Average Error: 1.2 → 1.3

Time: 17.4s

Precision: 64

Math

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

↓

\[x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{z - a}\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r431863 = x;
        double r431864 = y;
        double r431865 = z;
        double r431866 = t;
        double r431867 = r431865 - r431866;
        double r431868 = a;
        double r431869 = r431865 - r431868;
        double r431870 = r431867 / r431869;
        double r431871 = r431864 * r431870;
        double r431872 = r431863 + r431871;
        return r431872;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r431873 = x;
        double r431874 = y;
        double r431875 = z;
        double r431876 = t;
        double r431877 = r431875 - r431876;
        double r431878 = 1.0;
        double r431879 = a;
        double r431880 = r431875 - r431879;
        double r431881 = r431878 / r431880;
        double r431882 = r431877 * r431881;
        double r431883 = r431874 * r431882;
        double r431884 = r431873 + r431883;
        return r431884;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.2
Target	1.1
Herbie	1.3

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

Derivation

1. Initial program 1.2

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

3. Applied div-inv 1.3

   \[\leadsto x + y \cdot \color{blue}{\left(\left(z - t\right) \cdot \frac{1}{z - a}\right)}\]

4. Final simplification 1.3

   \[\leadsto x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{z - a}\right)\]

Reproduce

herbie shell --seed 2019305 
(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)))))