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

Average Error: 1.3 → 1.3

Time: 7.4s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r760788 = x;
        double r760789 = y;
        double r760790 = z;
        double r760791 = t;
        double r760792 = r760790 - r760791;
        double r760793 = a;
        double r760794 = r760790 - r760793;
        double r760795 = r760792 / r760794;
        double r760796 = r760789 * r760795;
        double r760797 = r760788 + r760796;
        return r760797;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r760798 = x;
        double r760799 = y;
        double r760800 = z;
        double r760801 = a;
        double r760802 = r760800 - r760801;
        double r760803 = r760800 / r760802;
        double r760804 = t;
        double r760805 = r760804 / r760802;
        double r760806 = r760803 - r760805;
        double r760807 = r760799 * r760806;
        double r760808 = r760798 + r760807;
        return r760808;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.3
Target	1.2
Herbie	1.3

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

Derivation

1. Initial program 1.3

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

3. Applied div-sub 1.3

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

4. Final simplification 1.3

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

Reproduce

herbie shell --seed 2020047 
(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)))))