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

Average Error: 10.9 → 1.2

Time: 8.2s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r1214765 = x;
        double r1214766 = y;
        double r1214767 = z;
        double r1214768 = t;
        double r1214769 = r1214767 - r1214768;
        double r1214770 = r1214766 * r1214769;
        double r1214771 = a;
        double r1214772 = r1214767 - r1214771;
        double r1214773 = r1214770 / r1214772;
        double r1214774 = r1214765 + r1214773;
        return r1214774;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r1214775 = x;
        double r1214776 = y;
        double r1214777 = z;
        double r1214778 = a;
        double r1214779 = r1214777 - r1214778;
        double r1214780 = t;
        double r1214781 = r1214777 - r1214780;
        double r1214782 = r1214779 / r1214781;
        double r1214783 = r1214776 / r1214782;
        double r1214784 = r1214775 + r1214783;
        return r1214784;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.9
Target	1.2
Herbie	1.2

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

Derivation

1. Initial program 10.9

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

3. Applied associate-/l* 1.2

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

4. Final simplification 1.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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