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

Average Error: 10.5 → 1.3

Time: 10.0s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r498209 = x;
        double r498210 = y;
        double r498211 = z;
        double r498212 = t;
        double r498213 = r498211 - r498212;
        double r498214 = r498210 * r498213;
        double r498215 = a;
        double r498216 = r498211 - r498215;
        double r498217 = r498214 / r498216;
        double r498218 = r498209 + r498217;
        return r498218;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r498219 = x;
        double r498220 = y;
        double r498221 = z;
        double r498222 = t;
        double r498223 = r498221 - r498222;
        double r498224 = r498221 / r498223;
        double r498225 = a;
        double r498226 = r498225 / r498223;
        double r498227 = r498224 - r498226;
        double r498228 = r498220 / r498227;
        double r498229 = r498219 + r498228;
        return r498229;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.5
Target	1.3
Herbie	1.3

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

Derivation

1. Initial program 10.5

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

3. Applied associate-/l* 1.3

   \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
4. Using strategy rm

5. Applied div-sub 1.3

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

6. Final simplification 1.3

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

Reproduce

herbie shell --seed 2020045 
(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))))