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

Average Error: 10.5 → 1.3

Time: 7.3s

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 r472321 = x;
        double r472322 = y;
        double r472323 = z;
        double r472324 = t;
        double r472325 = r472323 - r472324;
        double r472326 = r472322 * r472325;
        double r472327 = a;
        double r472328 = r472323 - r472327;
        double r472329 = r472326 / r472328;
        double r472330 = r472321 + r472329;
        return r472330;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r472331 = x;
        double r472332 = y;
        double r472333 = z;
        double r472334 = t;
        double r472335 = r472333 - r472334;
        double r472336 = r472333 / r472335;
        double r472337 = a;
        double r472338 = r472337 / r472335;
        double r472339 = r472336 - r472338;
        double r472340 = r472332 / r472339;
        double r472341 = r472331 + r472340;
        return r472341;
}

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))))