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

Average Error: 1.4 → 1.5

Time: 15.2s

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 r396299 = x;
        double r396300 = y;
        double r396301 = z;
        double r396302 = t;
        double r396303 = r396301 - r396302;
        double r396304 = a;
        double r396305 = r396301 - r396304;
        double r396306 = r396303 / r396305;
        double r396307 = r396300 * r396306;
        double r396308 = r396299 + r396307;
        return r396308;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r396309 = x;
        double r396310 = y;
        double r396311 = z;
        double r396312 = t;
        double r396313 = r396311 - r396312;
        double r396314 = 1.0;
        double r396315 = a;
        double r396316 = r396311 - r396315;
        double r396317 = r396314 / r396316;
        double r396318 = r396313 * r396317;
        double r396319 = r396310 * r396318;
        double r396320 = r396309 + r396319;
        return r396320;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.4
Target	1.4
Herbie	1.5

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

Derivation

1. Initial program 1.4

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

3. Applied div-inv 1.5

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

4. Final simplification 1.5

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

Reproduce

herbie shell --seed 2019325 
(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)))))