Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Average Error: 2.3 → 2.2

Time: 2.5s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r568435 = x;
        double r568436 = y;
        double r568437 = r568436 - r568435;
        double r568438 = z;
        double r568439 = t;
        double r568440 = r568438 / r568439;
        double r568441 = r568437 * r568440;
        double r568442 = r568435 + r568441;
        return r568442;
}

↓

double f(double x, double y, double z, double t) {
        double r568443 = x;
        double r568444 = y;
        double r568445 = r568444 - r568443;
        double r568446 = t;
        double r568447 = z;
        double r568448 = r568446 / r568447;
        double r568449 = r568445 / r568448;
        double r568450 = r568443 + r568449;
        return r568450;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.3
Target	2.3
Herbie	2.2

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

1. Initial program 2.3

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

3. Applied associate-*r/ 6.2

   \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot z}{t}}\]
4. Using strategy rm

5. Applied associate-/l* 2.2

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

6. Final simplification 2.2

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

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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