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

Average Error: 1.3 → 1.1

Time: 5.0s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \le 2.273435990876010059686839786084489960128 \cdot 10^{295}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r727828 = x;
        double r727829 = y;
        double r727830 = z;
        double r727831 = t;
        double r727832 = r727830 - r727831;
        double r727833 = a;
        double r727834 = r727833 - r727831;
        double r727835 = r727832 / r727834;
        double r727836 = r727829 * r727835;
        double r727837 = r727828 + r727836;
        return r727837;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r727838 = y;
        double r727839 = z;
        double r727840 = t;
        double r727841 = r727839 - r727840;
        double r727842 = a;
        double r727843 = r727842 - r727840;
        double r727844 = r727841 / r727843;
        double r727845 = r727838 * r727844;
        double r727846 = 2.27343599087601e+295;
        bool r727847 = r727845 <= r727846;
        double r727848 = x;
        double r727849 = r727848 + r727845;
        double r727850 = r727838 * r727841;
        double r727851 = 1.0;
        double r727852 = r727851 / r727843;
        double r727853 = r727850 * r727852;
        double r727854 = r727848 + r727853;
        double r727855 = r727847 ? r727849 : r727854;
        return r727855;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.3
Target	0.4
Herbie	1.1

\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (* y (/ (- z t) (- a t))) < 2.27343599087601e+295

   1. Initial program 0.8

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

   if 2.27343599087601e+295 < (* y (/ (- z t) (- a t)))

   1. Initial program 36.5

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

   3. Applied div-inv 36.5

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

   4. Applied associate-*r* 20.1

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \le 2.273435990876010059686839786084489960128 \cdot 10^{295}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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