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

Average Error: 1.3 → 1.1

Time: 4.3s

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 r778662 = x;
        double r778663 = y;
        double r778664 = z;
        double r778665 = t;
        double r778666 = r778664 - r778665;
        double r778667 = a;
        double r778668 = r778667 - r778665;
        double r778669 = r778666 / r778668;
        double r778670 = r778663 * r778669;
        double r778671 = r778662 + r778670;
        return r778671;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r778672 = y;
        double r778673 = z;
        double r778674 = t;
        double r778675 = r778673 - r778674;
        double r778676 = a;
        double r778677 = r778676 - r778674;
        double r778678 = r778675 / r778677;
        double r778679 = r778672 * r778678;
        double r778680 = 2.27343599087601e+295;
        bool r778681 = r778679 <= r778680;
        double r778682 = x;
        double r778683 = r778682 + r778679;
        double r778684 = r778672 * r778675;
        double r778685 = 1.0;
        double r778686 = r778685 / r778677;
        double r778687 = r778684 * r778686;
        double r778688 = r778682 + r778687;
        double r778689 = r778681 ? r778683 : r778688;
        return r778689;
}

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 
(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)))))