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

Average Error: 1.5 → 0.9

Time: 5.5s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \le -2.1155362594979767 \cdot 10^{165}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \end{array}\]

C

double code(double x, double y, double z, double t, double a) {
	return (x + (y * ((z - t) / (z - a))));
}

↓

double code(double x, double y, double z, double t, double a) {
	double temp;
	if ((((z - t) / (z - a)) <= -2.1155362594979767e+165)) {
		temp = (x + ((y * (z - t)) * (1.0 / (z - a))));
	} else {
		temp = (x + (y * ((z - t) / (z - a))));
	}
	return temp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.5
Target	1.3
Herbie	0.9

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

Derivation

1. Split input into 2 regimes

2. if (/ (- z t) (- z a)) < -2.1155362594979767e+165

   1. Initial program 15.9

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

   3. Applied div-inv 15.9

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

   4. Applied associate-*r* 1.5

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

   if -2.1155362594979767e+165 < (/ (- z t) (- z a))

   1. Initial program 0.8

      \[x + y \cdot \frac{z - t}{z - a}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{z - a} \le -2.1155362594979767 \cdot 10^{165}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020053 
(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)))))