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

Average Error: 10.7 → 0.4

Time: 4.4min

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -2.17530072959983735 \cdot 10^{259} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 6.29579517510261386 \cdot 10^{279}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((((((double) (y * ((double) (z - t)))) / ((double) (z - a))) <= -2.1753007295998373e+259) || !((((double) (y * ((double) (z - t)))) / ((double) (z - a))) <= 6.295795175102614e+279))) {
		VAR = ((double) (x + ((double) (y * ((double) ((z / ((double) (z - a))) - (t / ((double) (z - a)))))))));
	} else {
		VAR = ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (z - a)))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.7
Target	1.3
Herbie	0.4

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- z a)) < -2.17530072959983735e259 or 6.29579517510261386e279 < (/ (* y (- z t)) (- z a))

   1. Initial program 58.5

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

   3. Applied *-un-lft-identity 58.5

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

   4. Applied times-frac 1.1

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

   5. Simplified 1.1

      \[\leadsto x + \color{blue}{y} \cdot \frac{z - t}{z - a}\]
   6. Using strategy rm

   7. Applied div-sub 1.1

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

   if -2.17530072959983735e259 < (/ (* y (- z t)) (- z a)) < 6.29579517510261386e279

   1. Initial program 0.2

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

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -2.17530072959983735 \cdot 10^{259} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 6.29579517510261386 \cdot 10^{279}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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