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

Average Error: 1.5 → 0.7

Time: 6.8min

Precision: binary64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -530501686562953.62 \lor \neg \left(y \le 9.22165466596635165 \cdot 10^{59}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((y <= -530501686562953.6) || !(y <= 9.221654665966352e+59))) {
		VAR = ((double) (x + ((double) (y * ((double) ((z / ((double) (a - t))) - (t / ((double) (a - t)))))))));
	} else {
		VAR = ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (a - t)))));
	}
	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	1.5
Target	0.5
Herbie	0.7

\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if y < -530501686562953.62 or 9.22165466596635165e59 < y

   1. Initial program 0.6

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

   3. Applied div-sub 0.6

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

   if -530501686562953.62 < y < 9.22165466596635165e59

   1. Initial program 2.1

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

   3. Applied associate-*r/ 0.7

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

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -530501686562953.62 \lor \neg \left(y \le 9.22165466596635165 \cdot 10^{59}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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