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

Average Error: 11.0 → 0.2

Time: 3.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -inf.0:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 3.15913987496220917 \cdot 10^{278}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t)))) <= -inf.0)) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - t)) / ((double) (a - t))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t)))) <= 3.159139874962209e+278)) {
			VAR_1 = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t))))));
		} else {
			VAR_1 = ((double) (x + ((double) (y / ((double) (((double) (a - t)) / ((double) (z - t))))))));
		}
		VAR = VAR_1;
	}
	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	11.0
Target	1.1
Herbie	0.2

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

Derivation

1. Split input into 3 regimes

2. if (/ (* y (- z t)) (- a t)) < -inf.0

   1. Initial program 64.0

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

   3. Applied *-un-lft-identity 64.0

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

   4. Applied times-frac 0.1

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

   5. Simplified 0.1

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

   if -inf.0 < (/ (* y (- z t)) (- a t)) < 3.159139874962209e+278

   1. Initial program 0.2

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

   if 3.159139874962209e+278 < (/ (* y (- z t)) (- a t))

   1. Initial program 60.4

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

   3. Applied associate-/l* 0.5

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

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -inf.0:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 3.15913987496220917 \cdot 10^{278}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020126 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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