Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Average Error: 6.4 → 1.6

Time: 6.3s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -0.0263713862562576194:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;y \le -3.80871808056728307 \cdot 10^{-307}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{elif}\;y \le 2.7629859023376793 \cdot 10^{166}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{elif}\;y \le 1.41006685399171807 \cdot 10^{272}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if ((y <= -0.02637138625625762)) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - x)) / t))))));
	} else {
		double VAR_1;
		if ((y <= -3.808718080567283e-307)) {
			VAR_1 = ((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t))));
		} else {
			double VAR_2;
			if ((y <= 2.7629859023376793e+166)) {
				VAR_2 = ((double) (x + ((double) (((double) (y / t)) * ((double) (z - x))))));
			} else {
				double VAR_3;
				if ((y <= 1.410066853991718e+272)) {
					VAR_3 = ((double) (x + ((double) (y * ((double) (((double) (z - x)) / t))))));
				} else {
					VAR_3 = ((double) (x + ((double) (((double) (y / t)) * ((double) (z - x))))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.4
Target	2.0
Herbie	1.6

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

Derivation

1. Split input into 3 regimes

2. if y < -0.0263713862562576194 or 2.7629859023376793e166 < y < 1.41006685399171807e272

   1. Initial program 17.1

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

   3. Applied *-un-lft-identity 17.1

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

   4. Applied times-frac 2.3

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

   5. Simplified 2.3

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

   if -0.0263713862562576194 < y < -3.80871808056728307e-307

   1. Initial program 1.0

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

   if -3.80871808056728307e-307 < y < 2.7629859023376793e166 or 1.41006685399171807e272 < y

   1. Initial program 4.3

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

   3. Applied associate-/l* 6.3

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

   5. Applied associate-/r/ 1.7

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

4. Final simplification 1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -0.0263713862562576194:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;y \le -3.80871808056728307 \cdot 10^{-307}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{elif}\;y \le 2.7629859023376793 \cdot 10^{166}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{elif}\;y \le 1.41006685399171807 \cdot 10^{272}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020164 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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