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

Average Error: 6.6 → 1.3

Time: 4.6s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -inf.0:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.8845183729180806 \cdot 10^{-186}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array}\]

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 ((((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t)))) <= -inf.0)) {
		VAR = ((double) (x + ((double) (y / ((double) (t / ((double) (z - x))))))));
	} else {
		double VAR_1;
		if ((((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t)))) <= -3.884518372918081e-186)) {
			VAR_1 = ((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t))));
		} else {
			VAR_1 = ((double) (x + ((double) (((double) (z - x)) * ((double) (y / t))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.6
Target	2.1
Herbie	1.3

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.0

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

   2. Simplified 0.2

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

   4. Applied clear-num 0.2

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{t}{z - x}}}\]
   5. Using strategy rm

   6. Applied un-div-inv 0.2

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

   if -inf.0 < (+ x (/ (* y (- z x)) t)) < -3.8845183729180806e-186

   1. Initial program 0.3

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

   if -3.8845183729180806e-186 < (+ x (/ (* y (- z x)) t))

   1. Initial program 6.5

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

   2. Simplified 6.6

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

   4. Applied clear-num 6.8

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{t}{z - x}}}\]
   5. Using strategy rm

   6. Applied associate-/r/ 6.7

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

   7. Applied associate-*r* 2.2

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

   8. Simplified 2.1

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

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -inf.0:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.8845183729180806 \cdot 10^{-186}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(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)))