Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Average Error: 12.5 → 0.4

Time: 2.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{y \cdot \frac{1}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.9782176162867171 \cdot 10^{-240}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 7.842406589174579 \cdot 10^{-20}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{y - z}}{x}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.1537092818184106 \cdot 10^{302}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

C

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

↓

double code(double x, double y, double z) {
	double VAR;
	if ((((x * (y - z)) / y) <= -inf.0)) {
		VAR = (x / (y * (1.0 / (y - z))));
	} else {
		double VAR_1;
		if ((((x * (y - z)) / y) <= -1.9782176162867171e-240)) {
			VAR_1 = ((x * (y - z)) / y);
		} else {
			double VAR_2;
			if ((((x * (y - z)) / y) <= 7.842406589174579e-20)) {
				VAR_2 = (1.0 / ((y / (y - z)) / x));
			} else {
				double VAR_3;
				if ((((x * (y - z)) / y) <= 1.1537092818184106e+302)) {
					VAR_3 = ((x * (y - z)) / y);
				} else {
					VAR_3 = ((x / y) * (y - z));
				}
				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

Target

Original	12.5
Target	3.3
Herbie	0.4

\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 64.0

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

   3. Applied associate-/l* 0.1

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

   5. Applied div-inv 0.2

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

   if -inf.0 < (/ (* x (- y z)) y) < -1.9782176162867171e-240 or 7.842406589174579e-20 < (/ (* x (- y z)) y) < 1.1537092818184106e+302

   1. Initial program 0.3

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

   if -1.9782176162867171e-240 < (/ (* x (- y z)) y) < 7.842406589174579e-20

   1. Initial program 10.9

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

   3. Applied associate-/l* 0.1

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

   5. Applied clear-num 0.3

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

   if 1.1537092818184106e+302 < (/ (* x (- y z)) y)

   1. Initial program 62.1

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

   3. Applied associate-/l* 0.2

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

   5. Applied associate-/r/ 1.4

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(y - z\right)}\]
3. Recombined 4 regimes into one program.

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{y \cdot \frac{1}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.9782176162867171 \cdot 10^{-240}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 7.842406589174579 \cdot 10^{-20}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{y - z}}{x}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.1537092818184106 \cdot 10^{302}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020091 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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