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

Average Error: 12.2 → 1.1

Time: 1.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -7.6868885850443121 \cdot 10^{259}:\\ \;\;\;\;x + \frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -6.9464679095261849 \cdot 10^{107}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.2751829223193257 \cdot 10^{26}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.1047641663537662 \cdot 10^{302}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x}{y} \cdot \left(-z\right)\\ \end{array}\]

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) <= -7.686888585044312e+259)) {
		VAR = (x + ((x / y) * -z));
	} else {
		double VAR_1;
		if ((((x * (y - z)) / y) <= -6.946467909526185e+107)) {
			VAR_1 = ((x * (y - z)) / y);
		} else {
			double VAR_2;
			if ((((x * (y - z)) / y) <= 1.2751829223193257e+26)) {
				VAR_2 = (x / (y / (y - z)));
			} else {
				double VAR_3;
				if ((((x * (y - z)) / y) <= 1.1047641663537662e+302)) {
					VAR_3 = ((x * (y - z)) / y);
				} else {
					VAR_3 = (x + ((x / 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	12.2
Target	3.2
Herbie	1.1

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

Derivation

1. Split input into 3 regimes

2. if (/ (* x (- y z)) y) < -7.686888585044312e+259 or 1.1047641663537662e+302 < (/ (* x (- y z)) y)

   1. Initial program 53.3

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

   3. Applied associate-/l* 2.3

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

   5. Applied associate-/r/ 4.5

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(y - z\right)}\]
   6. Using strategy rm

   7. Applied sub-neg 4.5

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

   8. Applied distribute-lft-in 4.5

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

   9. Simplified 4.4

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

   if -7.686888585044312e+259 < (/ (* x (- y z)) y) < -6.946467909526185e+107 or 1.2751829223193257e+26 < (/ (* x (- y z)) y) < 1.1047641663537662e+302

   1. Initial program 0.2

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

   if -6.946467909526185e+107 < (/ (* x (- y z)) y) < 1.2751829223193257e+26

   1. Initial program 5.3

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

   3. Applied associate-/l* 0.5

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

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -7.6868885850443121 \cdot 10^{259}:\\ \;\;\;\;x + \frac{x}{y} \cdot \left(-z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -6.9464679095261849 \cdot 10^{107}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.2751829223193257 \cdot 10^{26}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.1047641663537662 \cdot 10^{302}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x}{y} \cdot \left(-z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020092 
(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))