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

Average Error: 12.7 → 0.4

Time: 2.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -5.74240735694960229 \cdot 10^{-106}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.0101904628573289 \cdot 10^{139}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.14880917404541375 \cdot 10^{307}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

C

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

↓

double code(double x, double y, double z) {
	double temp;
	if ((((x * (y - z)) / y) <= -inf.0)) {
		temp = (x / (y / (y - z)));
	} else {
		double temp_1;
		if ((((x * (y - z)) / y) <= -5.742407356949602e-106)) {
			temp_1 = ((x * (y - z)) / y);
		} else {
			double temp_2;
			if ((((x * (y - z)) / y) <= 1.0101904628573289e+139)) {
				temp_2 = (x / (y / (y - z)));
			} else {
				double temp_3;
				if ((((x * (y - z)) / y) <= 3.1488091740454137e+307)) {
					temp_3 = ((x * (y - z)) / y);
				} else {
					temp_3 = ((x / y) * (y - z));
				}
				temp_2 = temp_3;
			}
			temp_1 = temp_2;
		}
		temp = temp_1;
	}
	return temp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	12.7
Target	3.4
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 3 regimes

2. if (/ (* x (- y z)) y) < -inf.0 or -5.742407356949602e-106 < (/ (* x (- y z)) y) < 1.0101904628573289e+139

   1. Initial program 14.1

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

   3. Applied associate-/l* 0.6

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

   if -inf.0 < (/ (* x (- y z)) y) < -5.742407356949602e-106 or 1.0101904628573289e+139 < (/ (* x (- y z)) y) < 3.1488091740454137e+307

   1. Initial program 0.3

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

   if 3.1488091740454137e+307 < (/ (* x (- y z)) y)

   1. Initial program 63.7

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

   3. Applied associate-/l* 0.3

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

   5. Applied associate-/r/ 0.2

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

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -5.74240735694960229 \cdot 10^{-106}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.0101904628573289 \cdot 10^{139}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.14880917404541375 \cdot 10^{307}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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))