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

Average Error: 13.0 → 2.0

Time: 1.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.59894608005550967 \cdot 10^{49}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.73770528439198434 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.4257421418327737 \cdot 10^{275}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z) {
	double VAR;
	if ((((double) (((double) (x * ((double) (y - z)))) / y)) <= -1.5989460800555097e+49)) {
		VAR = ((double) (((double) (x / y)) * ((double) (y - z))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * ((double) (y - z)))) / y)) <= 1.7377052843919843e-46)) {
			VAR_1 = ((double) (x / ((double) (y / ((double) (y - z))))));
		} else {
			double VAR_2;
			if ((((double) (((double) (x * ((double) (y - z)))) / y)) <= 3.4257421418327737e+275)) {
				VAR_2 = ((double) (((double) (x * ((double) (y - z)))) / y));
			} else {
				VAR_2 = ((double) (x / ((double) (y / ((double) (y - z))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	13.0
Target	3.1
Herbie	2.0

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

Derivation

1. Split input into 3 regimes

2. if (/ (* x (- y z)) y) < -1.5989460800555097e+49

   1. Initial program 20.1

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

   3. Applied associate-/l* 5.7

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

   5. Applied associate-/r/ 6.4

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

   if -1.5989460800555097e+49 < (/ (* x (- y z)) y) < 1.7377052843919843e-46 or 3.4257421418327737e+275 < (/ (* x (- y z)) y)

   1. Initial program 15.1

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

   3. Applied associate-/l* 0.7

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

   if 1.7377052843919843e-46 < (/ (* x (- y z)) y) < 3.4257421418327737e+275

   1. Initial program 0.3

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

4. Final simplification 2.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.59894608005550967 \cdot 10^{49}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.73770528439198434 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.4257421418327737 \cdot 10^{275}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020123 +o rules:numerics
(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))