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

Average Error: 12.3 → 0.4

Time: 2.3s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -inf.0:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -2.6110579688521354 \cdot 10^{-15}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 664596070710589440:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.0525960320837076 \cdot 10^{285}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

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)) <= -inf.0)) {
		VAR = ((double) (x * ((double) (((double) (y - z)) / y))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * ((double) (y - z)))) / y)) <= -2.6110579688521354e-15)) {
			VAR_1 = ((double) (((double) (x * ((double) (y - z)))) / y));
		} else {
			double VAR_2;
			if ((((double) (((double) (x * ((double) (y - z)))) / y)) <= 6.645960707105894e+17)) {
				VAR_2 = ((double) (x / ((double) (y / ((double) (y - z))))));
			} else {
				double VAR_3;
				if ((((double) (((double) (x * ((double) (y - z)))) / y)) <= 1.0525960320837076e+285)) {
					VAR_3 = ((double) (((double) (x * ((double) (y - z)))) / y));
				} else {
					VAR_3 = ((double) (x / ((double) (y / ((double) (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	12.3
Target	3.1
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

   1. Initial program 64.0

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

   3. Applied *-un-lft-identity 64.0

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

   4. Applied times-frac 0.0

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

   5. Simplified 0.0

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

   if -inf.0 < (/ (* x (- y z)) y) < -2.6110579688521354e-15 or 664596070710589440 < (/ (* x (- y z)) y) < 1.0525960320837076e285

   1. Initial program 0.2

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

   if -2.6110579688521354e-15 < (/ (* x (- y z)) y) < 664596070710589440 or 1.0525960320837076e285 < (/ (* x (- y z)) y)

   1. Initial program 14.8

      \[\frac{x \cdot \left(y - z\right)}{y}\]
   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 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -inf.0:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -2.6110579688521354 \cdot 10^{-15}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 664596070710589440:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.0525960320837076 \cdot 10^{285}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020161 
(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))