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

Average Error: 11.9 → 0.8

Time: 2.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -4.72058132197552283 \cdot 10^{299} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -2.2834844323274411 \cdot 10^{95} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 3.7109574790270305 \cdot 10^{40} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.6948280499531564 \cdot 10^{272}\right)\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

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)) <= -4.720581321975523e+299) || !((((double) (((double) (x * ((double) (y - z)))) / y)) <= -2.283484432327441e+95) || !((((double) (((double) (x * ((double) (y - z)))) / y)) <= 3.7109574790270305e+40) || !(((double) (((double) (x * ((double) (y - z)))) / y)) <= 1.6948280499531564e+272))))) {
		VAR = ((double) (x * ((double) (1.0 - ((double) (z / y))))));
	} else {
		VAR = ((double) (((double) (x * ((double) (y - z)))) / y));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	11.9
Target	3.0
Herbie	0.8

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

Derivation

1. Split input into 2 regimes

2. if (/ (* x (- y z)) y) < -4.720581321975523e+299 or -2.283484432327441e+95 < (/ (* x (- y z)) y) < 3.7109574790270305e+40 or 1.6948280499531564e+272 < (/ (* x (- y z)) y)

   1. Initial program 16.7

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

   3. Applied *-un-lft-identity 16.7

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

   4. Applied times-frac 1.1

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

   5. Simplified 1.1

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

   7. Applied div-sub 1.1

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

   8. Simplified 1.1

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

   if -4.720581321975523e+299 < (/ (* x (- y z)) y) < -2.283484432327441e+95 or 3.7109574790270305e+40 < (/ (* x (- y z)) y) < 1.6948280499531564e+272

   1. Initial program 0.2

      \[\frac{x \cdot \left(y - z\right)}{y}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -4.72058132197552283 \cdot 10^{299} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -2.2834844323274411 \cdot 10^{95} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 3.7109574790270305 \cdot 10^{40} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.6948280499531564 \cdot 10^{272}\right)\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020128 
(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))