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

Average Error: 12.1 → 0.2

Time: 4.5s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq -5.933937315419125 \cdot 10^{+68} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq 2.4704900583474953 \cdot 10^{+48}\right) \land \frac{x \cdot \left(y - z\right)}{y} \leq 4.964536636908783 \cdot 10^{+305}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))

↓

(FPCore (x y z)
 :precision binary64
 (if (or (<= (/ (* x (- y z)) y) (- INFINITY))
         (not
          (or (<= (/ (* x (- y z)) y) -5.933937315419125e+68)
              (and (not (<= (/ (* x (- y z)) y) 2.4704900583474953e+48))
                   (<= (/ (* x (- y z)) y) 4.964536636908783e+305)))))
   (/ x (/ y (- y z)))
   (/ (* x (- y z)) y)))

C

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

↓

double code(double x, double y, double z) {
	double tmp;
	if ((((x * (y - z)) / y) <= -((double) INFINITY)) || !((((x * (y - z)) / y) <= -5.933937315419125e+68) || (!(((x * (y - z)) / y) <= 2.4704900583474953e+48) && (((x * (y - z)) / y) <= 4.964536636908783e+305)))) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (x * (y - z)) / y;
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	12.1
Target	3.0
Herbie	0.2

\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -inf.0 or -5.9339373154191252e68 < (/.f64 (*.f64 x (-.f64 y z)) y) < 2.47049005834749527e48 or 4.9645366369087834e305 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 17.9

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

   3. Applied associate-/l*_binary64 0.2

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

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < -5.9339373154191252e68 or 2.47049005834749527e48 < (/.f64 (*.f64 x (-.f64 y z)) y) < 4.9645366369087834e305

   1. Initial program 0.2

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

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq -5.933937315419125 \cdot 10^{+68} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq 2.4704900583474953 \cdot 10^{+48}\right) \land \frac{x \cdot \left(y - z\right)}{y} \leq 4.964536636908783 \cdot 10^{+305}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020299 
(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))