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

Average Error: 13.0 → 0.5

Time: 2.8s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -1.4772382854862037 \cdot 10^{+289} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq -1.6629232438593122 \cdot 10^{+49} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq 9.922968639006984 \cdot 10^{+52}\right) \land \frac{x \cdot \left(y - z\right)}{y} \leq 1.7756037105719044 \cdot 10^{+300}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y - z\right)\right) \cdot \frac{1}{y}\\ \end{array}\]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (if (or (<= (/ (* x (- y z)) y) -1.4772382854862037e+289)
         (not
          (or (<= (/ (* x (- y z)) y) -1.6629232438593122e+49)
              (and (not (<= (/ (* x (- y z)) y) 9.922968639006984e+52))
                   (<= (/ (* x (- y z)) y) 1.7756037105719044e+300)))))
   (* x (/ (- y z) y))
   (* (* x (- y z)) (/ 1.0 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) <= -1.4772382854862037e+289) || !((((x * (y - z)) / y) <= -1.6629232438593122e+49) || (!(((x * (y - z)) / y) <= 9.922968639006984e+52) && (((x * (y - z)) / y) <= 1.7756037105719044e+300)))) {
		tmp = x * ((y - z) / y);
	} else {
		tmp = (x * (y - z)) * (1.0 / y);
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	13.0
Target	3.1
Herbie	0.5

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -1.4772382854862037e289 or -1.6629232438593122e49 < (/.f64 (*.f64 x (-.f64 y z)) y) < 9.92296863900698404e52 or 1.77560371057190438e300 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 19.0

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

   3. Applied *-un-lft-identity_binary64 19.0

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

   4. Applied times-frac_binary64 0.5

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

   5. Simplified 0.5

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

   if -1.4772382854862037e289 < (/.f64 (*.f64 x (-.f64 y z)) y) < -1.6629232438593122e49 or 9.92296863900698404e52 < (/.f64 (*.f64 x (-.f64 y z)) y) < 1.77560371057190438e300

   1. Initial program 0.2

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

   3. Applied div-inv_binary64 0.3

      \[\leadsto \color{blue}{\left(x \cdot \left(y - z\right)\right) \cdot \frac{1}{y}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -1.4772382854862037 \cdot 10^{+289} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq -1.6629232438593122 \cdot 10^{+49} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq 9.922968639006984 \cdot 10^{+52}\right) \land \frac{x \cdot \left(y - z\right)}{y} \leq 1.7756037105719044 \cdot 10^{+300}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y - z\right)\right) \cdot \frac{1}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020231 
(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))