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

Average Error: 12.2 → 0.4

Time: 2.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -inf.0 \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -3.989301173799489 \cdot 10^{-11} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.3083941618729014 \cdot 10^{-35} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.22429215335421849 \cdot 10^{276}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

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)) <= -inf.0) || !((((double) (((double) (x * ((double) (y - z)))) / y)) <= -3.9893011737994894e-11) || !((((double) (((double) (x * ((double) (y - z)))) / y)) <= 1.3083941618729014e-35) || !(((double) (((double) (x * ((double) (y - z)))) / y)) <= 1.2242921533542185e+276))))) {
		VAR = ((double) (x * ((double) (((double) (y - z)) / y))));
	} else {
		VAR = ((double) (x - ((double) (((double) (x * z)) / y))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	12.2
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 2 regimes

2. if (/ (* x (- y z)) y) < -inf.0 or -3.9893011737994894e-11 < (/ (* x (- y z)) y) < 1.3083941618729014e-35 or 1.2242921533542185e+276 < (/ (* x (- y z)) y)

   1. Initial program 21.9

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

   3. Applied *-un-lft-identity 21.9

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

   4. Applied times-frac 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 -inf.0 < (/ (* x (- y z)) y) < -3.9893011737994894e-11 or 1.3083941618729014e-35 < (/ (* x (- y z)) y) < 1.2242921533542185e+276

   1. Initial program 0.2

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

   3. Applied associate-/l* 6.3

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

   4. Taylor expanded around 0 0.2

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

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -inf.0 \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -3.989301173799489 \cdot 10^{-11} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.3083941618729014 \cdot 10^{-35} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.22429215335421849 \cdot 10^{276}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020124 
(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))