Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B

Average Error: 0.1 → 0.1

Time: 6.4s

Precision: binary64

Cost: 13248

Math

\[\left(x + \cos y\right) - z \cdot \sin y\]

↓

\[\left(x + \cos y\right) - z \cdot \sin y\]

FPCore

(FPCore (x y z) :precision binary64 (- (+ x (cos y)) (* z (sin y))))

↓

(FPCore (x y z) :precision binary64 (- (+ x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(y));
}

↓

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(y));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Alternatives

Alternative 1
Error	6.9
Cost	13762

\[\begin{array}{l} \mathbf{if}\;x \leq -4.617795998451085 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.1853413812390224 \cdot 10^{-31}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array}\]

Alternative 2
Error	12.7
Cost	8453

\[\begin{array}{l} \mathbf{if}\;y \leq -1.518515463397373 \cdot 10^{+133}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq -2.4577894350339715 \cdot 10^{+88}:\\ \;\;\;\;-z \cdot \sin y\\ \mathbf{elif}\;y \leq -6.929473909826237 \cdot 10^{+24}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq -5.053716960464881:\\ \;\;\;\;-z \cdot \sin y\\ \mathbf{elif}\;y \leq 4.295310622478322 \cdot 10^{+26}:\\ \;\;\;\;\left(x + \cos y\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array}\]

Alternative 3
Error	12.9
Cost	8204

\[\begin{array}{l} \mathbf{if}\;y \leq -2.6612415537441975 \cdot 10^{+132}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq -2.5106536642892974 \cdot 10^{+88}:\\ \;\;\;\;-z \cdot \sin y\\ \mathbf{elif}\;y \leq -5.812743572593929 \cdot 10^{+24}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq -5.178985653066986:\\ \;\;\;\;-z \cdot \sin y\\ \mathbf{elif}\;y \leq -0.0003124677607253619 \lor \neg \left(y \leq 7.6669548423569 \cdot 10^{-14}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array}\]

Alternative 4
Error	12.3
Cost	6920

\[\begin{array}{l} \mathbf{if}\;y \leq -0.0002719120595556238 \lor \neg \left(y \leq 7.6669548423569 \cdot 10^{-14}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array}\]

Alternative 5
Error	19.4
Cost	1032

\[\begin{array}{l} \mathbf{if}\;y \leq -1.753118415588741 \cdot 10^{+30} \lor \neg \left(y \leq 4.083348596622708 \cdot 10^{+26}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot \left(z + y \cdot 0.5\right)\\ \end{array}\]

Alternative 6
Error	19.3
Cost	776

\[\begin{array}{l} \mathbf{if}\;y \leq -3.649977632017701 \lor \neg \left(y \leq 8.531729774650604 \cdot 10^{+29}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array}\]

Alternative 7
Error	24.7
Cost	192

\[x + 1\]

Alternative 8
Error	25.6
Cost	706

\[\begin{array}{l} \mathbf{if}\;x \leq -1.4886679085051663 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.0194997779622874:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Alternative 9
Error	50.4
Cost	64

\[1\]

Derivation

1. Initial program 0.1

   \[\left(x + \cos y\right) - z \cdot \sin y\]

2. Simplified 0.1

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

3. Final simplification 0.1

   \[\leadsto \left(x + \cos y\right) - z \cdot \sin y\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))