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

Average Error: 0.1 → 0.1

Time: 13.5s

Precision: binary64

Cost: 13248

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (sin(y) + (z * cos(y)))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

↓

public static double code(double x, double y, double z) {
	return x + (Math.sin(y) + (z * Math.cos(y)));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

↓

def code(x, y, z):
	return x + (math.sin(y) + (z * math.cos(y)))

Julia

function code(x, y, z)
	return Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
end

↓

function code(x, y, z)
	return Float64(x + Float64(sin(y) + Float64(z * cos(y))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + sin(y)) + (z * cos(y));
end

↓

function tmp = code(x, y, z)
	tmp = x + (sin(y) + (z * cos(y)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(x + N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.1

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

2. Simplified 0.1

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

   [Start] 0.1	\[ \left(x + \sin y\right) + z \cdot \cos y \]
   rational.json-simplify-1 [=>] 0.1	\[ \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]
   rational.json-simplify-41 [=>] 0.1	\[ \color{blue}{x + \left(\sin y + z \cdot \cos y\right)} \]

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	3.7
Cost	13384

\[\begin{array}{l} t_0 := x + \cos y \cdot z\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \cos y + \sin y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	18.8
Cost	7384

\[\begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{-9}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-157}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -9.4 \cdot 10^{-238}:\\ \;\;\;\;x + \left(y + z\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-149}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-123}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+61}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 3
Error	10.9
Cost	7120

\[\begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-94}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-92}:\\ \;\;\;\;\sin y + x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+89}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	4.0
Cost	6984

\[\begin{array}{l} t_0 := x + \cos y \cdot z\\ \mathbf{if}\;z \leq -3 \cdot 10^{-108}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-92}:\\ \;\;\;\;\sin y + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	20.0
Cost	6860

\[\begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-51}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-180}:\\ \;\;\;\;x + \left(y + z\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-116}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 6
Error	29.1
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-171}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-193}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+21}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	19.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+55}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 1000:\\ \;\;\;\;x + \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 8
Error	26.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+21}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	20.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-169}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-123}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 10
Error	35.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-171}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.96 \cdot 10^{-107}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	28.7
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{+21}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	37.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023074 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))