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

Average Error: 0.1 → 0.1

Time: 16.2s

Precision: binary64

Cost: 13248

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (+ (sin y) (+ x (* 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 sin(y) + (x + (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 = sin(y) + (x + (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 Math.sin(y) + (x + (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 math.sin(y) + (x + (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(sin(y) + Float64(x + 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 = sin(y) + (x + (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[(N[Sin[y], $MachinePrecision] + N[(x + 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

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

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	7.3
Cost	13384

\[\begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-5}:\\ \;\;\;\;\sin y + \left(x + z\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \cos y + \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 2
Error	6.8
Cost	7112

\[\begin{array}{l} t_0 := 0.5 \cdot \left(\cos y \cdot \left(z + z\right)\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+102}:\\ \;\;\;\;\sin y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	21.1
Cost	6860

\[\begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-221}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-145}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-68}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 4
Error	14.1
Cost	6856

\[\begin{array}{l} \mathbf{if}\;x \leq -0.00265:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-9}:\\ \;\;\;\;z + \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 5
Error	12.4
Cost	6856

\[\begin{array}{l} t_0 := \sin y + x\\ \mathbf{if}\;y \leq -19000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-5}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	11.3
Cost	6720

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

Alternative 7
Error	29.3
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-109}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-69}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+37}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	19.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -265000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2700:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 9
Error	20.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-221}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-99}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 10
Error	29.0
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+37}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	21.8
Cost	192

\[z + x \]

Alternative 12
Error	36.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023064 
(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))))