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

Average Accuracy: 99.9% → 99.9%

Time: 10.3s

Precision: binary64

Cost: 13248

Math

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

↓

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

FPCore

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 99.9%

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

3. Simplified 99.9%

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

   [Start] 99.9	\[ \left(\cos y + x\right) - z \cdot \sin y \]
   associate-+r- [<=] 99.9	\[ \color{blue}{\cos y + \left(x - z \cdot \sin y\right)} \]

4. Final simplification 99.9%

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

Alternatives

Alternative 1
Accuracy	90.3%
Cost	13385

\[\begin{array}{l} \mathbf{if}\;x \leq -0.0095 \lor \neg \left(x \leq 1.2 \cdot 10^{-15}\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]

Alternative 2
Accuracy	70.3%
Cost	6992

\[\begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-218}:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-184}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-15}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 3
Accuracy	82.4%
Cost	6921

\[\begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+109} \lor \neg \left(z \leq 3.3 \cdot 10^{+157}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]

Alternative 4
Accuracy	79.9%
Cost	6857

\[\begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-5} \lor \neg \left(y \leq 4.1 \cdot 10^{-25}\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 5
Accuracy	68.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+40}:\\ \;\;\;\;x + -1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+83}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 6
Accuracy	65.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.16:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-18}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 7
Accuracy	61.7%
Cost	388

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+250}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 8
Accuracy	60.4%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Accuracy	61.2%
Cost	192

\[x + 1 \]

Alternative 10
Accuracy	21.3%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023151 
(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))))