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

Percentage Accurate: 76.4% → 99.5%

Time: 13.7s

Alternatives: 13

Speedup: 1.5×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \frac{\left(\frac{8}{3} \cdot t_0\right) \cdot t_0}{\sin x} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5)))) (/ (* (* (/ 8.0 3.0) t_0) t_0) (sin x))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	return (((8.0 / 3.0) * t_0) * t_0) / sin(x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sin((x * 0.5d0))
    code = (((8.0d0 / 3.0d0) * t_0) * t_0) / sin(x)
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	return (((8.0 / 3.0) * t_0) * t_0) / Math.sin(x);
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	return (((8.0 / 3.0) * t_0) * t_0) / math.sin(x)

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	return Float64(Float64(Float64(Float64(8.0 / 3.0) * t_0) * t_0) / sin(x))
end

MATLAB

function tmp = code(x)
	t_0 = sin((x * 0.5));
	tmp = (((8.0 / 3.0) * t_0) * t_0) / sin(x);
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(N[(N[(N[(8.0 / 3.0), $MachinePrecision] * t$95$0), $MachinePrecision] * t$95$0), $MachinePrecision] / N[Sin[x], $MachinePrecision]), $MachinePrecision]]

Initial Program: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \frac{\left(\frac{8}{3} \cdot t_0\right) \cdot t_0}{\sin x} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5)))) (/ (* (* (/ 8.0 3.0) t_0) t_0) (sin x))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	return (((8.0 / 3.0) * t_0) * t_0) / sin(x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sin((x * 0.5d0))
    code = (((8.0d0 / 3.0d0) * t_0) * t_0) / sin(x)
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	return (((8.0 / 3.0) * t_0) * t_0) / Math.sin(x);
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	return (((8.0 / 3.0) * t_0) * t_0) / math.sin(x)

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	return Float64(Float64(Float64(Float64(8.0 / 3.0) * t_0) * t_0) / sin(x))
end

MATLAB

function tmp = code(x)
	t_0 = sin((x * 0.5));
	tmp = (((8.0 / 3.0) * t_0) * t_0) / sin(x);
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(N[(N[(N[(8.0 / 3.0), $MachinePrecision] * t$95$0), $MachinePrecision] * t$95$0), $MachinePrecision] / N[Sin[x], $MachinePrecision]), $MachinePrecision]]

Alternative 1: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \frac{t_0}{0.375 \cdot \frac{\sin x}{t_0}} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5)))) (/ t_0 (* 0.375 (/ (sin x) t_0)))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	return t_0 / (0.375 * (sin(x) / t_0));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sin((x * 0.5d0))
    code = t_0 / (0.375d0 * (sin(x) / t_0))
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	return t_0 / (0.375 * (Math.sin(x) / t_0));
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	return t_0 / (0.375 * (math.sin(x) / t_0))

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	return Float64(t_0 / Float64(0.375 * Float64(sin(x) / t_0)))
end

MATLAB

function tmp = code(x)
	t_0 = sin((x * 0.5));
	tmp = t_0 / (0.375 * (sin(x) / t_0));
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(t$95$0 / N[(0.375 * N[(N[Sin[x], $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 2: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ 2.6666666666666665 \cdot \left(t_0 \cdot \frac{t_0}{\sin x}\right) \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5)))) (* 2.6666666666666665 (* t_0 (/ t_0 (sin x))))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	return 2.6666666666666665 * (t_0 * (t_0 / sin(x)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sin((x * 0.5d0))
    code = 2.6666666666666665d0 * (t_0 * (t_0 / sin(x)))
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	return 2.6666666666666665 * (t_0 * (t_0 / Math.sin(x)));
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	return 2.6666666666666665 * (t_0 * (t_0 / math.sin(x)))

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	return Float64(2.6666666666666665 * Float64(t_0 * Float64(t_0 / sin(x))))
end

MATLAB

function tmp = code(x)
	t_0 = sin((x * 0.5));
	tmp = 2.6666666666666665 * (t_0 * (t_0 / sin(x)));
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(2.6666666666666665 * N[(t$95$0 * N[(t$95$0 / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 3: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \frac{t_0}{\sin x} \cdot \frac{t_0}{0.375} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5)))) (* (/ t_0 (sin x)) (/ t_0 0.375))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	return (t_0 / sin(x)) * (t_0 / 0.375);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sin((x * 0.5d0))
    code = (t_0 / sin(x)) * (t_0 / 0.375d0)
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	return (t_0 / Math.sin(x)) * (t_0 / 0.375);
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	return (t_0 / math.sin(x)) * (t_0 / 0.375)

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	return Float64(Float64(t_0 / sin(x)) * Float64(t_0 / 0.375))
end

MATLAB

function tmp = code(x)
	t_0 = sin((x * 0.5));
	tmp = (t_0 / sin(x)) * (t_0 / 0.375);
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(N[(t$95$0 / N[Sin[x], $MachinePrecision]), $MachinePrecision] * N[(t$95$0 / 0.375), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 4: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \mathbf{if}\;x \leq 10^{-8}:\\ \;\;\;\;\frac{t_0}{0.75}\\ \mathbf{else}:\\ \;\;\;\;2.6666666666666665 \cdot \frac{{t_0}^{2}}{\sin x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5))))
   (if (<= x 1e-8)
     (/ t_0 0.75)
     (* 2.6666666666666665 (/ (pow t_0 2.0) (sin x))))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	double tmp;
	if (x <= 1e-8) {
		tmp = t_0 / 0.75;
	} else {
		tmp = 2.6666666666666665 * (pow(t_0, 2.0) / sin(x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin((x * 0.5d0))
    if (x <= 1d-8) then
        tmp = t_0 / 0.75d0
    else
        tmp = 2.6666666666666665d0 * ((t_0 ** 2.0d0) / sin(x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	double tmp;
	if (x <= 1e-8) {
		tmp = t_0 / 0.75;
	} else {
		tmp = 2.6666666666666665 * (Math.pow(t_0, 2.0) / Math.sin(x));
	}
	return tmp;
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	tmp = 0
	if x <= 1e-8:
		tmp = t_0 / 0.75
	else:
		tmp = 2.6666666666666665 * (math.pow(t_0, 2.0) / math.sin(x))
	return tmp

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	tmp = 0.0
	if (x <= 1e-8)
		tmp = Float64(t_0 / 0.75);
	else
		tmp = Float64(2.6666666666666665 * Float64((t_0 ^ 2.0) / sin(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = sin((x * 0.5));
	tmp = 0.0;
	if (x <= 1e-8)
		tmp = t_0 / 0.75;
	else
		tmp = 2.6666666666666665 * ((t_0 ^ 2.0) / sin(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, 1e-8], N[(t$95$0 / 0.75), $MachinePrecision], N[(2.6666666666666665 * N[(N[Power[t$95$0, 2.0], $MachinePrecision] / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 5: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \mathbf{if}\;x \leq 10^{-9}:\\ \;\;\;\;\frac{t_0}{0.75}\\ \mathbf{else}:\\ \;\;\;\;{t_0}^{2} \cdot \frac{2.6666666666666665}{\sin x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5))))
   (if (<= x 1e-9)
     (/ t_0 0.75)
     (* (pow t_0 2.0) (/ 2.6666666666666665 (sin x))))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	double tmp;
	if (x <= 1e-9) {
		tmp = t_0 / 0.75;
	} else {
		tmp = pow(t_0, 2.0) * (2.6666666666666665 / sin(x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin((x * 0.5d0))
    if (x <= 1d-9) then
        tmp = t_0 / 0.75d0
    else
        tmp = (t_0 ** 2.0d0) * (2.6666666666666665d0 / sin(x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	double tmp;
	if (x <= 1e-9) {
		tmp = t_0 / 0.75;
	} else {
		tmp = Math.pow(t_0, 2.0) * (2.6666666666666665 / Math.sin(x));
	}
	return tmp;
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	tmp = 0
	if x <= 1e-9:
		tmp = t_0 / 0.75
	else:
		tmp = math.pow(t_0, 2.0) * (2.6666666666666665 / math.sin(x))
	return tmp

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	tmp = 0.0
	if (x <= 1e-9)
		tmp = Float64(t_0 / 0.75);
	else
		tmp = Float64((t_0 ^ 2.0) * Float64(2.6666666666666665 / sin(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = sin((x * 0.5));
	tmp = 0.0;
	if (x <= 1e-9)
		tmp = t_0 / 0.75;
	else
		tmp = (t_0 ^ 2.0) * (2.6666666666666665 / sin(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, 1e-9], N[(t$95$0 / 0.75), $MachinePrecision], N[(N[Power[t$95$0, 2.0], $MachinePrecision] * N[(2.6666666666666665 / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 6: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \mathbf{if}\;x \leq 7.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{t_0}{0.75}\\ \mathbf{else}:\\ \;\;\;\;\frac{2.6666666666666665 \cdot {t_0}^{2}}{\sin x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5))))
   (if (<= x 7.2e-9)
     (/ t_0 0.75)
     (/ (* 2.6666666666666665 (pow t_0 2.0)) (sin x)))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	double tmp;
	if (x <= 7.2e-9) {
		tmp = t_0 / 0.75;
	} else {
		tmp = (2.6666666666666665 * pow(t_0, 2.0)) / sin(x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin((x * 0.5d0))
    if (x <= 7.2d-9) then
        tmp = t_0 / 0.75d0
    else
        tmp = (2.6666666666666665d0 * (t_0 ** 2.0d0)) / sin(x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	double tmp;
	if (x <= 7.2e-9) {
		tmp = t_0 / 0.75;
	} else {
		tmp = (2.6666666666666665 * Math.pow(t_0, 2.0)) / Math.sin(x);
	}
	return tmp;
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	tmp = 0
	if x <= 7.2e-9:
		tmp = t_0 / 0.75
	else:
		tmp = (2.6666666666666665 * math.pow(t_0, 2.0)) / math.sin(x)
	return tmp

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	tmp = 0.0
	if (x <= 7.2e-9)
		tmp = Float64(t_0 / 0.75);
	else
		tmp = Float64(Float64(2.6666666666666665 * (t_0 ^ 2.0)) / sin(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = sin((x * 0.5));
	tmp = 0.0;
	if (x <= 7.2e-9)
		tmp = t_0 / 0.75;
	else
		tmp = (2.6666666666666665 * (t_0 ^ 2.0)) / sin(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, 7.2e-9], N[(t$95$0 / 0.75), $MachinePrecision], N[(N[(2.6666666666666665 * N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision] / N[Sin[x], $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 7: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \mathbf{if}\;x \leq 0.0006:\\ \;\;\;\;\frac{t_0}{0.75 + -0.09375 \cdot {x}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{t_0}^{2}}{\sin x}}{0.375}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5))))
   (if (<= x 0.0006)
     (/ t_0 (+ 0.75 (* -0.09375 (pow x 2.0))))
     (/ (/ (pow t_0 2.0) (sin x)) 0.375))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	double tmp;
	if (x <= 0.0006) {
		tmp = t_0 / (0.75 + (-0.09375 * pow(x, 2.0)));
	} else {
		tmp = (pow(t_0, 2.0) / sin(x)) / 0.375;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin((x * 0.5d0))
    if (x <= 0.0006d0) then
        tmp = t_0 / (0.75d0 + ((-0.09375d0) * (x ** 2.0d0)))
    else
        tmp = ((t_0 ** 2.0d0) / sin(x)) / 0.375d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	double tmp;
	if (x <= 0.0006) {
		tmp = t_0 / (0.75 + (-0.09375 * Math.pow(x, 2.0)));
	} else {
		tmp = (Math.pow(t_0, 2.0) / Math.sin(x)) / 0.375;
	}
	return tmp;
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	tmp = 0
	if x <= 0.0006:
		tmp = t_0 / (0.75 + (-0.09375 * math.pow(x, 2.0)))
	else:
		tmp = (math.pow(t_0, 2.0) / math.sin(x)) / 0.375
	return tmp

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	tmp = 0.0
	if (x <= 0.0006)
		tmp = Float64(t_0 / Float64(0.75 + Float64(-0.09375 * (x ^ 2.0))));
	else
		tmp = Float64(Float64((t_0 ^ 2.0) / sin(x)) / 0.375);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = sin((x * 0.5));
	tmp = 0.0;
	if (x <= 0.0006)
		tmp = t_0 / (0.75 + (-0.09375 * (x ^ 2.0)));
	else
		tmp = ((t_0 ^ 2.0) / sin(x)) / 0.375;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, 0.0006], N[(t$95$0 / N[(0.75 + N[(-0.09375 * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[t$95$0, 2.0], $MachinePrecision] / N[Sin[x], $MachinePrecision]), $MachinePrecision] / 0.375), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 8: 75.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0052:\\ \;\;\;\;\frac{\sin \left(x \cdot 0.5\right)}{0.75 + -0.09375 \cdot {x}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 - \frac{\cos x}{2}}{0.375 \cdot \sin x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 0.0052)
   (/ (sin (* x 0.5)) (+ 0.75 (* -0.09375 (pow x 2.0))))
   (/ (- 0.5 (/ (cos x) 2.0)) (* 0.375 (sin x)))))

C

double code(double x) {
	double tmp;
	if (x <= 0.0052) {
		tmp = sin((x * 0.5)) / (0.75 + (-0.09375 * pow(x, 2.0)));
	} else {
		tmp = (0.5 - (cos(x) / 2.0)) / (0.375 * sin(x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 0.0052d0) then
        tmp = sin((x * 0.5d0)) / (0.75d0 + ((-0.09375d0) * (x ** 2.0d0)))
    else
        tmp = (0.5d0 - (cos(x) / 2.0d0)) / (0.375d0 * sin(x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 0.0052) {
		tmp = Math.sin((x * 0.5)) / (0.75 + (-0.09375 * Math.pow(x, 2.0)));
	} else {
		tmp = (0.5 - (Math.cos(x) / 2.0)) / (0.375 * Math.sin(x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 0.0052:
		tmp = math.sin((x * 0.5)) / (0.75 + (-0.09375 * math.pow(x, 2.0)))
	else:
		tmp = (0.5 - (math.cos(x) / 2.0)) / (0.375 * math.sin(x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 0.0052)
		tmp = Float64(sin(Float64(x * 0.5)) / Float64(0.75 + Float64(-0.09375 * (x ^ 2.0))));
	else
		tmp = Float64(Float64(0.5 - Float64(cos(x) / 2.0)) / Float64(0.375 * sin(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 0.0052)
		tmp = sin((x * 0.5)) / (0.75 + (-0.09375 * (x ^ 2.0)));
	else
		tmp = (0.5 - (cos(x) / 2.0)) / (0.375 * sin(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 0.0052], N[(N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision] / N[(0.75 + N[(-0.09375 * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 - N[(N[Cos[x], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] / N[(0.375 * N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 77.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.000125:\\ \;\;\;\;\frac{\sin \left(x \cdot 0.5\right)}{0.75}\\ \mathbf{else}:\\ \;\;\;\;2.6666666666666665 \cdot \frac{0.5 - \frac{\cos x}{2}}{\sin x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 0.000125)
   (/ (sin (* x 0.5)) 0.75)
   (* 2.6666666666666665 (/ (- 0.5 (/ (cos x) 2.0)) (sin x)))))

C

double code(double x) {
	double tmp;
	if (x <= 0.000125) {
		tmp = sin((x * 0.5)) / 0.75;
	} else {
		tmp = 2.6666666666666665 * ((0.5 - (cos(x) / 2.0)) / sin(x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 0.000125d0) then
        tmp = sin((x * 0.5d0)) / 0.75d0
    else
        tmp = 2.6666666666666665d0 * ((0.5d0 - (cos(x) / 2.0d0)) / sin(x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 0.000125) {
		tmp = Math.sin((x * 0.5)) / 0.75;
	} else {
		tmp = 2.6666666666666665 * ((0.5 - (Math.cos(x) / 2.0)) / Math.sin(x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 0.000125:
		tmp = math.sin((x * 0.5)) / 0.75
	else:
		tmp = 2.6666666666666665 * ((0.5 - (math.cos(x) / 2.0)) / math.sin(x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 0.000125)
		tmp = Float64(sin(Float64(x * 0.5)) / 0.75);
	else
		tmp = Float64(2.6666666666666665 * Float64(Float64(0.5 - Float64(cos(x) / 2.0)) / sin(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 0.000125)
		tmp = sin((x * 0.5)) / 0.75;
	else
		tmp = 2.6666666666666665 * ((0.5 - (cos(x) / 2.0)) / sin(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 0.000125], N[(N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision] / 0.75), $MachinePrecision], N[(2.6666666666666665 * N[(N[(0.5 - N[(N[Cos[x], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 77.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.000125:\\ \;\;\;\;\frac{\sin \left(x \cdot 0.5\right)}{0.75}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 - \frac{\cos x}{2}}{0.375 \cdot \sin x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 0.000125)
   (/ (sin (* x 0.5)) 0.75)
   (/ (- 0.5 (/ (cos x) 2.0)) (* 0.375 (sin x)))))

C

double code(double x) {
	double tmp;
	if (x <= 0.000125) {
		tmp = sin((x * 0.5)) / 0.75;
	} else {
		tmp = (0.5 - (cos(x) / 2.0)) / (0.375 * sin(x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 0.000125d0) then
        tmp = sin((x * 0.5d0)) / 0.75d0
    else
        tmp = (0.5d0 - (cos(x) / 2.0d0)) / (0.375d0 * sin(x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 0.000125) {
		tmp = Math.sin((x * 0.5)) / 0.75;
	} else {
		tmp = (0.5 - (Math.cos(x) / 2.0)) / (0.375 * Math.sin(x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 0.000125:
		tmp = math.sin((x * 0.5)) / 0.75
	else:
		tmp = (0.5 - (math.cos(x) / 2.0)) / (0.375 * math.sin(x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 0.000125)
		tmp = Float64(sin(Float64(x * 0.5)) / 0.75);
	else
		tmp = Float64(Float64(0.5 - Float64(cos(x) / 2.0)) / Float64(0.375 * sin(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 0.000125)
		tmp = sin((x * 0.5)) / 0.75;
	else
		tmp = (0.5 - (cos(x) / 2.0)) / (0.375 * sin(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 0.000125], N[(N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision] / 0.75), $MachinePrecision], N[(N[(0.5 - N[(N[Cos[x], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] / N[(0.375 * N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 54.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \sin \left(x \cdot 0.5\right) \cdot 1.3333333333333333 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (sin (* x 0.5)) 1.3333333333333333))

C

double code(double x) {
	return sin((x * 0.5)) * 1.3333333333333333;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = sin((x * 0.5d0)) * 1.3333333333333333d0
end function

Java

public static double code(double x) {
	return Math.sin((x * 0.5)) * 1.3333333333333333;
}

Python

def code(x):
	return math.sin((x * 0.5)) * 1.3333333333333333

Julia

function code(x)
	return Float64(sin(Float64(x * 0.5)) * 1.3333333333333333)
end

MATLAB

function tmp = code(x)
	tmp = sin((x * 0.5)) * 1.3333333333333333;
end

Wolfram

code[x_] := N[(N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision] * 1.3333333333333333), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 54.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \frac{\sin \left(x \cdot 0.5\right)}{0.75} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (sin (* x 0.5)) 0.75))

C

double code(double x) {
	return sin((x * 0.5)) / 0.75;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = sin((x * 0.5d0)) / 0.75d0
end function

Java

public static double code(double x) {
	return Math.sin((x * 0.5)) / 0.75;
}

Python

def code(x):
	return math.sin((x * 0.5)) / 0.75

Julia

function code(x)
	return Float64(sin(Float64(x * 0.5)) / 0.75)
end

MATLAB

function tmp = code(x)
	tmp = sin((x * 0.5)) / 0.75;
end

Wolfram

code[x_] := N[(N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision] / 0.75), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 50.6% accurate, 104.3× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.6666666666666666 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* x 0.6666666666666666))

C

double code(double x) {
	return x * 0.6666666666666666;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * 0.6666666666666666d0
end function

Java

public static double code(double x) {
	return x * 0.6666666666666666;
}

Python

def code(x):
	return x * 0.6666666666666666

Julia

function code(x)
	return Float64(x * 0.6666666666666666)
end

MATLAB

function tmp = code(x)
	tmp = x * 0.6666666666666666;
end

Wolfram

code[x_] := N[(x * 0.6666666666666666), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \frac{\frac{8 \cdot t_0}{3}}{\frac{\sin x}{t_0}} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5)))) (/ (/ (* 8.0 t_0) 3.0) (/ (sin x) t_0))))

C

double code(double x) {
	double t_0 = sin((x * 0.5));
	return ((8.0 * t_0) / 3.0) / (sin(x) / t_0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sin((x * 0.5d0))
    code = ((8.0d0 * t_0) / 3.0d0) / (sin(x) / t_0)
end function

Java

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	return ((8.0 * t_0) / 3.0) / (Math.sin(x) / t_0);
}

Python

def code(x):
	t_0 = math.sin((x * 0.5))
	return ((8.0 * t_0) / 3.0) / (math.sin(x) / t_0)

Julia

function code(x)
	t_0 = sin(Float64(x * 0.5))
	return Float64(Float64(Float64(8.0 * t_0) / 3.0) / Float64(sin(x) / t_0))
end

MATLAB

function tmp = code(x)
	t_0 = sin((x * 0.5));
	tmp = ((8.0 * t_0) / 3.0) / (sin(x) / t_0);
end

Wolfram

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(N[(N[(8.0 * t$95$0), $MachinePrecision] / 3.0), $MachinePrecision] / N[(N[Sin[x], $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023343 
(FPCore (x)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A"
  :precision binary64

  :herbie-target
  (/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin x) (sin (* x 0.5))))

  (/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))