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

Percentage Accurate: 99.9% → 99.9%

Time: 1.4s

Alternatives: 6

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(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));
}

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

Java

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))

Julia

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

MATLAB

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]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(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));
}

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

Java

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))

Julia

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

MATLAB

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]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(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));
}

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

Java

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))

Julia

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

MATLAB

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]

Derivation

1. Initial program 100.0%

   \[\left(x + \sin y\right) + z \cdot \cos y \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 81.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sin y\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-47}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (sin y))))
   (if (<= x -2.8e-15) t_0 (if (<= x 5.7e-47) (+ (sin y) (* z (cos y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + sin(y);
	double tmp;
	if (x <= -2.8e-15) {
		tmp = t_0;
	} else if (x <= 5.7e-47) {
		tmp = sin(y) + (z * cos(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + sin(y)
    if (x <= (-2.8d-15)) then
        tmp = t_0
    else if (x <= 5.7d-47) then
        tmp = sin(y) + (z * cos(y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.sin(y);
	double tmp;
	if (x <= -2.8e-15) {
		tmp = t_0;
	} else if (x <= 5.7e-47) {
		tmp = Math.sin(y) + (z * Math.cos(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.sin(y)
	tmp = 0
	if x <= -2.8e-15:
		tmp = t_0
	elif x <= 5.7e-47:
		tmp = math.sin(y) + (z * math.cos(y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + sin(y))
	tmp = 0.0
	if (x <= -2.8e-15)
		tmp = t_0;
	elseif (x <= 5.7e-47)
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + sin(y);
	tmp = 0.0;
	if (x <= -2.8e-15)
		tmp = t_0;
	elseif (x <= 5.7e-47)
		tmp = sin(y) + (z * cos(y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e-15], t$95$0, If[LessEqual[x, 5.7e-47], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.80000000000000014e-15 or 5.70000000000000046e-47 < x

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 78.4%

      \[\leadsto \color{blue}{x + \sin y} \]

   if -2.80000000000000014e-15 < x < 5.70000000000000046e-47

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\sin y} + z \cdot \cos y \]

   5. Applied rewrites 95.3%

      \[\leadsto \color{blue}{\sin y} + z \cdot \cos y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 82.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -12:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+74}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -12.0) t_0 (if (<= z 7.5e+74) (+ x (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -12.0) {
		tmp = t_0;
	} else if (z <= 7.5e+74) {
		tmp = x + sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-12.0d0)) then
        tmp = t_0
    else if (z <= 7.5d+74) then
        tmp = x + sin(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -12.0) {
		tmp = t_0;
	} else if (z <= 7.5e+74) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -12.0:
		tmp = t_0
	elif z <= 7.5e+74:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -12.0)
		tmp = t_0;
	elseif (z <= 7.5e+74)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -12.0)
		tmp = t_0;
	elseif (z <= 7.5e+74)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -12.0], t$95$0, If[LessEqual[z, 7.5e+74], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -12 or 7.5e74 < z

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]

   5. Applied rewrites 2.5%

      \[\leadsto \color{blue}{\cos y} \]

   6. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]

   8. Applied rewrites 81.7%

      \[\leadsto \color{blue}{z \cdot \cos y} \]

   if -12 < z < 7.5e74

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.6%

      \[\leadsto \color{blue}{x + \sin y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 58.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ x + \sin y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x + 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 + sin(y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + \sin y\right) + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 59.6%

   \[\leadsto \color{blue}{x + \sin y} \]
6. Add Preprocessing

Alternative 5: 18.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (sin y))

C

double code(double x, double y, double z) {
	return 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 = sin(y)
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return sin(y)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Sin[y], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + \sin y\right) + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]

5. Applied rewrites 4.0%

   \[\leadsto \color{blue}{\cos y} \]

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]

8. Applied rewrites 16.4%

   \[\leadsto \color{blue}{\sin y} \]
9. Add Preprocessing

Alternative 6: 4.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (cos y))

C

double code(double x, double y, double z) {
	return 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 = cos(y)
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return cos(y)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Cos[y], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + \sin y\right) + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]

5. Applied rewrites 4.0%

   \[\leadsto \color{blue}{\cos y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  :pre (TRUE)
  (+ (+ x (sin y)) (* z (cos y))))