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

Percentage Accurate: 99.9% → 99.9%

Time: 7.0s

Alternatives: 5

Speedup: 1.0×

Specification

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. Final simplification 100.0%

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

Alternative 2: 85.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-106} \lor \neg \left(x \leq 2.8 \cdot 10^{-205}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.8e-106) (not (<= x 2.8e-205)))
   (+ x (* z (cos y)))
   (+ (sin y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.8e-106) || !(x <= 2.8e-205)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = sin(y) + z;
	}
	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) :: tmp
    if ((x <= (-7.8d-106)) .or. (.not. (x <= 2.8d-205))) then
        tmp = x + (z * cos(y))
    else
        tmp = sin(y) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.8e-106) || !(x <= 2.8e-205)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = Math.sin(y) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.8e-106) or not (x <= 2.8e-205):
		tmp = x + (z * math.cos(y))
	else:
		tmp = math.sin(y) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.8e-106) || !(x <= 2.8e-205))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(sin(y) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.8e-106) || ~((x <= 2.8e-205)))
		tmp = x + (z * cos(y));
	else
		tmp = sin(y) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.8e-106], N[Not[LessEqual[x, 2.8e-205]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.80000000000000019e-106 or 2.79999999999999991e-205 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 90.3%

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

   if -7.80000000000000019e-106 < x < 2.79999999999999991e-205

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.8%

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

   4. Taylor expanded in y around 0 86.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-106} \lor \neg \left(x \leq 2.8 \cdot 10^{-205}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+44} \lor \neg \left(z \leq 8.4 \cdot 10^{-22}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.65e+44) (not (<= z 8.4e-22)))
   (+ x (* z (cos y)))
   (+ (+ x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.65e+44) || !(z <= 8.4e-22)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = (x + sin(y)) + z;
	}
	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) :: tmp
    if ((z <= (-1.65d+44)) .or. (.not. (z <= 8.4d-22))) then
        tmp = x + (z * cos(y))
    else
        tmp = (x + sin(y)) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.65e+44) || !(z <= 8.4e-22)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.65e+44) or not (z <= 8.4e-22):
		tmp = x + (z * math.cos(y))
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.65e+44) || !(z <= 8.4e-22))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(Float64(x + sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.65e+44) || ~((z <= 8.4e-22)))
		tmp = x + (z * cos(y));
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.65e+44], N[Not[LessEqual[z, 8.4e-22]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65000000000000007e44 or 8.40000000000000031e-22 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 99.9%

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

   if -1.65000000000000007e44 < z < 8.40000000000000031e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.5%

      \[\leadsto \left(x + \sin y\right) + \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+44} \lor \neg \left(z \leq 8.4 \cdot 10^{-22}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-12} \lor \neg \left(x \leq 2.05 \cdot 10^{-78}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e-12) (not (<= x 2.05e-78))) (+ x z) (+ (sin y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-12) || !(x <= 2.05e-78)) {
		tmp = x + z;
	} else {
		tmp = sin(y) + z;
	}
	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) :: tmp
    if ((x <= (-2.1d-12)) .or. (.not. (x <= 2.05d-78))) then
        tmp = x + z
    else
        tmp = sin(y) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-12) || !(x <= 2.05e-78)) {
		tmp = x + z;
	} else {
		tmp = Math.sin(y) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e-12) or not (x <= 2.05e-78):
		tmp = x + z
	else:
		tmp = math.sin(y) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e-12) || !(x <= 2.05e-78))
		tmp = Float64(x + z);
	else
		tmp = Float64(sin(y) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.1e-12) || ~((x <= 2.05e-78)))
		tmp = x + z;
	else
		tmp = sin(y) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e-12], N[Not[LessEqual[x, 2.05e-78]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999994e-12 or 2.0499999999999999e-78 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 96.5%

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

   4. Taylor expanded in y around 0 79.9%

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

   if -2.09999999999999994e-12 < x < 2.0499999999999999e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 92.1%

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

   4. Taylor expanded in y around 0 75.9%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-12} \lor \neg \left(x \leq 2.05 \cdot 10^{-78}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.9% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + z \end{array} \]

FPCore

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

C

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

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 + z
end function

Java

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

Python

def code(x, y, z):
	return x + z

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + z), $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 82.7%

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

4. Taylor expanded in y around 0 66.3%

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

5. Final simplification 66.3%

   \[\leadsto x + z \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024024 
(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))))