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

Percentage Accurate: 99.9% → 99.9%

Time: 6.8s

Alternatives: 9

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 85.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-47} \lor \neg \left(x \leq 2.8 \cdot 10^{-153}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.6e-47) (not (<= x 2.8e-153)))
   (+ x (* z (cos y)))
   (+ (sin y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.6e-47) || !(x <= 2.8e-153)) {
		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 <= (-2.6d-47)) .or. (.not. (x <= 2.8d-153))) 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 <= -2.6e-47) || !(x <= 2.8e-153)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = Math.sin(y) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.6e-47) or not (x <= 2.8e-153):
		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 <= -2.6e-47) || !(x <= 2.8e-153))
		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 <= -2.6e-47) || ~((x <= 2.8e-153)))
		tmp = x + (z * cos(y));
	else
		tmp = sin(y) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.6e-47], N[Not[LessEqual[x, 2.8e-153]], $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 < -2.6e-47 or 2.8000000000000001e-153 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 90.9%

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

   if -2.6e-47 < x < 2.8000000000000001e-153

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.8%

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

   3. Taylor expanded in y around 0 79.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-47} \lor \neg \left(x \leq 2.8 \cdot 10^{-153}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \]

Alternative 3: 99.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -22.5 \lor \neg \left(z \leq 1.1\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -22.5) (not (<= z 1.1)))
   (+ x (* z (cos y)))
   (+ (+ x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -22.5) || !(z <= 1.1)) {
		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 <= (-22.5d0)) .or. (.not. (z <= 1.1d0))) 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 <= -22.5) || !(z <= 1.1)) {
		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 <= -22.5) or not (z <= 1.1):
		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 <= -22.5) || !(z <= 1.1))
		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 <= -22.5) || ~((z <= 1.1)))
		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, -22.5], N[Not[LessEqual[z, 1.1]], $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 < -22.5 or 1.1000000000000001 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 98.5%

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

   if -22.5 < z < 1.1000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22.5 \lor \neg \left(z \leq 1.1\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]

Alternative 4: 65.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+139}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+37}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+199}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+139)
   (sin y)
   (if (<= y 9.5e+37) (+ z (+ x y)) (if (<= y 8.5e+199) (sin y) (+ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+139) {
		tmp = sin(y);
	} else if (y <= 9.5e+37) {
		tmp = z + (x + y);
	} else if (y <= 8.5e+199) {
		tmp = sin(y);
	} else {
		tmp = x + 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 (y <= (-1.05d+139)) then
        tmp = sin(y)
    else if (y <= 9.5d+37) then
        tmp = z + (x + y)
    else if (y <= 8.5d+199) then
        tmp = sin(y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+139) {
		tmp = Math.sin(y);
	} else if (y <= 9.5e+37) {
		tmp = z + (x + y);
	} else if (y <= 8.5e+199) {
		tmp = Math.sin(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+139:
		tmp = math.sin(y)
	elif y <= 9.5e+37:
		tmp = z + (x + y)
	elif y <= 8.5e+199:
		tmp = math.sin(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+139)
		tmp = sin(y);
	elseif (y <= 9.5e+37)
		tmp = Float64(z + Float64(x + y));
	elseif (y <= 8.5e+199)
		tmp = sin(y);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.05e+139)
		tmp = sin(y);
	elseif (y <= 9.5e+37)
		tmp = z + (x + y);
	elseif (y <= 8.5e+199)
		tmp = sin(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+139], N[Sin[y], $MachinePrecision], If[LessEqual[y, 9.5e+37], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+199], N[Sin[y], $MachinePrecision], N[(x + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0499999999999999e139 or 9.4999999999999995e37 < y < 8.49999999999999923e199

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 75.0%

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

   3. Taylor expanded in z around 0 36.7%

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

   if -1.0499999999999999e139 < y < 9.4999999999999995e37

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.4%

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

   3. Taylor expanded in y around 0 86.1%

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

   if 8.49999999999999923e199 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 71.8%

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

   3. Taylor expanded in y around 0 47.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+139}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+37}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+199}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 5: 77.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-16}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-83}:\\ \;\;\;\;\sin y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.5e-16) (+ x z) (if (<= x 1.1e-83) (+ (sin y) z) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5e-16) {
		tmp = x + z;
	} else if (x <= 1.1e-83) {
		tmp = sin(y) + z;
	} else {
		tmp = x + 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 <= (-6.5d-16)) then
        tmp = x + z
    else if (x <= 1.1d-83) then
        tmp = sin(y) + z
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5e-16) {
		tmp = x + z;
	} else if (x <= 1.1e-83) {
		tmp = Math.sin(y) + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.5e-16:
		tmp = x + z
	elif x <= 1.1e-83:
		tmp = math.sin(y) + z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.5e-16)
		tmp = Float64(x + z);
	elseif (x <= 1.1e-83)
		tmp = Float64(sin(y) + z);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.5e-16)
		tmp = x + z;
	elseif (x <= 1.1e-83)
		tmp = sin(y) + z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.5e-16], N[(x + z), $MachinePrecision], If[LessEqual[x, 1.1e-83], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.50000000000000011e-16 or 1.10000000000000004e-83 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 95.4%

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

   3. Taylor expanded in y around 0 77.8%

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

   if -6.50000000000000011e-16 < x < 1.10000000000000004e-83

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 94.4%

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

   3. Taylor expanded in y around 0 73.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-16}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-83}:\\ \;\;\;\;\sin y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 6: 70.9% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1050000000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+53}:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1050000000000.0)
   (+ x z)
   (if (<= y 8e+53) (+ (+ x y) (* z (+ 1.0 (* -0.5 (* y y))))) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1050000000000.0) {
		tmp = x + z;
	} else if (y <= 8e+53) {
		tmp = (x + y) + (z * (1.0 + (-0.5 * (y * y))));
	} else {
		tmp = x + 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 (y <= (-1050000000000.0d0)) then
        tmp = x + z
    else if (y <= 8d+53) then
        tmp = (x + y) + (z * (1.0d0 + ((-0.5d0) * (y * y))))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1050000000000.0) {
		tmp = x + z;
	} else if (y <= 8e+53) {
		tmp = (x + y) + (z * (1.0 + (-0.5 * (y * y))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1050000000000.0:
		tmp = x + z
	elif y <= 8e+53:
		tmp = (x + y) + (z * (1.0 + (-0.5 * (y * y))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1050000000000.0)
		tmp = Float64(x + z);
	elseif (y <= 8e+53)
		tmp = Float64(Float64(x + y) + Float64(z * Float64(1.0 + Float64(-0.5 * Float64(y * y)))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1050000000000.0)
		tmp = x + z;
	elseif (y <= 8e+53)
		tmp = (x + y) + (z * (1.0 + (-0.5 * (y * y))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1050000000000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 8e+53], N[(N[(x + y), $MachinePrecision] + N[(z * N[(1.0 + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e12 or 7.9999999999999999e53 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 69.3%

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

   3. Taylor expanded in y around 0 34.5%

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

   if -1.05e12 < y < 7.9999999999999999e53

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.6%

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

   3. Taylor expanded in y around 0 91.5%

      \[\leadsto \left(y + x\right) + z \cdot \color{blue}{\left(1 + -0.5 \cdot {y}^{2}\right)} \]
   4. Step-by-step derivation

      1. unpow2 91.5%

         \[\leadsto \left(y + x\right) + z \cdot \left(1 + -0.5 \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

   5. Simplified 91.5%

      \[\leadsto \left(y + x\right) + z \cdot \color{blue}{\left(1 + -0.5 \cdot \left(y \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1050000000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+53}:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 7: 70.9% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+67}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+53}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7e+67) (+ x z) (if (<= y 8e+53) (+ z (+ x y)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+67) {
		tmp = x + z;
	} else if (y <= 8e+53) {
		tmp = z + (x + y);
	} else {
		tmp = x + 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 (y <= (-7d+67)) then
        tmp = x + z
    else if (y <= 8d+53) then
        tmp = z + (x + y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+67) {
		tmp = x + z;
	} else if (y <= 8e+53) {
		tmp = z + (x + y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7e+67:
		tmp = x + z
	elif y <= 8e+53:
		tmp = z + (x + y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7e+67)
		tmp = Float64(x + z);
	elseif (y <= 8e+53)
		tmp = Float64(z + Float64(x + y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7e+67)
		tmp = x + z;
	elseif (y <= 8e+53)
		tmp = z + (x + y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7e+67], N[(x + z), $MachinePrecision], If[LessEqual[y, 8e+53], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7e67 or 7.9999999999999999e53 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 69.1%

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

   3. Taylor expanded in y around 0 35.2%

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

   if -7e67 < y < 7.9999999999999999e53

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.9%

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

   3. Taylor expanded in y around 0 86.9%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+67}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+53}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 8: 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 99.9%

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

2. Taylor expanded in x around inf 80.6%

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

3. Taylor expanded in y around 0 62.2%

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

4. Final simplification 62.2%

   \[\leadsto x + z \]

Alternative 9: 42.8% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 68.8%

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

3. Taylor expanded in y around 0 53.6%

   \[\leadsto \left(y + x\right) + z \cdot \color{blue}{\left(1 + -0.5 \cdot {y}^{2}\right)} \]
4. Step-by-step derivation

   1. unpow2 53.6%

      \[\leadsto \left(y + x\right) + z \cdot \left(1 + -0.5 \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

5. Simplified 53.6%

   \[\leadsto \left(y + x\right) + z \cdot \color{blue}{\left(1 + -0.5 \cdot \left(y \cdot y\right)\right)} \]

6. Taylor expanded in x around inf 34.3%

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

7. Final simplification 34.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023196 
(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))))