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

Percentage Accurate: 99.9% → 99.9%

Time: 6.5s

Alternatives: 10

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 81.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -7 \cdot 10^{+198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+112}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-96}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+162}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -7e+198)
     t_0
     (if (<= z -4.5e+112)
       (+ x z)
       (if (<= z -5.8e+64)
         t_0
         (if (<= z 1.65e-96)
           (+ x (sin y))
           (if (<= z 3.4e+162) (+ x z) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -7e+198) {
		tmp = t_0;
	} else if (z <= -4.5e+112) {
		tmp = x + z;
	} else if (z <= -5.8e+64) {
		tmp = t_0;
	} else if (z <= 1.65e-96) {
		tmp = x + sin(y);
	} else if (z <= 3.4e+162) {
		tmp = x + z;
	} 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 <= (-7d+198)) then
        tmp = t_0
    else if (z <= (-4.5d+112)) then
        tmp = x + z
    else if (z <= (-5.8d+64)) then
        tmp = t_0
    else if (z <= 1.65d-96) then
        tmp = x + sin(y)
    else if (z <= 3.4d+162) then
        tmp = x + z
    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 <= -7e+198) {
		tmp = t_0;
	} else if (z <= -4.5e+112) {
		tmp = x + z;
	} else if (z <= -5.8e+64) {
		tmp = t_0;
	} else if (z <= 1.65e-96) {
		tmp = x + Math.sin(y);
	} else if (z <= 3.4e+162) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -7e+198:
		tmp = t_0
	elif z <= -4.5e+112:
		tmp = x + z
	elif z <= -5.8e+64:
		tmp = t_0
	elif z <= 1.65e-96:
		tmp = x + math.sin(y)
	elif z <= 3.4e+162:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -7e+198)
		tmp = t_0;
	elseif (z <= -4.5e+112)
		tmp = Float64(x + z);
	elseif (z <= -5.8e+64)
		tmp = t_0;
	elseif (z <= 1.65e-96)
		tmp = Float64(x + sin(y));
	elseif (z <= 3.4e+162)
		tmp = Float64(x + z);
	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 <= -7e+198)
		tmp = t_0;
	elseif (z <= -4.5e+112)
		tmp = x + z;
	elseif (z <= -5.8e+64)
		tmp = t_0;
	elseif (z <= 1.65e-96)
		tmp = x + sin(y);
	elseif (z <= 3.4e+162)
		tmp = x + z;
	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, -7e+198], t$95$0, If[LessEqual[z, -4.5e+112], N[(x + z), $MachinePrecision], If[LessEqual[z, -5.8e+64], t$95$0, If[LessEqual[z, 1.65e-96], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+162], N[(x + z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000026e198 or -4.4999999999999999e112 < z < -5.79999999999999986e64 or 3.40000000000000003e162 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 99.8%

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

   3. Taylor expanded in x around 0 92.4%

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

   if -7.00000000000000026e198 < z < -4.4999999999999999e112 or 1.64999999999999995e-96 < z < 3.40000000000000003e162

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 96.5%

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

   3. Taylor expanded in y around 0 85.3%

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

   if -5.79999999999999986e64 < z < 1.64999999999999995e-96

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.3%

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

      1. fma-def 76.3%

         \[\leadsto \left(x + \sin y\right) + \color{blue}{\mathsf{fma}\left(-0.5, {y}^{2} \cdot z, z\right)} \]

      2. *-commutative 76.3%

         \[\leadsto \left(x + \sin y\right) + \mathsf{fma}\left(-0.5, \color{blue}{z \cdot {y}^{2}}, z\right) \]

      3. unpow2 76.3%

         \[\leadsto \left(x + \sin y\right) + \mathsf{fma}\left(-0.5, z \cdot \color{blue}{\left(y \cdot y\right)}, z\right) \]

   4. Simplified 76.3%

      \[\leadsto \left(x + \sin y\right) + \color{blue}{\mathsf{fma}\left(-0.5, z \cdot \left(y \cdot y\right), z\right)} \]

   5. Taylor expanded in z around 0 93.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+198}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+112}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-96}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+162}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 3: 68.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -6 \cdot 10^{+203}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-97}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+158}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -6e+203)
     t_0
     (if (<= z 4.5e-97) (+ z (+ x y)) (if (<= z 9.5e+158) (+ x z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -6e+203) {
		tmp = t_0;
	} else if (z <= 4.5e-97) {
		tmp = z + (x + y);
	} else if (z <= 9.5e+158) {
		tmp = x + z;
	} 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 <= (-6d+203)) then
        tmp = t_0
    else if (z <= 4.5d-97) then
        tmp = z + (x + y)
    else if (z <= 9.5d+158) then
        tmp = x + z
    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 <= -6e+203) {
		tmp = t_0;
	} else if (z <= 4.5e-97) {
		tmp = z + (x + y);
	} else if (z <= 9.5e+158) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -6e+203:
		tmp = t_0
	elif z <= 4.5e-97:
		tmp = z + (x + y)
	elif z <= 9.5e+158:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -6e+203)
		tmp = t_0;
	elseif (z <= 4.5e-97)
		tmp = Float64(z + Float64(x + y));
	elseif (z <= 9.5e+158)
		tmp = Float64(x + z);
	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 <= -6e+203)
		tmp = t_0;
	elseif (z <= 4.5e-97)
		tmp = z + (x + y);
	elseif (z <= 9.5e+158)
		tmp = x + z;
	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, -6e+203], t$95$0, If[LessEqual[z, 4.5e-97], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+158], N[(x + z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.9999999999999999e203 or 9.49999999999999913e158 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 99.8%

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

   3. Taylor expanded in x around 0 91.2%

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

   if -5.9999999999999999e203 < z < 4.5000000000000001e-97

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.6%

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

   3. Taylor expanded in y around 0 75.0%

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

   if 4.5000000000000001e-97 < z < 9.49999999999999913e158

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 95.8%

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

   3. Taylor expanded in y around 0 84.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+203}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-97}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+158}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 4: 94.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.06 \lor \neg \left(z \leq 2.9 \cdot 10^{-114}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.06) (not (<= z 2.9e-114)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.06) || !(z <= 2.9e-114)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = x + sin(y);
	}
	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 <= (-0.06d0)) .or. (.not. (z <= 2.9d-114))) then
        tmp = x + (z * cos(y))
    else
        tmp = x + sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.06) || !(z <= 2.9e-114)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.06) or not (z <= 2.9e-114):
		tmp = x + (z * math.cos(y))
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.06) || !(z <= 2.9e-114))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.06) || ~((z <= 2.9e-114)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.06], N[Not[LessEqual[z, 2.9e-114]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.059999999999999998 or 2.89999999999999997e-114 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 97.6%

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

   if -0.059999999999999998 < z < 2.89999999999999997e-114

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.2%

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

      1. fma-def 78.2%

         \[\leadsto \left(x + \sin y\right) + \color{blue}{\mathsf{fma}\left(-0.5, {y}^{2} \cdot z, z\right)} \]

      2. *-commutative 78.2%

         \[\leadsto \left(x + \sin y\right) + \mathsf{fma}\left(-0.5, \color{blue}{z \cdot {y}^{2}}, z\right) \]

      3. unpow2 78.2%

         \[\leadsto \left(x + \sin y\right) + \mathsf{fma}\left(-0.5, z \cdot \color{blue}{\left(y \cdot y\right)}, z\right) \]

   4. Simplified 78.2%

      \[\leadsto \left(x + \sin y\right) + \color{blue}{\mathsf{fma}\left(-0.5, z \cdot \left(y \cdot y\right), z\right)} \]

   5. Taylor expanded in z around 0 96.1%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.06 \lor \neg \left(z \leq 2.9 \cdot 10^{-114}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 5: 98.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+37} \lor \neg \left(z \leq 2.65 \cdot 10^{-14}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.6e+37) (not (<= z 2.65e-14)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.6e+37) || !(z <= 2.65e-14)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = z + (x + sin(y));
	}
	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 <= (-9.6d+37)) .or. (.not. (z <= 2.65d-14))) then
        tmp = x + (z * cos(y))
    else
        tmp = z + (x + sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.6e+37) || !(z <= 2.65e-14)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.6e+37) or not (z <= 2.65e-14):
		tmp = x + (z * math.cos(y))
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.6e+37) || !(z <= 2.65e-14))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(z + Float64(x + sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.6e+37) || ~((z <= 2.65e-14)))
		tmp = x + (z * cos(y));
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.6e+37], N[Not[LessEqual[z, 2.65e-14]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5999999999999999e37 or 2.6500000000000001e-14 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 99.3%

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

   if -9.5999999999999999e37 < z < 2.6500000000000001e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+37} \lor \neg \left(z \leq 2.65 \cdot 10^{-14}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 6: 70.1% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -620000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.1:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -620000.0) (+ x z) (if (<= y 3.1) (+ z (+ x y)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -620000.0) {
		tmp = x + z;
	} else if (y <= 3.1) {
		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 <= (-620000.0d0)) then
        tmp = x + z
    else if (y <= 3.1d0) 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 <= -620000.0) {
		tmp = x + z;
	} else if (y <= 3.1) {
		tmp = z + (x + y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -620000.0:
		tmp = x + z
	elif y <= 3.1:
		tmp = z + (x + y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -620000.0)
		tmp = Float64(x + z);
	elseif (y <= 3.1)
		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 <= -620000.0)
		tmp = x + z;
	elseif (y <= 3.1)
		tmp = z + (x + y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -620000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 3.1], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2e5 or 3.10000000000000009 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 79.0%

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

   3. Taylor expanded in y around 0 47.6%

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

   if -6.2e5 < y < 3.10000000000000009

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.8%

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

   3. Taylor expanded in y around 0 99.3%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -620000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.1:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 7: 46.5% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-68}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.8e-14) x (if (<= x 4e-68) (+ x y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e-14) {
		tmp = x;
	} else if (x <= 4e-68) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	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 <= (-1.8d-14)) then
        tmp = x
    else if (x <= 4d-68) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e-14) {
		tmp = x;
	} else if (x <= 4e-68) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.8e-14:
		tmp = x
	elif x <= 4e-68:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.8e-14)
		tmp = x;
	elseif (x <= 4e-68)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.8e-14)
		tmp = x;
	elseif (x <= 4e-68)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.8e-14], x, If[LessEqual[x, 4e-68], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999999e-14 or 4.00000000000000027e-68 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 95.3%

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

   3. Taylor expanded in x around inf 68.6%

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

   if -1.7999999999999999e-14 < x < 4.00000000000000027e-68

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 67.4%

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

      1. fma-def 67.4%

         \[\leadsto \left(x + \sin y\right) + \color{blue}{\mathsf{fma}\left(-0.5, {y}^{2} \cdot z, z\right)} \]

      2. *-commutative 67.4%

         \[\leadsto \left(x + \sin y\right) + \mathsf{fma}\left(-0.5, \color{blue}{z \cdot {y}^{2}}, z\right) \]

      3. unpow2 67.4%

         \[\leadsto \left(x + \sin y\right) + \mathsf{fma}\left(-0.5, z \cdot \color{blue}{\left(y \cdot y\right)}, z\right) \]

   4. Simplified 67.4%

      \[\leadsto \left(x + \sin y\right) + \color{blue}{\mathsf{fma}\left(-0.5, z \cdot \left(y \cdot y\right), z\right)} \]

   5. Taylor expanded in z around 0 44.6%

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

   6. Taylor expanded in y around 0 28.7%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-68}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 67.6% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-164}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-83}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.2e-164) (+ x z) (if (<= x 1.8e-83) (+ y z) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.2e-164) {
		tmp = x + z;
	} else if (x <= 1.8e-83) {
		tmp = 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 <= (-9.2d-164)) then
        tmp = x + z
    else if (x <= 1.8d-83) then
        tmp = 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 <= -9.2e-164) {
		tmp = x + z;
	} else if (x <= 1.8e-83) {
		tmp = y + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.2e-164:
		tmp = x + z
	elif x <= 1.8e-83:
		tmp = y + z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.2e-164)
		tmp = Float64(x + z);
	elseif (x <= 1.8e-83)
		tmp = Float64(y + z);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.2e-164)
		tmp = x + z;
	elseif (x <= 1.8e-83)
		tmp = y + z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.2e-164], N[(x + z), $MachinePrecision], If[LessEqual[x, 1.8e-83], N[(y + z), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.19999999999999942e-164 or 1.80000000000000006e-83 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 91.9%

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

   3. Taylor expanded in y around 0 80.4%

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

   if -9.19999999999999942e-164 < x < 1.80000000000000006e-83

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.3%

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

   3. Taylor expanded in y around 0 57.9%

      \[\leadsto \color{blue}{y + z} \]
   4. Step-by-step derivation

      1. +-commutative 57.9%

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

   5. Simplified 57.9%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-164}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-83}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 9: 65.8% 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 84.1%

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

3. Taylor expanded in y around 0 70.4%

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

4. Final simplification 70.4%

   \[\leadsto x + z \]

Alternative 10: 42.5% 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 x around inf 84.1%

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

3. Taylor expanded in x around inf 46.3%

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

4. Final simplification 46.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023228 
(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))))