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

Percentage Accurate: 99.9% → 99.9%

Time: 9.2s

Alternatives: 11

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(z * N[Cos[y], $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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. fma-define 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, \cos y, x + \sin y\right)} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(z, \cos y, x + \sin y\right) \]
6. Add Preprocessing

Alternative 2: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0098 \lor \neg \left(x \leq 63000000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0098) (not (<= x 63000000.0)))
   (+ z x)
   (+ (sin y) (* z (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0098) || !(x <= 63000000.0)) {
		tmp = z + x;
	} else {
		tmp = sin(y) + (z * cos(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 ((x <= (-0.0098d0)) .or. (.not. (x <= 63000000.0d0))) then
        tmp = z + x
    else
        tmp = sin(y) + (z * cos(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0098) || !(x <= 63000000.0)) {
		tmp = z + x;
	} else {
		tmp = Math.sin(y) + (z * Math.cos(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0098) or not (x <= 63000000.0):
		tmp = z + x
	else:
		tmp = math.sin(y) + (z * math.cos(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0098) || !(x <= 63000000.0))
		tmp = Float64(z + x);
	else
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.0098) || ~((x <= 63000000.0)))
		tmp = z + x;
	else
		tmp = sin(y) + (z * cos(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0098], N[Not[LessEqual[x, 63000000.0]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0097999999999999997 or 6.3e7 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 86.0%

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

      1. +-commutative 86.0%

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

   5. Simplified 86.0%

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

   if -0.0097999999999999997 < x < 6.3e7

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 90.4%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0098 \lor \neg \left(x \leq 63000000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 4: 71.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+191}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-249}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+104}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.45e+191)
     t_0
     (if (<= z -4.1e-249) (+ z x) (if (<= z 5.3e+104) (+ z (+ y x)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -2.45e+191) {
		tmp = t_0;
	} else if (z <= -4.1e-249) {
		tmp = z + x;
	} else if (z <= 5.3e+104) {
		tmp = z + (y + x);
	} 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 <= (-2.45d+191)) then
        tmp = t_0
    else if (z <= (-4.1d-249)) then
        tmp = z + x
    else if (z <= 5.3d+104) then
        tmp = z + (y + x)
    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 <= -2.45e+191) {
		tmp = t_0;
	} else if (z <= -4.1e-249) {
		tmp = z + x;
	} else if (z <= 5.3e+104) {
		tmp = z + (y + x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -2.45e+191:
		tmp = t_0
	elif z <= -4.1e-249:
		tmp = z + x
	elif z <= 5.3e+104:
		tmp = z + (y + x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -2.45e+191)
		tmp = t_0;
	elseif (z <= -4.1e-249)
		tmp = Float64(z + x);
	elseif (z <= 5.3e+104)
		tmp = Float64(z + Float64(y + x));
	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 <= -2.45e+191)
		tmp = t_0;
	elseif (z <= -4.1e-249)
		tmp = z + x;
	elseif (z <= 5.3e+104)
		tmp = z + (y + x);
	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, -2.45e+191], t$95$0, If[LessEqual[z, -4.1e-249], N[(z + x), $MachinePrecision], If[LessEqual[z, 5.3e+104], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45e191 or 5.2999999999999999e104 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 90.3%

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

   if -2.45e191 < z < -4.10000000000000004e-249

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.7%

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

      1. +-commutative 70.7%

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

   5. Simplified 70.7%

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

   if -4.10000000000000004e-249 < z < 5.2999999999999999e104

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 67.8%

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

      1. +-commutative 67.8%

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

      2. +-commutative 67.8%

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

      3. associate-+l+ 67.8%

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

   5. Simplified 67.8%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+191}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-249}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+104}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+191}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-57}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 0.47:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.4e+191)
     t_0
     (if (<= z -5.5e-57) (+ z x) (if (<= z 0.47) (+ x (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -2.4e+191) {
		tmp = t_0;
	} else if (z <= -5.5e-57) {
		tmp = z + x;
	} else if (z <= 0.47) {
		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 <= (-2.4d+191)) then
        tmp = t_0
    else if (z <= (-5.5d-57)) then
        tmp = z + x
    else if (z <= 0.47d0) 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 <= -2.4e+191) {
		tmp = t_0;
	} else if (z <= -5.5e-57) {
		tmp = z + x;
	} else if (z <= 0.47) {
		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 <= -2.4e+191:
		tmp = t_0
	elif z <= -5.5e-57:
		tmp = z + x
	elif z <= 0.47:
		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 <= -2.4e+191)
		tmp = t_0;
	elseif (z <= -5.5e-57)
		tmp = Float64(z + x);
	elseif (z <= 0.47)
		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 <= -2.4e+191)
		tmp = t_0;
	elseif (z <= -5.5e-57)
		tmp = z + x;
	elseif (z <= 0.47)
		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, -2.4e+191], t$95$0, If[LessEqual[z, -5.5e-57], N[(z + x), $MachinePrecision], If[LessEqual[z, 0.47], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999986e191 or 0.46999999999999997 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 82.6%

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

   if -2.39999999999999986e191 < z < -5.50000000000000011e-57

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 78.4%

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

      1. +-commutative 78.4%

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

   5. Simplified 78.4%

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

   if -5.50000000000000011e-57 < z < 0.46999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.8%

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

      1. +-commutative 94.8%

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

   5. Simplified 94.8%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+191}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-57}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 0.47:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+85}:\\ \;\;\;\;t\_0 + \left(y + x\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 0.47:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.05e+85)
     (+ t_0 (+ y x))
     (if (<= z -2.3e-60) (+ z x) (if (<= z 0.47) (+ x (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.05e+85) {
		tmp = t_0 + (y + x);
	} else if (z <= -2.3e-60) {
		tmp = z + x;
	} else if (z <= 0.47) {
		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 <= (-1.05d+85)) then
        tmp = t_0 + (y + x)
    else if (z <= (-2.3d-60)) then
        tmp = z + x
    else if (z <= 0.47d0) 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 <= -1.05e+85) {
		tmp = t_0 + (y + x);
	} else if (z <= -2.3e-60) {
		tmp = z + x;
	} else if (z <= 0.47) {
		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 <= -1.05e+85:
		tmp = t_0 + (y + x)
	elif z <= -2.3e-60:
		tmp = z + x
	elif z <= 0.47:
		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 <= -1.05e+85)
		tmp = Float64(t_0 + Float64(y + x));
	elseif (z <= -2.3e-60)
		tmp = Float64(z + x);
	elseif (z <= 0.47)
		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 <= -1.05e+85)
		tmp = t_0 + (y + x);
	elseif (z <= -2.3e-60)
		tmp = z + x;
	elseif (z <= 0.47)
		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, -1.05e+85], N[(t$95$0 + N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-60], N[(z + x), $MachinePrecision], If[LessEqual[z, 0.47], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05000000000000005e85

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 91.2%

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

      1. +-commutative 91.2%

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

   5. Simplified 91.2%

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

   if -1.05000000000000005e85 < z < -2.3000000000000001e-60

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.1%

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

      1. +-commutative 79.1%

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

   5. Simplified 79.1%

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

   if -2.3000000000000001e-60 < z < 0.46999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.8%

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

      1. +-commutative 94.8%

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

   5. Simplified 94.8%

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

   if 0.46999999999999997 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 79.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \cos y + \left(y + x\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 0.47:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.5% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+86} \lor \neg \left(y \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+86) (not (<= y 2.8e+34))) (+ z x) (+ z (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+86) || !(y <= 2.8e+34)) {
		tmp = z + x;
	} else {
		tmp = z + (y + 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 ((y <= (-1d+86)) .or. (.not. (y <= 2.8d+34))) then
        tmp = z + x
    else
        tmp = z + (y + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+86) || !(y <= 2.8e+34)) {
		tmp = z + x;
	} else {
		tmp = z + (y + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e+86) or not (y <= 2.8e+34):
		tmp = z + x
	else:
		tmp = z + (y + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e+86) || !(y <= 2.8e+34))
		tmp = Float64(z + x);
	else
		tmp = Float64(z + Float64(y + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e+86) || ~((y <= 2.8e+34)))
		tmp = z + x;
	else
		tmp = z + (y + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e+86], N[Not[LessEqual[y, 2.8e+34]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1e86 or 2.80000000000000008e34 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 42.3%

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

      1. +-commutative 42.3%

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

   5. Simplified 42.3%

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

   if -1e86 < y < 2.80000000000000008e34

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.6%

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

      1. +-commutative 89.6%

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

      2. +-commutative 89.6%

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

      3. associate-+l+ 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+86} \lor \neg \left(y \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.3% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-247} \lor \neg \left(z \leq 1.32 \cdot 10^{-191}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.5e-247) (not (<= z 1.32e-191))) (+ z x) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e-247) || !(z <= 1.32e-191)) {
		tmp = z + x;
	} else {
		tmp = y + 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 ((z <= (-7.5d-247)) .or. (.not. (z <= 1.32d-191))) then
        tmp = z + x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e-247) || !(z <= 1.32e-191)) {
		tmp = z + x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.5e-247) or not (z <= 1.32e-191):
		tmp = z + x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.5e-247) || !(z <= 1.32e-191))
		tmp = Float64(z + x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.5e-247) || ~((z <= 1.32e-191)))
		tmp = z + x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.5e-247], N[Not[LessEqual[z, 1.32e-191]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e-247 or 1.31999999999999996e-191 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 66.6%

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

      1. +-commutative 66.6%

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

   5. Simplified 66.6%

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

   if -7.5e-247 < z < 1.31999999999999996e-191

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.3%

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

      1. +-commutative 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in z around 0 70.3%

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

      1. +-commutative 70.3%

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

   8. Simplified 70.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-247} \lor \neg \left(z \leq 1.32 \cdot 10^{-191}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.7% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+34}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+87) x (if (<= y 2.5e+34) (+ y x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+87) {
		tmp = x;
	} else if (y <= 2.5e+34) {
		tmp = y + x;
	} 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 (y <= (-1.05d+87)) then
        tmp = x
    else if (y <= 2.5d+34) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+87) {
		tmp = x;
	} else if (y <= 2.5e+34) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+87:
		tmp = x
	elif y <= 2.5e+34:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+87)
		tmp = x;
	elseif (y <= 2.5e+34)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.05e+87)
		tmp = x;
	elseif (y <= 2.5e+34)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+87], x, If[LessEqual[y, 2.5e+34], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e87 or 2.4999999999999999e34 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 38.7%

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

   if -1.05e87 < y < 2.4999999999999999e34

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.5%

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

      1. +-commutative 92.5%

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

   5. Simplified 92.5%

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

   6. Taylor expanded in z around 0 51.5%

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

      1. +-commutative 51.5%

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

   8. Simplified 51.5%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+34}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.2% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-127}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.4e-135) x (if (<= x 1.12e-127) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e-135) {
		tmp = x;
	} else if (x <= 1.12e-127) {
		tmp = 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 <= (-5.4d-135)) then
        tmp = x
    else if (x <= 1.12d-127) then
        tmp = 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 <= -5.4e-135) {
		tmp = x;
	} else if (x <= 1.12e-127) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.4e-135:
		tmp = x
	elif x <= 1.12e-127:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.4e-135)
		tmp = x;
	elseif (x <= 1.12e-127)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.4e-135)
		tmp = x;
	elseif (x <= 1.12e-127)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.4e-135], x, If[LessEqual[x, 1.12e-127], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.39999999999999997e-135 or 1.1199999999999999e-127 < 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 54.6%

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

   if -5.39999999999999997e-135 < x < 1.1199999999999999e-127

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 68.2%

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

      1. +-commutative 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in y around inf 17.7%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-127}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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. Add Preprocessing

3. Taylor expanded in x around inf 40.5%

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

4. Final simplification 40.5%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(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))))