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

Percentage Accurate: 99.9% → 99.9%

Time: 8.4s

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, 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 2: 88.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+64}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 41000:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \mathbf{else}:\\ \;\;\;\;\sin y + t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -3.7e+64)
     t_0
     (if (<= z 41000.0) (+ (+ x (sin y)) z) (+ (sin y) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -3.7e+64) {
		tmp = t_0;
	} else if (z <= 41000.0) {
		tmp = (x + sin(y)) + z;
	} else {
		tmp = sin(y) + 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 <= (-3.7d+64)) then
        tmp = t_0
    else if (z <= 41000.0d0) then
        tmp = (x + sin(y)) + z
    else
        tmp = sin(y) + 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 <= -3.7e+64) {
		tmp = t_0;
	} else if (z <= 41000.0) {
		tmp = (x + Math.sin(y)) + z;
	} else {
		tmp = Math.sin(y) + t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -3.7e+64:
		tmp = t_0
	elif z <= 41000.0:
		tmp = (x + math.sin(y)) + z
	else:
		tmp = math.sin(y) + t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -3.7e+64)
		tmp = t_0;
	elseif (z <= 41000.0)
		tmp = Float64(Float64(x + sin(y)) + z);
	else
		tmp = Float64(sin(y) + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -3.7e+64)
		tmp = t_0;
	elseif (z <= 41000.0)
		tmp = (x + sin(y)) + z;
	else
		tmp = sin(y) + 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, -3.7e+64], t$95$0, If[LessEqual[z, 41000.0], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.69999999999999983e64

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 89.5%

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

   if -3.69999999999999983e64 < z < 41000

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.6%

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

   if 41000 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 82.7%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 41000:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+65}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-132}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-181}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+24}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -3.8e+65)
     t_0
     (if (<= z -1.35e-132)
       (+ x z)
       (if (<= z -2.4e-181) (sin y) (if (<= z 2.8e+24) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -3.8e+65) {
		tmp = t_0;
	} else if (z <= -1.35e-132) {
		tmp = x + z;
	} else if (z <= -2.4e-181) {
		tmp = sin(y);
	} else if (z <= 2.8e+24) {
		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 <= (-3.8d+65)) then
        tmp = t_0
    else if (z <= (-1.35d-132)) then
        tmp = x + z
    else if (z <= (-2.4d-181)) then
        tmp = sin(y)
    else if (z <= 2.8d+24) 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 <= -3.8e+65) {
		tmp = t_0;
	} else if (z <= -1.35e-132) {
		tmp = x + z;
	} else if (z <= -2.4e-181) {
		tmp = Math.sin(y);
	} else if (z <= 2.8e+24) {
		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 <= -3.8e+65:
		tmp = t_0
	elif z <= -1.35e-132:
		tmp = x + z
	elif z <= -2.4e-181:
		tmp = math.sin(y)
	elif z <= 2.8e+24:
		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 <= -3.8e+65)
		tmp = t_0;
	elseif (z <= -1.35e-132)
		tmp = Float64(x + z);
	elseif (z <= -2.4e-181)
		tmp = sin(y);
	elseif (z <= 2.8e+24)
		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 <= -3.8e+65)
		tmp = t_0;
	elseif (z <= -1.35e-132)
		tmp = x + z;
	elseif (z <= -2.4e-181)
		tmp = sin(y);
	elseif (z <= 2.8e+24)
		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, -3.8e+65], t$95$0, If[LessEqual[z, -1.35e-132], N[(x + z), $MachinePrecision], If[LessEqual[z, -2.4e-181], N[Sin[y], $MachinePrecision], If[LessEqual[z, 2.8e+24], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000011e65 or 2.8000000000000002e24 < 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 86.1%

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

   if -3.80000000000000011e65 < z < -1.34999999999999995e-132 or -2.4000000000000001e-181 < z < 2.8000000000000002e24

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.7%

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

      1. +-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -1.34999999999999995e-132 < z < -2.4000000000000001e-181

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. add-cube-cbrt 100.0%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} \cdot z + \left(x + \sin y\right) \]

      4. associate-*l* 100.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \left(\sqrt[3]{\cos y} \cdot z\right)} + \left(x + \sin y\right) \]

      5. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

      6. pow2 100.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

   5. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
   6. Step-by-step derivation

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 81.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-132}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-181}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+24}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{-62}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-29}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+22}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -4.7e+23)
     t_0
     (if (<= z 3.85e-62)
       (+ x (sin y))
       (if (<= z 1.08e-29) (+ y (+ x z)) (if (<= z 4.2e+22) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -4.7e+23) {
		tmp = t_0;
	} else if (z <= 3.85e-62) {
		tmp = x + sin(y);
	} else if (z <= 1.08e-29) {
		tmp = y + (x + z);
	} else if (z <= 4.2e+22) {
		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 <= (-4.7d+23)) then
        tmp = t_0
    else if (z <= 3.85d-62) then
        tmp = x + sin(y)
    else if (z <= 1.08d-29) then
        tmp = y + (x + z)
    else if (z <= 4.2d+22) 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 <= -4.7e+23) {
		tmp = t_0;
	} else if (z <= 3.85e-62) {
		tmp = x + Math.sin(y);
	} else if (z <= 1.08e-29) {
		tmp = y + (x + z);
	} else if (z <= 4.2e+22) {
		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 <= -4.7e+23:
		tmp = t_0
	elif z <= 3.85e-62:
		tmp = x + math.sin(y)
	elif z <= 1.08e-29:
		tmp = y + (x + z)
	elif z <= 4.2e+22:
		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 <= -4.7e+23)
		tmp = t_0;
	elseif (z <= 3.85e-62)
		tmp = Float64(x + sin(y));
	elseif (z <= 1.08e-29)
		tmp = Float64(y + Float64(x + z));
	elseif (z <= 4.2e+22)
		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 <= -4.7e+23)
		tmp = t_0;
	elseif (z <= 3.85e-62)
		tmp = x + sin(y);
	elseif (z <= 1.08e-29)
		tmp = y + (x + z);
	elseif (z <= 4.2e+22)
		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, -4.7e+23], t$95$0, If[LessEqual[z, 3.85e-62], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e-29], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+22], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.6999999999999997e23 or 4.1999999999999996e22 < 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 84.5%

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

   if -4.6999999999999997e23 < z < 3.84999999999999998e-62

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 89.5%

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

      1. +-commutative 89.5%

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

   5. Simplified 89.5%

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

   if 3.84999999999999998e-62 < z < 1.07999999999999995e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-+l+ 99.7%

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

   5. Simplified 99.7%

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

   if 1.07999999999999995e-29 < z < 4.1999999999999996e22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.5%

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

      1. +-commutative 72.5%

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

   5. Simplified 72.5%

      \[\leadsto \color{blue}{z + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{-62}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-29}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+22}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+65} \lor \neg \left(z \leq 3.9 \cdot 10^{+24}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8e+65) (not (<= z 3.9e+24)))
   (* z (cos y))
   (+ (+ x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8e+65) || !(z <= 3.9e+24)) {
		tmp = 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 <= (-8d+65)) .or. (.not. (z <= 3.9d+24))) then
        tmp = 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 <= -8e+65) || !(z <= 3.9e+24)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8e+65) or not (z <= 3.9e+24):
		tmp = z * math.cos(y)
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8e+65) || !(z <= 3.9e+24))
		tmp = 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 <= -8e+65) || ~((z <= 3.9e+24)))
		tmp = z * cos(y);
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8e+65], N[Not[LessEqual[z, 3.9e+24]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999999e65 or 3.8999999999999998e24 < 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 86.1%

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

   if -7.9999999999999999e65 < z < 3.8999999999999998e24

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+65} \lor \neg \left(z \leq 3.9 \cdot 10^{+24}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.3% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4000000000000 \lor \neg \left(y \leq 24\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4000000000000.0) (not (<= y 24.0)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4000000000000.0) || !(y <= 24.0)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	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 <= (-4000000000000.0d0)) .or. (.not. (y <= 24.0d0))) then
        tmp = x + z
    else
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4000000000000.0) || !(y <= 24.0)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4000000000000.0) or not (y <= 24.0):
		tmp = x + z
	else:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4000000000000.0) || !(y <= 24.0))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4000000000000.0) || ~((y <= 24.0)))
		tmp = x + z;
	else
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4000000000000.0], N[Not[LessEqual[y, 24.0]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e12 or 24 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 42.9%

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

      1. +-commutative 42.9%

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

   5. Simplified 42.9%

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

   if -4e12 < y < 24

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.0%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot y\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4000000000000 \lor \neg \left(y \leq 24\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -140000000000 \lor \neg \left(y \leq 225\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -140000000000.0) (not (<= y 225.0)))
   (+ x z)
   (+ (+ x z) (* y (+ 1.0 (* -0.5 (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -140000000000.0) || !(y <= 225.0)) {
		tmp = x + z;
	} else {
		tmp = (x + z) + (y * (1.0 + (-0.5 * (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 ((y <= (-140000000000.0d0)) .or. (.not. (y <= 225.0d0))) then
        tmp = x + z
    else
        tmp = (x + z) + (y * (1.0d0 + ((-0.5d0) * (y * z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -140000000000.0) || !(y <= 225.0)) {
		tmp = x + z;
	} else {
		tmp = (x + z) + (y * (1.0 + (-0.5 * (y * z))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -140000000000.0) or not (y <= 225.0):
		tmp = x + z
	else:
		tmp = (x + z) + (y * (1.0 + (-0.5 * (y * z))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -140000000000.0) || !(y <= 225.0))
		tmp = Float64(x + z);
	else
		tmp = Float64(Float64(x + z) + Float64(y * Float64(1.0 + Float64(-0.5 * Float64(y * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -140000000000.0) || ~((y <= 225.0)))
		tmp = x + z;
	else
		tmp = (x + z) + (y * (1.0 + (-0.5 * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -140000000000.0], N[Not[LessEqual[y, 225.0]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(N[(x + z), $MachinePrecision] + N[(y * N[(1.0 + N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e11 or 225 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 42.6%

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

      1. +-commutative 42.6%

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

   5. Simplified 42.6%

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

   if -1.4e11 < y < 225

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.4%

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

      1. associate-+r+ 97.4%

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

      2. +-commutative 97.4%

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

      3. *-commutative 97.4%

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

   5. Simplified 97.4%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -140000000000 \lor \neg \left(y \leq 225\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.1% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -220000000000 \lor \neg \left(y \leq 5800\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -220000000000.0) (not (<= y 5800.0))) (+ x z) (+ y (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -220000000000.0) || !(y <= 5800.0)) {
		tmp = x + z;
	} else {
		tmp = y + (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 <= (-220000000000.0d0)) .or. (.not. (y <= 5800.0d0))) then
        tmp = x + z
    else
        tmp = y + (x + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -220000000000.0) || !(y <= 5800.0)) {
		tmp = x + z;
	} else {
		tmp = y + (x + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -220000000000.0) or not (y <= 5800.0):
		tmp = x + z
	else:
		tmp = y + (x + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -220000000000.0) || !(y <= 5800.0))
		tmp = Float64(x + z);
	else
		tmp = Float64(y + Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -220000000000.0) || ~((y <= 5800.0)))
		tmp = x + z;
	else
		tmp = y + (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -220000000000.0], N[Not[LessEqual[y, 5800.0]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e11 or 5800 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 42.4%

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

      1. +-commutative 42.4%

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

   5. Simplified 42.4%

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

   if -2.2e11 < y < 5800

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-+l+ 96.6%

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

   5. Simplified 96.6%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -220000000000 \lor \neg \left(y \leq 5800\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.5% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.9e-12) x (if (<= x 1.32e-56) (+ x y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.9e-12) {
		tmp = x;
	} else if (x <= 1.32e-56) {
		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 <= (-4.9d-12)) then
        tmp = x
    else if (x <= 1.32d-56) 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 <= -4.9e-12) {
		tmp = x;
	} else if (x <= 1.32e-56) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.9e-12:
		tmp = x
	elif x <= 1.32e-56:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.9e-12)
		tmp = x;
	elseif (x <= 1.32e-56)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.9e-12)
		tmp = x;
	elseif (x <= 1.32e-56)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.9e-12], x, If[LessEqual[x, 1.32e-56], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.89999999999999972e-12 or 1.3199999999999999e-56 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.3%

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

   if -4.89999999999999972e-12 < x < 1.3199999999999999e-56

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 64.5%

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

      1. +-commutative 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in z around 0 17.6%

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

      1. +-commutative 17.6%

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

   8. Simplified 17.6%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.1% 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. Add Preprocessing

3. Taylor expanded in y around 0 63.4%

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

   1. +-commutative 63.4%

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

5. Simplified 63.4%

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

6. Final simplification 63.4%

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

Alternative 11: 42.7% 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 39.7%

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

4. Final simplification 39.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(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))))