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

Percentage Accurate: 99.9% → 99.9%

Time: 12.8s

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

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

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 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-16}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.6e-16)
   (+ x z)
   (if (<= x 6.2e-15) (+ (sin y) (* z (cos y))) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.6e-16) {
		tmp = x + z;
	} else if (x <= 6.2e-15) {
		tmp = sin(y) + (z * cos(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 (x <= (-3.6d-16)) then
        tmp = x + z
    else if (x <= 6.2d-15) then
        tmp = sin(y) + (z * cos(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 (x <= -3.6e-16) {
		tmp = x + z;
	} else if (x <= 6.2e-15) {
		tmp = Math.sin(y) + (z * Math.cos(y));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.6e-16:
		tmp = x + z
	elif x <= 6.2e-15:
		tmp = math.sin(y) + (z * math.cos(y))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.6e-16)
		tmp = Float64(x + z);
	elseif (x <= 6.2e-15)
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.6e-16)
		tmp = x + z;
	elseif (x <= 6.2e-15)
		tmp = sin(y) + (z * cos(y));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.6e-16], N[(x + z), $MachinePrecision], If[LessEqual[x, 6.2e-15], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.59999999999999983e-16 or 6.1999999999999998e-15 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.7%

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

   if -3.59999999999999983e-16 < x < 6.1999999999999998e-15

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 88.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-16}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 3: 69.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+29}:\\ \;\;\;\;y + \left(\left(x + z\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+140}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -11.0)
   (+ x z)
   (if (<= y 1.7e+29)
     (+ y (+ (+ x z) (* -0.5 (* z (* y y)))))
     (if (<= y 8e+140) (sin y) (+ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -11.0) {
		tmp = x + z;
	} else if (y <= 1.7e+29) {
		tmp = y + ((x + z) + (-0.5 * (z * (y * y))));
	} else if (y <= 8e+140) {
		tmp = sin(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-11.0d0)) then
        tmp = x + z
    else if (y <= 1.7d+29) then
        tmp = y + ((x + z) + ((-0.5d0) * (z * (y * y))))
    else if (y <= 8d+140) then
        tmp = sin(y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -11.0) {
		tmp = x + z;
	} else if (y <= 1.7e+29) {
		tmp = y + ((x + z) + (-0.5 * (z * (y * y))));
	} else if (y <= 8e+140) {
		tmp = Math.sin(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -11.0:
		tmp = x + z
	elif y <= 1.7e+29:
		tmp = y + ((x + z) + (-0.5 * (z * (y * y))))
	elif y <= 8e+140:
		tmp = math.sin(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -11.0)
		tmp = Float64(x + z);
	elseif (y <= 1.7e+29)
		tmp = Float64(y + Float64(Float64(x + z) + Float64(-0.5 * Float64(z * Float64(y * y)))));
	elseif (y <= 8e+140)
		tmp = sin(y);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -11.0)
		tmp = x + z;
	elseif (y <= 1.7e+29)
		tmp = y + ((x + z) + (-0.5 * (z * (y * y))));
	elseif (y <= 8e+140)
		tmp = sin(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -11.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.7e+29], N[(y + N[(N[(x + z), $MachinePrecision] + N[(-0.5 * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+140], N[Sin[y], $MachinePrecision], N[(x + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -11 or 8.00000000000000047e140 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 43.3%

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

   if -11 < y < 1.69999999999999991e29

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. add-cube-cbrt 99.0%

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

      3. associate-*l* 99.0%

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

      4. fma-def 99.0%

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

      5. pow2 99.0%

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

   3. Applied egg-rr 99.0%

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

   4. Taylor expanded in y around 0 97.2%

      \[\leadsto \color{blue}{y + \left(-0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right) + \left({1}^{0.3333333333333333} \cdot z + x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 97.2%

         \[\leadsto y + \color{blue}{\left(\left({1}^{0.3333333333333333} \cdot z + x\right) + -0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]

      2. +-commutative 97.2%

         \[\leadsto y + \left(\color{blue}{\left(x + {1}^{0.3333333333333333} \cdot z\right)} + -0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      3. pow-base-1 97.2%

         \[\leadsto y + \left(\left(x + \color{blue}{1} \cdot z\right) + -0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      4. *-lft-identity 97.2%

         \[\leadsto y + \left(\left(x + \color{blue}{z}\right) + -0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      5. pow-base-1 97.2%

         \[\leadsto y + \left(\left(x + z\right) + -0.5 \cdot \left(\color{blue}{1} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      6. *-lft-identity 97.2%

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

      7. *-commutative 97.2%

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

      8. unpow2 97.2%

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

   6. Simplified 97.2%

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

   if 1.69999999999999991e29 < y < 8.00000000000000047e140

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 73.0%

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

      1. add-cube-cbrt 72.6%

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

      2. pow3 72.7%

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

   4. Applied egg-rr 72.7%

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

   5. Taylor expanded in z around 0 59.7%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+29}:\\ \;\;\;\;y + \left(\left(x + z\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+140}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 4: 73.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+54} \lor \neg \left(z \leq 5.5 \cdot 10^{+136}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.3e+54) (not (<= z 5.5e+136))) (* z (cos y)) (+ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e+54) || !(z <= 5.5e+136)) {
		tmp = z * cos(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 ((z <= (-1.3d+54)) .or. (.not. (z <= 5.5d+136))) then
        tmp = z * cos(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 ((z <= -1.3e+54) || !(z <= 5.5e+136)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.3e+54) or not (z <= 5.5e+136):
		tmp = z * math.cos(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.3e+54) || !(z <= 5.5e+136))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.3e+54) || ~((z <= 5.5e+136)))
		tmp = z * cos(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.3e+54], N[Not[LessEqual[z, 5.5e+136]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.30000000000000003e54 or 5.50000000000000039e136 < z

   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. add-sqr-sqrt 68.1%

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

      3. associate-*r* 68.1%

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

      4. fma-def 68.1%

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

   3. Applied egg-rr 68.1%

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

   4. Taylor expanded in z around inf 88.5%

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

   if -1.30000000000000003e54 < z < 5.50000000000000039e136

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+54} \lor \neg \left(z \leq 5.5 \cdot 10^{+136}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 5: 82.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3700000000000 \lor \neg \left(z \leq 3.3 \cdot 10^{-12}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3700000000000.0) (not (<= z 3.3e-12)))
   (* z (cos y))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3700000000000.0) || !(z <= 3.3e-12)) {
		tmp = 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 <= (-3700000000000.0d0)) .or. (.not. (z <= 3.3d-12))) then
        tmp = 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 <= -3700000000000.0) || !(z <= 3.3e-12)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3700000000000.0) or not (z <= 3.3e-12):
		tmp = z * math.cos(y)
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3700000000000.0) || !(z <= 3.3e-12))
		tmp = 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 <= -3700000000000.0) || ~((z <= 3.3e-12)))
		tmp = z * cos(y);
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3700000000000.0], N[Not[LessEqual[z, 3.3e-12]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7e12 or 3.3000000000000001e-12 < z

   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. add-sqr-sqrt 69.4%

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

      3. associate-*r* 69.4%

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

      4. fma-def 69.4%

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

   3. Applied egg-rr 69.4%

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

   4. Taylor expanded in z around inf 81.7%

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

   if -3.7e12 < z < 3.3000000000000001e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 92.0%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3700000000000 \lor \neg \left(z \leq 3.3 \cdot 10^{-12}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 6: 70.5% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 980000000000:\\ \;\;\;\;y + \left(\left(x + z\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -11.0)
   (+ x z)
   (if (<= y 980000000000.0)
     (+ y (+ (+ x z) (* -0.5 (* z (* y y)))))
     (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -11.0) {
		tmp = x + z;
	} else if (y <= 980000000000.0) {
		tmp = y + ((x + z) + (-0.5 * (z * (y * y))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-11.0d0)) then
        tmp = x + z
    else if (y <= 980000000000.0d0) then
        tmp = y + ((x + z) + ((-0.5d0) * (z * (y * y))))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -11.0) {
		tmp = x + z;
	} else if (y <= 980000000000.0) {
		tmp = y + ((x + z) + (-0.5 * (z * (y * y))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -11.0:
		tmp = x + z
	elif y <= 980000000000.0:
		tmp = y + ((x + z) + (-0.5 * (z * (y * y))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -11.0)
		tmp = Float64(x + z);
	elseif (y <= 980000000000.0)
		tmp = Float64(y + Float64(Float64(x + z) + Float64(-0.5 * Float64(z * Float64(y * y)))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -11.0)
		tmp = x + z;
	elseif (y <= 980000000000.0)
		tmp = y + ((x + z) + (-0.5 * (z * (y * y))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -11.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 980000000000.0], N[(y + N[(N[(x + z), $MachinePrecision] + N[(-0.5 * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -11 or 9.8e11 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 42.2%

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

   if -11 < y < 9.8e11

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. add-cube-cbrt 99.0%

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

      3. associate-*l* 99.0%

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

      4. fma-def 99.0%

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

      5. pow2 99.0%

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

   3. Applied egg-rr 99.0%

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

   4. Taylor expanded in y around 0 97.9%

      \[\leadsto \color{blue}{y + \left(-0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right) + \left({1}^{0.3333333333333333} \cdot z + x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 97.9%

         \[\leadsto y + \color{blue}{\left(\left({1}^{0.3333333333333333} \cdot z + x\right) + -0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]

      2. +-commutative 97.9%

         \[\leadsto y + \left(\color{blue}{\left(x + {1}^{0.3333333333333333} \cdot z\right)} + -0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      3. pow-base-1 97.9%

         \[\leadsto y + \left(\left(x + \color{blue}{1} \cdot z\right) + -0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      4. *-lft-identity 97.9%

         \[\leadsto y + \left(\left(x + \color{blue}{z}\right) + -0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      5. pow-base-1 97.9%

         \[\leadsto y + \left(\left(x + z\right) + -0.5 \cdot \left(\color{blue}{1} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      6. *-lft-identity 97.9%

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

      7. *-commutative 97.9%

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

      8. unpow2 97.9%

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

   6. Simplified 97.9%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 980000000000:\\ \;\;\;\;y + \left(\left(x + z\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 7: 70.4% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 0.0031:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+33) (+ x z) (if (<= y 0.0031) (+ y (+ x z)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+33) {
		tmp = x + z;
	} else if (y <= 0.0031) {
		tmp = y + (x + 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 (y <= (-1.4d+33)) then
        tmp = x + z
    else if (y <= 0.0031d0) then
        tmp = y + (x + 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 (y <= -1.4e+33) {
		tmp = x + z;
	} else if (y <= 0.0031) {
		tmp = y + (x + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e+33:
		tmp = x + z
	elif y <= 0.0031:
		tmp = y + (x + z)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+33)
		tmp = Float64(x + z);
	elseif (y <= 0.0031)
		tmp = Float64(y + Float64(x + z));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e+33)
		tmp = x + z;
	elseif (y <= 0.0031)
		tmp = y + (x + z);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e+33], N[(x + z), $MachinePrecision], If[LessEqual[y, 0.0031], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e33 or 0.00309999999999999989 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 42.3%

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

   if -1.4e33 < y < 0.00309999999999999989

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 0.0031:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 8: 58.6% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-34}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.42e+19) x (if (<= x 8.5e-34) (+ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42e+19) {
		tmp = x;
	} else if (x <= 8.5e-34) {
		tmp = y + z;
	} 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 <= (-1.42d+19)) then
        tmp = x
    else if (x <= 8.5d-34) then
        tmp = y + z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42e+19) {
		tmp = x;
	} else if (x <= 8.5e-34) {
		tmp = y + z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.42e+19:
		tmp = x
	elif x <= 8.5e-34:
		tmp = y + z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.42e+19)
		tmp = x;
	elseif (x <= 8.5e-34)
		tmp = Float64(y + z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.42e+19)
		tmp = x;
	elseif (x <= 8.5e-34)
		tmp = y + z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.42e+19], x, If[LessEqual[x, 8.5e-34], N[(y + z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.42e19 or 8.5000000000000001e-34 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.0%

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

   if -1.42e19 < x < 8.5000000000000001e-34

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 88.3%

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

      1. add-cube-cbrt 87.2%

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

      2. pow3 87.2%

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

   4. Applied egg-rr 87.2%

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

   5. Taylor expanded in y around 0 43.3%

      \[\leadsto \color{blue}{y + {1}^{0.3333333333333333} \cdot z} \]
   6. Step-by-step derivation

      1. pow-base-1 43.3%

         \[\leadsto y + \color{blue}{1} \cdot z \]

      2. *-lft-identity 43.3%

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

   7. Simplified 43.3%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-34}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 51.5% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+25}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.2e+25) z (if (<= z 5.8e+93) x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.2e+25) {
		tmp = z;
	} else if (z <= 5.8e+93) {
		tmp = x;
	} else {
		tmp = 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 <= (-6.2d+25)) then
        tmp = z
    else if (z <= 5.8d+93) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.2e+25) {
		tmp = z;
	} else if (z <= 5.8e+93) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.2e+25:
		tmp = z
	elif z <= 5.8e+93:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.2e+25)
		tmp = z;
	elseif (z <= 5.8e+93)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.2e+25)
		tmp = z;
	elseif (z <= 5.8e+93)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.2e+25], z, If[LessEqual[z, 5.8e+93], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999996e25 or 5.7999999999999997e93 < z

   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. add-sqr-sqrt 71.5%

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

      3. associate-*r* 71.5%

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

      4. fma-def 71.5%

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

   3. Applied egg-rr 71.5%

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

   4. Taylor expanded in z around inf 85.8%

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

   5. Taylor expanded in y around 0 51.5%

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

   if -6.1999999999999996e25 < z < 5.7999999999999997e93

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.2%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+25}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 10: 66.3% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0 67.7%

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

3. Final simplification 67.7%

   \[\leadsto x + z \]

Alternative 11: 42.3% 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 100.0%

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

2. Taylor expanded in x around inf 42.6%

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

3. Final simplification 42.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(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))))