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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

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. Add Preprocessing

Alternative 2: 84.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+174}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-23}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-16}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+165}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.25e+174)
     t_0
     (if (<= z -5.4e-23)
       (+ x z)
       (if (<= z 3e-16) (+ x (sin y)) (if (<= z 6.6e+165) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.25e+174) {
		tmp = t_0;
	} else if (z <= -5.4e-23) {
		tmp = x + z;
	} else if (z <= 3e-16) {
		tmp = x + sin(y);
	} else if (z <= 6.6e+165) {
		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 <= (-1.25d+174)) then
        tmp = t_0
    else if (z <= (-5.4d-23)) then
        tmp = x + z
    else if (z <= 3d-16) then
        tmp = x + sin(y)
    else if (z <= 6.6d+165) 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 <= -1.25e+174) {
		tmp = t_0;
	} else if (z <= -5.4e-23) {
		tmp = x + z;
	} else if (z <= 3e-16) {
		tmp = x + Math.sin(y);
	} else if (z <= 6.6e+165) {
		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 <= -1.25e+174:
		tmp = t_0
	elif z <= -5.4e-23:
		tmp = x + z
	elif z <= 3e-16:
		tmp = x + math.sin(y)
	elif z <= 6.6e+165:
		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 <= -1.25e+174)
		tmp = t_0;
	elseif (z <= -5.4e-23)
		tmp = Float64(x + z);
	elseif (z <= 3e-16)
		tmp = Float64(x + sin(y));
	elseif (z <= 6.6e+165)
		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 <= -1.25e+174)
		tmp = t_0;
	elseif (z <= -5.4e-23)
		tmp = x + z;
	elseif (z <= 3e-16)
		tmp = x + sin(y);
	elseif (z <= 6.6e+165)
		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, -1.25e+174], t$95$0, If[LessEqual[z, -5.4e-23], N[(x + z), $MachinePrecision], If[LessEqual[z, 3e-16], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+165], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2499999999999999e174 or 6.5999999999999997e165 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in x around inf 61.7%

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

      1. associate-/l* 61.6%

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

   6. Simplified 61.6%

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

   7. Taylor expanded in x around 0 94.4%

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

   if -1.2499999999999999e174 < z < -5.3999999999999997e-23 or 2.99999999999999994e-16 < z < 6.5999999999999997e165

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 98.7%

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

   4. Taylor expanded in y around 0 84.5%

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

      1. +-commutative 84.5%

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

   6. Simplified 84.5%

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

   if -5.3999999999999997e-23 < z < 2.99999999999999994e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around 0 95.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-23}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-16}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+165}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+175}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+165}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.3e+175)
     t_0
     (if (<= z 3.6e-94)
       (+ x z)
       (if (<= z 1.6e-57) (sin y) (if (<= z 6.5e+165) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.3e+175) {
		tmp = t_0;
	} else if (z <= 3.6e-94) {
		tmp = x + z;
	} else if (z <= 1.6e-57) {
		tmp = sin(y);
	} else if (z <= 6.5e+165) {
		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 <= (-1.3d+175)) then
        tmp = t_0
    else if (z <= 3.6d-94) then
        tmp = x + z
    else if (z <= 1.6d-57) then
        tmp = sin(y)
    else if (z <= 6.5d+165) 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 <= -1.3e+175) {
		tmp = t_0;
	} else if (z <= 3.6e-94) {
		tmp = x + z;
	} else if (z <= 1.6e-57) {
		tmp = Math.sin(y);
	} else if (z <= 6.5e+165) {
		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 <= -1.3e+175:
		tmp = t_0
	elif z <= 3.6e-94:
		tmp = x + z
	elif z <= 1.6e-57:
		tmp = math.sin(y)
	elif z <= 6.5e+165:
		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 <= -1.3e+175)
		tmp = t_0;
	elseif (z <= 3.6e-94)
		tmp = Float64(x + z);
	elseif (z <= 1.6e-57)
		tmp = sin(y);
	elseif (z <= 6.5e+165)
		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 <= -1.3e+175)
		tmp = t_0;
	elseif (z <= 3.6e-94)
		tmp = x + z;
	elseif (z <= 1.6e-57)
		tmp = sin(y);
	elseif (z <= 6.5e+165)
		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, -1.3e+175], t$95$0, If[LessEqual[z, 3.6e-94], N[(x + z), $MachinePrecision], If[LessEqual[z, 1.6e-57], N[Sin[y], $MachinePrecision], If[LessEqual[z, 6.5e+165], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e175 or 6.4999999999999999e165 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in x around inf 61.7%

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

      1. associate-/l* 61.6%

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

   6. Simplified 61.6%

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

   7. Taylor expanded in x around 0 94.4%

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

   if -1.3e175 < z < 3.6e-94 or 1.6e-57 < z < 6.4999999999999999e165

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 84.9%

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

   4. Taylor expanded in y around 0 79.0%

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

      1. +-commutative 79.0%

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

   6. Simplified 79.0%

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

   if 3.6e-94 < z < 1.6e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+175}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+165}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-12} \lor \neg \left(z \leq 4.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e-12) (not (<= z 4.5e+18)))
   (+ x (* z (cos y)))
   (+ (+ x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-12) || !(z <= 4.5e+18)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = (x + sin(y)) + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.7d-12)) .or. (.not. (z <= 4.5d+18))) then
        tmp = x + (z * cos(y))
    else
        tmp = (x + sin(y)) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-12) || !(z <= 4.5e+18)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e-12) or not (z <= 4.5e+18):
		tmp = x + (z * math.cos(y))
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e-12) || !(z <= 4.5e+18))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(Float64(x + sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.7e-12) || ~((z <= 4.5e+18)))
		tmp = x + (z * cos(y));
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e-12], N[Not[LessEqual[z, 4.5e+18]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e-12 or 4.5e18 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

   if -1.7e-12 < z < 4.5e18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.4%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-12} \lor \neg \left(z \leq 4.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-18} \lor \neg \left(z \leq 6 \cdot 10^{-16}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.3e-18) (not (<= z 6e-16)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.3e-18) || !(z <= 6e-16)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = x + sin(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.3d-18)) .or. (.not. (z <= 6d-16))) then
        tmp = x + (z * cos(y))
    else
        tmp = x + sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.3e-18) || !(z <= 6e-16)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.3e-18) or not (z <= 6e-16):
		tmp = x + (z * math.cos(y))
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.3e-18) || !(z <= 6e-16))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.3e-18) || ~((z <= 6e-16)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.3e-18], N[Not[LessEqual[z, 6e-16]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000002e-18 or 5.99999999999999987e-16 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.1%

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

   if -4.3000000000000002e-18 < z < 5.99999999999999987e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around 0 95.7%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-18} \lor \neg \left(z \leq 6 \cdot 10^{-16}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.0% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+20}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1)
   (+ x z)
   (if (<= y 1.45e+20) (+ z (+ x y)) (+ x (* z (* x (/ 1.0 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1) {
		tmp = x + z;
	} else if (y <= 1.45e+20) {
		tmp = z + (x + y);
	} else {
		tmp = x + (z * (x * (1.0 / 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 <= (-3.1d0)) then
        tmp = x + z
    else if (y <= 1.45d+20) then
        tmp = z + (x + y)
    else
        tmp = x + (z * (x * (1.0d0 / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1) {
		tmp = x + z;
	} else if (y <= 1.45e+20) {
		tmp = z + (x + y);
	} else {
		tmp = x + (z * (x * (1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.1:
		tmp = x + z
	elif y <= 1.45e+20:
		tmp = z + (x + y)
	else:
		tmp = x + (z * (x * (1.0 / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1)
		tmp = Float64(x + z);
	elseif (y <= 1.45e+20)
		tmp = Float64(z + Float64(x + y));
	else
		tmp = Float64(x + Float64(z * Float64(x * Float64(1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.1)
		tmp = x + z;
	elseif (y <= 1.45e+20)
		tmp = z + (x + y);
	else
		tmp = x + (z * (x * (1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.45e+20], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.10000000000000009

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 81.0%

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

   4. Taylor expanded in y around 0 53.8%

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

      1. +-commutative 53.8%

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

   6. Simplified 53.8%

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

   if -3.10000000000000009 < y < 1.45e20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.8%

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

   4. Taylor expanded in y around 0 96.7%

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

      1. +-commutative 96.7%

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

   6. Simplified 96.7%

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

   if 1.45e20 < 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 79.9%

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

   4. Taylor expanded in x around inf 74.7%

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

      1. associate-/l* 74.7%

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

   6. Simplified 74.7%

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

      1. +-commutative 74.7%

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

      2. distribute-rgt-in 74.7%

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

      3. associate-*l* 79.8%

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

      4. *-un-lft-identity 79.8%

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

   8. Applied egg-rr 79.8%

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

   9. Taylor expanded in y around 0 50.4%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+20}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.0% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \lor \neg \left(y \leq 3.4 \cdot 10^{+20}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1) (not (<= y 3.4e+20))) (+ x z) (+ z (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1) || !(y <= 3.4e+20)) {
		tmp = x + z;
	} else {
		tmp = z + (x + 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 ((y <= (-3.1d0)) .or. (.not. (y <= 3.4d+20))) then
        tmp = x + z
    else
        tmp = z + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1) || !(y <= 3.4e+20)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.1) or not (y <= 3.4e+20):
		tmp = x + z
	else:
		tmp = z + (x + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1) || !(y <= 3.4e+20))
		tmp = Float64(x + z);
	else
		tmp = Float64(z + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.1) || ~((y <= 3.4e+20)))
		tmp = x + z;
	else
		tmp = z + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.1], N[Not[LessEqual[y, 3.4e+20]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000009 or 3.4e20 < 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 80.5%

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

   4. Taylor expanded in y around 0 52.3%

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

      1. +-commutative 52.3%

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

   6. Simplified 52.3%

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

   if -3.10000000000000009 < y < 3.4e20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.8%

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

   4. Taylor expanded in y around 0 96.7%

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

      1. +-commutative 96.7%

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

   6. Simplified 96.7%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \lor \neg \left(y \leq 3.4 \cdot 10^{+20}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.8% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+52}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5) x (if (<= y 2e+52) (+ x y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5) {
		tmp = x;
	} else if (y <= 2e+52) {
		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 (y <= (-9.5d0)) then
        tmp = x
    else if (y <= 2d+52) 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 (y <= -9.5) {
		tmp = x;
	} else if (y <= 2e+52) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.5:
		tmp = x
	elif y <= 2e+52:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.5)
		tmp = x;
	elseif (y <= 2e+52)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.5)
		tmp = x;
	elseif (y <= 2e+52)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.5], x, If[LessEqual[y, 2e+52], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5 or 2e52 < 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 81.2%

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

   4. Taylor expanded in x around inf 50.9%

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

   if -9.5 < y < 2e52

   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%

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

   4. Taylor expanded in z around 0 54.4%

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

   5. Taylor expanded in y around 0 51.0%

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

      1. +-commutative 93.6%

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

   7. Simplified 51.0%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+52}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.7% 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 x around inf 85.8%

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

4. Taylor expanded in y around 0 71.4%

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

   1. +-commutative 71.4%

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

6. Simplified 71.4%

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

7. Final simplification 71.4%

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

Alternative 10: 41.7% 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 85.8%

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

4. Taylor expanded in x around inf 47.4%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024103 
(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))))