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 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 72.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+121}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-228}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-149}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+127}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -8.6e+121)
     t_0
     (if (<= z -2.8e-228)
       (+ x z)
       (if (<= z 2.4e-149) (+ z (+ x y)) (if (<= z 7e+127) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -8.6e+121) {
		tmp = t_0;
	} else if (z <= -2.8e-228) {
		tmp = x + z;
	} else if (z <= 2.4e-149) {
		tmp = z + (x + y);
	} else if (z <= 7e+127) {
		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 <= (-8.6d+121)) then
        tmp = t_0
    else if (z <= (-2.8d-228)) then
        tmp = x + z
    else if (z <= 2.4d-149) then
        tmp = z + (x + y)
    else if (z <= 7d+127) 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 <= -8.6e+121) {
		tmp = t_0;
	} else if (z <= -2.8e-228) {
		tmp = x + z;
	} else if (z <= 2.4e-149) {
		tmp = z + (x + y);
	} else if (z <= 7e+127) {
		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 <= -8.6e+121:
		tmp = t_0
	elif z <= -2.8e-228:
		tmp = x + z
	elif z <= 2.4e-149:
		tmp = z + (x + y)
	elif z <= 7e+127:
		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 <= -8.6e+121)
		tmp = t_0;
	elseif (z <= -2.8e-228)
		tmp = Float64(x + z);
	elseif (z <= 2.4e-149)
		tmp = Float64(z + Float64(x + y));
	elseif (z <= 7e+127)
		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 <= -8.6e+121)
		tmp = t_0;
	elseif (z <= -2.8e-228)
		tmp = x + z;
	elseif (z <= 2.4e-149)
		tmp = z + (x + y);
	elseif (z <= 7e+127)
		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, -8.6e+121], t$95$0, If[LessEqual[z, -2.8e-228], N[(x + z), $MachinePrecision], If[LessEqual[z, 2.4e-149], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+127], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5999999999999994e121 or 6.99999999999999956e127 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 88.5%

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

   if -8.5999999999999994e121 < z < -2.8000000000000003e-228 or 2.4000000000000001e-149 < z < 6.99999999999999956e127

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.5%

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

      1. +-commutative 73.5%

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

   5. Simplified 73.5%

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

   if -2.8000000000000003e-228 < z < 2.4000000000000001e-149

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.4%

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

      1. +-commutative 75.4%

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

      2. +-commutative 75.4%

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

      3. associate-+l+ 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-228}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-149}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+127}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+122}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 2800000000:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+127}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.8e+122)
     t_0
     (if (<= z -1.3e-24)
       (+ x z)
       (if (<= z 2800000000.0)
         (+ x (sin y))
         (if (<= z 7e+127) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.8e+122) {
		tmp = t_0;
	} else if (z <= -1.3e-24) {
		tmp = x + z;
	} else if (z <= 2800000000.0) {
		tmp = x + sin(y);
	} else if (z <= 7e+127) {
		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 <= (-1.8d+122)) then
        tmp = t_0
    else if (z <= (-1.3d-24)) then
        tmp = x + z
    else if (z <= 2800000000.0d0) then
        tmp = x + sin(y)
    else if (z <= 7d+127) 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 <= -1.8e+122) {
		tmp = t_0;
	} else if (z <= -1.3e-24) {
		tmp = x + z;
	} else if (z <= 2800000000.0) {
		tmp = x + Math.sin(y);
	} else if (z <= 7e+127) {
		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 <= -1.8e+122:
		tmp = t_0
	elif z <= -1.3e-24:
		tmp = x + z
	elif z <= 2800000000.0:
		tmp = x + math.sin(y)
	elif z <= 7e+127:
		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 <= -1.8e+122)
		tmp = t_0;
	elseif (z <= -1.3e-24)
		tmp = Float64(x + z);
	elseif (z <= 2800000000.0)
		tmp = Float64(x + sin(y));
	elseif (z <= 7e+127)
		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 <= -1.8e+122)
		tmp = t_0;
	elseif (z <= -1.3e-24)
		tmp = x + z;
	elseif (z <= 2800000000.0)
		tmp = x + sin(y);
	elseif (z <= 7e+127)
		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, -1.8e+122], t$95$0, If[LessEqual[z, -1.3e-24], N[(x + z), $MachinePrecision], If[LessEqual[z, 2800000000.0], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+127], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8000000000000001e122 or 6.99999999999999956e127 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 88.5%

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

   if -1.8000000000000001e122 < z < -1.3e-24 or 2.8e9 < z < 6.99999999999999956e127

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.3%

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

      1. +-commutative 87.3%

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

   5. Simplified 87.3%

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

   if -1.3e-24 < z < 2.8e9

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.5%

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

      1. +-commutative 92.5%

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

   5. Simplified 92.5%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+122}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 2800000000:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+127}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-25} \lor \neg \left(z \leq 7 \cdot 10^{-31}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.05e-25) (not (<= z 7e-31)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.05e-25) || !(z <= 7e-31)) {
		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 <= (-2.05d-25)) .or. (.not. (z <= 7d-31))) 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 <= -2.05e-25) || !(z <= 7e-31)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.05e-25) or not (z <= 7e-31):
		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 <= -2.05e-25) || !(z <= 7e-31))
		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 <= -2.05e-25) || ~((z <= 7e-31)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.05e-25], N[Not[LessEqual[z, 7e-31]], $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 < -2.04999999999999994e-25 or 6.99999999999999971e-31 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 99.9%

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

   4. Taylor expanded in x around inf 97.4%

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

   if -2.04999999999999994e-25 < z < 6.99999999999999971e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.7%

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

      1. +-commutative 94.7%

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

   5. Simplified 94.7%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-25} \lor \neg \left(z \leq 7 \cdot 10^{-31}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -23 \lor \neg \left(z \leq 0.084\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -23.0) (not (<= z 0.084)))
   (+ x (* z (cos y)))
   (+ (+ x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -23.0) || !(z <= 0.084)) {
		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 <= (-23.0d0)) .or. (.not. (z <= 0.084d0))) 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 <= -23.0) || !(z <= 0.084)) {
		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 <= -23.0) or not (z <= 0.084):
		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 <= -23.0) || !(z <= 0.084))
		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 <= -23.0) || ~((z <= 0.084)))
		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, -23.0], N[Not[LessEqual[z, 0.084]], $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 < -23 or 0.0840000000000000052 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 99.9%

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

   4. Taylor expanded in x around inf 98.6%

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

   if -23 < z < 0.0840000000000000052

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -23 \lor \neg \left(z \leq 0.084\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.9% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \lor \neg \left(y \leq 30000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.8) (not (<= y 30000.0)))
   (+ 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 <= -4.8) || !(y <= 30000.0)) {
		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 <= (-4.8d0)) .or. (.not. (y <= 30000.0d0))) 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 <= -4.8) || !(y <= 30000.0)) {
		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 <= -4.8) or not (y <= 30000.0):
		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 <= -4.8) || !(y <= 30000.0))
		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 <= -4.8) || ~((y <= 30000.0)))
		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, -4.8], N[Not[LessEqual[y, 30000.0]], $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 < -4.79999999999999982 or 3e4 < 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 45.2%

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

      1. +-commutative 45.2%

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

   5. Simplified 45.2%

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

   if -4.79999999999999982 < y < 3e4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.5%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \lor \neg \left(y \leq 30000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.3 \lor \neg \left(y \leq 3.75 \cdot 10^{+31}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.3) (not (<= y 3.75e+31)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* y (* y -0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.3) || !(y <= 3.75e+31)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * (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 <= (-6.3d0)) .or. (.not. (y <= 3.75d+31))) then
        tmp = x + z
    else
        tmp = x + (z + (y * (1.0d0 + (y * (y * (-0.16666666666666666d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.3) || !(y <= 3.75e+31)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.3) or not (y <= 3.75e+31):
		tmp = x + z
	else:
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.3) || !(y <= 3.75e+31))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(y * -0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.3) || ~((y <= 3.75e+31)))
		tmp = x + z;
	else
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.3], N[Not[LessEqual[y, 3.75e+31]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.29999999999999982 or 3.75e31 < 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 45.9%

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

      1. +-commutative 45.9%

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

   5. Simplified 45.9%

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

   if -6.29999999999999982 < y < 3.75e31

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.7%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot y\right)\right)\right)} \]

   4. Taylor expanded in z around 0 96.7%

      \[\leadsto x + \left(z + y \cdot \left(1 + y \cdot \color{blue}{\left(-0.16666666666666666 \cdot y\right)}\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 96.7%

         \[\leadsto x + \left(z + y \cdot \left(1 + y \cdot \color{blue}{\left(y \cdot -0.16666666666666666\right)}\right)\right) \]

   6. Simplified 96.7%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.3 \lor \neg \left(y \leq 3.75 \cdot 10^{+31}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.7% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8000000000000 \lor \neg \left(y \leq 1.5 \cdot 10^{+63}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8000000000000.0) (not (<= y 1.5e+63))) (+ x z) (+ z (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8000000000000.0) || !(y <= 1.5e+63)) {
		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 <= (-8000000000000.0d0)) .or. (.not. (y <= 1.5d+63))) 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 <= -8000000000000.0) || !(y <= 1.5e+63)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8000000000000.0) or not (y <= 1.5e+63):
		tmp = x + z
	else:
		tmp = z + (x + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8000000000000.0) || !(y <= 1.5e+63))
		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 <= -8000000000000.0) || ~((y <= 1.5e+63)))
		tmp = x + z;
	else
		tmp = z + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8000000000000.0], N[Not[LessEqual[y, 1.5e+63]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8e12 or 1.5e63 < 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 46.0%

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

      1. +-commutative 46.0%

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

   5. Simplified 46.0%

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

   if -8e12 < y < 1.5e63

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.3%

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

      1. +-commutative 92.3%

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

      2. +-commutative 92.3%

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

      3. associate-+l+ 92.3%

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

   5. Simplified 92.3%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8000000000000 \lor \neg \left(y \leq 1.5 \cdot 10^{+63}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.7% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-150}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3500000000000.0) x (if (<= x 3.5e-150) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3500000000000.0) {
		tmp = x;
	} else if (x <= 3.5e-150) {
		tmp = 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 <= (-3500000000000.0d0)) then
        tmp = x
    else if (x <= 3.5d-150) then
        tmp = 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 <= -3500000000000.0) {
		tmp = x;
	} else if (x <= 3.5e-150) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3500000000000.0:
		tmp = x
	elif x <= 3.5e-150:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3500000000000.0)
		tmp = x;
	elseif (x <= 3.5e-150)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3500000000000.0)
		tmp = x;
	elseif (x <= 3.5e-150)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3500000000000.0], x, If[LessEqual[x, 3.5e-150], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e12 or 3.4999999999999998e-150 < 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 66.6%

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

   if -3.5e12 < x < 3.4999999999999998e-150

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.3%

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

      1. associate-/l* 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in y around 0 33.4%

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

   7. Taylor expanded in x around 0 37.6%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-150}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.8% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 66.7%

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

   1. +-commutative 66.7%

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

5. Simplified 66.7%

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

6. Final simplification 66.7%

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

Alternative 11: 42.1% 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. Add Preprocessing

3. Taylor expanded in x around inf 43.9%

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

4. Final simplification 43.9%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(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))))