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

Percentage Accurate: 99.9% → 99.9%

Time: 6.8s

Alternatives: 13

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. Final simplification 99.9%

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

Alternative 2: 71.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -3 \cdot 10^{+209}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-211}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-177}:\\ \;\;\;\;\sin y + z\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+101}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -3e+209)
     t_0
     (if (<= z 1.06e-211)
       (+ x z)
       (if (<= z 6.8e-177) (+ (sin y) z) (if (<= z 3.7e+101) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -3e+209) {
		tmp = t_0;
	} else if (z <= 1.06e-211) {
		tmp = x + z;
	} else if (z <= 6.8e-177) {
		tmp = sin(y) + z;
	} else if (z <= 3.7e+101) {
		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 <= (-3d+209)) then
        tmp = t_0
    else if (z <= 1.06d-211) then
        tmp = x + z
    else if (z <= 6.8d-177) then
        tmp = sin(y) + z
    else if (z <= 3.7d+101) 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 <= -3e+209) {
		tmp = t_0;
	} else if (z <= 1.06e-211) {
		tmp = x + z;
	} else if (z <= 6.8e-177) {
		tmp = Math.sin(y) + z;
	} else if (z <= 3.7e+101) {
		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 <= -3e+209:
		tmp = t_0
	elif z <= 1.06e-211:
		tmp = x + z
	elif z <= 6.8e-177:
		tmp = math.sin(y) + z
	elif z <= 3.7e+101:
		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 <= -3e+209)
		tmp = t_0;
	elseif (z <= 1.06e-211)
		tmp = Float64(x + z);
	elseif (z <= 6.8e-177)
		tmp = Float64(sin(y) + z);
	elseif (z <= 3.7e+101)
		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 <= -3e+209)
		tmp = t_0;
	elseif (z <= 1.06e-211)
		tmp = x + z;
	elseif (z <= 6.8e-177)
		tmp = sin(y) + z;
	elseif (z <= 3.7e+101)
		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, -3e+209], t$95$0, If[LessEqual[z, 1.06e-211], N[(x + z), $MachinePrecision], If[LessEqual[z, 6.8e-177], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision], If[LessEqual[z, 3.7e+101], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999985e209 or 3.6999999999999997e101 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 99.9%

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

   3. Taylor expanded in x around 0 95.2%

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

   if -2.99999999999999985e209 < z < 1.0600000000000001e-211 or 6.8000000000000001e-177 < z < 3.6999999999999997e101

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.0%

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

   if 1.0600000000000001e-211 < z < 6.8000000000000001e-177

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.3%

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

   3. Taylor expanded in y around 0 90.3%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+209}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-211}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-177}:\\ \;\;\;\;\sin y + z\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+101}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 3: 83.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+209}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-96}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 650000:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.22e+209)
     t_0
     (if (<= z -1.52e-96) (+ x z) (if (<= z 650000.0) (+ x (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.22e+209) {
		tmp = t_0;
	} else if (z <= -1.52e-96) {
		tmp = x + z;
	} else if (z <= 650000.0) {
		tmp = x + sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-1.22d+209)) then
        tmp = t_0
    else if (z <= (-1.52d-96)) then
        tmp = x + z
    else if (z <= 650000.0d0) then
        tmp = x + sin(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -1.22e+209) {
		tmp = t_0;
	} else if (z <= -1.52e-96) {
		tmp = x + z;
	} else if (z <= 650000.0) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1.22e+209:
		tmp = t_0
	elif z <= -1.52e-96:
		tmp = x + z
	elif z <= 650000.0:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1.22e+209)
		tmp = t_0;
	elseif (z <= -1.52e-96)
		tmp = Float64(x + z);
	elseif (z <= 650000.0)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -1.22e+209)
		tmp = t_0;
	elseif (z <= -1.52e-96)
		tmp = x + z;
	elseif (z <= 650000.0)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e+209], t$95$0, If[LessEqual[z, -1.52e-96], N[(x + z), $MachinePrecision], If[LessEqual[z, 650000.0], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.21999999999999995e209 or 6.5e5 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 98.4%

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

   3. Taylor expanded in x around 0 90.1%

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

   if -1.21999999999999995e209 < z < -1.52e-96

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 81.5%

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

   if -1.52e-96 < z < 6.5e5

   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. *-commutative 100.0%

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

      3. add-sqr-sqrt 67.1%

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

      4. associate-*r* 67.1%

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

      5. fma-def 67.2%

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

   3. Applied egg-rr 67.2%

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

   4. Taylor expanded in z around 0 92.3%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+209}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-96}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 650000:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 4: 94.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-96} \lor \neg \left(z \leq 5.2 \cdot 10^{-63}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.4e-96) (not (<= z 5.2e-63)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.4e-96) || !(z <= 5.2e-63)) {
		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 <= (-6.4d-96)) .or. (.not. (z <= 5.2d-63))) 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 <= -6.4e-96) || !(z <= 5.2e-63)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.4e-96) or not (z <= 5.2e-63):
		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 <= -6.4e-96) || !(z <= 5.2e-63))
		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 <= -6.4e-96) || ~((z <= 5.2e-63)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.4e-96], N[Not[LessEqual[z, 5.2e-63]], $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 < -6.40000000000000023e-96 or 5.2000000000000003e-63 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 95.3%

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

   if -6.40000000000000023e-96 < z < 5.2000000000000003e-63

   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. *-commutative 100.0%

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

      3. add-sqr-sqrt 61.7%

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

      4. associate-*r* 61.7%

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

      5. fma-def 61.7%

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

   3. Applied egg-rr 61.7%

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

   4. Taylor expanded in z around 0 95.4%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-96} \lor \neg \left(z \leq 5.2 \cdot 10^{-63}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 5: 99.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -80000000 \lor \neg \left(z \leq 1.6 \cdot 10^{-5}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -80000000.0) (not (<= z 1.6e-5)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -80000000.0) || !(z <= 1.6e-5)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = z + (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 <= (-80000000.0d0)) .or. (.not. (z <= 1.6d-5))) then
        tmp = x + (z * cos(y))
    else
        tmp = z + (x + sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -80000000.0) || !(z <= 1.6e-5)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -80000000.0) or not (z <= 1.6e-5):
		tmp = x + (z * math.cos(y))
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -80000000.0) || !(z <= 1.6e-5))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(z + Float64(x + sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -80000000.0) || ~((z <= 1.6e-5)))
		tmp = x + (z * cos(y));
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -80000000.0], N[Not[LessEqual[z, 1.6e-5]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8e7 or 1.59999999999999993e-5 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 98.8%

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

   if -8e7 < z < 1.59999999999999993e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.2%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -80000000 \lor \neg \left(z \leq 1.6 \cdot 10^{-5}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 6: 69.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7000000000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 27500:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+69}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7000000000000.0)
   (+ x z)
   (if (<= y 27500.0) (+ z (+ x y)) (if (<= y 9e+69) (sin y) (+ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7000000000000.0) {
		tmp = x + z;
	} else if (y <= 27500.0) {
		tmp = z + (x + y);
	} else if (y <= 9e+69) {
		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 <= (-7000000000000.0d0)) then
        tmp = x + z
    else if (y <= 27500.0d0) then
        tmp = z + (x + y)
    else if (y <= 9d+69) 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 <= -7000000000000.0) {
		tmp = x + z;
	} else if (y <= 27500.0) {
		tmp = z + (x + y);
	} else if (y <= 9e+69) {
		tmp = Math.sin(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7000000000000.0:
		tmp = x + z
	elif y <= 27500.0:
		tmp = z + (x + y)
	elif y <= 9e+69:
		tmp = math.sin(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7000000000000.0)
		tmp = Float64(x + z);
	elseif (y <= 27500.0)
		tmp = Float64(z + Float64(x + y));
	elseif (y <= 9e+69)
		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 <= -7000000000000.0)
		tmp = x + z;
	elseif (y <= 27500.0)
		tmp = z + (x + y);
	elseif (y <= 9e+69)
		tmp = sin(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7000000000000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 27500.0], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+69], N[Sin[y], $MachinePrecision], N[(x + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7e12 or 8.9999999999999999e69 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 43.1%

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

   if -7e12 < y < 27500

   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. *-commutative 100.0%

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

      3. add-sqr-sqrt 52.2%

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

      4. associate-*r* 52.2%

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

      5. fma-def 52.3%

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

   3. Applied egg-rr 52.3%

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

   4. Taylor expanded in y around 0 98.3%

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

      1. associate-+r+ 98.3%

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

      2. +-commutative 98.3%

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

      3. associate-+l+ 98.4%

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

   6. Simplified 98.4%

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

   if 27500 < y < 8.9999999999999999e69

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 96.7%

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

   3. Taylor expanded in z around 0 54.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7000000000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 27500:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+69}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 7: 71.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+209} \lor \neg \left(z \leq 3.7 \cdot 10^{+101}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e+209) (not (<= z 3.7e+101))) (* z (cos y)) (+ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+209) || !(z <= 3.7e+101)) {
		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 <= (-2.5d+209)) .or. (.not. (z <= 3.7d+101))) 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 <= -2.5e+209) || !(z <= 3.7e+101)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e+209) or not (z <= 3.7e+101):
		tmp = z * math.cos(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e+209) || !(z <= 3.7e+101))
		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 <= -2.5e+209) || ~((z <= 3.7e+101)))
		tmp = z * cos(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e+209], N[Not[LessEqual[z, 3.7e+101]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999982e209 or 3.6999999999999997e101 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 99.9%

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

   3. Taylor expanded in x around 0 95.2%

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

   if -2.49999999999999982e209 < z < 3.6999999999999997e101

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.3%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+209} \lor \neg \left(z \leq 3.7 \cdot 10^{+101}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 8: 69.9% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+15}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+69}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+15) (+ x z) (if (<= y 9e+69) (+ y (+ x z)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+15) {
		tmp = x + z;
	} else if (y <= 9e+69) {
		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 <= (-3.4d+15)) then
        tmp = x + z
    else if (y <= 9d+69) 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 <= -3.4e+15) {
		tmp = x + z;
	} else if (y <= 9e+69) {
		tmp = y + (x + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.4e+15:
		tmp = x + z
	elif y <= 9e+69:
		tmp = y + (x + z)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+15)
		tmp = Float64(x + z);
	elseif (y <= 9e+69)
		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 <= -3.4e+15)
		tmp = x + z;
	elseif (y <= 9e+69)
		tmp = y + (x + z);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.4e+15], N[(x + z), $MachinePrecision], If[LessEqual[y, 9e+69], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4e15 or 8.9999999999999999e69 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 43.1%

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

   if -3.4e15 < y < 8.9999999999999999e69

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 92.7%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+15}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+69}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 9: 69.9% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7500000000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+69}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7500000000000.0)
   (+ x z)
   (if (<= y 9.2e+69) (+ z (+ x y)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7500000000000.0) {
		tmp = x + z;
	} else if (y <= 9.2e+69) {
		tmp = z + (x + 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 <= (-7500000000000.0d0)) then
        tmp = x + z
    else if (y <= 9.2d+69) then
        tmp = z + (x + 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 <= -7500000000000.0) {
		tmp = x + z;
	} else if (y <= 9.2e+69) {
		tmp = z + (x + y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7500000000000.0:
		tmp = x + z
	elif y <= 9.2e+69:
		tmp = z + (x + y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7500000000000.0)
		tmp = Float64(x + z);
	elseif (y <= 9.2e+69)
		tmp = Float64(z + Float64(x + y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7500000000000.0)
		tmp = x + z;
	elseif (y <= 9.2e+69)
		tmp = z + (x + y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7500000000000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 9.2e+69], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e12 or 9.20000000000000067e69 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 43.1%

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

   if -7.5e12 < y < 9.20000000000000067e69

   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. *-commutative 100.0%

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

      3. add-sqr-sqrt 53.4%

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

      4. associate-*r* 53.4%

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

      5. fma-def 53.4%

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

   3. Applied egg-rr 53.4%

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

   4. Taylor expanded in y around 0 92.7%

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

      1. associate-+r+ 92.7%

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

      2. +-commutative 92.7%

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

      3. associate-+l+ 92.7%

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

   6. Simplified 92.7%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7500000000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+69}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 10: 67.4% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-169}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-216}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e-169) (+ x z) (if (<= x 1.55e-216) (+ y z) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e-169) {
		tmp = x + z;
	} else if (x <= 1.55e-216) {
		tmp = y + 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 (x <= (-4.6d-169)) then
        tmp = x + z
    else if (x <= 1.55d-216) then
        tmp = y + 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 (x <= -4.6e-169) {
		tmp = x + z;
	} else if (x <= 1.55e-216) {
		tmp = y + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e-169:
		tmp = x + z
	elif x <= 1.55e-216:
		tmp = y + z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e-169)
		tmp = Float64(x + z);
	elseif (x <= 1.55e-216)
		tmp = Float64(y + z);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.6e-169)
		tmp = x + z;
	elseif (x <= 1.55e-216)
		tmp = y + z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e-169], N[(x + z), $MachinePrecision], If[LessEqual[x, 1.55e-216], N[(y + z), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6000000000000002e-169 or 1.5500000000000001e-216 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.2%

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

   if -4.6000000000000002e-169 < x < 1.5500000000000001e-216

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.2%

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

   3. Taylor expanded in y around 0 64.4%

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

      1. +-commutative 64.4%

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

   5. Simplified 64.4%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-169}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-216}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 11: 53.9% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-61}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2e-31) x (if (<= x 1.42e-61) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e-31) {
		tmp = x;
	} else if (x <= 1.42e-61) {
		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 <= (-2d-31)) then
        tmp = x
    else if (x <= 1.42d-61) 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 <= -2e-31) {
		tmp = x;
	} else if (x <= 1.42e-61) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2e-31:
		tmp = x
	elif x <= 1.42e-61:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2e-31)
		tmp = x;
	elseif (x <= 1.42e-61)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2e-31)
		tmp = x;
	elseif (x <= 1.42e-61)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2e-31], x, If[LessEqual[x, 1.42e-61], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2e-31 or 1.42e-61 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 93.9%

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

   3. Taylor expanded in x around inf 69.5%

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

   if -2e-31 < x < 1.42e-61

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 73.0%

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

   3. Taylor expanded in x around 0 64.4%

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

   4. Taylor expanded in y around 0 46.9%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-61}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 65.5% 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. Taylor expanded in y around 0 68.5%

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

3. Final simplification 68.5%

   \[\leadsto x + z \]

Alternative 13: 42.0% 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. Taylor expanded in x around inf 84.4%

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

3. Taylor expanded in x around inf 42.9%

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

4. Final simplification 42.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023174 
(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))))