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

Percentage Accurate: 99.9% → 99.9%

Time: 7.8s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-10} \lor \neg \left(x \leq 3.2 \cdot 10^{-26}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e-10) (not (<= x 3.2e-26)))
   (+ x z)
   (+ (sin y) (* z (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-10) || !(x <= 3.2e-26)) {
		tmp = x + z;
	} else {
		tmp = sin(y) + (z * cos(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 ((x <= (-5.5d-10)) .or. (.not. (x <= 3.2d-26))) then
        tmp = x + z
    else
        tmp = sin(y) + (z * cos(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-10) || !(x <= 3.2e-26)) {
		tmp = x + z;
	} else {
		tmp = Math.sin(y) + (z * Math.cos(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e-10) or not (x <= 3.2e-26):
		tmp = x + z
	else:
		tmp = math.sin(y) + (z * math.cos(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e-10) || !(x <= 3.2e-26))
		tmp = Float64(x + z);
	else
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5e-10) || ~((x <= 3.2e-26)))
		tmp = x + z;
	else
		tmp = sin(y) + (z * cos(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e-10], N[Not[LessEqual[x, 3.2e-26]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4999999999999996e-10 or 3.2000000000000001e-26 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 91.1%

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

      1. +-commutative 91.1%

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

   5. Simplified 91.1%

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

   if -5.4999999999999996e-10 < x < 3.2000000000000001e-26

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 91.5%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-10} \lor \neg \left(x \leq 3.2 \cdot 10^{-26}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+114}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-285}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-141}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+149}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.8e+114)
     t_0
     (if (<= z -8e-285)
       (+ x z)
       (if (<= z 5.4e-141) (+ y (+ x z)) (if (<= z 4.4e+149) (+ 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+114) {
		tmp = t_0;
	} else if (z <= -8e-285) {
		tmp = x + z;
	} else if (z <= 5.4e-141) {
		tmp = y + (x + z);
	} else if (z <= 4.4e+149) {
		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+114)) then
        tmp = t_0
    else if (z <= (-8d-285)) then
        tmp = x + z
    else if (z <= 5.4d-141) then
        tmp = y + (x + z)
    else if (z <= 4.4d+149) 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+114) {
		tmp = t_0;
	} else if (z <= -8e-285) {
		tmp = x + z;
	} else if (z <= 5.4e-141) {
		tmp = y + (x + z);
	} else if (z <= 4.4e+149) {
		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+114:
		tmp = t_0
	elif z <= -8e-285:
		tmp = x + z
	elif z <= 5.4e-141:
		tmp = y + (x + z)
	elif z <= 4.4e+149:
		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+114)
		tmp = t_0;
	elseif (z <= -8e-285)
		tmp = Float64(x + z);
	elseif (z <= 5.4e-141)
		tmp = Float64(y + Float64(x + z));
	elseif (z <= 4.4e+149)
		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+114)
		tmp = t_0;
	elseif (z <= -8e-285)
		tmp = x + z;
	elseif (z <= 5.4e-141)
		tmp = y + (x + z);
	elseif (z <= 4.4e+149)
		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+114], t$95$0, If[LessEqual[z, -8e-285], N[(x + z), $MachinePrecision], If[LessEqual[z, 5.4e-141], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+149], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e114 or 4.4e149 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 91.4%

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

   if -1.8e114 < z < -8.00000000000000059e-285 or 5.4000000000000005e-141 < z < 4.4e149

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.8%

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

      1. +-commutative 77.8%

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

   5. Simplified 77.8%

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

   if -8.00000000000000059e-285 < z < 5.4000000000000005e-141

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. associate-+l+ 76.3%

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

   5. Simplified 76.3%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-285}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-141}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+149}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+115}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-82}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-36}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+148}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -4.2e+115)
     t_0
     (if (<= z -2.25e-82)
       (+ x z)
       (if (<= z 8.8e-36) (+ x (sin y)) (if (<= z 2.2e+148) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -4.2e+115) {
		tmp = t_0;
	} else if (z <= -2.25e-82) {
		tmp = x + z;
	} else if (z <= 8.8e-36) {
		tmp = x + sin(y);
	} else if (z <= 2.2e+148) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-4.2d+115)) then
        tmp = t_0
    else if (z <= (-2.25d-82)) then
        tmp = x + z
    else if (z <= 8.8d-36) then
        tmp = x + sin(y)
    else if (z <= 2.2d+148) then
        tmp = x + z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -4.2e+115) {
		tmp = t_0;
	} else if (z <= -2.25e-82) {
		tmp = x + z;
	} else if (z <= 8.8e-36) {
		tmp = x + Math.sin(y);
	} else if (z <= 2.2e+148) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -4.2e+115:
		tmp = t_0
	elif z <= -2.25e-82:
		tmp = x + z
	elif z <= 8.8e-36:
		tmp = x + math.sin(y)
	elif z <= 2.2e+148:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -4.2e+115)
		tmp = t_0;
	elseif (z <= -2.25e-82)
		tmp = Float64(x + z);
	elseif (z <= 8.8e-36)
		tmp = Float64(x + sin(y));
	elseif (z <= 2.2e+148)
		tmp = Float64(x + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -4.2e+115)
		tmp = t_0;
	elseif (z <= -2.25e-82)
		tmp = x + z;
	elseif (z <= 8.8e-36)
		tmp = x + sin(y);
	elseif (z <= 2.2e+148)
		tmp = x + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+115], t$95$0, If[LessEqual[z, -2.25e-82], N[(x + z), $MachinePrecision], If[LessEqual[z, 8.8e-36], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+148], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000007e115 or 2.1999999999999999e148 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 91.4%

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

   if -4.20000000000000007e115 < z < -2.2499999999999999e-82 or 8.7999999999999997e-36 < z < 2.1999999999999999e148

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.4%

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

      1. +-commutative 84.4%

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

   5. Simplified 84.4%

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

   if -2.2499999999999999e-82 < z < 8.7999999999999997e-36

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.2%

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

      1. +-commutative 96.2%

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

   5. Simplified 96.2%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-82}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-36}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+148}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.6% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+117}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-283}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.24 \cdot 10^{+215}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.4e+117)
   z
   (if (<= z -6.6e-283)
     x
     (if (<= z 1.05e-136) (+ x y) (if (<= z 1.24e+215) x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.4e+117) {
		tmp = z;
	} else if (z <= -6.6e-283) {
		tmp = x;
	} else if (z <= 1.05e-136) {
		tmp = x + y;
	} else if (z <= 1.24e+215) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-4.4d+117)) then
        tmp = z
    else if (z <= (-6.6d-283)) then
        tmp = x
    else if (z <= 1.05d-136) then
        tmp = x + y
    else if (z <= 1.24d+215) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.4e+117) {
		tmp = z;
	} else if (z <= -6.6e-283) {
		tmp = x;
	} else if (z <= 1.05e-136) {
		tmp = x + y;
	} else if (z <= 1.24e+215) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.4e+117:
		tmp = z
	elif z <= -6.6e-283:
		tmp = x
	elif z <= 1.05e-136:
		tmp = x + y
	elif z <= 1.24e+215:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.4e+117)
		tmp = z;
	elseif (z <= -6.6e-283)
		tmp = x;
	elseif (z <= 1.05e-136)
		tmp = Float64(x + y);
	elseif (z <= 1.24e+215)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.4e+117)
		tmp = z;
	elseif (z <= -6.6e-283)
		tmp = x;
	elseif (z <= 1.05e-136)
		tmp = x + y;
	elseif (z <= 1.24e+215)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.4e+117], z, If[LessEqual[z, -6.6e-283], x, If[LessEqual[z, 1.05e-136], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.24e+215], x, z]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.40000000000000028e117 or 1.23999999999999991e215 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 97.5%

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

   4. Taylor expanded in y around 0 61.2%

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

   if -4.40000000000000028e117 < z < -6.60000000000000039e-283 or 1.0499999999999999e-136 < z < 1.23999999999999991e215

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 54.5%

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

   if -6.60000000000000039e-283 < z < 1.0499999999999999e-136

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 76.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+117}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-283}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.24 \cdot 10^{+215}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.0% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+21} \lor \neg \left(y \leq 3.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e+21) (not (<= y 3.5e-5))) (+ x z) (+ y (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+21) || !(y <= 3.5e-5)) {
		tmp = x + z;
	} else {
		tmp = y + (x + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4d+21)) .or. (.not. (y <= 3.5d-5))) then
        tmp = x + z
    else
        tmp = y + (x + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+21) || !(y <= 3.5e-5)) {
		tmp = x + z;
	} else {
		tmp = y + (x + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e+21) or not (y <= 3.5e-5):
		tmp = x + z
	else:
		tmp = y + (x + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e+21) || !(y <= 3.5e-5))
		tmp = Float64(x + z);
	else
		tmp = Float64(y + Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e+21) || ~((y <= 3.5e-5)))
		tmp = x + z;
	else
		tmp = y + (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e+21], N[Not[LessEqual[y, 3.5e-5]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e21 or 3.4999999999999997e-5 < 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 44.9%

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

      1. +-commutative 44.9%

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

   5. Simplified 44.9%

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

   if -4e21 < y < 3.4999999999999997e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.4%

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

      1. +-commutative 97.4%

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

      2. associate-+l+ 97.4%

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

   5. Simplified 97.4%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+21} \lor \neg \left(y \leq 3.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.5% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+115}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.24 \cdot 10^{+215}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.8e+115) z (if (<= z 1.24e+215) x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+115) {
		tmp = z;
	} else if (z <= 1.24e+215) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.8d+115)) then
        tmp = z
    else if (z <= 1.24d+215) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+115) {
		tmp = z;
	} else if (z <= 1.24e+215) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.8e+115:
		tmp = z
	elif z <= 1.24e+215:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.8e+115)
		tmp = z;
	elseif (z <= 1.24e+215)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.8e+115)
		tmp = z;
	elseif (z <= 1.24e+215)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.8e+115], z, If[LessEqual[z, 1.24e+215], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -5.80000000000000009e115 or 1.23999999999999991e215 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 97.5%

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

   4. Taylor expanded in y around 0 61.2%

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

   if -5.80000000000000009e115 < z < 1.23999999999999991e215

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.3%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+115}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.24 \cdot 10^{+215}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% 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. Add Preprocessing

3. Taylor expanded in y around 0 69.0%

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

   1. +-commutative 69.0%

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

5. Simplified 69.0%

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

6. Final simplification 69.0%

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

Alternative 9: 42.7% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf 43.0%

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

4. Final simplification 43.0%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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))))