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

Percentage Accurate: 99.9% → 99.9%

Time: 7.5s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * 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 = (x + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * 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 = (x + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * 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 = (x + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+14} \lor \neg \left(x \leq 0.56\right):\\ \;\;\;\;x - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -6.6e+14) (not (<= x 0.56))) (- x t_0) (- (cos y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if ((x <= -6.6e+14) || !(x <= 0.56)) {
		tmp = x - t_0;
	} else {
		tmp = cos(y) - 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 * sin(y)
    if ((x <= (-6.6d+14)) .or. (.not. (x <= 0.56d0))) then
        tmp = x - t_0
    else
        tmp = cos(y) - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if ((x <= -6.6e+14) || !(x <= 0.56)) {
		tmp = x - t_0;
	} else {
		tmp = Math.cos(y) - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if (x <= -6.6e+14) or not (x <= 0.56):
		tmp = x - t_0
	else:
		tmp = math.cos(y) - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if ((x <= -6.6e+14) || !(x <= 0.56))
		tmp = Float64(x - t_0);
	else
		tmp = Float64(cos(y) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if ((x <= -6.6e+14) || ~((x <= 0.56)))
		tmp = x - t_0;
	else
		tmp = cos(y) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -6.6e+14], N[Not[LessEqual[x, 0.56]], $MachinePrecision]], N[(x - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6e14 or 0.56000000000000005 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.5%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   if -6.6e14 < x < 0.56000000000000005

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.5%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+14} \lor \neg \left(x \leq 0.56\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-303}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.8e+37)
   x
   (if (<= x -5.6e-303)
     (- (+ x 1.0) (* y z))
     (if (<= x 1.3e-189) (* z (- (sin y))) (if (<= x 0.65) (cos y) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+37) {
		tmp = x;
	} else if (x <= -5.6e-303) {
		tmp = (x + 1.0) - (y * z);
	} else if (x <= 1.3e-189) {
		tmp = z * -sin(y);
	} else if (x <= 0.65) {
		tmp = cos(y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-6.8d+37)) then
        tmp = x
    else if (x <= (-5.6d-303)) then
        tmp = (x + 1.0d0) - (y * z)
    else if (x <= 1.3d-189) then
        tmp = z * -sin(y)
    else if (x <= 0.65d0) then
        tmp = cos(y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+37) {
		tmp = x;
	} else if (x <= -5.6e-303) {
		tmp = (x + 1.0) - (y * z);
	} else if (x <= 1.3e-189) {
		tmp = z * -Math.sin(y);
	} else if (x <= 0.65) {
		tmp = Math.cos(y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.8e+37:
		tmp = x
	elif x <= -5.6e-303:
		tmp = (x + 1.0) - (y * z)
	elif x <= 1.3e-189:
		tmp = z * -math.sin(y)
	elif x <= 0.65:
		tmp = math.cos(y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.8e+37)
		tmp = x;
	elseif (x <= -5.6e-303)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	elseif (x <= 1.3e-189)
		tmp = Float64(z * Float64(-sin(y)));
	elseif (x <= 0.65)
		tmp = cos(y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.8e+37)
		tmp = x;
	elseif (x <= -5.6e-303)
		tmp = (x + 1.0) - (y * z);
	elseif (x <= 1.3e-189)
		tmp = z * -sin(y);
	elseif (x <= 0.65)
		tmp = cos(y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.8e+37], x, If[LessEqual[x, -5.6e-303], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-189], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 0.65], N[Cos[y], $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.80000000000000011e37 or 0.650000000000000022 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.5%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   4. Taylor expanded in x around inf 88.5%

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

   if -6.80000000000000011e37 < x < -5.6e-303

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 83.8%

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

   4. Taylor expanded in y around 0 64.2%

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

   if -5.6e-303 < x < 1.2999999999999999e-189

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 63.1%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   4. Taylor expanded in x around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. *-commutative 63.1%

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

      3. distribute-rgt-neg-in 63.1%

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

   6. Simplified 63.1%

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

   if 1.2999999999999999e-189 < x < 0.650000000000000022

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.6%

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

   4. Taylor expanded in y around 0 66.7%

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

   5. Taylor expanded in z around 0 64.3%

      \[\leadsto \color{blue}{\cos y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-303}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := x - t\_0\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-104}:\\ \;\;\;\;1 - t\_0\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-15}:\\ \;\;\;\;\cos y - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))) (t_1 (- x t_0)))
   (if (<= x -6.6e+14)
     t_1
     (if (<= x 2.5e-104)
       (- 1.0 t_0)
       (if (<= x 2.6e-15) (- (cos y) (* y z)) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double t_1 = x - t_0;
	double tmp;
	if (x <= -6.6e+14) {
		tmp = t_1;
	} else if (x <= 2.5e-104) {
		tmp = 1.0 - t_0;
	} else if (x <= 2.6e-15) {
		tmp = cos(y) - (y * z);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = z * sin(y)
    t_1 = x - t_0
    if (x <= (-6.6d+14)) then
        tmp = t_1
    else if (x <= 2.5d-104) then
        tmp = 1.0d0 - t_0
    else if (x <= 2.6d-15) then
        tmp = cos(y) - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double t_1 = x - t_0;
	double tmp;
	if (x <= -6.6e+14) {
		tmp = t_1;
	} else if (x <= 2.5e-104) {
		tmp = 1.0 - t_0;
	} else if (x <= 2.6e-15) {
		tmp = Math.cos(y) - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	t_1 = x - t_0
	tmp = 0
	if x <= -6.6e+14:
		tmp = t_1
	elif x <= 2.5e-104:
		tmp = 1.0 - t_0
	elif x <= 2.6e-15:
		tmp = math.cos(y) - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	t_1 = Float64(x - t_0)
	tmp = 0.0
	if (x <= -6.6e+14)
		tmp = t_1;
	elseif (x <= 2.5e-104)
		tmp = Float64(1.0 - t_0);
	elseif (x <= 2.6e-15)
		tmp = Float64(cos(y) - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	t_1 = x - t_0;
	tmp = 0.0;
	if (x <= -6.6e+14)
		tmp = t_1;
	elseif (x <= 2.5e-104)
		tmp = 1.0 - t_0;
	elseif (x <= 2.6e-15)
		tmp = cos(y) - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x - t$95$0), $MachinePrecision]}, If[LessEqual[x, -6.6e+14], t$95$1, If[LessEqual[x, 2.5e-104], N[(1.0 - t$95$0), $MachinePrecision], If[LessEqual[x, 2.6e-15], N[(N[Cos[y], $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.6e14 or 2.60000000000000004e-15 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.1%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   if -6.6e14 < x < 2.49999999999999989e-104

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 81.2%

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

   4. Taylor expanded in x around 0 80.8%

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

   if 2.49999999999999989e-104 < x < 2.60000000000000004e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in y around 0 77.2%

      \[\leadsto \cos y - \color{blue}{y \cdot z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 92.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-39} \lor \neg \left(z \leq 3.3 \cdot 10^{-110}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \cos y\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5e-39) (not (<= z 3.3e-110)))
   (- (+ x 1.0) (* z (sin y)))
   (- (+ x (cos y)) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5e-39) || !(z <= 3.3e-110)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = (x + cos(y)) - (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 <= (-5.5d-39)) .or. (.not. (z <= 3.3d-110))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = (x + cos(y)) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5e-39) || !(z <= 3.3e-110)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = (x + Math.cos(y)) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5e-39) or not (z <= 3.3e-110):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = (x + math.cos(y)) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5e-39) || !(z <= 3.3e-110))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(Float64(x + cos(y)) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.5e-39) || ~((z <= 3.3e-110)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = (x + cos(y)) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5e-39], N[Not[LessEqual[z, 3.3e-110]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000018e-39 or 3.2999999999999999e-110 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 94.1%

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

   if -5.50000000000000018e-39 < z < 3.2999999999999999e-110

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.5%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-39} \lor \neg \left(z \leq 3.3 \cdot 10^{-110}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \cos y\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3 \cdot 10^{-105} \lor \neg \left(x \leq 7.5 \cdot 10^{-28}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x 3e-105) (not (<= x 7.5e-28)))
   (- (+ x 1.0) (* z (sin y)))
   (- (cos y) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= 3e-105) || !(x <= 7.5e-28)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = cos(y) - (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 ((x <= 3d-105) .or. (.not. (x <= 7.5d-28))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = cos(y) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= 3e-105) || !(x <= 7.5e-28)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = Math.cos(y) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= 3e-105) or not (x <= 7.5e-28):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = math.cos(y) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= 3e-105) || !(x <= 7.5e-28))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(cos(y) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= 3e-105) || ~((x <= 7.5e-28)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = cos(y) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, 3e-105], N[Not[LessEqual[x, 7.5e-28]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.0000000000000001e-105 or 7.5000000000000003e-28 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 90.4%

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

   if 3.0000000000000001e-105 < x < 7.5000000000000003e-28

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 78.4%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3 \cdot 10^{-105} \lor \neg \left(x \leq 7.5 \cdot 10^{-28}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-287}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;x \leq 0.68:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e+38)
   x
   (if (<= x -2.9e-287) (- (+ x 1.0) (* y z)) (if (<= x 0.68) (cos y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e+38) {
		tmp = x;
	} else if (x <= -2.9e-287) {
		tmp = (x + 1.0) - (y * z);
	} else if (x <= 0.68) {
		tmp = cos(y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.4d+38)) then
        tmp = x
    else if (x <= (-2.9d-287)) then
        tmp = (x + 1.0d0) - (y * z)
    else if (x <= 0.68d0) then
        tmp = cos(y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e+38) {
		tmp = x;
	} else if (x <= -2.9e-287) {
		tmp = (x + 1.0) - (y * z);
	} else if (x <= 0.68) {
		tmp = Math.cos(y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e+38:
		tmp = x
	elif x <= -2.9e-287:
		tmp = (x + 1.0) - (y * z)
	elif x <= 0.68:
		tmp = math.cos(y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e+38)
		tmp = x;
	elseif (x <= -2.9e-287)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	elseif (x <= 0.68)
		tmp = cos(y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.4e+38)
		tmp = x;
	elseif (x <= -2.9e-287)
		tmp = (x + 1.0) - (y * z);
	elseif (x <= 0.68)
		tmp = cos(y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e+38], x, If[LessEqual[x, -2.9e-287], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.68], N[Cos[y], $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4e38 or 0.680000000000000049 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.5%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   4. Taylor expanded in x around inf 88.5%

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

   if -1.4e38 < x < -2.8999999999999998e-287

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 84.0%

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

   4. Taylor expanded in y around 0 63.4%

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

   if -2.8999999999999998e-287 < x < 0.680000000000000049

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.4%

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

   4. Taylor expanded in y around 0 55.5%

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

   5. Taylor expanded in z around 0 57.6%

      \[\leadsto \color{blue}{\cos y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 86.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+14} \lor \neg \left(x \leq 1.55\right):\\ \;\;\;\;x - t\_0\\ \mathbf{else}:\\ \;\;\;\;1 - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -6.6e+14) (not (<= x 1.55))) (- x t_0) (- 1.0 t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if ((x <= -6.6e+14) || !(x <= 1.55)) {
		tmp = x - t_0;
	} else {
		tmp = 1.0 - 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 * sin(y)
    if ((x <= (-6.6d+14)) .or. (.not. (x <= 1.55d0))) then
        tmp = x - t_0
    else
        tmp = 1.0d0 - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if ((x <= -6.6e+14) || !(x <= 1.55)) {
		tmp = x - t_0;
	} else {
		tmp = 1.0 - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if (x <= -6.6e+14) or not (x <= 1.55):
		tmp = x - t_0
	else:
		tmp = 1.0 - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if ((x <= -6.6e+14) || !(x <= 1.55))
		tmp = Float64(x - t_0);
	else
		tmp = Float64(1.0 - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if ((x <= -6.6e+14) || ~((x <= 1.55)))
		tmp = x - t_0;
	else
		tmp = 1.0 - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -6.6e+14], N[Not[LessEqual[x, 1.55]], $MachinePrecision]], N[(x - t$95$0), $MachinePrecision], N[(1.0 - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6e14 or 1.55000000000000004 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.5%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   if -6.6e14 < x < 1.55000000000000004

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.8%

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

   4. Taylor expanded in x around 0 75.6%

      \[\leadsto \color{blue}{1 - z \cdot \sin y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+14} \lor \neg \left(x \leq 1.55\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+64}:\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.8e+16) x (if (<= x 8.6e+64) (- 1.0 (* z (sin y))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.8e+16) {
		tmp = x;
	} else if (x <= 8.6e+64) {
		tmp = 1.0 - (z * sin(y));
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (x <= (-3.8d+16)) then
        tmp = x
    else if (x <= 8.6d+64) then
        tmp = 1.0d0 - (z * sin(y))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.8e+16) {
		tmp = x;
	} else if (x <= 8.6e+64) {
		tmp = 1.0 - (z * Math.sin(y));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.8e+16:
		tmp = x
	elif x <= 8.6e+64:
		tmp = 1.0 - (z * math.sin(y))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.8e+16)
		tmp = x;
	elseif (x <= 8.6e+64)
		tmp = Float64(1.0 - Float64(z * sin(y)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.8e+16)
		tmp = x;
	elseif (x <= 8.6e+64)
		tmp = 1.0 - (z * sin(y));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.8e+16], x, If[LessEqual[x, 8.6e+64], N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.8e16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   4. Taylor expanded in x around inf 93.3%

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

   if -3.8e16 < x < 8.5999999999999995e64

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.4%

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

   4. Taylor expanded in x around 0 74.4%

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

   if 8.5999999999999995e64 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around 0 94.7%

      \[\leadsto \color{blue}{1 + x} \]
   5. Step-by-step derivation

      1. +-commutative 94.7%

         \[\leadsto \color{blue}{x + 1} \]

   6. Simplified 94.7%

      \[\leadsto \color{blue}{x + 1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 67.9% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+69}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5e+37) x (if (<= x 2.2e+69) (- (+ x 1.0) (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5e+37) {
		tmp = x;
	} else if (x <= 2.2e+69) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (x <= (-5d+37)) then
        tmp = x
    else if (x <= 2.2d+69) then
        tmp = (x + 1.0d0) - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5e+37) {
		tmp = x;
	} else if (x <= 2.2e+69) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5e+37:
		tmp = x
	elif x <= 2.2e+69:
		tmp = (x + 1.0) - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5e+37)
		tmp = x;
	elseif (x <= 2.2e+69)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5e+37)
		tmp = x;
	elseif (x <= 2.2e+69)
		tmp = (x + 1.0) - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5e+37], x, If[LessEqual[x, 2.2e+69], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.99999999999999989e37

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   4. Taylor expanded in x around inf 93.2%

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

   if -4.99999999999999989e37 < x < 2.2000000000000002e69

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.6%

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

   4. Taylor expanded in y around 0 50.8%

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

   if 2.2000000000000002e69 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around 0 94.7%

      \[\leadsto \color{blue}{1 + x} \]
   5. Step-by-step derivation

      1. +-commutative 94.7%

         \[\leadsto \color{blue}{x + 1} \]

   6. Simplified 94.7%

      \[\leadsto \color{blue}{x + 1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 66.9% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 49000000:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7e+14) x (if (<= x 49000000.0) (- 1.0 (* y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e+14) {
		tmp = x;
	} else if (x <= 49000000.0) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-7d+14)) then
        tmp = x
    else if (x <= 49000000.0d0) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e+14) {
		tmp = x;
	} else if (x <= 49000000.0) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7e+14:
		tmp = x
	elif x <= 49000000.0:
		tmp = 1.0 - (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7e+14)
		tmp = x;
	elseif (x <= 49000000.0)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7e+14)
		tmp = x;
	elseif (x <= 49000000.0)
		tmp = 1.0 - (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7e+14], x, If[LessEqual[x, 49000000.0], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -7e14 or 4.9e7 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   4. Taylor expanded in x around inf 89.6%

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

   if -7e14 < x < 4.9e7

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.8%

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

   4. Taylor expanded in y around 0 61.0%

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

   5. Taylor expanded in y around 0 49.0%

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

      1. *-commutative 49.0%

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

      2. neg-mul-1 49.0%

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

      3. unsub-neg 49.0%

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

   7. Simplified 49.0%

      \[\leadsto \color{blue}{1 - z \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 49000000:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.6% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.013:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -0.013) x (if (<= x 1.1) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.013) {
		tmp = x;
	} else if (x <= 1.1) {
		tmp = 1.0;
	} 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 <= (-0.013d0)) then
        tmp = x
    else if (x <= 1.1d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.013) {
		tmp = x;
	} else if (x <= 1.1) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.013:
		tmp = x
	elif x <= 1.1:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.013)
		tmp = x;
	elseif (x <= 1.1)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.013)
		tmp = x;
	elseif (x <= 1.1)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.013], x, If[LessEqual[x, 1.1], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0129999999999999994 or 1.1000000000000001 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.5%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   4. Taylor expanded in x around inf 86.5%

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

   if -0.0129999999999999994 < x < 1.1000000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.5%

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

   4. Taylor expanded in y around 0 61.0%

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

   5. Taylor expanded in y around 0 32.5%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 63.1% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+263}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e+263) (* z (- y)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+263) {
		tmp = z * -y;
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (z <= (-4.1d+263)) then
        tmp = z * -y
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+263) {
		tmp = z * -y;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.1e+263:
		tmp = z * -y
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.1e+263)
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.1e+263)
		tmp = z * -y;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.1e+263], N[(z * (-y)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999986e263

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.8%

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

   4. Taylor expanded in y around 0 71.6%

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

   5. Taylor expanded in y around inf 71.6%

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

      1. associate-*r* 71.6%

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

      2. neg-mul-1 71.6%

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

      3. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   if -4.09999999999999986e263 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.8%

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

   4. Taylor expanded in z around 0 61.7%

      \[\leadsto \color{blue}{1 + x} \]
   5. Step-by-step derivation

      1. +-commutative 61.7%

         \[\leadsto \color{blue}{x + 1} \]

   6. Simplified 61.7%

      \[\leadsto \color{blue}{x + 1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 62.5% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

double code(double x, double y, double z) {
	return x + 1.0;
}

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 + 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return x + 1.0;
}

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 87.4%

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

4. Taylor expanded in z around 0 59.6%

   \[\leadsto \color{blue}{1 + x} \]
5. Step-by-step derivation

   1. +-commutative 59.6%

      \[\leadsto \color{blue}{x + 1} \]

6. Simplified 59.6%

   \[\leadsto \color{blue}{x + 1} \]
7. Add Preprocessing

Alternative 15: 21.9% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 57.1%

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

4. Taylor expanded in y around 0 34.7%

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

5. Taylor expanded in y around 0 17.7%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024086 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))