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

Percentage Accurate: 99.9% → 99.9%

Time: 6.7s

Alternatives: 12

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 99.9%

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

Alternative 2: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-22} \lor \neg \left(x \leq 0.00029\right):\\ \;\;\;\;\left(x + 1\right) - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -7.5e-22) (not (<= x 0.00029)))
     (- (+ x 1.0) 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 <= -7.5e-22) || !(x <= 0.00029)) {
		tmp = (x + 1.0) - 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 <= (-7.5d-22)) .or. (.not. (x <= 0.00029d0))) then
        tmp = (x + 1.0d0) - 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 <= -7.5e-22) || !(x <= 0.00029)) {
		tmp = (x + 1.0) - 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 <= -7.5e-22) or not (x <= 0.00029):
		tmp = (x + 1.0) - 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 <= -7.5e-22) || !(x <= 0.00029))
		tmp = Float64(Float64(x + 1.0) - 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 <= -7.5e-22) || ~((x <= 0.00029)))
		tmp = (x + 1.0) - 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, -7.5e-22], N[Not[LessEqual[x, 0.00029]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.49999999999999978e-22 or 2.9e-4 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.8%

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

      1. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   if -7.49999999999999978e-22 < x < 2.9e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.7%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-22} \lor \neg \left(x \leq 0.00029\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;x \leq -0.08:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-195}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-212}:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-137}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-9}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (<= x -0.08)
     (+ x 1.0)
     (if (<= x -2.6e-195)
       t_0
       (if (<= x 2.25e-212)
         (cos y)
         (if (<= x 2.6e-137) t_0 (if (<= x 1.6e-9) (cos y) (+ x 1.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (x <= -0.08) {
		tmp = x + 1.0;
	} else if (x <= -2.6e-195) {
		tmp = t_0;
	} else if (x <= 2.25e-212) {
		tmp = cos(y);
	} else if (x <= 2.6e-137) {
		tmp = t_0;
	} else if (x <= 1.6e-9) {
		tmp = cos(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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y * z)
    if (x <= (-0.08d0)) then
        tmp = x + 1.0d0
    else if (x <= (-2.6d-195)) then
        tmp = t_0
    else if (x <= 2.25d-212) then
        tmp = cos(y)
    else if (x <= 2.6d-137) then
        tmp = t_0
    else if (x <= 1.6d-9) then
        tmp = cos(y)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (x <= -0.08) {
		tmp = x + 1.0;
	} else if (x <= -2.6e-195) {
		tmp = t_0;
	} else if (x <= 2.25e-212) {
		tmp = Math.cos(y);
	} else if (x <= 2.6e-137) {
		tmp = t_0;
	} else if (x <= 1.6e-9) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if x <= -0.08:
		tmp = x + 1.0
	elif x <= -2.6e-195:
		tmp = t_0
	elif x <= 2.25e-212:
		tmp = math.cos(y)
	elif x <= 2.6e-137:
		tmp = t_0
	elif x <= 1.6e-9:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if (x <= -0.08)
		tmp = Float64(x + 1.0);
	elseif (x <= -2.6e-195)
		tmp = t_0;
	elseif (x <= 2.25e-212)
		tmp = cos(y);
	elseif (x <= 2.6e-137)
		tmp = t_0;
	elseif (x <= 1.6e-9)
		tmp = cos(y);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if (x <= -0.08)
		tmp = x + 1.0;
	elseif (x <= -2.6e-195)
		tmp = t_0;
	elseif (x <= 2.25e-212)
		tmp = cos(y);
	elseif (x <= 2.6e-137)
		tmp = t_0;
	elseif (x <= 1.6e-9)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.08], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, -2.6e-195], t$95$0, If[LessEqual[x, 2.25e-212], N[Cos[y], $MachinePrecision], If[LessEqual[x, 2.6e-137], t$95$0, If[LessEqual[x, 1.6e-9], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0800000000000000017 or 1.60000000000000006e-9 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.8%

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

   4. Taylor expanded in y around 0 86.1%

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

      1. +-commutative 86.1%

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

   6. Simplified 86.1%

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

   if -0.0800000000000000017 < x < -2.6000000000000002e-195 or 2.2499999999999999e-212 < x < 2.6e-137

   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 62.4%

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

      1. mul-1-neg 62.4%

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

      2. *-commutative 62.4%

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

      3. unsub-neg 62.4%

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

   6. Simplified 62.4%

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

   if -2.6000000000000002e-195 < x < 2.2499999999999999e-212 or 2.6e-137 < x < 1.60000000000000006e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.5%

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

   4. Taylor expanded in z around 0 77.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.08:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-195}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-212}:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-137}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-9}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-12} \lor \neg \left(z \leq 4.5 \cdot 10^{+18}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e-12) (not (<= z 4.5e+18)))
   (- (+ x 1.0) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-12) || !(z <= 4.5e+18)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = x + 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 ((z <= (-1.7d-12)) .or. (.not. (z <= 4.5d+18))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-12) || !(z <= 4.5e+18)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e-12) or not (z <= 4.5e+18):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e-12) || !(z <= 4.5e+18))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.7e-12) || ~((z <= 4.5e+18)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e-12], N[Not[LessEqual[z, 4.5e+18]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.8%

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

      1. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   if -1.7e-12 < z < 4.5e18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.5%

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

   4. Taylor expanded in z around 0 99.4%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-12} \lor \neg \left(z \leq 4.5 \cdot 10^{+18}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+16} \lor \neg \left(z \leq 8 \cdot 10^{+117}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e+16) (not (<= z 8e+117)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e+16) || !(z <= 8e+117)) {
		tmp = x - (z * sin(y));
	} else {
		tmp = x + 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 ((z <= (-4.8d+16)) .or. (.not. (z <= 8d+117))) then
        tmp = x - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e+16) || !(z <= 8e+117)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e+16) or not (z <= 8e+117):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e+16) || !(z <= 8e+117))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e+16) || ~((z <= 8e+117)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e+16], N[Not[LessEqual[z, 8e+117]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e16 or 8.0000000000000004e117 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 87.4%

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

   if -4.8e16 < z < 8.0000000000000004e117

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.0%

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

   4. Taylor expanded in z around 0 97.1%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+16} \lor \neg \left(z \leq 8 \cdot 10^{+117}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+174} \lor \neg \left(z \leq 1.85 \cdot 10^{+163}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e+174) (not (<= z 1.85e+163)))
   (* (sin y) (- z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e+174) || !(z <= 1.85e+163)) {
		tmp = sin(y) * -z;
	} else {
		tmp = x + 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 ((z <= (-4.5d+174)) .or. (.not. (z <= 1.85d+163))) then
        tmp = sin(y) * -z
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e+174) || !(z <= 1.85e+163)) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e+174) or not (z <= 1.85e+163):
		tmp = math.sin(y) * -z
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e+174) || !(z <= 1.85e+163))
		tmp = Float64(sin(y) * Float64(-z));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5e+174) || ~((z <= 1.85e+163)))
		tmp = sin(y) * -z;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e+174], N[Not[LessEqual[z, 1.85e+163]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.50000000000000042e174 or 1.84999999999999996e163 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 93.6%

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

   4. Taylor expanded in x around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. *-commutative 82.3%

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

      3. distribute-rgt-neg-in 82.3%

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

   6. Simplified 82.3%

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

   if -4.50000000000000042e174 < z < 1.84999999999999996e163

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.4%

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

   4. Taylor expanded in z around 0 88.9%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+174} \lor \neg \left(z \leq 1.85 \cdot 10^{+163}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+212} \lor \neg \left(z \leq 9.6 \cdot 10^{+161}\right):\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e+212) (not (<= z 9.6e+161))) (- x (* y z)) (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+212) || !(z <= 9.6e+161)) {
		tmp = x - (y * z);
	} else {
		tmp = x + 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 ((z <= (-2.5d+212)) .or. (.not. (z <= 9.6d+161))) then
        tmp = x - (y * z)
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+212) || !(z <= 9.6e+161)) {
		tmp = x - (y * z);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e+212) or not (z <= 9.6e+161):
		tmp = x - (y * z)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e+212) || !(z <= 9.6e+161))
		tmp = Float64(x - Float64(y * z));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.5e+212) || ~((z <= 9.6e+161)))
		tmp = x - (y * z);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e+212], N[Not[LessEqual[z, 9.6e+161]], $MachinePrecision]], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999996e212 or 9.5999999999999996e161 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 94.9%

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

   4. Taylor expanded in y around 0 46.6%

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

      1. associate-*r* 46.6%

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

      2. neg-mul-1 46.6%

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

      3. cancel-sign-sub-inv 46.6%

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

      4. *-commutative 46.6%

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

   6. Simplified 46.6%

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

   if -2.49999999999999996e212 < z < 9.5999999999999996e161

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.7%

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

   4. Taylor expanded in z around 0 87.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+212} \lor \neg \left(z \leq 9.6 \cdot 10^{+161}\right):\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.3% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.08 \lor \neg \left(x \leq 2.3 \cdot 10^{-18}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.08) (not (<= x 2.3e-18))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.08) || !(x <= 2.3e-18)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (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 <= (-0.08d0)) .or. (.not. (x <= 2.3d-18))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.08) || !(x <= 2.3e-18)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.08) or not (x <= 2.3e-18):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.08) || !(x <= 2.3e-18))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.08) || ~((x <= 2.3e-18)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.08], N[Not[LessEqual[x, 2.3e-18]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0800000000000000017 or 2.3000000000000001e-18 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.2%

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

   4. Taylor expanded in y around 0 85.6%

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

      1. +-commutative 85.6%

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

   6. Simplified 85.6%

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

   if -0.0800000000000000017 < x < 2.3000000000000001e-18

   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 58.7%

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

      1. mul-1-neg 58.7%

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

      2. *-commutative 58.7%

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

      3. unsub-neg 58.7%

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

   6. Simplified 58.7%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.08 \lor \neg \left(x \leq 2.3 \cdot 10^{-18}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.1% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e-9) x (if (<= x 1.0) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e-9) {
		tmp = x;
	} else if (x <= 1.0) {
		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 <= (-1.55d-9)) then
        tmp = x
    else if (x <= 1.0d0) 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 <= -1.55e-9) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.55e-9:
		tmp = x
	elif x <= 1.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e-9)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.55e-9)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e-9], x, If[LessEqual[x, 1.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000002e-9 or 1 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 98.7%

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

   4. Taylor expanded in x around inf 83.7%

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

   if -1.55000000000000002e-9 < x < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.7%

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

   4. Taylor expanded in y around 0 44.9%

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

Alternative 10: 61.5% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+215}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.25e+215) (* y (- z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.25e+215) {
		tmp = 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 (z <= (-1.25d+215)) then
        tmp = 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 (z <= -1.25e+215) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.25e+215:
		tmp = y * -z
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.25e+215)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.25e+215)
		tmp = y * -z;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.25e+215], N[(y * (-z)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e215

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 52.8%

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

   4. Taylor expanded in y around inf 40.8%

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

      1. associate-*r* 40.8%

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

      2. neg-mul-1 40.8%

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

      3. *-commutative 40.8%

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

   6. Simplified 40.8%

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

   if -1.25e215 < 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 71.0%

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

   4. Taylor expanded in y around 0 69.6%

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

      1. +-commutative 69.6%

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

   6. Simplified 69.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+215}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% 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 99.9%

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

3. Taylor expanded in y around 0 69.4%

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

4. Taylor expanded in y around 0 64.6%

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

   1. +-commutative 64.6%

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

6. Simplified 64.6%

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

Alternative 12: 21.5% 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 99.9%

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

3. Taylor expanded in x around 0 59.1%

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

4. Taylor expanded in y around 0 24.1%

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

Reproduce

herbie shell --seed 2024103 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))