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

Percentage Accurate: 99.9% → 99.9%

Time: 8.7s

Alternatives: 12

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: 69.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -112000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+23}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+209}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -112000.0)
   (+ x z)
   (if (<= y 4.1e+23)
     (+ x (+ z (* y (+ 1.0 (* y (* y -0.16666666666666666))))))
     (if (<= y 2.8e+209) (* z (cos y)) (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -112000.0) {
		tmp = x + z;
	} else if (y <= 4.1e+23) {
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	} else if (y <= 2.8e+209) {
		tmp = z * cos(y);
	} else {
		tmp = sin(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-112000.0d0)) then
        tmp = x + z
    else if (y <= 4.1d+23) then
        tmp = x + (z + (y * (1.0d0 + (y * (y * (-0.16666666666666666d0))))))
    else if (y <= 2.8d+209) then
        tmp = z * cos(y)
    else
        tmp = sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -112000.0) {
		tmp = x + z;
	} else if (y <= 4.1e+23) {
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	} else if (y <= 2.8e+209) {
		tmp = z * Math.cos(y);
	} else {
		tmp = Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -112000.0:
		tmp = x + z
	elif y <= 4.1e+23:
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))))
	elif y <= 2.8e+209:
		tmp = z * math.cos(y)
	else:
		tmp = math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -112000.0)
		tmp = Float64(x + z);
	elseif (y <= 4.1e+23)
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(y * -0.16666666666666666))))));
	elseif (y <= 2.8e+209)
		tmp = Float64(z * cos(y));
	else
		tmp = sin(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -112000.0)
		tmp = x + z;
	elseif (y <= 4.1e+23)
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	elseif (y <= 2.8e+209)
		tmp = z * cos(y);
	else
		tmp = sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -112000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.1e+23], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+209], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[Sin[y], $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -112000

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 43.9%

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

   if -112000 < y < 4.09999999999999996e23

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.0%

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

   4. Taylor expanded in z around 0 97.0%

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

      1. *-commutative 97.0%

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

   6. Simplified 97.0%

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

   if 4.09999999999999996e23 < y < 2.80000000000000013e209

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 46.5%

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

   if 2.80000000000000013e209 < 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 73.9%

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

   4. Taylor expanded in x around 0 52.2%

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

   5. Taylor expanded in z around 0 48.1%

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

Alternative 3: 99.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+15} \lor \neg \left(z \leq 7 \cdot 10^{-12}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.4e+15) (not (<= z 7e-12)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.4e+15) || !(z <= 7e-12)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = z + (x + sin(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-6.4d+15)) .or. (.not. (z <= 7d-12))) then
        tmp = x + (z * cos(y))
    else
        tmp = z + (x + sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.4e+15) || !(z <= 7e-12)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.4e+15) or not (z <= 7e-12):
		tmp = x + (z * math.cos(y))
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.4e+15) || !(z <= 7e-12))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(z + Float64(x + sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.4e+15) || ~((z <= 7e-12)))
		tmp = x + (z * cos(y));
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.4e+15], N[Not[LessEqual[z, 7e-12]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4e15 or 7.0000000000000001e-12 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 99.9%

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

   if -6.4e15 < z < 7.0000000000000001e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.6%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+15} \lor \neg \left(z \leq 7 \cdot 10^{-12}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-46} \lor \neg \left(z \leq 4.3 \cdot 10^{-13}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1e-46) (not (<= z 4.3e-13)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e-46) || !(z <= 4.3e-13)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = x + sin(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.1d-46)) .or. (.not. (z <= 4.3d-13))) then
        tmp = x + (z * cos(y))
    else
        tmp = x + sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e-46) || !(z <= 4.3e-13)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1e-46) or not (z <= 4.3e-13):
		tmp = x + (z * math.cos(y))
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1e-46) || !(z <= 4.3e-13))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.1e-46) || ~((z <= 4.3e-13)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1e-46], N[Not[LessEqual[z, 4.3e-13]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e-46 or 4.2999999999999999e-13 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 96.9%

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

   if -1.1e-46 < z < 4.2999999999999999e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 91.6%

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

      1. +-commutative 91.6%

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

   5. Simplified 91.6%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-46} \lor \neg \left(z \leq 4.3 \cdot 10^{-13}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -106000 \lor \neg \left(y \leq 2.5\right):\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -106000.0) (not (<= y 2.5)))
   (+ x (sin y))
   (+ x (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -106000.0) || !(y <= 2.5)) {
		tmp = x + sin(y);
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-106000.0d0)) .or. (.not. (y <= 2.5d0))) then
        tmp = x + sin(y)
    else
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -106000.0) || !(y <= 2.5)) {
		tmp = x + Math.sin(y);
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -106000.0) or not (y <= 2.5):
		tmp = x + math.sin(y)
	else:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -106000.0) || !(y <= 2.5))
		tmp = Float64(x + sin(y));
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -106000.0) || ~((y <= 2.5)))
		tmp = x + sin(y);
	else
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -106000.0], N[Not[LessEqual[y, 2.5]], $MachinePrecision]], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -106000 or 2.5 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 64.7%

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

      1. +-commutative 64.7%

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

   5. Simplified 64.7%

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

   if -106000 < y < 2.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.4%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -106000 \lor \neg \left(y \leq 2.5\right):\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6400000000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+21}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6400000000000.0)
   (+ x z)
   (if (<= y 3.3e+21)
     (+ x (+ z (* y (+ 1.0 (* y (* y -0.16666666666666666))))))
     (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6400000000000.0) {
		tmp = x + z;
	} else if (y <= 3.3e+21) {
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	} else {
		tmp = sin(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6400000000000.0d0)) then
        tmp = x + z
    else if (y <= 3.3d+21) then
        tmp = x + (z + (y * (1.0d0 + (y * (y * (-0.16666666666666666d0))))))
    else
        tmp = sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6400000000000.0) {
		tmp = x + z;
	} else if (y <= 3.3e+21) {
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	} else {
		tmp = Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6400000000000.0:
		tmp = x + z
	elif y <= 3.3e+21:
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))))
	else:
		tmp = math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6400000000000.0)
		tmp = Float64(x + z);
	elseif (y <= 3.3e+21)
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(y * -0.16666666666666666))))));
	else
		tmp = sin(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6400000000000.0)
		tmp = x + z;
	elseif (y <= 3.3e+21)
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	else
		tmp = sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6400000000000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 3.3e+21], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sin[y], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4e12

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 43.9%

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

   if -6.4e12 < y < 3.3e21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.6%

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

   4. Taylor expanded in z around 0 97.6%

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

      1. *-commutative 97.6%

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

   6. Simplified 97.6%

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

   if 3.3e21 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 66.4%

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

   4. Taylor expanded in x around 0 42.6%

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

   5. Taylor expanded in z around 0 38.1%

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

Alternative 7: 71.0% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3400000 \lor \neg \left(y \leq 45000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3400000.0) (not (<= y 45000.0)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3400000.0) || !(y <= 45000.0)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3400000.0d0)) .or. (.not. (y <= 45000.0d0))) then
        tmp = x + z
    else
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3400000.0) || !(y <= 45000.0)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3400000.0) or not (y <= 45000.0):
		tmp = x + z
	else:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3400000.0) || !(y <= 45000.0))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3400000.0) || ~((y <= 45000.0)))
		tmp = x + z;
	else
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3400000.0], N[Not[LessEqual[y, 45000.0]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4e6 or 45000 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 38.2%

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

   if -3.4e6 < y < 45000

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.8%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3400000 \lor \neg \left(y \leq 45000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -32000000 \lor \neg \left(y \leq 1.25 \cdot 10^{+22}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -32000000.0) (not (<= y 1.25e+22)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* y (* y -0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -32000000.0) || !(y <= 1.25e+22)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-32000000.0d0)) .or. (.not. (y <= 1.25d+22))) then
        tmp = x + z
    else
        tmp = x + (z + (y * (1.0d0 + (y * (y * (-0.16666666666666666d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -32000000.0) || !(y <= 1.25e+22)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -32000000.0) or not (y <= 1.25e+22):
		tmp = x + z
	else:
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -32000000.0) || !(y <= 1.25e+22))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(y * -0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -32000000.0) || ~((y <= 1.25e+22)))
		tmp = x + z;
	else
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -32000000.0], N[Not[LessEqual[y, 1.25e+22]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e7 or 1.2499999999999999e22 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 37.1%

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

   if -3.2e7 < y < 1.2499999999999999e22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.0%

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

   4. Taylor expanded in z around 0 97.0%

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

      1. *-commutative 97.0%

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

   6. Simplified 97.0%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -32000000 \lor \neg \left(y \leq 1.25 \cdot 10^{+22}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -200000 \lor \neg \left(y \leq 9.5\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -200000.0) (not (<= y 9.5))) (+ x z) (+ z (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -200000.0) || !(y <= 9.5)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-200000.0d0)) .or. (.not. (y <= 9.5d0))) then
        tmp = x + z
    else
        tmp = z + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -200000.0) || !(y <= 9.5)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -200000.0) or not (y <= 9.5):
		tmp = x + z
	else:
		tmp = z + (x + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -200000.0) || !(y <= 9.5))
		tmp = Float64(x + z);
	else
		tmp = Float64(z + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -200000.0) || ~((y <= 9.5)))
		tmp = x + z;
	else
		tmp = z + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -200000.0], N[Not[LessEqual[y, 9.5]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2e5 or 9.5 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 37.9%

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

   if -2e5 < y < 9.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.9%

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

      1. associate-+r+ 98.9%

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

      2. +-commutative 98.9%

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

   5. Simplified 98.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -200000 \lor \neg \left(y \leq 9.5\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.6% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-20}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.6e-69) x (if (<= x 3.8e-20) (+ x y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.6e-69) {
		tmp = x;
	} else if (x <= 3.8e-20) {
		tmp = x + 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 <= (-3.6d-69)) then
        tmp = x
    else if (x <= 3.8d-20) then
        tmp = x + 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 <= -3.6e-69) {
		tmp = x;
	} else if (x <= 3.8e-20) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.6e-69:
		tmp = x
	elif x <= 3.8e-20:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.6e-69)
		tmp = x;
	elseif (x <= 3.8e-20)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.6e-69)
		tmp = x;
	elseif (x <= 3.8e-20)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.6e-69], x, If[LessEqual[x, 3.8e-20], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.60000000000000018e-69 or 3.7999999999999998e-20 < x

   1. Initial program 100.0%

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

      1. add-cbrt-cube 99.9%

         \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\sqrt[3]{\left(\cos y \cdot \cos y\right) \cdot \cos y}} \]

      2. pow3 99.9%

         \[\leadsto \left(x + \sin y\right) + z \cdot \sqrt[3]{\color{blue}{{\cos y}^{3}}} \]

   4. Applied egg-rr 99.9%

      \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\sqrt[3]{{\cos y}^{3}}} \]

   5. Taylor expanded in x around inf 60.1%

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

   if -3.60000000000000018e-69 < x < 3.7999999999999998e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 56.1%

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

      1. associate-+r+ 56.1%

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

      2. +-commutative 56.1%

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

   5. Simplified 56.1%

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

   6. Taylor expanded in z around 0 20.1%

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

Alternative 11: 66.7% 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 68.9%

   \[\leadsto \color{blue}{x + z} \]
4. Add Preprocessing

Alternative 12: 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. Step-by-step derivation

   1. add-cbrt-cube 99.8%

      \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\sqrt[3]{\left(\cos y \cdot \cos y\right) \cdot \cos y}} \]

   2. pow3 99.9%

      \[\leadsto \left(x + \sin y\right) + z \cdot \sqrt[3]{\color{blue}{{\cos y}^{3}}} \]

4. Applied egg-rr 99.9%

   \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\sqrt[3]{{\cos y}^{3}}} \]

5. Taylor expanded in x around inf 39.2%

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

Reproduce

herbie shell --seed 2024165 
(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))))