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

Percentage Accurate: 99.9% → 99.9%

Time: 8.0s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 71.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -1.16 \cdot 10^{+18}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-177}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-249}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-125}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-78}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= x -1.16e+18)
     (+ x z)
     (if (<= x -1.6e-177)
       t_0
       (if (<= x -6.2e-249)
         (sin y)
         (if (<= x 2.3e-125)
           t_0
           (if (<= x 7.4e-78)
             (+ y (+ x z))
             (if (<= x 1.2e-19) t_0 (+ x z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (x <= -1.16e+18) {
		tmp = x + z;
	} else if (x <= -1.6e-177) {
		tmp = t_0;
	} else if (x <= -6.2e-249) {
		tmp = sin(y);
	} else if (x <= 2.3e-125) {
		tmp = t_0;
	} else if (x <= 7.4e-78) {
		tmp = y + (x + z);
	} else if (x <= 1.2e-19) {
		tmp = t_0;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (x <= (-1.16d+18)) then
        tmp = x + z
    else if (x <= (-1.6d-177)) then
        tmp = t_0
    else if (x <= (-6.2d-249)) then
        tmp = sin(y)
    else if (x <= 2.3d-125) then
        tmp = t_0
    else if (x <= 7.4d-78) then
        tmp = y + (x + z)
    else if (x <= 1.2d-19) then
        tmp = t_0
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (x <= -1.16e+18) {
		tmp = x + z;
	} else if (x <= -1.6e-177) {
		tmp = t_0;
	} else if (x <= -6.2e-249) {
		tmp = Math.sin(y);
	} else if (x <= 2.3e-125) {
		tmp = t_0;
	} else if (x <= 7.4e-78) {
		tmp = y + (x + z);
	} else if (x <= 1.2e-19) {
		tmp = t_0;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if x <= -1.16e+18:
		tmp = x + z
	elif x <= -1.6e-177:
		tmp = t_0
	elif x <= -6.2e-249:
		tmp = math.sin(y)
	elif x <= 2.3e-125:
		tmp = t_0
	elif x <= 7.4e-78:
		tmp = y + (x + z)
	elif x <= 1.2e-19:
		tmp = t_0
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (x <= -1.16e+18)
		tmp = Float64(x + z);
	elseif (x <= -1.6e-177)
		tmp = t_0;
	elseif (x <= -6.2e-249)
		tmp = sin(y);
	elseif (x <= 2.3e-125)
		tmp = t_0;
	elseif (x <= 7.4e-78)
		tmp = Float64(y + Float64(x + z));
	elseif (x <= 1.2e-19)
		tmp = t_0;
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (x <= -1.16e+18)
		tmp = x + z;
	elseif (x <= -1.6e-177)
		tmp = t_0;
	elseif (x <= -6.2e-249)
		tmp = sin(y);
	elseif (x <= 2.3e-125)
		tmp = t_0;
	elseif (x <= 7.4e-78)
		tmp = y + (x + z);
	elseif (x <= 1.2e-19)
		tmp = t_0;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.16e+18], N[(x + z), $MachinePrecision], If[LessEqual[x, -1.6e-177], t$95$0, If[LessEqual[x, -6.2e-249], N[Sin[y], $MachinePrecision], If[LessEqual[x, 2.3e-125], t$95$0, If[LessEqual[x, 7.4e-78], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e-19], t$95$0, N[(x + z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.16e18 or 1.20000000000000011e-19 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 90.9%

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

   if -1.16e18 < x < -1.5999999999999999e-177 or -6.19999999999999971e-249 < x < 2.2999999999999999e-125 or 7.40000000000000011e-78 < x < 1.20000000000000011e-19

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 78.5%

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

   3. Taylor expanded in x around 0 76.6%

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

   if -1.5999999999999999e-177 < x < -6.19999999999999971e-249

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around 0 61.0%

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

   if 2.2999999999999999e-125 < x < 7.40000000000000011e-78

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 90.5%

      \[\leadsto \color{blue}{y + \left(z + x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+18}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-177}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-249}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-78}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 3: 77.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{-23}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-209}:\\ \;\;\;\;\sin y + z\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-126}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-77}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= x -1.65e-23)
     (+ x z)
     (if (<= x 1.65e-209)
       (+ (sin y) z)
       (if (<= x 3.6e-126)
         t_0
         (if (<= x 1.3e-77)
           (+ y (+ x z))
           (if (<= x 1.15e-19) t_0 (+ x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (x <= -1.65e-23) {
		tmp = x + z;
	} else if (x <= 1.65e-209) {
		tmp = sin(y) + z;
	} else if (x <= 3.6e-126) {
		tmp = t_0;
	} else if (x <= 1.3e-77) {
		tmp = y + (x + z);
	} else if (x <= 1.15e-19) {
		tmp = t_0;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (x <= (-1.65d-23)) then
        tmp = x + z
    else if (x <= 1.65d-209) then
        tmp = sin(y) + z
    else if (x <= 3.6d-126) then
        tmp = t_0
    else if (x <= 1.3d-77) then
        tmp = y + (x + z)
    else if (x <= 1.15d-19) then
        tmp = t_0
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (x <= -1.65e-23) {
		tmp = x + z;
	} else if (x <= 1.65e-209) {
		tmp = Math.sin(y) + z;
	} else if (x <= 3.6e-126) {
		tmp = t_0;
	} else if (x <= 1.3e-77) {
		tmp = y + (x + z);
	} else if (x <= 1.15e-19) {
		tmp = t_0;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if x <= -1.65e-23:
		tmp = x + z
	elif x <= 1.65e-209:
		tmp = math.sin(y) + z
	elif x <= 3.6e-126:
		tmp = t_0
	elif x <= 1.3e-77:
		tmp = y + (x + z)
	elif x <= 1.15e-19:
		tmp = t_0
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (x <= -1.65e-23)
		tmp = Float64(x + z);
	elseif (x <= 1.65e-209)
		tmp = Float64(sin(y) + z);
	elseif (x <= 3.6e-126)
		tmp = t_0;
	elseif (x <= 1.3e-77)
		tmp = Float64(y + Float64(x + z));
	elseif (x <= 1.15e-19)
		tmp = t_0;
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (x <= -1.65e-23)
		tmp = x + z;
	elseif (x <= 1.65e-209)
		tmp = sin(y) + z;
	elseif (x <= 3.6e-126)
		tmp = t_0;
	elseif (x <= 1.3e-77)
		tmp = y + (x + z);
	elseif (x <= 1.15e-19)
		tmp = t_0;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e-23], N[(x + z), $MachinePrecision], If[LessEqual[x, 1.65e-209], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision], If[LessEqual[x, 3.6e-126], t$95$0, If[LessEqual[x, 1.3e-77], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-19], t$95$0, N[(x + z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6500000000000001e-23 or 1.1499999999999999e-19 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.8%

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

   if -1.6500000000000001e-23 < x < 1.64999999999999987e-209

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 98.6%

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

   3. Taylor expanded in y around 0 82.2%

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

   if 1.64999999999999987e-209 < x < 3.5999999999999999e-126 or 1.3000000000000001e-77 < x < 1.1499999999999999e-19

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 85.5%

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

   3. Taylor expanded in x around 0 85.7%

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

   if 3.5999999999999999e-126 < x < 1.3000000000000001e-77

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.4%

      \[\leadsto \color{blue}{y + \left(z + x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-23}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-209}:\\ \;\;\;\;\sin y + z\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-77}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 4: 83.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1450000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-16}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+199}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1450000.0)
     t_0
     (if (<= z 7.5e-16) (+ x (sin y)) (if (<= z 9.8e+199) (+ x z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1450000.0) {
		tmp = t_0;
	} else if (z <= 7.5e-16) {
		tmp = x + sin(y);
	} else if (z <= 9.8e+199) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-1450000.0d0)) then
        tmp = t_0
    else if (z <= 7.5d-16) then
        tmp = x + sin(y)
    else if (z <= 9.8d+199) then
        tmp = x + z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -1450000.0) {
		tmp = t_0;
	} else if (z <= 7.5e-16) {
		tmp = x + Math.sin(y);
	} else if (z <= 9.8e+199) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1450000.0:
		tmp = t_0
	elif z <= 7.5e-16:
		tmp = x + math.sin(y)
	elif z <= 9.8e+199:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1450000.0)
		tmp = t_0;
	elseif (z <= 7.5e-16)
		tmp = Float64(x + sin(y));
	elseif (z <= 9.8e+199)
		tmp = Float64(x + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -1450000.0)
		tmp = t_0;
	elseif (z <= 7.5e-16)
		tmp = x + sin(y);
	elseif (z <= 9.8e+199)
		tmp = x + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1450000.0], t$95$0, If[LessEqual[z, 7.5e-16], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+199], N[(x + z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e6 or 9.7999999999999993e199 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 99.9%

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

   3. Taylor expanded in x around 0 82.8%

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

   if -1.45e6 < z < 7.5e-16

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. add-cube-cbrt 99.8%

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

      3. associate-*l* 99.8%

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

      4. fma-def 99.8%

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

      5. pow2 99.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right) \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right)} \]

   4. Taylor expanded in z around 0 91.9%

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

   if 7.5e-16 < z < 9.7999999999999993e199

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.7%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1450000:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-16}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+199}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 5: 94.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-52} \lor \neg \left(z \leq 5.6 \cdot 10^{-16}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.3e-52) (not (<= z 5.6e-16)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e-52) || !(z <= 5.6e-16)) {
		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 <= (-2.3d-52)) .or. (.not. (z <= 5.6d-16))) 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 <= -2.3e-52) || !(z <= 5.6e-16)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.3e-52) or not (z <= 5.6e-16):
		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 <= -2.3e-52) || !(z <= 5.6e-16))
		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 <= -2.3e-52) || ~((z <= 5.6e-16)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.3e-52], N[Not[LessEqual[z, 5.6e-16]], $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 < -2.29999999999999994e-52 or 5.6000000000000003e-16 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 98.0%

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

   if -2.29999999999999994e-52 < z < 5.6000000000000003e-16

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. add-cube-cbrt 99.8%

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

      3. associate-*l* 99.8%

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

      4. fma-def 99.8%

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

      5. pow2 99.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right) \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right)} \]

   4. Taylor expanded in z around 0 93.6%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-52} \lor \neg \left(z \leq 5.6 \cdot 10^{-16}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 6: 99.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+14} \lor \neg \left(z \leq 1.35 \cdot 10^{-15}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e+14) (not (<= z 1.35e-15)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+14) || !(z <= 1.35e-15)) {
		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 <= (-6d+14)) .or. (.not. (z <= 1.35d-15))) 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 <= -6e+14) || !(z <= 1.35e-15)) {
		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 <= -6e+14) or not (z <= 1.35e-15):
		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 <= -6e+14) || !(z <= 1.35e-15))
		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 <= -6e+14) || ~((z <= 1.35e-15)))
		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, -6e+14], N[Not[LessEqual[z, 1.35e-15]], $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 < -6e14 or 1.35000000000000005e-15 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 99.9%

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

   if -6e14 < z < 1.35000000000000005e-15

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.6%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+14} \lor \neg \left(z \leq 1.35 \cdot 10^{-15}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 7: 70.8% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 108000:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5) (+ x z) (if (<= y 108000.0) (+ y (+ x z)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5) {
		tmp = x + z;
	} else if (y <= 108000.0) {
		tmp = y + (x + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9.5d0)) then
        tmp = x + z
    else if (y <= 108000.0d0) then
        tmp = y + (x + z)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5) {
		tmp = x + z;
	} else if (y <= 108000.0) {
		tmp = y + (x + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.5:
		tmp = x + z
	elif y <= 108000.0:
		tmp = y + (x + z)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.5)
		tmp = Float64(x + z);
	elseif (y <= 108000.0)
		tmp = Float64(y + Float64(x + z));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.5)
		tmp = x + z;
	elseif (y <= 108000.0)
		tmp = y + (x + z);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.5], N[(x + z), $MachinePrecision], If[LessEqual[y, 108000.0], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5 or 108000 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 45.0%

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

   if -9.5 < y < 108000

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.1%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 108000:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 8: 54.5% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.3e+63) x (if (<= x 4.2e-8) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.3e+63) {
		tmp = x;
	} else if (x <= 4.2e-8) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.3d+63)) then
        tmp = x
    else if (x <= 4.2d-8) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.3e+63) {
		tmp = x;
	} else if (x <= 4.2e-8) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.3e+63:
		tmp = x
	elif x <= 4.2e-8:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.3e+63)
		tmp = x;
	elseif (x <= 4.2e-8)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.3e+63)
		tmp = x;
	elseif (x <= 4.2e-8)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.3e+63], x, If[LessEqual[x, 4.2e-8], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.29999999999999993e63 or 4.19999999999999989e-8 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.6%

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

      3. associate-*l* 99.6%

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

      4. fma-def 99.6%

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

      5. pow2 99.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right) \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right)} \]

   4. Taylor expanded in x around inf 81.0%

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

   if -2.29999999999999993e63 < x < 4.19999999999999989e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 93.2%

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

   3. Taylor expanded in y around 0 72.7%

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

   4. Taylor expanded in z around inf 47.2%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 66.9% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 71.0%

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

3. Final simplification 71.0%

   \[\leadsto x + z \]

Alternative 10: 42.9% 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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. add-cube-cbrt 99.2%

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

   3. associate-*l* 99.2%

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

   4. fma-def 99.2%

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

   5. pow2 99.2%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right) \]

3. Applied egg-rr 99.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \cos y, x + \sin y\right)} \]

4. Taylor expanded in x around inf 42.6%

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

5. Final simplification 42.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023268 
(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))))