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

Percentage Accurate: 99.9% → 99.9%

Time: 10.6s

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(z * N[Cos[y], $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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(z, \cos y, x + \sin y\right) \]

Alternative 2: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y + z \cdot \cos y\\ \mathbf{if}\;x \leq -0.13:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-35}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+38}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (sin y) (* z (cos y)))))
   (if (<= x -0.13)
     (+ z x)
     (if (<= x 1.75e-113)
       t_0
       (if (<= x 4.4e-35) (+ x (sin y)) (if (<= x 9.6e+38) t_0 (+ z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) + (z * cos(y));
	double tmp;
	if (x <= -0.13) {
		tmp = z + x;
	} else if (x <= 1.75e-113) {
		tmp = t_0;
	} else if (x <= 4.4e-35) {
		tmp = x + sin(y);
	} else if (x <= 9.6e+38) {
		tmp = t_0;
	} else {
		tmp = z + 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) :: t_0
    real(8) :: tmp
    t_0 = sin(y) + (z * cos(y))
    if (x <= (-0.13d0)) then
        tmp = z + x
    else if (x <= 1.75d-113) then
        tmp = t_0
    else if (x <= 4.4d-35) then
        tmp = x + sin(y)
    else if (x <= 9.6d+38) then
        tmp = t_0
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) + (z * Math.cos(y));
	double tmp;
	if (x <= -0.13) {
		tmp = z + x;
	} else if (x <= 1.75e-113) {
		tmp = t_0;
	} else if (x <= 4.4e-35) {
		tmp = x + Math.sin(y);
	} else if (x <= 9.6e+38) {
		tmp = t_0;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) + (z * math.cos(y))
	tmp = 0
	if x <= -0.13:
		tmp = z + x
	elif x <= 1.75e-113:
		tmp = t_0
	elif x <= 4.4e-35:
		tmp = x + math.sin(y)
	elif x <= 9.6e+38:
		tmp = t_0
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) + Float64(z * cos(y)))
	tmp = 0.0
	if (x <= -0.13)
		tmp = Float64(z + x);
	elseif (x <= 1.75e-113)
		tmp = t_0;
	elseif (x <= 4.4e-35)
		tmp = Float64(x + sin(y));
	elseif (x <= 9.6e+38)
		tmp = t_0;
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) + (z * cos(y));
	tmp = 0.0;
	if (x <= -0.13)
		tmp = z + x;
	elseif (x <= 1.75e-113)
		tmp = t_0;
	elseif (x <= 4.4e-35)
		tmp = x + sin(y);
	elseif (x <= 9.6e+38)
		tmp = t_0;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.13], N[(z + x), $MachinePrecision], If[LessEqual[x, 1.75e-113], t$95$0, If[LessEqual[x, 4.4e-35], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.6e+38], t$95$0, N[(z + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.13 or 9.60000000000000069e38 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 92.4%

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

      1. +-commutative 92.4%

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

   4. Simplified 92.4%

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

   if -0.13 < x < 1.75000000000000014e-113 or 4.39999999999999987e-35 < x < 9.60000000000000069e38

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 91.2%

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

   if 1.75000000000000014e-113 < x < 4.39999999999999987e-35

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 88.4%

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

      1. +-commutative 88.4%

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

   4. Simplified 88.4%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.13:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-113}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-35}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+38}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 3: 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 4: 83.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-33}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-7}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.6e+91)
     t_0
     (if (<= z -1.1e-33) (+ z x) (if (<= z 2.65e-7) (+ x (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.6e+91) {
		tmp = t_0;
	} else if (z <= -1.1e-33) {
		tmp = z + x;
	} else if (z <= 2.65e-7) {
		tmp = x + sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-1.6d+91)) then
        tmp = t_0
    else if (z <= (-1.1d-33)) then
        tmp = z + x
    else if (z <= 2.65d-7) then
        tmp = x + sin(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -1.6e+91) {
		tmp = t_0;
	} else if (z <= -1.1e-33) {
		tmp = z + x;
	} else if (z <= 2.65e-7) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1.6e+91:
		tmp = t_0
	elif z <= -1.1e-33:
		tmp = z + x
	elif z <= 2.65e-7:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1.6e+91)
		tmp = t_0;
	elseif (z <= -1.1e-33)
		tmp = Float64(z + x);
	elseif (z <= 2.65e-7)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -1.6e+91)
		tmp = t_0;
	elseif (z <= -1.1e-33)
		tmp = z + x;
	elseif (z <= 2.65e-7)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+91], t$95$0, If[LessEqual[z, -1.1e-33], N[(z + x), $MachinePrecision], If[LessEqual[z, 2.65e-7], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999995e91 or 2.65e-7 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 79.7%

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

   if -1.59999999999999995e91 < z < -1.10000000000000003e-33

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 75.4%

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

      1. +-commutative 75.4%

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

   4. Simplified 75.4%

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

   if -1.10000000000000003e-33 < z < 2.65e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 92.0%

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

      1. +-commutative 92.0%

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

   4. Simplified 92.0%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-33}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-7}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 5: 69.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+72} \lor \neg \left(y \leq 7.5 \cdot 10^{+37}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.8e+72) (not (<= y 7.5e+37))) (* z (cos y)) (+ z (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e+72) || !(y <= 7.5e+37)) {
		tmp = z * cos(y);
	} else {
		tmp = z + (y + 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 ((y <= (-3.8d+72)) .or. (.not. (y <= 7.5d+37))) then
        tmp = z * cos(y)
    else
        tmp = z + (y + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e+72) || !(y <= 7.5e+37)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (y + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.8e+72) or not (y <= 7.5e+37):
		tmp = z * math.cos(y)
	else:
		tmp = z + (y + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.8e+72) || !(y <= 7.5e+37))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + Float64(y + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.8e+72) || ~((y <= 7.5e+37)))
		tmp = z * cos(y);
	else
		tmp = z + (y + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.8e+72], N[Not[LessEqual[y, 7.5e+37]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000006e72 or 7.5000000000000003e37 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 44.0%

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

   if -3.80000000000000006e72 < y < 7.5000000000000003e37

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.5%

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

      1. +-commutative 91.5%

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

      2. +-commutative 91.5%

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

      3. associate-+l+ 91.5%

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

   4. Simplified 91.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+72} \lor \neg \left(y \leq 7.5 \cdot 10^{+37}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \]

Alternative 6: 56.8% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+58} \lor \neg \left(x \leq -5.9 \cdot 10^{-15}\right) \land x \leq 4 \cdot 10^{-90}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.16e+97)
   x
   (if (or (<= x -2.25e+58) (and (not (<= x -5.9e-15)) (<= x 4e-90)))
     (+ z y)
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.16e+97) {
		tmp = x;
	} else if ((x <= -2.25e+58) || (!(x <= -5.9e-15) && (x <= 4e-90))) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.16d+97)) then
        tmp = x
    else if ((x <= (-2.25d+58)) .or. (.not. (x <= (-5.9d-15))) .and. (x <= 4d-90)) then
        tmp = z + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.16e+97) {
		tmp = x;
	} else if ((x <= -2.25e+58) || (!(x <= -5.9e-15) && (x <= 4e-90))) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.16e+97:
		tmp = x
	elif (x <= -2.25e+58) or (not (x <= -5.9e-15) and (x <= 4e-90)):
		tmp = z + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.16e+97)
		tmp = x;
	elseif ((x <= -2.25e+58) || (!(x <= -5.9e-15) && (x <= 4e-90)))
		tmp = Float64(z + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.16e+97)
		tmp = x;
	elseif ((x <= -2.25e+58) || (~((x <= -5.9e-15)) && (x <= 4e-90)))
		tmp = z + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.16e+97], x, If[Or[LessEqual[x, -2.25e+58], And[N[Not[LessEqual[x, -5.9e-15]], $MachinePrecision], LessEqual[x, 4e-90]]], N[(z + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15999999999999991e97 or -2.2499999999999999e58 < x < -5.89999999999999963e-15 or 3.99999999999999998e-90 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 68.8%

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

   if -1.15999999999999991e97 < x < -2.2499999999999999e58 or -5.89999999999999963e-15 < x < 3.99999999999999998e-90

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 93.3%

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

   3. Taylor expanded in y around 0 53.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+58} \lor \neg \left(x \leq -5.9 \cdot 10^{-15}\right) \land x \leq 4 \cdot 10^{-90}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 69.7% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+132} \lor \neg \left(y \leq 1.15 \cdot 10^{+19}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e+132) (not (<= y 1.15e+19))) (+ z x) (+ z (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+132) || !(y <= 1.15e+19)) {
		tmp = z + x;
	} else {
		tmp = z + (y + 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 ((y <= (-1.4d+132)) .or. (.not. (y <= 1.15d+19))) then
        tmp = z + x
    else
        tmp = z + (y + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+132) || !(y <= 1.15e+19)) {
		tmp = z + x;
	} else {
		tmp = z + (y + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.4e+132) or not (y <= 1.15e+19):
		tmp = z + x
	else:
		tmp = z + (y + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e+132) || !(y <= 1.15e+19))
		tmp = Float64(z + x);
	else
		tmp = Float64(z + Float64(y + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.4e+132) || ~((y <= 1.15e+19)))
		tmp = z + x;
	else
		tmp = z + (y + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e+132], N[Not[LessEqual[y, 1.15e+19]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e132 or 1.15e19 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 37.3%

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

      1. +-commutative 37.3%

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

   4. Simplified 37.3%

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

   if -1.4e132 < y < 1.15e19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.9%

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

      1. +-commutative 88.9%

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

      2. +-commutative 88.9%

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

      3. associate-+l+ 88.9%

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

   4. Simplified 88.9%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+132} \lor \neg \left(y \leq 1.15 \cdot 10^{+19}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \]

Alternative 8: 68.1% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-89} \lor \neg \left(x \leq 3 \cdot 10^{-127}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8e-89) (not (<= x 3e-127))) (+ z x) (+ z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e-89) || !(x <= 3e-127)) {
		tmp = z + x;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-8d-89)) .or. (.not. (x <= 3d-127))) then
        tmp = z + x
    else
        tmp = z + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e-89) || !(x <= 3e-127)) {
		tmp = z + x;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8e-89) or not (x <= 3e-127):
		tmp = z + x
	else:
		tmp = z + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8e-89) || !(x <= 3e-127))
		tmp = Float64(z + x);
	else
		tmp = Float64(z + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8e-89) || ~((x <= 3e-127)))
		tmp = z + x;
	else
		tmp = z + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8e-89], N[Not[LessEqual[x, 3e-127]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.00000000000000031e-89 or 3.00000000000000009e-127 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 75.3%

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

      1. +-commutative 75.3%

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

   4. Simplified 75.3%

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

   if -8.00000000000000031e-89 < x < 3.00000000000000009e-127

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 98.4%

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

   3. Taylor expanded in y around 0 55.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-89} \lor \neg \left(x \leq 3 \cdot 10^{-127}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \]

Alternative 9: 45.6% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+19}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+132) x (if (<= y 2.4e+19) (+ y x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+132) {
		tmp = x;
	} else if (y <= 2.4e+19) {
		tmp = y + x;
	} 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 (y <= (-1.4d+132)) then
        tmp = x
    else if (y <= 2.4d+19) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+132) {
		tmp = x;
	} else if (y <= 2.4e+19) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e+132:
		tmp = x
	elif y <= 2.4e+19:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+132)
		tmp = x;
	elseif (y <= 2.4e+19)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e+132)
		tmp = x;
	elseif (y <= 2.4e+19)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e+132], x, If[LessEqual[y, 2.4e+19], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e132 or 2.4e19 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 33.6%

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

   if -1.4e132 < y < 2.4e19

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 57.1%

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

      1. +-commutative 57.1%

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

   4. Simplified 57.1%

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

   5. Taylor expanded in y around 0 51.0%

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

      1. +-commutative 51.0%

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

   7. Simplified 51.0%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+19}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 42.2% 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. Taylor expanded in x around inf 39.6%

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

3. Final simplification 39.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023322 
(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))))