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

Percentage Accurate: 99.9% → 99.9%

Time: 7.3s

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-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 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 3: 85.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+136}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-6}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-54}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+79}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.8e+136)
     t_0
     (if (<= z -3.1e-6)
       (+ z x)
       (if (<= z 9e-54) (+ x (sin y)) (if (<= z 9.2e+79) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -2.8e+136) {
		tmp = t_0;
	} else if (z <= -3.1e-6) {
		tmp = z + x;
	} else if (z <= 9e-54) {
		tmp = x + sin(y);
	} else if (z <= 9.2e+79) {
		tmp = z + x;
	} 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 <= (-2.8d+136)) then
        tmp = t_0
    else if (z <= (-3.1d-6)) then
        tmp = z + x
    else if (z <= 9d-54) then
        tmp = x + sin(y)
    else if (z <= 9.2d+79) then
        tmp = z + x
    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 <= -2.8e+136) {
		tmp = t_0;
	} else if (z <= -3.1e-6) {
		tmp = z + x;
	} else if (z <= 9e-54) {
		tmp = x + Math.sin(y);
	} else if (z <= 9.2e+79) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -2.8e+136:
		tmp = t_0
	elif z <= -3.1e-6:
		tmp = z + x
	elif z <= 9e-54:
		tmp = x + math.sin(y)
	elif z <= 9.2e+79:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -2.8e+136)
		tmp = t_0;
	elseif (z <= -3.1e-6)
		tmp = Float64(z + x);
	elseif (z <= 9e-54)
		tmp = Float64(x + sin(y));
	elseif (z <= 9.2e+79)
		tmp = Float64(z + x);
	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 <= -2.8e+136)
		tmp = t_0;
	elseif (z <= -3.1e-6)
		tmp = z + x;
	elseif (z <= 9e-54)
		tmp = x + sin(y);
	elseif (z <= 9.2e+79)
		tmp = z + x;
	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, -2.8e+136], t$95$0, If[LessEqual[z, -3.1e-6], N[(z + x), $MachinePrecision], If[LessEqual[z, 9e-54], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+79], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8000000000000002e136 or 9.2000000000000002e79 < z

   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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 86.0%

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

   if -2.8000000000000002e136 < z < -3.1e-6 or 8.9999999999999997e-54 < z < 9.2000000000000002e79

   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-define 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. Add Preprocessing

   5. Taylor expanded in y around 0 84.2%

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

   if -3.1e-6 < z < 8.9999999999999997e-54

   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-define 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. Add Preprocessing

   5. Taylor expanded in z around 0 94.3%

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

      1. +-commutative 94.3%

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

   7. Simplified 94.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+136}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-6}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-54}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+79}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -3 \cdot 10^{+136}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-255}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-202}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+79}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -3e+136)
     t_0
     (if (<= z -4.8e-255)
       (+ z x)
       (if (<= z 5.8e-202) (sin y) (if (<= z 9.2e+79) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -3e+136) {
		tmp = t_0;
	} else if (z <= -4.8e-255) {
		tmp = z + x;
	} else if (z <= 5.8e-202) {
		tmp = sin(y);
	} else if (z <= 9.2e+79) {
		tmp = z + x;
	} 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 <= (-3d+136)) then
        tmp = t_0
    else if (z <= (-4.8d-255)) then
        tmp = z + x
    else if (z <= 5.8d-202) then
        tmp = sin(y)
    else if (z <= 9.2d+79) then
        tmp = z + x
    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 <= -3e+136) {
		tmp = t_0;
	} else if (z <= -4.8e-255) {
		tmp = z + x;
	} else if (z <= 5.8e-202) {
		tmp = Math.sin(y);
	} else if (z <= 9.2e+79) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -3e+136:
		tmp = t_0
	elif z <= -4.8e-255:
		tmp = z + x
	elif z <= 5.8e-202:
		tmp = math.sin(y)
	elif z <= 9.2e+79:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -3e+136)
		tmp = t_0;
	elseif (z <= -4.8e-255)
		tmp = Float64(z + x);
	elseif (z <= 5.8e-202)
		tmp = sin(y);
	elseif (z <= 9.2e+79)
		tmp = Float64(z + x);
	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 <= -3e+136)
		tmp = t_0;
	elseif (z <= -4.8e-255)
		tmp = z + x;
	elseif (z <= 5.8e-202)
		tmp = sin(y);
	elseif (z <= 9.2e+79)
		tmp = z + x;
	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, -3e+136], t$95$0, If[LessEqual[z, -4.8e-255], N[(z + x), $MachinePrecision], If[LessEqual[z, 5.8e-202], N[Sin[y], $MachinePrecision], If[LessEqual[z, 9.2e+79], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999979e136 or 9.2000000000000002e79 < z

   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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 86.0%

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

   if -2.99999999999999979e136 < z < -4.7999999999999997e-255 or 5.79999999999999976e-202 < z < 9.2000000000000002e79

   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-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 71.3%

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

   if -4.7999999999999997e-255 < z < 5.79999999999999976e-202

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 66.2%

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

   4. Taylor expanded in z around 0 66.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+136}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-255}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-202}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+79}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+74}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;y \leq 550000:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+125}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3e+74)
   (sin y)
   (if (<= y 550000.0) (+ z (+ y x)) (if (<= y 4.9e+125) (sin y) (+ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e+74) {
		tmp = sin(y);
	} else if (y <= 550000.0) {
		tmp = z + (y + x);
	} else if (y <= 4.9e+125) {
		tmp = sin(y);
	} 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) :: tmp
    if (y <= (-3d+74)) then
        tmp = sin(y)
    else if (y <= 550000.0d0) then
        tmp = z + (y + x)
    else if (y <= 4.9d+125) then
        tmp = sin(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e+74) {
		tmp = Math.sin(y);
	} else if (y <= 550000.0) {
		tmp = z + (y + x);
	} else if (y <= 4.9e+125) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3e+74:
		tmp = math.sin(y)
	elif y <= 550000.0:
		tmp = z + (y + x)
	elif y <= 4.9e+125:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3e+74)
		tmp = sin(y);
	elseif (y <= 550000.0)
		tmp = Float64(z + Float64(y + x));
	elseif (y <= 4.9e+125)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3e+74)
		tmp = sin(y);
	elseif (y <= 550000.0)
		tmp = z + (y + x);
	elseif (y <= 4.9e+125)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3e+74], N[Sin[y], $MachinePrecision], If[LessEqual[y, 550000.0], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+125], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e74 or 5.5e5 < y < 4.90000000000000016e125

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 75.1%

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

   4. Taylor expanded in z around 0 40.9%

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

   if -3e74 < y < 5.5e5

   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. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 94.5%

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

      1. associate-+r+ 94.5%

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

      2. +-commutative 94.5%

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

   7. Simplified 94.5%

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

   if 4.90000000000000016e125 < y

   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-define 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. Add Preprocessing

   5. Taylor expanded in y around 0 47.0%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+74}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;y \leq 550000:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+125}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+17} \lor \neg \left(z \leq 1.25 \cdot 10^{-5}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.6e+17) (not (<= z 1.25e-5)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.6e+17) || !(z <= 1.25e-5)) {
		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 <= (-3.6d+17)) .or. (.not. (z <= 1.25d-5))) 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 <= -3.6e+17) || !(z <= 1.25e-5)) {
		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 <= -3.6e+17) or not (z <= 1.25e-5):
		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 <= -3.6e+17) || !(z <= 1.25e-5))
		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 <= -3.6e+17) || ~((z <= 1.25e-5)))
		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, -3.6e+17], N[Not[LessEqual[z, 1.25e-5]], $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 < -3.6e17 or 1.25000000000000006e-5 < 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 99.5%

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

   if -3.6e17 < z < 1.25000000000000006e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.3%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+17} \lor \neg \left(z \leq 1.25 \cdot 10^{-5}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-5} \lor \neg \left(z \leq 2.3 \cdot 10^{-55}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.8e-5) (not (<= z 2.3e-55)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e-5) || !(z <= 2.3e-55)) {
		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 <= (-2.8d-5)) .or. (.not. (z <= 2.3d-55))) 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 <= -2.8e-5) || !(z <= 2.3e-55)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.8e-5) or not (z <= 2.3e-55):
		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 <= -2.8e-5) || !(z <= 2.3e-55))
		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 <= -2.8e-5) || ~((z <= 2.3e-55)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.8e-5], N[Not[LessEqual[z, 2.3e-55]], $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 < -2.79999999999999996e-5 or 2.30000000000000011e-55 < 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 98.5%

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

   if -2.79999999999999996e-5 < z < 2.30000000000000011e-55

   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-define 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. Add Preprocessing

   5. Taylor expanded in z around 0 94.3%

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

      1. +-commutative 94.3%

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

   7. Simplified 94.3%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-5} \lor \neg \left(z \leq 2.3 \cdot 10^{-55}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.3% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-38}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.3e+18) x (if (<= x 1.2e-38) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.3e+18) {
		tmp = x;
	} else if (x <= 1.2e-38) {
		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 <= (-4.3d+18)) then
        tmp = x
    else if (x <= 1.2d-38) 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 <= -4.3e+18) {
		tmp = x;
	} else if (x <= 1.2e-38) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.3e+18:
		tmp = x
	elif x <= 1.2e-38:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.3e+18)
		tmp = x;
	elseif (x <= 1.2e-38)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.3e+18)
		tmp = x;
	elseif (x <= 1.2e-38)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.3e+18], x, If[LessEqual[x, 1.2e-38], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3e18 or 1.20000000000000011e-38 < x

   1. Initial program 99.9%

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

      1. expm1-log1p-u 99.9%

         \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} \]

   4. Applied egg-rr 99.9%

      \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} \]

   5. Taylor expanded in x around inf 71.1%

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

   if -4.3e18 < x < 1.20000000000000011e-38

   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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 51.6%

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

   6. Taylor expanded in y around 0 36.2%

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

Alternative 9: 66.4% accurate, 69.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return z + 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 = z + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(z + x), $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-define 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. Add Preprocessing

5. Taylor expanded in y around 0 64.0%

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

6. Final simplification 64.0%

   \[\leadsto z + x \]
7. Add Preprocessing

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. Add Preprocessing
3. Step-by-step derivation

   1. expm1-log1p-u 99.9%

      \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} \]

4. Applied egg-rr 99.9%

   \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} \]

5. Taylor expanded in x around inf 41.5%

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

Reproduce

herbie shell --seed 2024129 
(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))))