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

Percentage Accurate: 99.9% → 99.9%

Time: 6.9s

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: 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. Final simplification 99.9%

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

Alternative 3: 72.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-162}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-212}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+97}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.45e+101)
     t_0
     (if (<= z -1.85e-162)
       (+ z x)
       (if (<= z -4.7e-212) (sin y) (if (<= z 2.5e+97) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.45e+101) {
		tmp = t_0;
	} else if (z <= -1.85e-162) {
		tmp = z + x;
	} else if (z <= -4.7e-212) {
		tmp = sin(y);
	} else if (z <= 2.5e+97) {
		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 <= (-1.45d+101)) then
        tmp = t_0
    else if (z <= (-1.85d-162)) then
        tmp = z + x
    else if (z <= (-4.7d-212)) then
        tmp = sin(y)
    else if (z <= 2.5d+97) 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 <= -1.45e+101) {
		tmp = t_0;
	} else if (z <= -1.85e-162) {
		tmp = z + x;
	} else if (z <= -4.7e-212) {
		tmp = Math.sin(y);
	} else if (z <= 2.5e+97) {
		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 <= -1.45e+101:
		tmp = t_0
	elif z <= -1.85e-162:
		tmp = z + x
	elif z <= -4.7e-212:
		tmp = math.sin(y)
	elif z <= 2.5e+97:
		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 <= -1.45e+101)
		tmp = t_0;
	elseif (z <= -1.85e-162)
		tmp = Float64(z + x);
	elseif (z <= -4.7e-212)
		tmp = sin(y);
	elseif (z <= 2.5e+97)
		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 <= -1.45e+101)
		tmp = t_0;
	elseif (z <= -1.85e-162)
		tmp = z + x;
	elseif (z <= -4.7e-212)
		tmp = sin(y);
	elseif (z <= 2.5e+97)
		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, -1.45e+101], t$95$0, If[LessEqual[z, -1.85e-162], N[(z + x), $MachinePrecision], If[LessEqual[z, -4.7e-212], N[Sin[y], $MachinePrecision], If[LessEqual[z, 2.5e+97], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.44999999999999994e101 or 2.49999999999999999e97 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 93.8%

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

   5. Taylor expanded in z around inf 93.8%

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

   if -1.44999999999999994e101 < z < -1.8500000000000001e-162 or -4.69999999999999998e-212 < z < 2.49999999999999999e97

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.1%

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

   if -1.8500000000000001e-162 < z < -4.69999999999999998e-212

   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-def 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. Taylor expanded in x around 0 71.9%

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

   5. Taylor expanded in z around 0 65.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-162}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-212}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+97}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 4: 84.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -3.75 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-46}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-115}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+98}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -3.75e+102)
     t_0
     (if (<= z -1.7e-46)
       (+ z x)
       (if (<= z 2.6e-115) (+ x (sin y)) (if (<= z 7.5e+98) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -3.75e+102) {
		tmp = t_0;
	} else if (z <= -1.7e-46) {
		tmp = z + x;
	} else if (z <= 2.6e-115) {
		tmp = x + sin(y);
	} else if (z <= 7.5e+98) {
		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 <= (-3.75d+102)) then
        tmp = t_0
    else if (z <= (-1.7d-46)) then
        tmp = z + x
    else if (z <= 2.6d-115) then
        tmp = x + sin(y)
    else if (z <= 7.5d+98) 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 <= -3.75e+102) {
		tmp = t_0;
	} else if (z <= -1.7e-46) {
		tmp = z + x;
	} else if (z <= 2.6e-115) {
		tmp = x + Math.sin(y);
	} else if (z <= 7.5e+98) {
		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 <= -3.75e+102:
		tmp = t_0
	elif z <= -1.7e-46:
		tmp = z + x
	elif z <= 2.6e-115:
		tmp = x + math.sin(y)
	elif z <= 7.5e+98:
		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 <= -3.75e+102)
		tmp = t_0;
	elseif (z <= -1.7e-46)
		tmp = Float64(z + x);
	elseif (z <= 2.6e-115)
		tmp = Float64(x + sin(y));
	elseif (z <= 7.5e+98)
		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 <= -3.75e+102)
		tmp = t_0;
	elseif (z <= -1.7e-46)
		tmp = z + x;
	elseif (z <= 2.6e-115)
		tmp = x + sin(y);
	elseif (z <= 7.5e+98)
		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, -3.75e+102], t$95$0, If[LessEqual[z, -1.7e-46], N[(z + x), $MachinePrecision], If[LessEqual[z, 2.6e-115], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+98], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.75e102 or 7.50000000000000036e98 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 93.8%

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

   5. Taylor expanded in z around inf 93.8%

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

   if -3.75e102 < z < -1.69999999999999998e-46 or 2.60000000000000004e-115 < z < 7.50000000000000036e98

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.9%

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

   if -1.69999999999999998e-46 < z < 2.60000000000000004e-115

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.75 \cdot 10^{+102}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-46}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-115}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+98}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 5: 94.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-43} \lor \neg \left(z \leq 2.6 \cdot 10^{-115}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.6e-43) (not (<= z 2.6e-115)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.6e-43) || !(z <= 2.6e-115)) {
		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 <= (-8.6d-43)) .or. (.not. (z <= 2.6d-115))) 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 <= -8.6e-43) || !(z <= 2.6e-115)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.6e-43) or not (z <= 2.6e-115):
		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 <= -8.6e-43) || !(z <= 2.6e-115))
		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 <= -8.6e-43) || ~((z <= 2.6e-115)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.6e-43], N[Not[LessEqual[z, 2.6e-115]], $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 < -8.59999999999999927e-43 or 2.60000000000000004e-115 < z

   1. Initial program 99.9%

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

      1. flip-+ 83.8%

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

      2. div-inv 83.8%

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

      3. fma-def 83.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot x - \sin y \cdot \sin y, \frac{1}{x - \sin y}, z \cdot \cos y\right)} \]

      4. pow2 83.7%

         \[\leadsto \mathsf{fma}\left(x \cdot x - \color{blue}{{\sin y}^{2}}, \frac{1}{x - \sin y}, z \cdot \cos y\right) \]

   3. Applied egg-rr 83.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot x - {\sin y}^{2}, \frac{1}{x - \sin y}, z \cdot \cos y\right)} \]
   4. Step-by-step derivation

      1. fma-udef 83.8%

         \[\leadsto \color{blue}{\left(x \cdot x - {\sin y}^{2}\right) \cdot \frac{1}{x - \sin y} + z \cdot \cos y} \]

      2. +-commutative 83.8%

         \[\leadsto \color{blue}{z \cdot \cos y + \left(x \cdot x - {\sin y}^{2}\right) \cdot \frac{1}{x - \sin y}} \]

      3. *-commutative 83.8%

         \[\leadsto \color{blue}{\cos y \cdot z} + \left(x \cdot x - {\sin y}^{2}\right) \cdot \frac{1}{x - \sin y} \]

      4. associate-*r/ 83.8%

         \[\leadsto \cos y \cdot z + \color{blue}{\frac{\left(x \cdot x - {\sin y}^{2}\right) \cdot 1}{x - \sin y}} \]

      5. *-rgt-identity 83.8%

         \[\leadsto \cos y \cdot z + \frac{\color{blue}{x \cdot x - {\sin y}^{2}}}{x - \sin y} \]

   5. Simplified 83.8%

      \[\leadsto \color{blue}{\cos y \cdot z + \frac{x \cdot x - {\sin y}^{2}}{x - \sin y}} \]

   6. Taylor expanded in x around inf 96.7%

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

   if -8.59999999999999927e-43 < z < 2.60000000000000004e-115

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.1%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-43} \lor \neg \left(z \leq 2.6 \cdot 10^{-115}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 6: 99.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2400000000 \lor \neg \left(z \leq 1.2\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2400000000.0) (not (<= z 1.2)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2400000000.0) || !(z <= 1.2)) {
		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 <= (-2400000000.0d0)) .or. (.not. (z <= 1.2d0))) 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 <= -2400000000.0) || !(z <= 1.2)) {
		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 <= -2400000000.0) or not (z <= 1.2):
		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 <= -2400000000.0) || !(z <= 1.2))
		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 <= -2400000000.0) || ~((z <= 1.2)))
		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, -2400000000.0], N[Not[LessEqual[z, 1.2]], $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 < -2.4e9 or 1.19999999999999996 < z

   1. Initial program 99.9%

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

      1. flip-+ 86.2%

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

      2. div-inv 86.2%

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

      3. fma-def 86.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot x - \sin y \cdot \sin y, \frac{1}{x - \sin y}, z \cdot \cos y\right)} \]

      4. pow2 86.2%

         \[\leadsto \mathsf{fma}\left(x \cdot x - \color{blue}{{\sin y}^{2}}, \frac{1}{x - \sin y}, z \cdot \cos y\right) \]

   3. Applied egg-rr 86.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot x - {\sin y}^{2}, \frac{1}{x - \sin y}, z \cdot \cos y\right)} \]
   4. Step-by-step derivation

      1. fma-udef 86.2%

         \[\leadsto \color{blue}{\left(x \cdot x - {\sin y}^{2}\right) \cdot \frac{1}{x - \sin y} + z \cdot \cos y} \]

      2. +-commutative 86.2%

         \[\leadsto \color{blue}{z \cdot \cos y + \left(x \cdot x - {\sin y}^{2}\right) \cdot \frac{1}{x - \sin y}} \]

      3. *-commutative 86.2%

         \[\leadsto \color{blue}{\cos y \cdot z} + \left(x \cdot x - {\sin y}^{2}\right) \cdot \frac{1}{x - \sin y} \]

      4. associate-*r/ 86.2%

         \[\leadsto \cos y \cdot z + \color{blue}{\frac{\left(x \cdot x - {\sin y}^{2}\right) \cdot 1}{x - \sin y}} \]

      5. *-rgt-identity 86.2%

         \[\leadsto \cos y \cdot z + \frac{\color{blue}{x \cdot x - {\sin y}^{2}}}{x - \sin y} \]

   5. Simplified 86.2%

      \[\leadsto \color{blue}{\cos y \cdot z + \frac{x \cdot x - {\sin y}^{2}}{x - \sin y}} \]

   6. Taylor expanded in x around inf 98.9%

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

   if -2.4e9 < z < 1.19999999999999996

   1. Initial program 100.0%

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

   2. 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 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2400000000 \lor \neg \left(z \leq 1.2\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 7: 70.1% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-72}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-19}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.7e-72) (+ z x) (if (<= x 3.3e-19) (+ y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e-72) {
		tmp = z + x;
	} else if (x <= 3.3e-19) {
		tmp = y + (z + x);
	} 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 (x <= (-1.7d-72)) then
        tmp = z + x
    else if (x <= 3.3d-19) then
        tmp = y + (z + x)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e-72) {
		tmp = z + x;
	} else if (x <= 3.3e-19) {
		tmp = y + (z + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.7e-72:
		tmp = z + x
	elif x <= 3.3e-19:
		tmp = y + (z + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.7e-72)
		tmp = Float64(z + x);
	elseif (x <= 3.3e-19)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.7e-72)
		tmp = z + x;
	elseif (x <= 3.3e-19)
		tmp = y + (z + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.7e-72], N[(z + x), $MachinePrecision], If[LessEqual[x, 3.3e-19], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6999999999999999e-72 or 3.2999999999999998e-19 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.9%

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

   if -1.6999999999999999e-72 < x < 3.2999999999999998e-19

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 54.5%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-72}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-19}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 8: 54.9% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-80}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.4e-42) x (if (<= x 4.1e-80) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e-42) {
		tmp = x;
	} else if (x <= 4.1e-80) {
		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 <= (-2.4d-42)) then
        tmp = x
    else if (x <= 4.1d-80) 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 <= -2.4e-42) {
		tmp = x;
	} else if (x <= 4.1e-80) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.4e-42:
		tmp = x
	elif x <= 4.1e-80:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.4e-42)
		tmp = x;
	elseif (x <= 4.1e-80)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.4e-42)
		tmp = x;
	elseif (x <= 4.1e-80)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.4e-42], x, If[LessEqual[x, 4.1e-80], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.40000000000000003e-42 or 4.0999999999999999e-80 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 72.3%

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

   if -2.40000000000000003e-42 < x < 4.0999999999999999e-80

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 97.3%

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

      1. *-commutative 97.3%

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

      2. fma-def 97.3%

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

   4. Simplified 97.3%

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

   5. Taylor expanded in y around 0 44.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-80}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 66.5% 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. Taylor expanded in y around 0 69.9%

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

3. Final simplification 69.9%

   \[\leadsto z + x \]

Alternative 10: 42.8% 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 44.4%

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

3. Final simplification 44.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023257 
(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))))