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

Percentage Accurate: 99.9% → 99.9%

Time: 6.8s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+33}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.6e+33)
   (+ x z)
   (if (<= x 5e+32) (+ (sin y) (* z (cos y))) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e+33) {
		tmp = x + z;
	} else if (x <= 5e+32) {
		tmp = sin(y) + (z * cos(y));
	} 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 (x <= (-2.6d+33)) then
        tmp = x + z
    else if (x <= 5d+32) then
        tmp = sin(y) + (z * cos(y))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e+33) {
		tmp = x + z;
	} else if (x <= 5e+32) {
		tmp = Math.sin(y) + (z * Math.cos(y));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.6e+33:
		tmp = x + z
	elif x <= 5e+32:
		tmp = math.sin(y) + (z * math.cos(y))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.6e+33)
		tmp = Float64(x + z);
	elseif (x <= 5e+32)
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.6e+33)
		tmp = x + z;
	elseif (x <= 5e+32)
		tmp = sin(y) + (z * cos(y));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.6e+33], N[(x + z), $MachinePrecision], If[LessEqual[x, 5e+32], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999997e33 or 4.9999999999999997e32 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.7%

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

      1. +-commutative 88.7%

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

   4. Simplified 88.7%

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

   if -2.5999999999999997e33 < x < 4.9999999999999997e32

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 92.5%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+33}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 3: 70.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-222}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-193}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+56}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -5.8e+63)
     t_0
     (if (<= z 5e-222)
       (+ z (+ x y))
       (if (<= z 2.15e-193) (sin y) (if (<= z 3.3e+56) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -5.8e+63) {
		tmp = t_0;
	} else if (z <= 5e-222) {
		tmp = z + (x + y);
	} else if (z <= 2.15e-193) {
		tmp = sin(y);
	} else if (z <= 3.3e+56) {
		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 <= (-5.8d+63)) then
        tmp = t_0
    else if (z <= 5d-222) then
        tmp = z + (x + y)
    else if (z <= 2.15d-193) then
        tmp = sin(y)
    else if (z <= 3.3d+56) 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 <= -5.8e+63) {
		tmp = t_0;
	} else if (z <= 5e-222) {
		tmp = z + (x + y);
	} else if (z <= 2.15e-193) {
		tmp = Math.sin(y);
	} else if (z <= 3.3e+56) {
		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 <= -5.8e+63:
		tmp = t_0
	elif z <= 5e-222:
		tmp = z + (x + y)
	elif z <= 2.15e-193:
		tmp = math.sin(y)
	elif z <= 3.3e+56:
		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 <= -5.8e+63)
		tmp = t_0;
	elseif (z <= 5e-222)
		tmp = Float64(z + Float64(x + y));
	elseif (z <= 2.15e-193)
		tmp = sin(y);
	elseif (z <= 3.3e+56)
		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 <= -5.8e+63)
		tmp = t_0;
	elseif (z <= 5e-222)
		tmp = z + (x + y);
	elseif (z <= 2.15e-193)
		tmp = sin(y);
	elseif (z <= 3.3e+56)
		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, -5.8e+63], t$95$0, If[LessEqual[z, 5e-222], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-193], N[Sin[y], $MachinePrecision], If[LessEqual[z, 3.3e+56], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.7999999999999999e63 or 3.30000000000000002e56 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 85.9%

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

   if -5.7999999999999999e63 < z < 5.00000000000000008e-222

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 63.0%

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

      1. +-commutative 63.0%

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

      2. +-commutative 63.0%

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

      3. associate-+l+ 63.0%

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

   4. Simplified 63.0%

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

   if 5.00000000000000008e-222 < z < 2.1500000000000001e-193

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

   if 2.1500000000000001e-193 < z < 3.30000000000000002e56

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.4%

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

      1. +-commutative 79.4%

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

   4. Simplified 79.4%

      \[\leadsto \color{blue}{z + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-222}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-193}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+56}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 4: 83.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-20}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+56}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1000000000.0)
     t_0
     (if (<= z 1.32e-20) (+ x (sin y)) (if (<= z 3e+56) (+ x z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1000000000.0) {
		tmp = t_0;
	} else if (z <= 1.32e-20) {
		tmp = x + sin(y);
	} else if (z <= 3e+56) {
		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 <= (-1000000000.0d0)) then
        tmp = t_0
    else if (z <= 1.32d-20) then
        tmp = x + sin(y)
    else if (z <= 3d+56) 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 <= -1000000000.0) {
		tmp = t_0;
	} else if (z <= 1.32e-20) {
		tmp = x + Math.sin(y);
	} else if (z <= 3e+56) {
		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 <= -1000000000.0:
		tmp = t_0
	elif z <= 1.32e-20:
		tmp = x + math.sin(y)
	elif z <= 3e+56:
		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 <= -1000000000.0)
		tmp = t_0;
	elseif (z <= 1.32e-20)
		tmp = Float64(x + sin(y));
	elseif (z <= 3e+56)
		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 <= -1000000000.0)
		tmp = t_0;
	elseif (z <= 1.32e-20)
		tmp = x + sin(y);
	elseif (z <= 3e+56)
		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, -1000000000.0], t$95$0, If[LessEqual[z, 1.32e-20], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+56], N[(x + z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e9 or 3.00000000000000006e56 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 83.4%

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

   if -1e9 < z < 1.32000000000000004e-20

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 94.9%

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

      1. +-commutative 94.9%

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

   4. Simplified 94.9%

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

   if 1.32000000000000004e-20 < z < 3.00000000000000006e56

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.7%

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

      1. +-commutative 83.7%

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

   4. Simplified 83.7%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1000000000:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-20}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+56}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 5: 70.3% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-98}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 0.9:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.4e-98) (+ x z) (if (<= x 0.9) (+ z (+ x y)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e-98) {
		tmp = x + z;
	} else if (x <= 0.9) {
		tmp = z + (x + y);
	} 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 (x <= (-3.4d-98)) then
        tmp = x + z
    else if (x <= 0.9d0) then
        tmp = z + (x + y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e-98) {
		tmp = x + z;
	} else if (x <= 0.9) {
		tmp = z + (x + y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.4e-98:
		tmp = x + z
	elif x <= 0.9:
		tmp = z + (x + y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e-98)
		tmp = Float64(x + z);
	elseif (x <= 0.9)
		tmp = Float64(z + Float64(x + y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.4e-98)
		tmp = x + z;
	elseif (x <= 0.9)
		tmp = z + (x + y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.4e-98], N[(x + z), $MachinePrecision], If[LessEqual[x, 0.9], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4000000000000001e-98 or 0.900000000000000022 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.4%

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

      1. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   if -3.4000000000000001e-98 < x < 0.900000000000000022

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 51.8%

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

      1. +-commutative 51.8%

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

      2. +-commutative 51.8%

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

      3. associate-+l+ 51.8%

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

   4. Simplified 51.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-98}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 0.9:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 6: 44.4% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.75 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-70}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.75e-90) x (if (<= x 7e-70) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.75e-90) {
		tmp = x;
	} else if (x <= 7e-70) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-3.75d-90)) then
        tmp = x
    else if (x <= 7d-70) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.75e-90) {
		tmp = x;
	} else if (x <= 7e-70) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.75e-90:
		tmp = x
	elif x <= 7e-70:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.75e-90)
		tmp = x;
	elseif (x <= 7e-70)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.75e-90)
		tmp = x;
	elseif (x <= 7e-70)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.75e-90], x, If[LessEqual[x, 7e-70], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7499999999999999e-90 or 6.99999999999999949e-70 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 61.6%

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

   if -3.7499999999999999e-90 < x < 6.99999999999999949e-70

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 50.1%

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

      1. +-commutative 50.1%

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

      2. +-commutative 50.1%

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

      3. associate-+l+ 50.1%

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

   4. Simplified 50.1%

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

   5. Taylor expanded in y around inf 16.7%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.75 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-70}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 54.6% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+23}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e+33) x (if (<= x 1.25e+23) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e+33) {
		tmp = x;
	} else if (x <= 1.25e+23) {
		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 <= (-1.5d+33)) then
        tmp = x
    else if (x <= 1.25d+23) 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 <= -1.5e+33) {
		tmp = x;
	} else if (x <= 1.25e+23) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5e+33:
		tmp = x
	elif x <= 1.25e+23:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e+33)
		tmp = x;
	elseif (x <= 1.25e+23)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5e+33)
		tmp = x;
	elseif (x <= 1.25e+23)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e+33], x, If[LessEqual[x, 1.25e+23], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999992e33 or 1.25e23 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 77.4%

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

   if -1.49999999999999992e33 < x < 1.25e23

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 61.9%

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

   3. Taylor expanded in y around 0 37.7%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+23}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 66.7% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 62.1%

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

   1. +-commutative 62.1%

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

4. Simplified 62.1%

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

5. Final simplification 62.1%

   \[\leadsto x + z \]

Alternative 9: 42.5% 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 38.1%

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

3. Final simplification 38.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023290 
(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))))