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

Percentage Accurate: 99.9% → 99.9%

Time: 13.8s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 82.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+161}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+25}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-21}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+17}:\\ \;\;\;\;\sin y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -3.1e+161)
     t_0
     (if (<= z -2.4e+25)
       (+ z x)
       (if (<= z -4.8e-21) t_0 (if (<= z 1.2e+17) (+ (sin y) x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -3.1e+161) {
		tmp = t_0;
	} else if (z <= -2.4e+25) {
		tmp = z + x;
	} else if (z <= -4.8e-21) {
		tmp = t_0;
	} else if (z <= 1.2e+17) {
		tmp = sin(y) + 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 <= (-3.1d+161)) then
        tmp = t_0
    else if (z <= (-2.4d+25)) then
        tmp = z + x
    else if (z <= (-4.8d-21)) then
        tmp = t_0
    else if (z <= 1.2d+17) then
        tmp = sin(y) + 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 <= -3.1e+161) {
		tmp = t_0;
	} else if (z <= -2.4e+25) {
		tmp = z + x;
	} else if (z <= -4.8e-21) {
		tmp = t_0;
	} else if (z <= 1.2e+17) {
		tmp = Math.sin(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -3.1e+161:
		tmp = t_0
	elif z <= -2.4e+25:
		tmp = z + x
	elif z <= -4.8e-21:
		tmp = t_0
	elif z <= 1.2e+17:
		tmp = math.sin(y) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -3.1e+161)
		tmp = t_0;
	elseif (z <= -2.4e+25)
		tmp = Float64(z + x);
	elseif (z <= -4.8e-21)
		tmp = t_0;
	elseif (z <= 1.2e+17)
		tmp = Float64(sin(y) + 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 <= -3.1e+161)
		tmp = t_0;
	elseif (z <= -2.4e+25)
		tmp = z + x;
	elseif (z <= -4.8e-21)
		tmp = t_0;
	elseif (z <= 1.2e+17)
		tmp = sin(y) + 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, -3.1e+161], t$95$0, If[LessEqual[z, -2.4e+25], N[(z + x), $MachinePrecision], If[LessEqual[z, -4.8e-21], t$95$0, If[LessEqual[z, 1.2e+17], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000007e161 or -2.39999999999999996e25 < z < -4.7999999999999999e-21 or 1.2e17 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.10000000000000007e161 < z < -2.39999999999999996e25

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.7999999999999999e-21 < z < 1.2e17

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 72.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+161}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-236}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-136}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+196}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.8e+161)
     t_0
     (if (<= z -9e-236)
       (+ z x)
       (if (<= z 2.45e-136) (+ z (+ y x)) (if (<= z 5.8e+196) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.8e+161) {
		tmp = t_0;
	} else if (z <= -9e-236) {
		tmp = z + x;
	} else if (z <= 2.45e-136) {
		tmp = z + (y + x);
	} else if (z <= 5.8e+196) {
		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 <= (-1.8d+161)) then
        tmp = t_0
    else if (z <= (-9d-236)) then
        tmp = z + x
    else if (z <= 2.45d-136) then
        tmp = z + (y + x)
    else if (z <= 5.8d+196) 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 <= -1.8e+161) {
		tmp = t_0;
	} else if (z <= -9e-236) {
		tmp = z + x;
	} else if (z <= 2.45e-136) {
		tmp = z + (y + x);
	} else if (z <= 5.8e+196) {
		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 <= -1.8e+161:
		tmp = t_0
	elif z <= -9e-236:
		tmp = z + x
	elif z <= 2.45e-136:
		tmp = z + (y + x)
	elif z <= 5.8e+196:
		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 <= -1.8e+161)
		tmp = t_0;
	elseif (z <= -9e-236)
		tmp = Float64(z + x);
	elseif (z <= 2.45e-136)
		tmp = Float64(z + Float64(y + x));
	elseif (z <= 5.8e+196)
		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 <= -1.8e+161)
		tmp = t_0;
	elseif (z <= -9e-236)
		tmp = z + x;
	elseif (z <= 2.45e-136)
		tmp = z + (y + x);
	elseif (z <= 5.8e+196)
		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, -1.8e+161], t$95$0, If[LessEqual[z, -9e-236], N[(z + x), $MachinePrecision], If[LessEqual[z, 2.45e-136], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+196], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999992e161 or 5.8e196 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.79999999999999992e161 < z < -8.99999999999999997e-236 or 2.45e-136 < z < 5.8e196

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -8.99999999999999997e-236 < z < 2.45e-136

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 95.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + z \cdot \cos y\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-24}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.017:\\ \;\;\;\;\sin y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* z (cos y)))))
   (if (<= z -1.15e-24) t_0 (if (<= z 0.017) (+ (sin y) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (z * cos(y));
	double tmp;
	if (z <= -1.15e-24) {
		tmp = t_0;
	} else if (z <= 0.017) {
		tmp = sin(y) + 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 = x + (z * cos(y))
    if (z <= (-1.15d-24)) then
        tmp = t_0
    else if (z <= 0.017d0) then
        tmp = sin(y) + 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 = x + (z * Math.cos(y));
	double tmp;
	if (z <= -1.15e-24) {
		tmp = t_0;
	} else if (z <= 0.017) {
		tmp = Math.sin(y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (z * math.cos(y))
	tmp = 0
	if z <= -1.15e-24:
		tmp = t_0
	elif z <= 0.017:
		tmp = math.sin(y) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(z * cos(y)))
	tmp = 0.0
	if (z <= -1.15e-24)
		tmp = t_0;
	elseif (z <= 0.017)
		tmp = Float64(sin(y) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (z * cos(y));
	tmp = 0.0;
	if (z <= -1.15e-24)
		tmp = t_0;
	elseif (z <= 0.017)
		tmp = sin(y) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e-24], t$95$0, If[LessEqual[z, 0.017], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1500000000000001e-24 or 0.017000000000000001 < 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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.1500000000000001e-24 < z < 0.017000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 70.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+236}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+32}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 1800000000000:\\ \;\;\;\;\left(x + \left(y + z\right)\right) + \left(y \cdot -0.16666666666666666 + z \cdot -0.5\right) \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.2e+236)
   (sin y)
   (if (<= y -2.4e+32)
     (+ z x)
     (if (<= y 1800000000000.0)
       (+ (+ x (+ y z)) (* (+ (* y -0.16666666666666666) (* z -0.5)) (* y y)))
       (+ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+236) {
		tmp = sin(y);
	} else if (y <= -2.4e+32) {
		tmp = z + x;
	} else if (y <= 1800000000000.0) {
		tmp = (x + (y + z)) + (((y * -0.16666666666666666) + (z * -0.5)) * (y * 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 <= (-1.2d+236)) then
        tmp = sin(y)
    else if (y <= (-2.4d+32)) then
        tmp = z + x
    else if (y <= 1800000000000.0d0) then
        tmp = (x + (y + z)) + (((y * (-0.16666666666666666d0)) + (z * (-0.5d0))) * (y * 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 <= -1.2e+236) {
		tmp = Math.sin(y);
	} else if (y <= -2.4e+32) {
		tmp = z + x;
	} else if (y <= 1800000000000.0) {
		tmp = (x + (y + z)) + (((y * -0.16666666666666666) + (z * -0.5)) * (y * y));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.2e+236:
		tmp = math.sin(y)
	elif y <= -2.4e+32:
		tmp = z + x
	elif y <= 1800000000000.0:
		tmp = (x + (y + z)) + (((y * -0.16666666666666666) + (z * -0.5)) * (y * y))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2e+236)
		tmp = sin(y);
	elseif (y <= -2.4e+32)
		tmp = Float64(z + x);
	elseif (y <= 1800000000000.0)
		tmp = Float64(Float64(x + Float64(y + z)) + Float64(Float64(Float64(y * -0.16666666666666666) + Float64(z * -0.5)) * Float64(y * y)));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.2e+236)
		tmp = sin(y);
	elseif (y <= -2.4e+32)
		tmp = z + x;
	elseif (y <= 1800000000000.0)
		tmp = (x + (y + z)) + (((y * -0.16666666666666666) + (z * -0.5)) * (y * y));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.2e+236], N[Sin[y], $MachinePrecision], If[LessEqual[y, -2.4e+32], N[(z + x), $MachinePrecision], If[LessEqual[y, 1800000000000.0], N[(N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * -0.16666666666666666), $MachinePrecision] + N[(z * -0.5), $MachinePrecision]), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.20000000000000006e236

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.20000000000000006e236 < y < -2.39999999999999991e32 or 1.8e12 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.39999999999999991e32 < y < 1.8e12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 70.9% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+31}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 10000000:\\ \;\;\;\;\left(x + \left(y + z\right)\right) + \left(y \cdot -0.16666666666666666 + z \cdot -0.5\right) \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+31)
   (+ z x)
   (if (<= y 10000000.0)
     (+ (+ x (+ y z)) (* (+ (* y -0.16666666666666666) (* z -0.5)) (* y y)))
     (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+31) {
		tmp = z + x;
	} else if (y <= 10000000.0) {
		tmp = (x + (y + z)) + (((y * -0.16666666666666666) + (z * -0.5)) * (y * 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 <= (-2.8d+31)) then
        tmp = z + x
    else if (y <= 10000000.0d0) then
        tmp = (x + (y + z)) + (((y * (-0.16666666666666666d0)) + (z * (-0.5d0))) * (y * 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 <= -2.8e+31) {
		tmp = z + x;
	} else if (y <= 10000000.0) {
		tmp = (x + (y + z)) + (((y * -0.16666666666666666) + (z * -0.5)) * (y * y));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+31:
		tmp = z + x
	elif y <= 10000000.0:
		tmp = (x + (y + z)) + (((y * -0.16666666666666666) + (z * -0.5)) * (y * y))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+31)
		tmp = Float64(z + x);
	elseif (y <= 10000000.0)
		tmp = Float64(Float64(x + Float64(y + z)) + Float64(Float64(Float64(y * -0.16666666666666666) + Float64(z * -0.5)) * Float64(y * y)));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e+31)
		tmp = z + x;
	elseif (y <= 10000000.0)
		tmp = (x + (y + z)) + (((y * -0.16666666666666666) + (z * -0.5)) * (y * y));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+31], N[(z + x), $MachinePrecision], If[LessEqual[y, 10000000.0], N[(N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * -0.16666666666666666), $MachinePrecision] + N[(z * -0.5), $MachinePrecision]), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.80000000000000017e31 or 1e7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.80000000000000017e31 < y < 1e7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 70.9% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+31}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 4600000:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+31)
   (+ z x)
   (if (<= y 4600000.0)
     (+ x (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))
     (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+31) {
		tmp = z + x;
	} else if (y <= 4600000.0) {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	} 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 <= (-2.8d+31)) then
        tmp = z + x
    else if (y <= 4600000.0d0) then
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    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 <= -2.8e+31) {
		tmp = z + x;
	} else if (y <= 4600000.0) {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+31:
		tmp = z + x
	elif y <= 4600000.0:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+31)
		tmp = Float64(z + x);
	elseif (y <= 4600000.0)
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e+31)
		tmp = z + x;
	elseif (y <= 4600000.0)
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+31], N[(z + x), $MachinePrecision], If[LessEqual[y, 4600000.0], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.80000000000000017e31 or 4.6e6 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.80000000000000017e31 < y < 4.6e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 70.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+40}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 260000000000:\\ \;\;\;\;y + \left(x + z \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+40)
   (+ z x)
   (if (<= y 260000000000.0)
     (+ y (+ x (* z (+ 1.0 (* -0.5 (* y y))))))
     (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+40) {
		tmp = z + x;
	} else if (y <= 260000000000.0) {
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * 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 <= (-3.4d+40)) then
        tmp = z + x
    else if (y <= 260000000000.0d0) then
        tmp = y + (x + (z * (1.0d0 + ((-0.5d0) * (y * 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 <= -3.4e+40) {
		tmp = z + x;
	} else if (y <= 260000000000.0) {
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * y)))));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.4e+40:
		tmp = z + x
	elif y <= 260000000000.0:
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * y)))))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+40)
		tmp = Float64(z + x);
	elseif (y <= 260000000000.0)
		tmp = Float64(y + Float64(x + Float64(z * Float64(1.0 + Float64(-0.5 * Float64(y * y))))));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e+40)
		tmp = z + x;
	elseif (y <= 260000000000.0)
		tmp = y + (x + (z * (1.0 + (-0.5 * (y * y)))));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.4e+40], N[(z + x), $MachinePrecision], If[LessEqual[y, 260000000000.0], N[(y + N[(x + N[(z * N[(1.0 + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999989e40 or 2.6e11 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.39999999999999989e40 < y < 2.6e11

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 70.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+31}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 62:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.8e+31)
   (+ z x)
   (if (<= y 62.0)
     (+ x (+ z (* y (+ 1.0 (* y (* y -0.16666666666666666))))))
     (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.8e+31) {
		tmp = z + x;
	} else if (y <= 62.0) {
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	} 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 <= (-7.8d+31)) then
        tmp = z + x
    else if (y <= 62.0d0) then
        tmp = x + (z + (y * (1.0d0 + (y * (y * (-0.16666666666666666d0))))))
    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 <= -7.8e+31) {
		tmp = z + x;
	} else if (y <= 62.0) {
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.8e+31:
		tmp = z + x
	elif y <= 62.0:
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.8e+31)
		tmp = Float64(z + x);
	elseif (y <= 62.0)
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(y * -0.16666666666666666))))));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.8e+31)
		tmp = z + x;
	elseif (y <= 62.0)
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.8e+31], N[(z + x), $MachinePrecision], If[LessEqual[y, 62.0], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.79999999999999999e31 or 62 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -7.79999999999999999e31 < y < 62

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 54.6% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-179}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-90}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 0.44:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.9e-52)
   x
   (if (<= x 3.2e-179) z (if (<= x 8.2e-90) (+ y x) (if (<= x 0.44) z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.9e-52) {
		tmp = x;
	} else if (x <= 3.2e-179) {
		tmp = z;
	} else if (x <= 8.2e-90) {
		tmp = y + x;
	} else if (x <= 0.44) {
		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 <= (-4.9d-52)) then
        tmp = x
    else if (x <= 3.2d-179) then
        tmp = z
    else if (x <= 8.2d-90) then
        tmp = y + x
    else if (x <= 0.44d0) 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 <= -4.9e-52) {
		tmp = x;
	} else if (x <= 3.2e-179) {
		tmp = z;
	} else if (x <= 8.2e-90) {
		tmp = y + x;
	} else if (x <= 0.44) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.9e-52:
		tmp = x
	elif x <= 3.2e-179:
		tmp = z
	elif x <= 8.2e-90:
		tmp = y + x
	elif x <= 0.44:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.9e-52)
		tmp = x;
	elseif (x <= 3.2e-179)
		tmp = z;
	elseif (x <= 8.2e-90)
		tmp = Float64(y + x);
	elseif (x <= 0.44)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.9e-52)
		tmp = x;
	elseif (x <= 3.2e-179)
		tmp = z;
	elseif (x <= 8.2e-90)
		tmp = y + x;
	elseif (x <= 0.44)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.9e-52], x, If[LessEqual[x, 3.2e-179], z, If[LessEqual[x, 8.2e-90], N[(y + x), $MachinePrecision], If[LessEqual[x, 0.44], z, x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.90000000000000019e-52 or 0.440000000000000002 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.90000000000000019e-52 < x < 3.2000000000000001e-179 or 8.2000000000000007e-90 < x < 0.440000000000000002

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 3.2000000000000001e-179 < x < 8.2000000000000007e-90

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 70.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -60:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-14}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -60.0) (+ z x) (if (<= y 8.2e-14) (+ z (+ y x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -60.0) {
		tmp = z + x;
	} else if (y <= 8.2e-14) {
		tmp = z + (y + 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 (y <= (-60.0d0)) then
        tmp = z + x
    else if (y <= 8.2d-14) then
        tmp = z + (y + 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 (y <= -60.0) {
		tmp = z + x;
	} else if (y <= 8.2e-14) {
		tmp = z + (y + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -60.0:
		tmp = z + x
	elif y <= 8.2e-14:
		tmp = z + (y + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -60.0)
		tmp = Float64(z + x);
	elseif (y <= 8.2e-14)
		tmp = Float64(z + Float64(y + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -60.0)
		tmp = z + x;
	elseif (y <= 8.2e-14)
		tmp = z + (y + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -60.0], N[(z + x), $MachinePrecision], If[LessEqual[y, 8.2e-14], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -60 or 8.2000000000000004e-14 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -60 < y < 8.2000000000000004e-14

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 68.6% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-139}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-93}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4e-139) (+ z x) (if (<= x 4.5e-93) (+ z y) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4e-139) {
		tmp = z + x;
	} else if (x <= 4.5e-93) {
		tmp = z + 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 (x <= (-4d-139)) then
        tmp = z + x
    else if (x <= 4.5d-93) then
        tmp = z + 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 (x <= -4e-139) {
		tmp = z + x;
	} else if (x <= 4.5e-93) {
		tmp = z + y;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4e-139:
		tmp = z + x
	elif x <= 4.5e-93:
		tmp = z + y
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4e-139)
		tmp = Float64(z + x);
	elseif (x <= 4.5e-93)
		tmp = Float64(z + y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4e-139)
		tmp = z + x;
	elseif (x <= 4.5e-93)
		tmp = z + y;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4e-139], N[(z + x), $MachinePrecision], If[LessEqual[x, 4.5e-93], N[(z + y), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000012e-139 or 4.5000000000000002e-93 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.00000000000000012e-139 < x < 4.5000000000000002e-93

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 55.9% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.29:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e-52) x (if (<= x 0.29) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e-52) {
		tmp = x;
	} else if (x <= 0.29) {
		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 <= (-3.2d-52)) then
        tmp = x
    else if (x <= 0.29d0) 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 <= -3.2e-52) {
		tmp = x;
	} else if (x <= 0.29) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.2e-52:
		tmp = x
	elif x <= 0.29:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e-52)
		tmp = x;
	elseif (x <= 0.29)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.2e-52)
		tmp = x;
	elseif (x <= 0.29)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e-52], x, If[LessEqual[x, 0.29], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2000000000000001e-52 or 0.28999999999999998 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.2000000000000001e-52 < x < 0.28999999999999998

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 45.0% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-93}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.4e-134) x (if (<= x 6e-93) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.4e-134) {
		tmp = x;
	} else if (x <= 6e-93) {
		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 <= (-4.4d-134)) then
        tmp = x
    else if (x <= 6d-93) 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 <= -4.4e-134) {
		tmp = x;
	} else if (x <= 6e-93) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.4e-134:
		tmp = x
	elif x <= 6e-93:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.4e-134)
		tmp = x;
	elseif (x <= 6e-93)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.4e-134)
		tmp = x;
	elseif (x <= 6e-93)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.4e-134], x, If[LessEqual[x, 6e-93], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3999999999999999e-134 or 6.0000000000000003e-93 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.3999999999999999e-134 < x < 6.0000000000000003e-93

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 67.1% 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. Add Preprocessing

3. Taylor expanded in y around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 16: 43.2% 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. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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))))