Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4

Percentage Accurate: 99.9% → 100.0%

Time: 12.4s

Alternatives: 12

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 3, y \cdot 2 + z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma x 3.0 (+ (* y 2.0) z)))

C

double code(double x, double y, double z) {
	return fma(x, 3.0, ((y * 2.0) + z));
}

Julia

function code(x, y, z)
	return fma(x, 3.0, Float64(Float64(y * 2.0) + z))
end

Wolfram

code[x_, y_, z_] := N[(x * 3.0 + N[(N[(y * 2.0), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]
7. Add Preprocessing

Alternative 2: 54.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot y + x\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-163}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-238}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-223}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-26}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+100}:\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* 2.0 y) x)))
   (if (<= y -4.2e+123)
     t_0
     (if (<= y -8.6e-163)
       (* 3.0 x)
       (if (<= y -4.6e-238)
         (+ z x)
         (if (<= y 5.4e-223)
           (* 3.0 x)
           (if (<= y 7.6e-26) (+ z x) (if (<= y 4e+100) (* 3.0 x) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 * y) + x;
	double tmp;
	if (y <= -4.2e+123) {
		tmp = t_0;
	} else if (y <= -8.6e-163) {
		tmp = 3.0 * x;
	} else if (y <= -4.6e-238) {
		tmp = z + x;
	} else if (y <= 5.4e-223) {
		tmp = 3.0 * x;
	} else if (y <= 7.6e-26) {
		tmp = z + x;
	} else if (y <= 4e+100) {
		tmp = 3.0 * 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 = (2.0d0 * y) + x
    if (y <= (-4.2d+123)) then
        tmp = t_0
    else if (y <= (-8.6d-163)) then
        tmp = 3.0d0 * x
    else if (y <= (-4.6d-238)) then
        tmp = z + x
    else if (y <= 5.4d-223) then
        tmp = 3.0d0 * x
    else if (y <= 7.6d-26) then
        tmp = z + x
    else if (y <= 4d+100) then
        tmp = 3.0d0 * 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 = (2.0 * y) + x;
	double tmp;
	if (y <= -4.2e+123) {
		tmp = t_0;
	} else if (y <= -8.6e-163) {
		tmp = 3.0 * x;
	} else if (y <= -4.6e-238) {
		tmp = z + x;
	} else if (y <= 5.4e-223) {
		tmp = 3.0 * x;
	} else if (y <= 7.6e-26) {
		tmp = z + x;
	} else if (y <= 4e+100) {
		tmp = 3.0 * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (2.0 * y) + x
	tmp = 0
	if y <= -4.2e+123:
		tmp = t_0
	elif y <= -8.6e-163:
		tmp = 3.0 * x
	elif y <= -4.6e-238:
		tmp = z + x
	elif y <= 5.4e-223:
		tmp = 3.0 * x
	elif y <= 7.6e-26:
		tmp = z + x
	elif y <= 4e+100:
		tmp = 3.0 * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 * y) + x)
	tmp = 0.0
	if (y <= -4.2e+123)
		tmp = t_0;
	elseif (y <= -8.6e-163)
		tmp = Float64(3.0 * x);
	elseif (y <= -4.6e-238)
		tmp = Float64(z + x);
	elseif (y <= 5.4e-223)
		tmp = Float64(3.0 * x);
	elseif (y <= 7.6e-26)
		tmp = Float64(z + x);
	elseif (y <= 4e+100)
		tmp = Float64(3.0 * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (2.0 * y) + x;
	tmp = 0.0;
	if (y <= -4.2e+123)
		tmp = t_0;
	elseif (y <= -8.6e-163)
		tmp = 3.0 * x;
	elseif (y <= -4.6e-238)
		tmp = z + x;
	elseif (y <= 5.4e-223)
		tmp = 3.0 * x;
	elseif (y <= 7.6e-26)
		tmp = z + x;
	elseif (y <= 4e+100)
		tmp = 3.0 * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 * y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -4.2e+123], t$95$0, If[LessEqual[y, -8.6e-163], N[(3.0 * x), $MachinePrecision], If[LessEqual[y, -4.6e-238], N[(z + x), $MachinePrecision], If[LessEqual[y, 5.4e-223], N[(3.0 * x), $MachinePrecision], If[LessEqual[y, 7.6e-26], N[(z + x), $MachinePrecision], If[LessEqual[y, 4e+100], N[(3.0 * x), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.19999999999999988e123 or 4.00000000000000006e100 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.19999999999999988e123 < y < -8.60000000000000017e-163 or -4.60000000000000009e-238 < y < 5.39999999999999977e-223 or 7.60000000000000029e-26 < y < 4.00000000000000006e100

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -8.60000000000000017e-163 < y < -4.60000000000000009e-238 or 5.39999999999999977e-223 < y < 7.60000000000000029e-26

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 3: 53.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-161}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-240}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-224}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+112}:\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e+123)
   (* 2.0 y)
   (if (<= y -2.7e-161)
     (* 3.0 x)
     (if (<= y -2.2e-240)
       (+ z x)
       (if (<= y 2.7e-224)
         (* 3.0 x)
         (if (<= y 4.5e-27)
           (+ z x)
           (if (<= y 2.7e+112) (* 3.0 x) (* 2.0 y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+123) {
		tmp = 2.0 * y;
	} else if (y <= -2.7e-161) {
		tmp = 3.0 * x;
	} else if (y <= -2.2e-240) {
		tmp = z + x;
	} else if (y <= 2.7e-224) {
		tmp = 3.0 * x;
	} else if (y <= 4.5e-27) {
		tmp = z + x;
	} else if (y <= 2.7e+112) {
		tmp = 3.0 * x;
	} else {
		tmp = 2.0 * 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 (y <= (-4.2d+123)) then
        tmp = 2.0d0 * y
    else if (y <= (-2.7d-161)) then
        tmp = 3.0d0 * x
    else if (y <= (-2.2d-240)) then
        tmp = z + x
    else if (y <= 2.7d-224) then
        tmp = 3.0d0 * x
    else if (y <= 4.5d-27) then
        tmp = z + x
    else if (y <= 2.7d+112) then
        tmp = 3.0d0 * x
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+123) {
		tmp = 2.0 * y;
	} else if (y <= -2.7e-161) {
		tmp = 3.0 * x;
	} else if (y <= -2.2e-240) {
		tmp = z + x;
	} else if (y <= 2.7e-224) {
		tmp = 3.0 * x;
	} else if (y <= 4.5e-27) {
		tmp = z + x;
	} else if (y <= 2.7e+112) {
		tmp = 3.0 * x;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e+123:
		tmp = 2.0 * y
	elif y <= -2.7e-161:
		tmp = 3.0 * x
	elif y <= -2.2e-240:
		tmp = z + x
	elif y <= 2.7e-224:
		tmp = 3.0 * x
	elif y <= 4.5e-27:
		tmp = z + x
	elif y <= 2.7e+112:
		tmp = 3.0 * x
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e+123)
		tmp = Float64(2.0 * y);
	elseif (y <= -2.7e-161)
		tmp = Float64(3.0 * x);
	elseif (y <= -2.2e-240)
		tmp = Float64(z + x);
	elseif (y <= 2.7e-224)
		tmp = Float64(3.0 * x);
	elseif (y <= 4.5e-27)
		tmp = Float64(z + x);
	elseif (y <= 2.7e+112)
		tmp = Float64(3.0 * x);
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e+123)
		tmp = 2.0 * y;
	elseif (y <= -2.7e-161)
		tmp = 3.0 * x;
	elseif (y <= -2.2e-240)
		tmp = z + x;
	elseif (y <= 2.7e-224)
		tmp = 3.0 * x;
	elseif (y <= 4.5e-27)
		tmp = z + x;
	elseif (y <= 2.7e+112)
		tmp = 3.0 * x;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e+123], N[(2.0 * y), $MachinePrecision], If[LessEqual[y, -2.7e-161], N[(3.0 * x), $MachinePrecision], If[LessEqual[y, -2.2e-240], N[(z + x), $MachinePrecision], If[LessEqual[y, 2.7e-224], N[(3.0 * x), $MachinePrecision], If[LessEqual[y, 4.5e-27], N[(z + x), $MachinePrecision], If[LessEqual[y, 2.7e+112], N[(3.0 * x), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.19999999999999988e123 or 2.7000000000000001e112 < y

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -4.19999999999999988e123 < y < -2.6999999999999999e-161 or -2.1999999999999999e-240 < y < 2.69999999999999998e-224 or 4.5000000000000002e-27 < y < 2.7000000000000001e112

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2.6999999999999999e-161 < y < -2.1999999999999999e-240 or 2.69999999999999998e-224 < y < 4.5000000000000002e-27

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 4: 51.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+125}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-162}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-211}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-223}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-22}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+112}:\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.85e+125)
   (* 2.0 y)
   (if (<= y -1.55e-162)
     (* 3.0 x)
     (if (<= y -6e-211)
       z
       (if (<= y 2.2e-223)
         (* 3.0 x)
         (if (<= y 3e-22) z (if (<= y 2.4e+112) (* 3.0 x) (* 2.0 y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.85e+125) {
		tmp = 2.0 * y;
	} else if (y <= -1.55e-162) {
		tmp = 3.0 * x;
	} else if (y <= -6e-211) {
		tmp = z;
	} else if (y <= 2.2e-223) {
		tmp = 3.0 * x;
	} else if (y <= 3e-22) {
		tmp = z;
	} else if (y <= 2.4e+112) {
		tmp = 3.0 * x;
	} else {
		tmp = 2.0 * 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 (y <= (-1.85d+125)) then
        tmp = 2.0d0 * y
    else if (y <= (-1.55d-162)) then
        tmp = 3.0d0 * x
    else if (y <= (-6d-211)) then
        tmp = z
    else if (y <= 2.2d-223) then
        tmp = 3.0d0 * x
    else if (y <= 3d-22) then
        tmp = z
    else if (y <= 2.4d+112) then
        tmp = 3.0d0 * x
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.85e+125) {
		tmp = 2.0 * y;
	} else if (y <= -1.55e-162) {
		tmp = 3.0 * x;
	} else if (y <= -6e-211) {
		tmp = z;
	} else if (y <= 2.2e-223) {
		tmp = 3.0 * x;
	} else if (y <= 3e-22) {
		tmp = z;
	} else if (y <= 2.4e+112) {
		tmp = 3.0 * x;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.85e+125:
		tmp = 2.0 * y
	elif y <= -1.55e-162:
		tmp = 3.0 * x
	elif y <= -6e-211:
		tmp = z
	elif y <= 2.2e-223:
		tmp = 3.0 * x
	elif y <= 3e-22:
		tmp = z
	elif y <= 2.4e+112:
		tmp = 3.0 * x
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.85e+125)
		tmp = Float64(2.0 * y);
	elseif (y <= -1.55e-162)
		tmp = Float64(3.0 * x);
	elseif (y <= -6e-211)
		tmp = z;
	elseif (y <= 2.2e-223)
		tmp = Float64(3.0 * x);
	elseif (y <= 3e-22)
		tmp = z;
	elseif (y <= 2.4e+112)
		tmp = Float64(3.0 * x);
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.85e+125)
		tmp = 2.0 * y;
	elseif (y <= -1.55e-162)
		tmp = 3.0 * x;
	elseif (y <= -6e-211)
		tmp = z;
	elseif (y <= 2.2e-223)
		tmp = 3.0 * x;
	elseif (y <= 3e-22)
		tmp = z;
	elseif (y <= 2.4e+112)
		tmp = 3.0 * x;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.85e+125], N[(2.0 * y), $MachinePrecision], If[LessEqual[y, -1.55e-162], N[(3.0 * x), $MachinePrecision], If[LessEqual[y, -6e-211], z, If[LessEqual[y, 2.2e-223], N[(3.0 * x), $MachinePrecision], If[LessEqual[y, 3e-22], z, If[LessEqual[y, 2.4e+112], N[(3.0 * x), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8499999999999999e125 or 2.4e112 < y

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.8499999999999999e125 < y < -1.5499999999999999e-162 or -6.00000000000000009e-211 < y < 2.20000000000000009e-223 or 2.9999999999999999e-22 < y < 2.4e112

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.5499999999999999e-162 < y < -6.00000000000000009e-211 or 2.20000000000000009e-223 < y < 2.9999999999999999e-22

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 5: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot y + z\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+16}:\\ \;\;\;\;2 \cdot \left(x + y\right) + x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + x\right) + z\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e-23)
   (+ (* 2.0 y) z)
   (if (<= z 2.95e+16) (+ (* 2.0 (+ x y)) x) (+ (+ (+ x x) z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e-23) {
		tmp = (2.0 * y) + z;
	} else if (z <= 2.95e+16) {
		tmp = (2.0 * (x + y)) + x;
	} else {
		tmp = ((x + x) + 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 (z <= (-2d-23)) then
        tmp = (2.0d0 * y) + z
    else if (z <= 2.95d+16) then
        tmp = (2.0d0 * (x + y)) + x
    else
        tmp = ((x + x) + z) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e-23) {
		tmp = (2.0 * y) + z;
	} else if (z <= 2.95e+16) {
		tmp = (2.0 * (x + y)) + x;
	} else {
		tmp = ((x + x) + z) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e-23:
		tmp = (2.0 * y) + z
	elif z <= 2.95e+16:
		tmp = (2.0 * (x + y)) + x
	else:
		tmp = ((x + x) + z) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e-23)
		tmp = Float64(Float64(2.0 * y) + z);
	elseif (z <= 2.95e+16)
		tmp = Float64(Float64(2.0 * Float64(x + y)) + x);
	else
		tmp = Float64(Float64(Float64(x + x) + z) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2e-23)
		tmp = (2.0 * y) + z;
	elseif (z <= 2.95e+16)
		tmp = (2.0 * (x + y)) + x;
	else
		tmp = ((x + x) + z) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e-23], N[(N[(2.0 * y), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[z, 2.95e+16], N[(N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x + x), $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.99999999999999992e-23

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.99999999999999992e-23 < z < 2.95e16

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.95e16 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 6: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-21}:\\ \;\;\;\;2 \cdot y + z\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+17}:\\ \;\;\;\;2 \cdot \left(x + y\right) + x\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.6e-21)
   (+ (* 2.0 y) z)
   (if (<= z 1.42e+17) (+ (* 2.0 (+ x y)) x) (+ (* 3.0 x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.6e-21) {
		tmp = (2.0 * y) + z;
	} else if (z <= 1.42e+17) {
		tmp = (2.0 * (x + y)) + x;
	} else {
		tmp = (3.0 * 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 (z <= (-4.6d-21)) then
        tmp = (2.0d0 * y) + z
    else if (z <= 1.42d+17) then
        tmp = (2.0d0 * (x + y)) + x
    else
        tmp = (3.0d0 * x) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.6e-21) {
		tmp = (2.0 * y) + z;
	} else if (z <= 1.42e+17) {
		tmp = (2.0 * (x + y)) + x;
	} else {
		tmp = (3.0 * x) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.6e-21:
		tmp = (2.0 * y) + z
	elif z <= 1.42e+17:
		tmp = (2.0 * (x + y)) + x
	else:
		tmp = (3.0 * x) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.6e-21)
		tmp = Float64(Float64(2.0 * y) + z);
	elseif (z <= 1.42e+17)
		tmp = Float64(Float64(2.0 * Float64(x + y)) + x);
	else
		tmp = Float64(Float64(3.0 * x) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.6e-21)
		tmp = (2.0 * y) + z;
	elseif (z <= 1.42e+17)
		tmp = (2.0 * (x + y)) + x;
	else
		tmp = (3.0 * x) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.6e-21], N[(N[(2.0 * y), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[z, 1.42e+17], N[(N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(3.0 * x), $MachinePrecision] + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.59999999999999999e-21

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -4.59999999999999999e-21 < z < 1.42e17

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.42e17 < z

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 7: 84.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot y + z\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+124}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+112}:\\ \;\;\;\;3 \cdot x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* 2.0 y) z)))
   (if (<= y -1.5e+124) t_0 (if (<= y 5.5e+112) (+ (* 3.0 x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 * y) + z;
	double tmp;
	if (y <= -1.5e+124) {
		tmp = t_0;
	} else if (y <= 5.5e+112) {
		tmp = (3.0 * 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 = (2.0d0 * y) + z
    if (y <= (-1.5d+124)) then
        tmp = t_0
    else if (y <= 5.5d+112) then
        tmp = (3.0d0 * 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 = (2.0 * y) + z;
	double tmp;
	if (y <= -1.5e+124) {
		tmp = t_0;
	} else if (y <= 5.5e+112) {
		tmp = (3.0 * x) + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (2.0 * y) + z
	tmp = 0
	if y <= -1.5e+124:
		tmp = t_0
	elif y <= 5.5e+112:
		tmp = (3.0 * x) + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 * y) + z)
	tmp = 0.0
	if (y <= -1.5e+124)
		tmp = t_0;
	elseif (y <= 5.5e+112)
		tmp = Float64(Float64(3.0 * x) + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (2.0 * y) + z;
	tmp = 0.0;
	if (y <= -1.5e+124)
		tmp = t_0;
	elseif (y <= 5.5e+112)
		tmp = (3.0 * x) + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 * y), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[y, -1.5e+124], t$95$0, If[LessEqual[y, 5.5e+112], N[(N[(3.0 * x), $MachinePrecision] + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e124 or 5.50000000000000026e112 < y

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.5e124 < y < 5.50000000000000026e112

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 8: 79.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+106}:\\ \;\;\;\;2 \cdot y + z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.7e+60) (* 3.0 x) (if (<= x 2.9e+106) (+ (* 2.0 y) z) (* 3.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.7e+60) {
		tmp = 3.0 * x;
	} else if (x <= 2.9e+106) {
		tmp = (2.0 * y) + z;
	} else {
		tmp = 3.0 * 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 <= (-4.7d+60)) then
        tmp = 3.0d0 * x
    else if (x <= 2.9d+106) then
        tmp = (2.0d0 * y) + z
    else
        tmp = 3.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.7e+60) {
		tmp = 3.0 * x;
	} else if (x <= 2.9e+106) {
		tmp = (2.0 * y) + z;
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.7e+60:
		tmp = 3.0 * x
	elif x <= 2.9e+106:
		tmp = (2.0 * y) + z
	else:
		tmp = 3.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.7e+60)
		tmp = Float64(3.0 * x);
	elseif (x <= 2.9e+106)
		tmp = Float64(Float64(2.0 * y) + z);
	else
		tmp = Float64(3.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.7e+60)
		tmp = 3.0 * x;
	elseif (x <= 2.9e+106)
		tmp = (2.0 * y) + z;
	else
		tmp = 3.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.7e+60], N[(3.0 * x), $MachinePrecision], If[LessEqual[x, 2.9e+106], N[(N[(2.0 * y), $MachinePrecision] + z), $MachinePrecision], N[(3.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6999999999999998e60 or 2.9000000000000002e106 < x

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -4.6999999999999998e60 < x < 2.9000000000000002e106

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 9: 51.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-21}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+16}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.15e-21) z (if (<= z 3.25e+16) (* 2.0 y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e-21) {
		tmp = z;
	} else if (z <= 3.25e+16) {
		tmp = 2.0 * y;
	} else {
		tmp = 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 (z <= (-1.15d-21)) then
        tmp = z
    else if (z <= 3.25d+16) then
        tmp = 2.0d0 * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e-21) {
		tmp = z;
	} else if (z <= 3.25e+16) {
		tmp = 2.0 * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.15e-21:
		tmp = z
	elif z <= 3.25e+16:
		tmp = 2.0 * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.15e-21)
		tmp = z;
	elseif (z <= 3.25e+16)
		tmp = Float64(2.0 * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.15e-21)
		tmp = z;
	elseif (z <= 3.25e+16)
		tmp = 2.0 * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.15e-21], z, If[LessEqual[z, 3.25e+16], N[(2.0 * y), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e-21 or 3.25e16 < z

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.15e-21 < z < 3.25e16

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 10: 99.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ z + \left(y \cdot 2 + x \cdot 3\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z (+ (* y 2.0) (* x 3.0))))

C

double code(double x, double y, double z) {
	return z + ((y * 2.0) + (x * 3.0));
}

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 + ((y * 2.0d0) + (x * 3.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return z + ((y * 2.0) + (x * 3.0));
}

Python

def code(x, y, z):
	return z + ((y * 2.0) + (x * 3.0))

Julia

function code(x, y, z)
	return Float64(z + Float64(Float64(y * 2.0) + Float64(x * 3.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + ((y * 2.0) + (x * 3.0));
end

Wolfram

code[x_, y_, z_] := N[(z + N[(N[(y * 2.0), $MachinePrecision] + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing
5. Add Preprocessing

Alternative 11: 33.8% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in z around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Alternative 12: 8.0% accurate, 11.0× 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%

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

3. Taylor expanded in z around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in z around 0 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  :precision binary64
  (+ (+ (+ (+ (+ x y) y) x) z) x))