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

Percentage Accurate: 99.9% → 99.9%

Time: 8.0s

Alternatives: 8

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: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (2.0 * (x + y)) + (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 = (2.0d0 * (x + y)) + (x + z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

   5. +-commutative 99.9%

      \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

   6. +-commutative 99.9%

      \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
4. Add Preprocessing

5. Final simplification 99.9%

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

Alternative 2: 51.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+131}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-178}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-241}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-191}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-129}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-44}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 0.078:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+26}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.95e+131)
   (* x 3.0)
   (if (<= x -1.1e-178)
     (* 2.0 y)
     (if (<= x 2.15e-241)
       z
       (if (<= x 3.2e-191)
         (* 2.0 y)
         (if (<= x 8.2e-129)
           z
           (if (<= x 2.9e-44)
             (* 2.0 y)
             (if (<= x 0.078) z (if (<= x 3.5e+26) (* 2.0 y) (* x 3.0))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e+131) {
		tmp = x * 3.0;
	} else if (x <= -1.1e-178) {
		tmp = 2.0 * y;
	} else if (x <= 2.15e-241) {
		tmp = z;
	} else if (x <= 3.2e-191) {
		tmp = 2.0 * y;
	} else if (x <= 8.2e-129) {
		tmp = z;
	} else if (x <= 2.9e-44) {
		tmp = 2.0 * y;
	} else if (x <= 0.078) {
		tmp = z;
	} else if (x <= 3.5e+26) {
		tmp = 2.0 * y;
	} else {
		tmp = x * 3.0;
	}
	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) :: tmp
    if (x <= (-1.95d+131)) then
        tmp = x * 3.0d0
    else if (x <= (-1.1d-178)) then
        tmp = 2.0d0 * y
    else if (x <= 2.15d-241) then
        tmp = z
    else if (x <= 3.2d-191) then
        tmp = 2.0d0 * y
    else if (x <= 8.2d-129) then
        tmp = z
    else if (x <= 2.9d-44) then
        tmp = 2.0d0 * y
    else if (x <= 0.078d0) then
        tmp = z
    else if (x <= 3.5d+26) then
        tmp = 2.0d0 * y
    else
        tmp = x * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e+131) {
		tmp = x * 3.0;
	} else if (x <= -1.1e-178) {
		tmp = 2.0 * y;
	} else if (x <= 2.15e-241) {
		tmp = z;
	} else if (x <= 3.2e-191) {
		tmp = 2.0 * y;
	} else if (x <= 8.2e-129) {
		tmp = z;
	} else if (x <= 2.9e-44) {
		tmp = 2.0 * y;
	} else if (x <= 0.078) {
		tmp = z;
	} else if (x <= 3.5e+26) {
		tmp = 2.0 * y;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.95e+131:
		tmp = x * 3.0
	elif x <= -1.1e-178:
		tmp = 2.0 * y
	elif x <= 2.15e-241:
		tmp = z
	elif x <= 3.2e-191:
		tmp = 2.0 * y
	elif x <= 8.2e-129:
		tmp = z
	elif x <= 2.9e-44:
		tmp = 2.0 * y
	elif x <= 0.078:
		tmp = z
	elif x <= 3.5e+26:
		tmp = 2.0 * y
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.95e+131)
		tmp = Float64(x * 3.0);
	elseif (x <= -1.1e-178)
		tmp = Float64(2.0 * y);
	elseif (x <= 2.15e-241)
		tmp = z;
	elseif (x <= 3.2e-191)
		tmp = Float64(2.0 * y);
	elseif (x <= 8.2e-129)
		tmp = z;
	elseif (x <= 2.9e-44)
		tmp = Float64(2.0 * y);
	elseif (x <= 0.078)
		tmp = z;
	elseif (x <= 3.5e+26)
		tmp = Float64(2.0 * y);
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.95e+131)
		tmp = x * 3.0;
	elseif (x <= -1.1e-178)
		tmp = 2.0 * y;
	elseif (x <= 2.15e-241)
		tmp = z;
	elseif (x <= 3.2e-191)
		tmp = 2.0 * y;
	elseif (x <= 8.2e-129)
		tmp = z;
	elseif (x <= 2.9e-44)
		tmp = 2.0 * y;
	elseif (x <= 0.078)
		tmp = z;
	elseif (x <= 3.5e+26)
		tmp = 2.0 * y;
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.95e+131], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, -1.1e-178], N[(2.0 * y), $MachinePrecision], If[LessEqual[x, 2.15e-241], z, If[LessEqual[x, 3.2e-191], N[(2.0 * y), $MachinePrecision], If[LessEqual[x, 8.2e-129], z, If[LessEqual[x, 2.9e-44], N[(2.0 * y), $MachinePrecision], If[LessEqual[x, 0.078], z, If[LessEqual[x, 3.5e+26], N[(2.0 * y), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.95e131 or 3.4999999999999999e26 < x

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 99.9%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 99.9%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.4%

      \[\leadsto \color{blue}{3 \cdot x} \]

   if -1.95e131 < x < -1.1000000000000001e-178 or 2.1499999999999999e-241 < x < 3.2000000000000003e-191 or 8.1999999999999999e-129 < x < 2.9000000000000001e-44 or 0.0779999999999999999 < x < 3.4999999999999999e26

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 100.0%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 100.0%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.9%

      \[\leadsto \color{blue}{2 \cdot y} \]

   if -1.1000000000000001e-178 < x < 2.1499999999999999e-241 or 3.2000000000000003e-191 < x < 8.1999999999999999e-129 or 2.9000000000000001e-44 < x < 0.0779999999999999999

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 100.0%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 100.0%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.7%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+131}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-178}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-241}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-191}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-129}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-44}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 0.078:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+26}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \left(z + 2 \cdot x\right)\\ t_1 := z - y \cdot -2\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+151}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-54}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (+ z (* 2.0 x)))) (t_1 (- z (* y -2.0))))
   (if (<= x -3.9e+151)
     t_0
     (if (<= x -3.8e+78)
       t_1
       (if (<= x -3.3e-54)
         (+ x (* 2.0 (+ x y)))
         (if (<= x 3.5e+17) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (z + (2.0 * x));
	double t_1 = z - (y * -2.0);
	double tmp;
	if (x <= -3.9e+151) {
		tmp = t_0;
	} else if (x <= -3.8e+78) {
		tmp = t_1;
	} else if (x <= -3.3e-54) {
		tmp = x + (2.0 * (x + y));
	} else if (x <= 3.5e+17) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x + (z + (2.0d0 * x))
    t_1 = z - (y * (-2.0d0))
    if (x <= (-3.9d+151)) then
        tmp = t_0
    else if (x <= (-3.8d+78)) then
        tmp = t_1
    else if (x <= (-3.3d-54)) then
        tmp = x + (2.0d0 * (x + y))
    else if (x <= 3.5d+17) then
        tmp = t_1
    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 + (2.0 * x));
	double t_1 = z - (y * -2.0);
	double tmp;
	if (x <= -3.9e+151) {
		tmp = t_0;
	} else if (x <= -3.8e+78) {
		tmp = t_1;
	} else if (x <= -3.3e-54) {
		tmp = x + (2.0 * (x + y));
	} else if (x <= 3.5e+17) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (z + (2.0 * x))
	t_1 = z - (y * -2.0)
	tmp = 0
	if x <= -3.9e+151:
		tmp = t_0
	elif x <= -3.8e+78:
		tmp = t_1
	elif x <= -3.3e-54:
		tmp = x + (2.0 * (x + y))
	elif x <= 3.5e+17:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(z + Float64(2.0 * x)))
	t_1 = Float64(z - Float64(y * -2.0))
	tmp = 0.0
	if (x <= -3.9e+151)
		tmp = t_0;
	elseif (x <= -3.8e+78)
		tmp = t_1;
	elseif (x <= -3.3e-54)
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	elseif (x <= 3.5e+17)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (z + (2.0 * x));
	t_1 = z - (y * -2.0);
	tmp = 0.0;
	if (x <= -3.9e+151)
		tmp = t_0;
	elseif (x <= -3.8e+78)
		tmp = t_1;
	elseif (x <= -3.3e-54)
		tmp = x + (2.0 * (x + y));
	elseif (x <= 3.5e+17)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(z + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z - N[(y * -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e+151], t$95$0, If[LessEqual[x, -3.8e+78], t$95$1, If[LessEqual[x, -3.3e-54], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+17], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.89999999999999976e151 or 3.5e17 < x

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 99.9%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 99.9%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 91.5%

      \[\leadsto \color{blue}{x + \left(z + 2 \cdot x\right)} \]

   if -3.89999999999999976e151 < x < -3.7999999999999999e78 or -3.29999999999999993e-54 < x < 3.5e17

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 100.0%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 100.0%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 94.1%

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   6. Step-by-step derivation

      1. metadata-eval 94.1%

         \[\leadsto z + \color{blue}{\left(--2\right)} \cdot y \]

      2. cancel-sign-sub-inv 94.1%

         \[\leadsto \color{blue}{z - -2 \cdot y} \]

      3. *-commutative 94.1%

         \[\leadsto z - \color{blue}{y \cdot -2} \]

   7. Simplified 94.1%

      \[\leadsto \color{blue}{z - y \cdot -2} \]

   if -3.7999999999999999e78 < x < -3.29999999999999993e-54

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 99.8%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 99.8%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 94.5%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+151}:\\ \;\;\;\;x + \left(z + 2 \cdot x\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+78}:\\ \;\;\;\;z - y \cdot -2\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-54}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;z - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z - x \cdot -3\\ t_1 := z - y \cdot -2\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+151}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-53}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- z (* x -3.0))) (t_1 (- z (* y -2.0))))
   (if (<= x -4.2e+151)
     t_0
     (if (<= x -1.6e+78)
       t_1
       (if (<= x -1.85e-53)
         (+ x (* 2.0 (+ x y)))
         (if (<= x 1.95e+26) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z - (x * -3.0);
	double t_1 = z - (y * -2.0);
	double tmp;
	if (x <= -4.2e+151) {
		tmp = t_0;
	} else if (x <= -1.6e+78) {
		tmp = t_1;
	} else if (x <= -1.85e-53) {
		tmp = x + (2.0 * (x + y));
	} else if (x <= 1.95e+26) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z - (x * (-3.0d0))
    t_1 = z - (y * (-2.0d0))
    if (x <= (-4.2d+151)) then
        tmp = t_0
    else if (x <= (-1.6d+78)) then
        tmp = t_1
    else if (x <= (-1.85d-53)) then
        tmp = x + (2.0d0 * (x + y))
    else if (x <= 1.95d+26) then
        tmp = t_1
    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 - (x * -3.0);
	double t_1 = z - (y * -2.0);
	double tmp;
	if (x <= -4.2e+151) {
		tmp = t_0;
	} else if (x <= -1.6e+78) {
		tmp = t_1;
	} else if (x <= -1.85e-53) {
		tmp = x + (2.0 * (x + y));
	} else if (x <= 1.95e+26) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z - (x * -3.0)
	t_1 = z - (y * -2.0)
	tmp = 0
	if x <= -4.2e+151:
		tmp = t_0
	elif x <= -1.6e+78:
		tmp = t_1
	elif x <= -1.85e-53:
		tmp = x + (2.0 * (x + y))
	elif x <= 1.95e+26:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z - Float64(x * -3.0))
	t_1 = Float64(z - Float64(y * -2.0))
	tmp = 0.0
	if (x <= -4.2e+151)
		tmp = t_0;
	elseif (x <= -1.6e+78)
		tmp = t_1;
	elseif (x <= -1.85e-53)
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	elseif (x <= 1.95e+26)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z - (x * -3.0);
	t_1 = z - (y * -2.0);
	tmp = 0.0;
	if (x <= -4.2e+151)
		tmp = t_0;
	elseif (x <= -1.6e+78)
		tmp = t_1;
	elseif (x <= -1.85e-53)
		tmp = x + (2.0 * (x + y));
	elseif (x <= 1.95e+26)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z - N[(y * -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+151], t$95$0, If[LessEqual[x, -1.6e+78], t$95$1, If[LessEqual[x, -1.85e-53], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e+26], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2000000000000001e151 or 1.95e26 < x

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. remove-double-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-+r+ 99.8%

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

      9. associate-+r+ 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. distribute-neg-out 99.8%

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

      12. neg-mul-1 99.8%

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

      13. count-2 99.8%

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

      14. distribute-lft-neg-in 99.8%

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

      15. metadata-eval 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-rgt-out 99.8%

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

      18. distribute-neg-out 99.8%

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

      19. fma-define 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{z - \mathsf{fma}\left(x, -3, y \cdot -2\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 91.4%

      \[\leadsto \color{blue}{z - -3 \cdot x} \]

   if -4.2000000000000001e151 < x < -1.59999999999999997e78 or -1.84999999999999991e-53 < x < 1.95e26

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 100.0%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 100.0%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 94.1%

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   6. Step-by-step derivation

      1. metadata-eval 94.1%

         \[\leadsto z + \color{blue}{\left(--2\right)} \cdot y \]

      2. cancel-sign-sub-inv 94.1%

         \[\leadsto \color{blue}{z - -2 \cdot y} \]

      3. *-commutative 94.1%

         \[\leadsto z - \color{blue}{y \cdot -2} \]

   7. Simplified 94.1%

      \[\leadsto \color{blue}{z - y \cdot -2} \]

   if -1.59999999999999997e78 < x < -1.84999999999999991e-53

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 99.8%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 99.8%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 94.5%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+151}:\\ \;\;\;\;z - x \cdot -3\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+78}:\\ \;\;\;\;z - y \cdot -2\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-53}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+26}:\\ \;\;\;\;z - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+82} \lor \neg \left(y \leq 1.45 \cdot 10^{+133}\right):\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e+82) (not (<= y 1.45e+133))) (* 2.0 y) (- z (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+82) || !(y <= 1.45e+133)) {
		tmp = 2.0 * y;
	} else {
		tmp = z - (x * -3.0);
	}
	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) :: tmp
    if ((y <= (-1.8d+82)) .or. (.not. (y <= 1.45d+133))) then
        tmp = 2.0d0 * y
    else
        tmp = z - (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+82) || !(y <= 1.45e+133)) {
		tmp = 2.0 * y;
	} else {
		tmp = z - (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e+82) or not (y <= 1.45e+133):
		tmp = 2.0 * y
	else:
		tmp = z - (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e+82) || !(y <= 1.45e+133))
		tmp = Float64(2.0 * y);
	else
		tmp = Float64(z - Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.8e+82) || ~((y <= 1.45e+133)))
		tmp = 2.0 * y;
	else
		tmp = z - (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e+82], N[Not[LessEqual[y, 1.45e+133]], $MachinePrecision]], N[(2.0 * y), $MachinePrecision], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.80000000000000007e82 or 1.4500000000000001e133 < y

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 100.0%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 100.0%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.8%

      \[\leadsto \color{blue}{2 \cdot y} \]

   if -1.80000000000000007e82 < y < 1.4500000000000001e133

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. remove-double-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+r+ 99.9%

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

      9. associate-+r+ 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. distribute-neg-out 99.8%

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

      12. neg-mul-1 99.8%

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

      13. count-2 99.8%

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

      14. distribute-lft-neg-in 99.8%

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

      15. metadata-eval 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-rgt-out 99.8%

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

      18. distribute-neg-out 99.8%

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

      19. fma-define 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z - \mathsf{fma}\left(x, -3, y \cdot -2\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 83.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+82} \lor \neg \left(y \leq 1.45 \cdot 10^{+133}\right):\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+151} \lor \neg \left(x \leq 5.8 \cdot 10^{+19}\right):\\ \;\;\;\;z - x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.9e+151) (not (<= x 5.8e+19)))
   (- z (* x -3.0))
   (- z (* y -2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.9e+151) || !(x <= 5.8e+19)) {
		tmp = z - (x * -3.0);
	} else {
		tmp = z - (y * -2.0);
	}
	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) :: tmp
    if ((x <= (-3.9d+151)) .or. (.not. (x <= 5.8d+19))) then
        tmp = z - (x * (-3.0d0))
    else
        tmp = z - (y * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.9e+151) || !(x <= 5.8e+19)) {
		tmp = z - (x * -3.0);
	} else {
		tmp = z - (y * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.9e+151) or not (x <= 5.8e+19):
		tmp = z - (x * -3.0)
	else:
		tmp = z - (y * -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.9e+151) || !(x <= 5.8e+19))
		tmp = Float64(z - Float64(x * -3.0));
	else
		tmp = Float64(z - Float64(y * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.9e+151) || ~((x <= 5.8e+19)))
		tmp = z - (x * -3.0);
	else
		tmp = z - (y * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.9e+151], N[Not[LessEqual[x, 5.8e+19]], $MachinePrecision]], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(z - N[(y * -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.89999999999999976e151 or 5.8e19 < x

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. remove-double-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-+r+ 99.8%

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

      9. associate-+r+ 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. distribute-neg-out 99.8%

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

      12. neg-mul-1 99.8%

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

      13. count-2 99.8%

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

      14. distribute-lft-neg-in 99.8%

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

      15. metadata-eval 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-rgt-out 99.8%

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

      18. distribute-neg-out 99.8%

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

      19. fma-define 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{z - \mathsf{fma}\left(x, -3, y \cdot -2\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 91.4%

      \[\leadsto \color{blue}{z - -3 \cdot x} \]

   if -3.89999999999999976e151 < x < 5.8e19

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 100.0%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 100.0%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 89.5%

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   6. Step-by-step derivation

      1. metadata-eval 89.5%

         \[\leadsto z + \color{blue}{\left(--2\right)} \cdot y \]

      2. cancel-sign-sub-inv 89.5%

         \[\leadsto \color{blue}{z - -2 \cdot y} \]

      3. *-commutative 89.5%

         \[\leadsto z - \color{blue}{y \cdot -2} \]

   7. Simplified 89.5%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+151} \lor \neg \left(x \leq 5.8 \cdot 10^{+19}\right):\\ \;\;\;\;z - x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+167}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.32e+167) z (if (<= z 3.9e+59) (* 2.0 y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.32e+167) {
		tmp = z;
	} else if (z <= 3.9e+59) {
		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 <= (-1.32d+167)) then
        tmp = z
    else if (z <= 3.9d+59) 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 <= -1.32e+167) {
		tmp = z;
	} else if (z <= 3.9e+59) {
		tmp = 2.0 * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.32e+167:
		tmp = z
	elif z <= 3.9e+59:
		tmp = 2.0 * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.32e+167)
		tmp = z;
	elseif (z <= 3.9e+59)
		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 <= -1.32e+167)
		tmp = z;
	elseif (z <= 3.9e+59)
		tmp = 2.0 * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.32e+167], z, If[LessEqual[z, 3.9e+59], N[(2.0 * y), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3200000000000001e167 or 3.90000000000000021e59 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 99.9%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 99.9%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 67.3%

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

   if -1.3200000000000001e167 < z < 3.90000000000000021e59

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

         \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

      5. +-commutative 99.9%

         \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

      6. +-commutative 99.9%

         \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 46.6%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+167}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.3% 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%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(y + x\right)} + \left(z + x\right) \]

   5. +-commutative 99.9%

      \[\leadsto 2 \cdot \color{blue}{\left(x + y\right)} + \left(z + x\right) \]

   6. +-commutative 99.9%

      \[\leadsto 2 \cdot \left(x + y\right) + \color{blue}{\left(x + z\right)} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 32.4%

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

6. Final simplification 32.4%

   \[\leadsto z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(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))