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

Percentage Accurate: 99.9% → 100.0%

Time: 8.0s

Alternatives: 10

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(z - N[(x * -3.0 + N[(y * -2.0), $MachinePrecision]), $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. +-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+ 99.9%

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

   10. distribute-neg-in 99.9%

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

   11. distribute-neg-out 99.9%

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

   12. neg-mul-1 99.9%

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

   13. count-2 99.9%

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

   14. distribute-lft-neg-in 99.9%

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

   15. metadata-eval 99.9%

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

   16. metadata-eval 99.9%

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

   17. distribute-rgt-out 99.9%

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

   18. distribute-neg-out 99.9%

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

   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. Final simplification 99.9%

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

Alternative 2: 53.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+50}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-91}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-156}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-231}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-99}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+57}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+50)
   (* x 3.0)
   (if (<= x -4.5e-91)
     (* y 2.0)
     (if (<= x -1.95e-156)
       z
       (if (<= x 3.5e-231)
         (* y 2.0)
         (if (<= x 1.2e-99) z (if (<= x 1.2e+57) (* y 2.0) (* x 3.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+50) {
		tmp = x * 3.0;
	} else if (x <= -4.5e-91) {
		tmp = y * 2.0;
	} else if (x <= -1.95e-156) {
		tmp = z;
	} else if (x <= 3.5e-231) {
		tmp = y * 2.0;
	} else if (x <= 1.2e-99) {
		tmp = z;
	} else if (x <= 1.2e+57) {
		tmp = y * 2.0;
	} 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 <= (-1.55d+50)) then
        tmp = x * 3.0d0
    else if (x <= (-4.5d-91)) then
        tmp = y * 2.0d0
    else if (x <= (-1.95d-156)) then
        tmp = z
    else if (x <= 3.5d-231) then
        tmp = y * 2.0d0
    else if (x <= 1.2d-99) then
        tmp = z
    else if (x <= 1.2d+57) then
        tmp = y * 2.0d0
    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 <= -1.55e+50) {
		tmp = x * 3.0;
	} else if (x <= -4.5e-91) {
		tmp = y * 2.0;
	} else if (x <= -1.95e-156) {
		tmp = z;
	} else if (x <= 3.5e-231) {
		tmp = y * 2.0;
	} else if (x <= 1.2e-99) {
		tmp = z;
	} else if (x <= 1.2e+57) {
		tmp = y * 2.0;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.55e+50:
		tmp = x * 3.0
	elif x <= -4.5e-91:
		tmp = y * 2.0
	elif x <= -1.95e-156:
		tmp = z
	elif x <= 3.5e-231:
		tmp = y * 2.0
	elif x <= 1.2e-99:
		tmp = z
	elif x <= 1.2e+57:
		tmp = y * 2.0
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+50)
		tmp = Float64(x * 3.0);
	elseif (x <= -4.5e-91)
		tmp = Float64(y * 2.0);
	elseif (x <= -1.95e-156)
		tmp = z;
	elseif (x <= 3.5e-231)
		tmp = Float64(y * 2.0);
	elseif (x <= 1.2e-99)
		tmp = z;
	elseif (x <= 1.2e+57)
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.55e+50)
		tmp = x * 3.0;
	elseif (x <= -4.5e-91)
		tmp = y * 2.0;
	elseif (x <= -1.95e-156)
		tmp = z;
	elseif (x <= 3.5e-231)
		tmp = y * 2.0;
	elseif (x <= 1.2e-99)
		tmp = z;
	elseif (x <= 1.2e+57)
		tmp = y * 2.0;
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+50], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, -4.5e-91], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, -1.95e-156], z, If[LessEqual[x, 3.5e-231], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 1.2e-99], z, If[LessEqual[x, 1.2e+57], N[(y * 2.0), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55000000000000001e50 or 1.20000000000000002e57 < 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%

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

      2. associate-+l+ 99.8%

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

      3. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 76.6%

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

   if -1.55000000000000001e50 < x < -4.49999999999999976e-91 or -1.9500000000000001e-156 < x < 3.5000000000000001e-231 or 1.2e-99 < x < 1.20000000000000002e57

   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%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 57.0%

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

   if -4.49999999999999976e-91 < x < -1.9500000000000001e-156 or 3.5000000000000001e-231 < x < 1.2e-99

   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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 64.8%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+50}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-91}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-156}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-231}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-99}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+57}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+39}:\\ \;\;\;\;z - x \cdot -3\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+20}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e+39)
   (- z (* x -3.0))
   (if (<= z 4.7e+20) (+ x (* 2.0 (+ x y))) (- z (* y -2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+39) {
		tmp = z - (x * -3.0);
	} else if (z <= 4.7e+20) {
		tmp = x + (2.0 * (x + y));
	} 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 (z <= (-2.5d+39)) then
        tmp = z - (x * (-3.0d0))
    else if (z <= 4.7d+20) then
        tmp = x + (2.0d0 * (x + y))
    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 (z <= -2.5e+39) {
		tmp = z - (x * -3.0);
	} else if (z <= 4.7e+20) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z - (y * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e+39:
		tmp = z - (x * -3.0)
	elif z <= 4.7e+20:
		tmp = x + (2.0 * (x + y))
	else:
		tmp = z - (y * -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e+39)
		tmp = Float64(z - Float64(x * -3.0));
	elseif (z <= 4.7e+20)
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	else
		tmp = Float64(z - Float64(y * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.5e+39)
		tmp = z - (x * -3.0);
	elseif (z <= 4.7e+20)
		tmp = x + (2.0 * (x + y));
	else
		tmp = z - (y * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e+39], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+20], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z - N[(y * -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000008e39

   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+ 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. distribute-neg-out 99.9%

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

      12. neg-mul-1 99.9%

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

      13. count-2 99.9%

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

      14. distribute-lft-neg-in 99.9%

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

      15. metadata-eval 99.9%

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

      16. metadata-eval 99.9%

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

      17. distribute-rgt-out 99.9%

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

      18. distribute-neg-out 99.9%

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

      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 79.5%

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

   if -2.50000000000000008e39 < z < 4.7e20

   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%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 91.4%

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

   7. Simplified 91.4%

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

   if 4.7e20 < 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. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 84.7%

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

   7. Simplified 84.7%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+39}:\\ \;\;\;\;z - x \cdot -3\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+20}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;x + \left(z + x \cdot 2\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+20}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e+40)
   (+ x (+ z (* x 2.0)))
   (if (<= z 4.8e+20) (+ x (* 2.0 (+ x y))) (- z (* y -2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+40) {
		tmp = x + (z + (x * 2.0));
	} else if (z <= 4.8e+20) {
		tmp = x + (2.0 * (x + y));
	} 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 (z <= (-1.05d+40)) then
        tmp = x + (z + (x * 2.0d0))
    else if (z <= 4.8d+20) then
        tmp = x + (2.0d0 * (x + y))
    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 (z <= -1.05e+40) {
		tmp = x + (z + (x * 2.0));
	} else if (z <= 4.8e+20) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z - (y * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05e+40:
		tmp = x + (z + (x * 2.0))
	elif z <= 4.8e+20:
		tmp = x + (2.0 * (x + y))
	else:
		tmp = z - (y * -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05e+40)
		tmp = Float64(x + Float64(z + Float64(x * 2.0)));
	elseif (z <= 4.8e+20)
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	else
		tmp = Float64(z - Float64(y * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05e+40)
		tmp = x + (z + (x * 2.0));
	elseif (z <= 4.8e+20)
		tmp = x + (2.0 * (x + y));
	else
		tmp = z - (y * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05e+40], N[(x + N[(z + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+20], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z - N[(y * -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000005e40

   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%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 79.5%

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

   if -1.05000000000000005e40 < z < 4.8e20

   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%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 91.4%

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

   7. Simplified 91.4%

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

   if 4.8e20 < 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. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 84.7%

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

   7. Simplified 84.7%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;x + \left(z + x \cdot 2\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+20}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+39}:\\ \;\;\;\;x + \left(z + x \cdot 2\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+20}:\\ \;\;\;\;x \cdot 3 - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.1e+39)
   (+ x (+ z (* x 2.0)))
   (if (<= z 7.2e+20) (- (* x 3.0) (* y -2.0)) (- z (* y -2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e+39) {
		tmp = x + (z + (x * 2.0));
	} else if (z <= 7.2e+20) {
		tmp = (x * 3.0) - (y * -2.0);
	} 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 (z <= (-2.1d+39)) then
        tmp = x + (z + (x * 2.0d0))
    else if (z <= 7.2d+20) then
        tmp = (x * 3.0d0) - (y * (-2.0d0))
    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 (z <= -2.1e+39) {
		tmp = x + (z + (x * 2.0));
	} else if (z <= 7.2e+20) {
		tmp = (x * 3.0) - (y * -2.0);
	} else {
		tmp = z - (y * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.1e+39:
		tmp = x + (z + (x * 2.0))
	elif z <= 7.2e+20:
		tmp = (x * 3.0) - (y * -2.0)
	else:
		tmp = z - (y * -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.1e+39)
		tmp = Float64(x + Float64(z + Float64(x * 2.0)));
	elseif (z <= 7.2e+20)
		tmp = Float64(Float64(x * 3.0) - Float64(y * -2.0));
	else
		tmp = Float64(z - Float64(y * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.1e+39)
		tmp = x + (z + (x * 2.0));
	elseif (z <= 7.2e+20)
		tmp = (x * 3.0) - (y * -2.0);
	else
		tmp = z - (y * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.1e+39], N[(x + N[(z + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+20], N[(N[(x * 3.0), $MachinePrecision] - N[(y * -2.0), $MachinePrecision]), $MachinePrecision], N[(z - N[(y * -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0999999999999999e39

   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%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 79.5%

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

   if -2.0999999999999999e39 < z < 7.2e20

   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+ 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. distribute-neg-out 99.9%

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

      12. neg-mul-1 99.9%

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

      13. count-2 99.9%

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

      14. distribute-lft-neg-in 99.9%

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

      15. metadata-eval 99.9%

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

      16. metadata-eval 99.9%

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

      17. distribute-rgt-out 99.9%

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

      18. distribute-neg-out 99.9%

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

      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 x around 0 99.9%

      \[\leadsto \color{blue}{\left(z + 3 \cdot x\right) - -2 \cdot y} \]

   6. Taylor expanded in z around 0 91.4%

      \[\leadsto \color{blue}{3 \cdot x} - -2 \cdot y \]

   if 7.2e20 < 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. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 84.7%

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

   7. Simplified 84.7%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+39}:\\ \;\;\;\;x + \left(z + x \cdot 2\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+20}:\\ \;\;\;\;x \cdot 3 - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+193} \lor \neg \left(y \leq 3.6 \cdot 10^{+50}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.5e+193) (not (<= y 3.6e+50))) (* y 2.0) (- z (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e+193) || !(y <= 3.6e+50)) {
		tmp = y * 2.0;
	} 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 <= (-4.5d+193)) .or. (.not. (y <= 3.6d+50))) then
        tmp = y * 2.0d0
    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 <= -4.5e+193) || !(y <= 3.6e+50)) {
		tmp = y * 2.0;
	} else {
		tmp = z - (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.5e+193) or not (y <= 3.6e+50):
		tmp = y * 2.0
	else:
		tmp = z - (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.5e+193) || !(y <= 3.6e+50))
		tmp = Float64(y * 2.0);
	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 <= -4.5e+193) || ~((y <= 3.6e+50)))
		tmp = y * 2.0;
	else
		tmp = z - (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.5e+193], N[Not[LessEqual[y, 3.6e+50]], $MachinePrecision]], N[(y * 2.0), $MachinePrecision], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.49999999999999999e193 or 3.59999999999999986e50 < 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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 77.8%

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

   if -4.49999999999999999e193 < y < 3.59999999999999986e50

   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+ 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. distribute-neg-out 99.9%

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

      12. neg-mul-1 99.9%

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

      13. count-2 99.9%

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

      14. distribute-lft-neg-in 99.9%

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

      15. metadata-eval 99.9%

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

      16. metadata-eval 99.9%

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

      17. distribute-rgt-out 99.9%

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

      18. distribute-neg-out 99.9%

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

      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 84.0%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+193} \lor \neg \left(y \leq 3.6 \cdot 10^{+50}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+50} \lor \neg \left(x \leq 1.15 \cdot 10^{+57}\right):\\ \;\;\;\;z - x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.5e+50) (not (<= x 1.15e+57)))
   (- z (* x -3.0))
   (- z (* y -2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e+50) || !(x <= 1.15e+57)) {
		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 <= (-2.5d+50)) .or. (.not. (x <= 1.15d+57))) 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 <= -2.5e+50) || !(x <= 1.15e+57)) {
		tmp = z - (x * -3.0);
	} else {
		tmp = z - (y * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.5e+50) or not (x <= 1.15e+57):
		tmp = z - (x * -3.0)
	else:
		tmp = z - (y * -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.5e+50) || !(x <= 1.15e+57))
		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 <= -2.5e+50) || ~((x <= 1.15e+57)))
		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, -2.5e+50], N[Not[LessEqual[x, 1.15e+57]], $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 < -2.5e50 or 1.1499999999999999e57 < 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 99.9%

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

   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 89.3%

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

   if -2.5e50 < x < 1.1499999999999999e57

   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. +-commutative 100.0%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 87.1%

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

   7. Simplified 87.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+50} \lor \neg \left(x \leq 1.15 \cdot 10^{+57}\right):\\ \;\;\;\;z - x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+38}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+15}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.65e+38) z (if (<= z 1.65e+15) (* y 2.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.65e+38) {
		tmp = z;
	} else if (z <= 1.65e+15) {
		tmp = y * 2.0;
	} 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 <= (-1.65d+38)) then
        tmp = z
    else if (z <= 1.65d+15) then
        tmp = y * 2.0d0
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.65e+38) {
		tmp = z;
	} else if (z <= 1.65e+15) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.65e+38:
		tmp = z
	elif z <= 1.65e+15:
		tmp = y * 2.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.65e+38)
		tmp = z;
	elseif (z <= 1.65e+15)
		tmp = Float64(y * 2.0);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.65e+38)
		tmp = z;
	elseif (z <= 1.65e+15)
		tmp = y * 2.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.65e+38], z, If[LessEqual[z, 1.65e+15], N[(y * 2.0), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e38 or 1.65e15 < 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. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 58.1%

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

   if -1.65e38 < z < 1.65e15

   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%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 43.0%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+38}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+15}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 10: 34.9% 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. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 29.8%

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

6. Final simplification 29.8%

   \[\leadsto z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024066 
(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))