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

Percentage Accurate: 99.9% → 100.0%

Time: 7.9s

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: 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 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 51.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-24}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-157}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-282}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-170}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-111}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 48000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.1e-24)
   (* x 3.0)
   (if (<= x -4.4e-157)
     z
     (if (<= x 1.7e-282)
       (* y 2.0)
       (if (<= x 1.5e-170)
         z
         (if (<= x 2.4e-111) (* y 2.0) (if (<= x 48000.0) z (* x 3.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.1e-24) {
		tmp = x * 3.0;
	} else if (x <= -4.4e-157) {
		tmp = z;
	} else if (x <= 1.7e-282) {
		tmp = y * 2.0;
	} else if (x <= 1.5e-170) {
		tmp = z;
	} else if (x <= 2.4e-111) {
		tmp = y * 2.0;
	} else if (x <= 48000.0) {
		tmp = z;
	} 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 <= (-1.1d-24)) then
        tmp = x * 3.0d0
    else if (x <= (-4.4d-157)) then
        tmp = z
    else if (x <= 1.7d-282) then
        tmp = y * 2.0d0
    else if (x <= 1.5d-170) then
        tmp = z
    else if (x <= 2.4d-111) then
        tmp = y * 2.0d0
    else if (x <= 48000.0d0) then
        tmp = z
    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 <= -1.1e-24) {
		tmp = x * 3.0;
	} else if (x <= -4.4e-157) {
		tmp = z;
	} else if (x <= 1.7e-282) {
		tmp = y * 2.0;
	} else if (x <= 1.5e-170) {
		tmp = z;
	} else if (x <= 2.4e-111) {
		tmp = y * 2.0;
	} else if (x <= 48000.0) {
		tmp = z;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.1e-24:
		tmp = x * 3.0
	elif x <= -4.4e-157:
		tmp = z
	elif x <= 1.7e-282:
		tmp = y * 2.0
	elif x <= 1.5e-170:
		tmp = z
	elif x <= 2.4e-111:
		tmp = y * 2.0
	elif x <= 48000.0:
		tmp = z
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.1e-24)
		tmp = Float64(x * 3.0);
	elseif (x <= -4.4e-157)
		tmp = z;
	elseif (x <= 1.7e-282)
		tmp = Float64(y * 2.0);
	elseif (x <= 1.5e-170)
		tmp = z;
	elseif (x <= 2.4e-111)
		tmp = Float64(y * 2.0);
	elseif (x <= 48000.0)
		tmp = z;
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.1e-24)
		tmp = x * 3.0;
	elseif (x <= -4.4e-157)
		tmp = z;
	elseif (x <= 1.7e-282)
		tmp = y * 2.0;
	elseif (x <= 1.5e-170)
		tmp = z;
	elseif (x <= 2.4e-111)
		tmp = y * 2.0;
	elseif (x <= 48000.0)
		tmp = z;
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.1e-24], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, -4.4e-157], z, If[LessEqual[x, 1.7e-282], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 1.5e-170], z, If[LessEqual[x, 2.4e-111], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 48000.0], z, N[(x * 3.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.10000000000000001e-24 or 48000 < 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+ 99.8%

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

      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 x around inf 66.6%

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

   if -1.10000000000000001e-24 < x < -4.4000000000000002e-157 or 1.69999999999999999e-282 < x < 1.50000000000000007e-170 or 2.4000000000000001e-111 < x < 48000

   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 64.1%

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

   if -4.4000000000000002e-157 < x < 1.69999999999999999e-282 or 1.50000000000000007e-170 < x < 2.4000000000000001e-111

   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 72.0%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-24}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-157}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-282}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-170}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-111}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 48000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+121} \lor \neg \left(y \leq 9.2 \cdot 10^{+156}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.05e+121) (not (<= y 9.2e+156))) (* y 2.0) (- z (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e+121) || !(y <= 9.2e+156)) {
		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 <= (-1.05d+121)) .or. (.not. (y <= 9.2d+156))) 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 <= -1.05e+121) || !(y <= 9.2e+156)) {
		tmp = y * 2.0;
	} else {
		tmp = z - (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.05e+121) or not (y <= 9.2e+156):
		tmp = y * 2.0
	else:
		tmp = z - (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.05e+121) || !(y <= 9.2e+156))
		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 <= -1.05e+121) || ~((y <= 9.2e+156)))
		tmp = y * 2.0;
	else
		tmp = z - (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.05e+121], N[Not[LessEqual[y, 9.2e+156]], $MachinePrecision]], N[(y * 2.0), $MachinePrecision], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0500000000000001e121 or 9.1999999999999995e156 < 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 70.0%

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

   if -1.0500000000000001e121 < y < 9.1999999999999995e156

   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 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 86.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+121} \lor \neg \left(y \leq 9.2 \cdot 10^{+156}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-44} \lor \neg \left(x \leq 9.5 \cdot 10^{-28}\right):\\ \;\;\;\;z - x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.2e-44) (not (<= x 9.5e-28)))
   (- z (* x -3.0))
   (- z (* y -2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e-44) || !(x <= 9.5e-28)) {
		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 <= (-2.2d-44)) .or. (.not. (x <= 9.5d-28))) 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 <= -2.2e-44) || !(x <= 9.5e-28)) {
		tmp = z - (x * -3.0);
	} else {
		tmp = z - (y * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.2e-44) or not (x <= 9.5e-28):
		tmp = z - (x * -3.0)
	else:
		tmp = z - (y * -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.2e-44) || !(x <= 9.5e-28))
		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 <= -2.2e-44) || ~((x <= 9.5e-28)))
		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, -2.2e-44], N[Not[LessEqual[x, 9.5e-28]], $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 < -2.20000000000000012e-44 or 9.50000000000000001e-28 < 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 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 84.4%

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

   if -2.20000000000000012e-44 < x < 9.50000000000000001e-28

   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 95.7%

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

      1. metadata-eval 95.7%

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

      2. cancel-sign-sub-inv 95.7%

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

      3. *-commutative 95.7%

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

   7. Simplified 95.7%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-44} \lor \neg \left(x \leq 9.5 \cdot 10^{-28}\right):\\ \;\;\;\;z - x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-16}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-28}:\\ \;\;\;\;z - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.8e-16)
   (+ x (* 2.0 (+ x y)))
   (if (<= x 9e-28) (- z (* y -2.0)) (- z (* x -3.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.8e-16) {
		tmp = x + (2.0 * (x + y));
	} else if (x <= 9e-28) {
		tmp = z - (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 (x <= (-5.8d-16)) then
        tmp = x + (2.0d0 * (x + y))
    else if (x <= 9d-28) then
        tmp = z - (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 (x <= -5.8e-16) {
		tmp = x + (2.0 * (x + y));
	} else if (x <= 9e-28) {
		tmp = z - (y * -2.0);
	} else {
		tmp = z - (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.8e-16:
		tmp = x + (2.0 * (x + y))
	elif x <= 9e-28:
		tmp = z - (y * -2.0)
	else:
		tmp = z - (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.8e-16)
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	elseif (x <= 9e-28)
		tmp = Float64(z - 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 (x <= -5.8e-16)
		tmp = x + (2.0 * (x + y));
	elseif (x <= 9e-28)
		tmp = z - (y * -2.0);
	else
		tmp = z - (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.8e-16], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-28], N[(z - N[(y * -2.0), $MachinePrecision]), $MachinePrecision], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.7999999999999996e-16

   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 89.4%

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

   if -5.7999999999999996e-16 < x < 8.9999999999999996e-28

   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 95.0%

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

      1. metadata-eval 95.0%

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

      2. cancel-sign-sub-inv 95.0%

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

      3. *-commutative 95.0%

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

   7. Simplified 95.0%

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

   if 8.9999999999999996e-28 < x

   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 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 85.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-16}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-28}:\\ \;\;\;\;z - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+49}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.2e+49) z (if (<= z 1.6e+19) (* y 2.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.2e+49) {
		tmp = z;
	} else if (z <= 1.6e+19) {
		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 <= (-2.2d+49)) then
        tmp = z
    else if (z <= 1.6d+19) 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 <= -2.2e+49) {
		tmp = z;
	} else if (z <= 1.6e+19) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.2e+49:
		tmp = z
	elif z <= 1.6e+19:
		tmp = y * 2.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.2e+49)
		tmp = z;
	elseif (z <= 1.6e+19)
		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 <= -2.2e+49)
		tmp = z;
	elseif (z <= 1.6e+19)
		tmp = y * 2.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.2e+49], z, If[LessEqual[z, 1.6e+19], N[(y * 2.0), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e49 or 1.6e19 < 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 66.3%

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

   if -2.2000000000000001e49 < z < 1.6e19

   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 41.1%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+49}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 8: 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. 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 33.3%

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

6. Final simplification 33.3%

   \[\leadsto z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024082 
(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))