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

Percentage Accurate: 99.9% → 100.0%

Time: 6.1s

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 99.8%

   \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
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+ 99.9%

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

   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: 52.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+85}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-214}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-123}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-39}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1150000000:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e+85)
   (* x 3.0)
   (if (<= x -1.7e-257)
     (* y 2.0)
     (if (<= x 1.22e-214)
       z
       (if (<= x 7e-123)
         (* y 2.0)
         (if (<= x 2.5e-39)
           z
           (if (<= x 1150000000.0) (* y 2.0) (* x 3.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e+85) {
		tmp = x * 3.0;
	} else if (x <= -1.7e-257) {
		tmp = y * 2.0;
	} else if (x <= 1.22e-214) {
		tmp = z;
	} else if (x <= 7e-123) {
		tmp = y * 2.0;
	} else if (x <= 2.5e-39) {
		tmp = z;
	} else if (x <= 1150000000.0) {
		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 <= (-1.4d+85)) then
        tmp = x * 3.0d0
    else if (x <= (-1.7d-257)) then
        tmp = y * 2.0d0
    else if (x <= 1.22d-214) then
        tmp = z
    else if (x <= 7d-123) then
        tmp = y * 2.0d0
    else if (x <= 2.5d-39) then
        tmp = z
    else if (x <= 1150000000.0d0) 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 <= -1.4e+85) {
		tmp = x * 3.0;
	} else if (x <= -1.7e-257) {
		tmp = y * 2.0;
	} else if (x <= 1.22e-214) {
		tmp = z;
	} else if (x <= 7e-123) {
		tmp = y * 2.0;
	} else if (x <= 2.5e-39) {
		tmp = z;
	} else if (x <= 1150000000.0) {
		tmp = y * 2.0;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e+85:
		tmp = x * 3.0
	elif x <= -1.7e-257:
		tmp = y * 2.0
	elif x <= 1.22e-214:
		tmp = z
	elif x <= 7e-123:
		tmp = y * 2.0
	elif x <= 2.5e-39:
		tmp = z
	elif x <= 1150000000.0:
		tmp = y * 2.0
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e+85)
		tmp = Float64(x * 3.0);
	elseif (x <= -1.7e-257)
		tmp = Float64(y * 2.0);
	elseif (x <= 1.22e-214)
		tmp = z;
	elseif (x <= 7e-123)
		tmp = Float64(y * 2.0);
	elseif (x <= 2.5e-39)
		tmp = z;
	elseif (x <= 1150000000.0)
		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 <= -1.4e+85)
		tmp = x * 3.0;
	elseif (x <= -1.7e-257)
		tmp = y * 2.0;
	elseif (x <= 1.22e-214)
		tmp = z;
	elseif (x <= 7e-123)
		tmp = y * 2.0;
	elseif (x <= 2.5e-39)
		tmp = z;
	elseif (x <= 1150000000.0)
		tmp = y * 2.0;
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e+85], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, -1.7e-257], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 1.22e-214], z, If[LessEqual[x, 7e-123], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 2.5e-39], z, If[LessEqual[x, 1150000000.0], N[(y * 2.0), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4e85 or 1.15e9 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. count-2 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 64.7%

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

   if -1.4e85 < x < -1.6999999999999999e-257 or 1.22000000000000004e-214 < x < 6.9999999999999997e-123 or 2.4999999999999999e-39 < x < 1.15e9

   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 54.5%

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

   if -1.6999999999999999e-257 < x < 1.22000000000000004e-214 or 6.9999999999999997e-123 < x < 2.4999999999999999e-39

   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 67.1%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+85}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-214}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-123}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-39}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1150000000:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+66}:\\ \;\;\;\;z - x \cdot -3\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+102}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.5e+66)
   (- z (* x -3.0))
   (if (<= z 4.3e+102) (+ x (* 2.0 (+ x y))) (- z (* y -2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e+66) {
		tmp = z - (x * -3.0);
	} else if (z <= 4.3e+102) {
		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 <= (-1.5d+66)) then
        tmp = z - (x * (-3.0d0))
    else if (z <= 4.3d+102) 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 <= -1.5e+66) {
		tmp = z - (x * -3.0);
	} else if (z <= 4.3e+102) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z - (y * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.5e+66:
		tmp = z - (x * -3.0)
	elif z <= 4.3e+102:
		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 <= -1.5e+66)
		tmp = Float64(z - Float64(x * -3.0));
	elseif (z <= 4.3e+102)
		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 <= -1.5e+66)
		tmp = z - (x * -3.0);
	elseif (z <= 4.3e+102)
		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, -1.5e+66], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+102], 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 < -1.50000000000000001e66

   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%

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

      2. associate-+l+ 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+r+ 100.0%

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

      9. associate-+r+ 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. distribute-neg-out 100.0%

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

      12. neg-mul-1 100.0%

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

      13. count-2 100.0%

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

      14. distribute-lft-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

      16. metadata-eval 100.0%

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

      17. distribute-rgt-out 100.0%

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

      18. distribute-neg-out 100.0%

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

      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 89.9%

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

   if -1.50000000000000001e66 < z < 4.3000000000000001e102

   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 88.0%

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

   if 4.3000000000000001e102 < z

   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%

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

      2. associate-+l+ 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+r+ 100.0%

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

      9. associate-+r+ 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. distribute-neg-out 100.0%

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

      12. neg-mul-1 100.0%

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

      13. count-2 100.0%

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

      14. distribute-lft-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

      16. metadata-eval 100.0%

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

      17. distribute-rgt-out 100.0%

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

      18. distribute-neg-out 100.0%

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

      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 x around 0 92.2%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+66}:\\ \;\;\;\;z - x \cdot -3\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+102}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+65}:\\ \;\;\;\;z - x \cdot -3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+103}:\\ \;\;\;\;x \cdot 3 - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.1e+65)
   (- z (* x -3.0))
   (if (<= z 3.1e+103) (- (* 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+65) {
		tmp = z - (x * -3.0);
	} else if (z <= 3.1e+103) {
		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+65)) then
        tmp = z - (x * (-3.0d0))
    else if (z <= 3.1d+103) 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+65) {
		tmp = z - (x * -3.0);
	} else if (z <= 3.1e+103) {
		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+65:
		tmp = z - (x * -3.0)
	elif z <= 3.1e+103:
		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+65)
		tmp = Float64(z - Float64(x * -3.0));
	elseif (z <= 3.1e+103)
		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+65)
		tmp = z - (x * -3.0);
	elseif (z <= 3.1e+103)
		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+65], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+103], 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 < -2.09999999999999991e65

   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%

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

      2. associate-+l+ 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+r+ 100.0%

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

      9. associate-+r+ 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. distribute-neg-out 100.0%

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

      12. neg-mul-1 100.0%

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

      13. count-2 100.0%

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

      14. distribute-lft-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

      16. metadata-eval 100.0%

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

      17. distribute-rgt-out 100.0%

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

      18. distribute-neg-out 100.0%

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

      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 89.9%

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

   if -2.09999999999999991e65 < z < 3.1000000000000002e103

   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 x around 0 99.8%

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

   6. Taylor expanded in z around 0 88.0%

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

   if 3.1000000000000002e103 < z

   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%

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

      2. associate-+l+ 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+r+ 100.0%

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

      9. associate-+r+ 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. distribute-neg-out 100.0%

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

      12. neg-mul-1 100.0%

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

      13. count-2 100.0%

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

      14. distribute-lft-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

      16. metadata-eval 100.0%

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

      17. distribute-rgt-out 100.0%

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

      18. distribute-neg-out 100.0%

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

      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 x around 0 92.2%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+65}:\\ \;\;\;\;z - x \cdot -3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+103}:\\ \;\;\;\;x \cdot 3 - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+132} \lor \neg \left(y \leq 1.45 \cdot 10^{+172}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.4e+132) (not (<= y 1.45e+172))) (* y 2.0) (- z (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e+132) || !(y <= 1.45e+172)) {
		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 <= (-4.4d+132)) .or. (.not. (y <= 1.45d+172))) 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 <= -4.4e+132) || !(y <= 1.45e+172)) {
		tmp = y * 2.0;
	} else {
		tmp = z - (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.4e+132) or not (y <= 1.45e+172):
		tmp = y * 2.0
	else:
		tmp = z - (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.4e+132) || !(y <= 1.45e+172))
		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 <= -4.4e+132) || ~((y <= 1.45e+172)))
		tmp = y * 2.0;
	else
		tmp = z - (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.4e+132], N[Not[LessEqual[y, 1.45e+172]], $MachinePrecision]], N[(y * 2.0), $MachinePrecision], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.39999999999999977e132 or 1.45e172 < y

   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+ 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 72.4%

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

   if -4.39999999999999977e132 < y < 1.45e172

   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+ 99.9%

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

      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+ 99.8%

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

      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 78.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+132} \lor \neg \left(y \leq 1.45 \cdot 10^{+172}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+86} \lor \neg \left(x \leq 3500000000\right):\\ \;\;\;\;z - x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.4e+86) (not (<= x 3500000000.0)))
   (- z (* x -3.0))
   (- z (* y -2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.4e+86) || !(x <= 3500000000.0)) {
		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 <= (-8.4d+86)) .or. (.not. (x <= 3500000000.0d0))) 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 <= -8.4e+86) || !(x <= 3500000000.0)) {
		tmp = z - (x * -3.0);
	} else {
		tmp = z - (y * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.4e+86) or not (x <= 3500000000.0):
		tmp = z - (x * -3.0)
	else:
		tmp = z - (y * -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.4e+86) || !(x <= 3500000000.0))
		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 <= -8.4e+86) || ~((x <= 3500000000.0)))
		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, -8.4e+86], N[Not[LessEqual[x, 3500000000.0]], $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 < -8.3999999999999996e86 or 3.5e9 < x

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-+l+ 99.7%

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

      3. remove-double-neg 99.7%

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

      4. unsub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. associate-+r+ 99.7%

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

      9. associate-+r+ 99.7%

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

      10. distribute-neg-in 99.7%

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

      11. distribute-neg-out 99.7%

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

      12. neg-mul-1 99.7%

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

      13. count-2 99.7%

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

      14. distribute-lft-neg-in 99.7%

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

      15. metadata-eval 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-rgt-out 99.7%

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

      18. distribute-neg-out 99.7%

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

      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 82.6%

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

   if -8.3999999999999996e86 < x < 3.5e9

   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%

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

      2. associate-+l+ 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+r+ 100.0%

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

      9. associate-+r+ 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. distribute-neg-out 100.0%

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

      12. neg-mul-1 100.0%

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

      13. count-2 100.0%

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

      14. distribute-lft-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

      16. metadata-eval 100.0%

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

      17. distribute-rgt-out 100.0%

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

      18. distribute-neg-out 100.0%

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

      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 x around 0 89.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+86} \lor \neg \left(x \leq 3500000000\right):\\ \;\;\;\;z - x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+81}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+117}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.5e+81) z (if (<= z 8.4e+117) (* y 2.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.5e+81) {
		tmp = z;
	} else if (z <= 8.4e+117) {
		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 <= (-6.5d+81)) then
        tmp = z
    else if (z <= 8.4d+117) 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 <= -6.5e+81) {
		tmp = z;
	} else if (z <= 8.4e+117) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.5e+81:
		tmp = z
	elif z <= 8.4e+117:
		tmp = y * 2.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.5e+81)
		tmp = z;
	elseif (z <= 8.4e+117)
		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 <= -6.5e+81)
		tmp = z;
	elseif (z <= 8.4e+117)
		tmp = y * 2.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.5e+81], z, If[LessEqual[z, 8.4e+117], N[(y * 2.0), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999996e81 or 8.4000000000000005e117 < z

   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 73.9%

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

   if -6.4999999999999996e81 < z < 8.4000000000000005e117

   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 y around inf 47.1%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+81}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+117}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 99.8%

   \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
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 9: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (z + (x * 3.0d0)) - (y * (-2.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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+ 99.9%

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

   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 x around 0 99.9%

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

6. Final simplification 99.9%

   \[\leadsto \left(z + x \cdot 3\right) - y \cdot -2 \]
7. Add Preprocessing

Alternative 10: 33.8% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
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 33.0%

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

6. Final simplification 33.0%

   \[\leadsto z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(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))