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

Percentage Accurate: 99.9% → 100.0%

Time: 6.7s

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. +-commutative 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. associate-+r+ 99.9%

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

   7. associate-+r+ 99.9%

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

   8. *-lft-identity 99.9%

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

   9. metadata-eval 99.9%

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

   10. count-2 99.9%

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

   11. distribute-rgt-out 99.9%

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

   12. fma-define 100.0%

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

   13. metadata-eval 100.0%

       \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

   14. metadata-eval 100.0%

       \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

   15. count-2 100.0%

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

   16. *-commutative 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 52.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+83}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-89}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+15}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+105} \lor \neg \left(z \leq 3.5 \cdot 10^{+156}\right):\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.02e+83)
   z
   (if (<= z 9.2e-89)
     (* y 2.0)
     (if (<= z 2e+15)
       (* x 3.0)
       (if (or (<= z 1.4e+105) (not (<= z 3.5e+156))) z (* y 2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.02e+83) {
		tmp = z;
	} else if (z <= 9.2e-89) {
		tmp = y * 2.0;
	} else if (z <= 2e+15) {
		tmp = x * 3.0;
	} else if ((z <= 1.4e+105) || !(z <= 3.5e+156)) {
		tmp = z;
	} else {
		tmp = 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 <= (-1.02d+83)) then
        tmp = z
    else if (z <= 9.2d-89) then
        tmp = y * 2.0d0
    else if (z <= 2d+15) then
        tmp = x * 3.0d0
    else if ((z <= 1.4d+105) .or. (.not. (z <= 3.5d+156))) then
        tmp = z
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.02e+83) {
		tmp = z;
	} else if (z <= 9.2e-89) {
		tmp = y * 2.0;
	} else if (z <= 2e+15) {
		tmp = x * 3.0;
	} else if ((z <= 1.4e+105) || !(z <= 3.5e+156)) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.02e+83:
		tmp = z
	elif z <= 9.2e-89:
		tmp = y * 2.0
	elif z <= 2e+15:
		tmp = x * 3.0
	elif (z <= 1.4e+105) or not (z <= 3.5e+156):
		tmp = z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.02e+83)
		tmp = z;
	elseif (z <= 9.2e-89)
		tmp = Float64(y * 2.0);
	elseif (z <= 2e+15)
		tmp = Float64(x * 3.0);
	elseif ((z <= 1.4e+105) || !(z <= 3.5e+156))
		tmp = z;
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.02e+83)
		tmp = z;
	elseif (z <= 9.2e-89)
		tmp = y * 2.0;
	elseif (z <= 2e+15)
		tmp = x * 3.0;
	elseif ((z <= 1.4e+105) || ~((z <= 3.5e+156)))
		tmp = z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.02e+83], z, If[LessEqual[z, 9.2e-89], N[(y * 2.0), $MachinePrecision], If[LessEqual[z, 2e+15], N[(x * 3.0), $MachinePrecision], If[Or[LessEqual[z, 1.4e+105], N[Not[LessEqual[z, 3.5e+156]], $MachinePrecision]], z, N[(y * 2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0200000000000001e83 or 2e15 < z < 1.4000000000000001e105 or 3.5000000000000003e156 < 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+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. *-lft-identity 99.9%

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

      9. metadata-eval 99.9%

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

      10. count-2 99.9%

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

      11. distribute-rgt-out 99.9%

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

      12. fma-define 100.0%

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

      13. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

      14. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

      15. count-2 100.0%

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

      16. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 67.6%

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

   if -1.0200000000000001e83 < z < 9.200000000000001e-89 or 1.4000000000000001e105 < z < 3.5000000000000003e156

   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. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. *-lft-identity 99.9%

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

      9. metadata-eval 99.9%

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

      10. count-2 99.9%

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

      11. distribute-rgt-out 99.9%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

      14. metadata-eval 99.9%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 59.9%

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

   if 9.200000000000001e-89 < z < 2e15

   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+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. associate-+r+ 99.8%

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

      7. associate-+r+ 99.8%

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

      8. *-lft-identity 99.8%

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

      9. metadata-eval 99.8%

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

      10. count-2 99.8%

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

      11. distribute-rgt-out 99.8%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

      14. metadata-eval 99.9%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 53.1%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+83}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-89}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+15}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+105} \lor \neg \left(z \leq 3.5 \cdot 10^{+156}\right):\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+83} \lor \neg \left(z \leq 5.4 \cdot 10^{-18}\right) \land \left(z \leq 1.2 \cdot 10^{+104} \lor \neg \left(z \leq 2.2 \cdot 10^{+156}\right)\right):\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.02e+83)
         (and (not (<= z 5.4e-18)) (or (<= z 1.2e+104) (not (<= z 2.2e+156)))))
   z
   (* y 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.02e+83) || (!(z <= 5.4e-18) && ((z <= 1.2e+104) || !(z <= 2.2e+156)))) {
		tmp = z;
	} else {
		tmp = 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 <= (-1.02d+83)) .or. (.not. (z <= 5.4d-18)) .and. (z <= 1.2d+104) .or. (.not. (z <= 2.2d+156))) then
        tmp = z
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.02e+83) || (!(z <= 5.4e-18) && ((z <= 1.2e+104) || !(z <= 2.2e+156)))) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.02e+83) or (not (z <= 5.4e-18) and ((z <= 1.2e+104) or not (z <= 2.2e+156))):
		tmp = z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.02e+83) || (!(z <= 5.4e-18) && ((z <= 1.2e+104) || !(z <= 2.2e+156))))
		tmp = z;
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.02e+83) || (~((z <= 5.4e-18)) && ((z <= 1.2e+104) || ~((z <= 2.2e+156)))))
		tmp = z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.02e+83], And[N[Not[LessEqual[z, 5.4e-18]], $MachinePrecision], Or[LessEqual[z, 1.2e+104], N[Not[LessEqual[z, 2.2e+156]], $MachinePrecision]]]], z, N[(y * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0200000000000001e83 or 5.39999999999999977e-18 < z < 1.2e104 or 2.20000000000000004e156 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. *-lft-identity 99.9%

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

      9. metadata-eval 99.9%

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

      10. count-2 99.9%

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

      11. distribute-rgt-out 99.9%

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

      12. fma-define 100.0%

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

      13. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

      14. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

      15. count-2 100.0%

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

      16. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 64.9%

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

   if -1.0200000000000001e83 < z < 5.39999999999999977e-18 or 1.2e104 < z < 2.20000000000000004e156

   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. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. *-lft-identity 99.9%

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

      9. metadata-eval 99.9%

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

      10. count-2 99.9%

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

      11. distribute-rgt-out 99.9%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

      14. metadata-eval 99.9%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 56.2%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+83} \lor \neg \left(z \leq 5.4 \cdot 10^{-18}\right) \land \left(z \leq 1.2 \cdot 10^{+104} \lor \neg \left(z \leq 2.2 \cdot 10^{+156}\right)\right):\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+129}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+96}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + \left(x + x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.8e+129)
   (+ z (* x 3.0))
   (if (<= x 3.6e+96) (+ z (* y 2.0)) (+ x (+ z (+ x x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e+129) {
		tmp = z + (x * 3.0);
	} else if (x <= 3.6e+96) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x + (z + (x + x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.8d+129)) then
        tmp = z + (x * 3.0d0)
    else if (x <= 3.6d+96) then
        tmp = z + (y * 2.0d0)
    else
        tmp = x + (z + (x + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e+129) {
		tmp = z + (x * 3.0);
	} else if (x <= 3.6e+96) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x + (z + (x + x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.8e+129:
		tmp = z + (x * 3.0)
	elif x <= 3.6e+96:
		tmp = z + (y * 2.0)
	else:
		tmp = x + (z + (x + x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.8e+129)
		tmp = Float64(z + Float64(x * 3.0));
	elseif (x <= 3.6e+96)
		tmp = Float64(z + Float64(y * 2.0));
	else
		tmp = Float64(x + Float64(z + Float64(x + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.8e+129)
		tmp = z + (x * 3.0);
	elseif (x <= 3.6e+96)
		tmp = z + (y * 2.0);
	else
		tmp = x + (z + (x + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.8e+129], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+96], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.7999999999999997e129

   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. +-commutative 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+l+ 99.7%

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

      6. associate-+r+ 99.7%

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

      7. associate-+r+ 99.7%

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

      8. *-lft-identity 99.7%

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

      9. metadata-eval 99.7%

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

      10. count-2 99.7%

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

      11. distribute-rgt-out 99.7%

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

      12. fma-define 100.0%

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

      13. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

      14. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

      15. count-2 100.0%

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

      16. *-commutative 100.0%

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

   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 87.4%

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

   if -4.7999999999999997e129 < x < 3.60000000000000013e96

   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. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+r+ 100.0%

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

      8. *-lft-identity 100.0%

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

      9. metadata-eval 100.0%

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

      10. count-2 100.0%

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

      11. distribute-rgt-out 100.0%

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

      12. fma-define 100.0%

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

      13. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

      14. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

      15. count-2 100.0%

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

      16. *-commutative 100.0%

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

   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 92.3%

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

   if 3.60000000000000013e96 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 85.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+129}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+96}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + \left(x + x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+129} \lor \neg \left(x \leq 1.7 \cdot 10^{+97}\right):\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.2e+129) (not (<= x 1.7e+97)))
   (+ z (* x 3.0))
   (+ z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e+129) || !(x <= 1.7e+97)) {
		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 <= (-8.2d+129)) .or. (.not. (x <= 1.7d+97))) 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 <= -8.2e+129) || !(x <= 1.7e+97)) {
		tmp = z + (x * 3.0);
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.2e+129) or not (x <= 1.7e+97):
		tmp = z + (x * 3.0)
	else:
		tmp = z + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.2e+129) || !(x <= 1.7e+97))
		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 <= -8.2e+129) || ~((x <= 1.7e+97)))
		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, -8.2e+129], N[Not[LessEqual[x, 1.7e+97]], $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 < -8.2000000000000005e129 or 1.70000000000000005e97 < 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. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. associate-+r+ 99.8%

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

      7. associate-+r+ 99.8%

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

      8. *-lft-identity 99.8%

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

      9. metadata-eval 99.8%

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

      10. count-2 99.8%

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

      11. distribute-rgt-out 99.8%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

      14. metadata-eval 99.9%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 86.1%

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

   if -8.2000000000000005e129 < x < 1.70000000000000005e97

   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. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+r+ 100.0%

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

      8. *-lft-identity 100.0%

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

      9. metadata-eval 100.0%

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

      10. count-2 100.0%

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

      11. distribute-rgt-out 100.0%

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

      12. fma-define 100.0%

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

      13. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

      14. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

      15. count-2 100.0%

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

      16. *-commutative 100.0%

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

   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 92.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+129} \lor \neg \left(x \leq 1.7 \cdot 10^{+97}\right):\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+129} \lor \neg \left(x \leq 3.4 \cdot 10^{+100}\right):\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.5e+129) (not (<= x 3.4e+100))) (* x 3.0) (+ z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e+129) || !(x <= 3.4e+100)) {
		tmp = 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 <= (-6.5d+129)) .or. (.not. (x <= 3.4d+100))) then
        tmp = 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 <= -6.5e+129) || !(x <= 3.4e+100)) {
		tmp = x * 3.0;
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.5e+129) or not (x <= 3.4e+100):
		tmp = x * 3.0
	else:
		tmp = z + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.5e+129) || !(x <= 3.4e+100))
		tmp = 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 <= -6.5e+129) || ~((x <= 3.4e+100)))
		tmp = x * 3.0;
	else
		tmp = z + (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.5e+129], N[Not[LessEqual[x, 3.4e+100]], $MachinePrecision]], N[(x * 3.0), $MachinePrecision], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4999999999999995e129 or 3.39999999999999994e100 < 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. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. associate-+r+ 99.8%

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

      7. associate-+r+ 99.8%

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

      8. *-lft-identity 99.8%

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

      9. metadata-eval 99.8%

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

      10. count-2 99.8%

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

      11. distribute-rgt-out 99.8%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

      14. metadata-eval 99.9%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 70.1%

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

   if -6.4999999999999995e129 < x < 3.39999999999999994e100

   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. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+r+ 100.0%

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

      8. *-lft-identity 100.0%

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

      9. metadata-eval 100.0%

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

      10. count-2 100.0%

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

      11. distribute-rgt-out 100.0%

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

      12. fma-define 100.0%

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

      13. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

      14. metadata-eval 100.0%

          \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

      15. count-2 100.0%

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

      16. *-commutative 100.0%

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

   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 92.3%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+129} \lor \neg \left(x \leq 3.4 \cdot 10^{+100}\right):\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. *-un-lft-identity 99.9%

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

   3. +-commutative 99.9%

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

   4. *-un-lft-identity 99.9%

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

   5. distribute-rgt-out 99.9%

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

   6. metadata-eval 99.9%

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

4. Applied egg-rr 99.9%

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

5. Final simplification 99.9%

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

Alternative 8: 33.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. associate-+r+ 99.9%

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

   7. associate-+r+ 99.9%

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

   8. *-lft-identity 99.9%

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

   9. metadata-eval 99.9%

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

   10. count-2 99.9%

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

   11. distribute-rgt-out 99.9%

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

   12. fma-define 100.0%

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

   13. metadata-eval 100.0%

       \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{1} + 2, y + y\right) \]

   14. metadata-eval 100.0%

       \[\leadsto z + \mathsf{fma}\left(x, \color{blue}{3}, y + y\right) \]

   15. count-2 100.0%

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

   16. *-commutative 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in z around inf 35.8%

   \[\leadsto \color{blue}{z} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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))