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

Percentage Accurate: 99.9% → 100.0%

Time: 4.9s

Alternatives: 8

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. remove-double-neg 99.9%

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

   4. distribute-neg-in 99.9%

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

   5. distribute-neg-in 99.9%

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

   6. remove-double-neg 99.9%

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

   7. sub-neg 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. associate-+r+ 99.9%

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

   11. associate--l+ 99.9%

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

   12. count-2 99.9%

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

   13. *-commutative 99.9%

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

   14. fma-def 99.9%

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

   15. count-2 99.9%

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

   16. neg-mul-1 99.9%

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

   17. distribute-rgt-out-- 99.9%

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

   18. metadata-eval 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{z + \mathsf{fma}\left(y, 2, x \cdot 3\right)} \]
4. Step-by-step derivation

   1. add-log-exp 27.7%

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

   2. *-un-lft-identity 27.7%

      \[\leadsto z + \log \color{blue}{\left(1 \cdot e^{\mathsf{fma}\left(y, 2, x \cdot 3\right)}\right)} \]

   3. log-prod 27.7%

      \[\leadsto z + \color{blue}{\left(\log 1 + \log \left(e^{\mathsf{fma}\left(y, 2, x \cdot 3\right)}\right)\right)} \]

   4. metadata-eval 27.7%

      \[\leadsto z + \left(\color{blue}{0} + \log \left(e^{\mathsf{fma}\left(y, 2, x \cdot 3\right)}\right)\right) \]

   5. add-log-exp 99.9%

      \[\leadsto z + \left(0 + \color{blue}{\mathsf{fma}\left(y, 2, x \cdot 3\right)}\right) \]

   6. fma-udef 99.9%

      \[\leadsto z + \left(0 + \color{blue}{\left(y \cdot 2 + x \cdot 3\right)}\right) \]

   7. +-commutative 99.9%

      \[\leadsto z + \left(0 + \color{blue}{\left(x \cdot 3 + y \cdot 2\right)}\right) \]

   8. fma-def 99.9%

      \[\leadsto z + \left(0 + \color{blue}{\mathsf{fma}\left(x, 3, y \cdot 2\right)}\right) \]

   9. *-commutative 99.9%

      \[\leadsto z + \left(0 + \mathsf{fma}\left(x, 3, \color{blue}{2 \cdot y}\right)\right) \]

5. Applied egg-rr 99.9%

   \[\leadsto z + \color{blue}{\left(0 + \mathsf{fma}\left(x, 3, 2 \cdot y\right)\right)} \]

6. Final simplification 99.9%

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

Alternative 2: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-13}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-82}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-178}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-255}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-6}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+114}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.4e+63)
   (* x 3.0)
   (if (<= x -5.4e-13)
     z
     (if (<= x -3.3e-82)
       (* 2.0 y)
       (if (<= x -2e-178)
         z
         (if (<= x -3.7e-255)
           (* 2.0 y)
           (if (<= x 1.35e-6) z (if (<= x 1.9e+114) (* 2.0 y) (* x 3.0)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e+63) {
		tmp = x * 3.0;
	} else if (x <= -5.4e-13) {
		tmp = z;
	} else if (x <= -3.3e-82) {
		tmp = 2.0 * y;
	} else if (x <= -2e-178) {
		tmp = z;
	} else if (x <= -3.7e-255) {
		tmp = 2.0 * y;
	} else if (x <= 1.35e-6) {
		tmp = z;
	} else if (x <= 1.9e+114) {
		tmp = 2.0 * y;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-3.4d+63)) then
        tmp = x * 3.0d0
    else if (x <= (-5.4d-13)) then
        tmp = z
    else if (x <= (-3.3d-82)) then
        tmp = 2.0d0 * y
    else if (x <= (-2d-178)) then
        tmp = z
    else if (x <= (-3.7d-255)) then
        tmp = 2.0d0 * y
    else if (x <= 1.35d-6) then
        tmp = z
    else if (x <= 1.9d+114) then
        tmp = 2.0d0 * y
    else
        tmp = x * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e+63) {
		tmp = x * 3.0;
	} else if (x <= -5.4e-13) {
		tmp = z;
	} else if (x <= -3.3e-82) {
		tmp = 2.0 * y;
	} else if (x <= -2e-178) {
		tmp = z;
	} else if (x <= -3.7e-255) {
		tmp = 2.0 * y;
	} else if (x <= 1.35e-6) {
		tmp = z;
	} else if (x <= 1.9e+114) {
		tmp = 2.0 * y;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.4e+63:
		tmp = x * 3.0
	elif x <= -5.4e-13:
		tmp = z
	elif x <= -3.3e-82:
		tmp = 2.0 * y
	elif x <= -2e-178:
		tmp = z
	elif x <= -3.7e-255:
		tmp = 2.0 * y
	elif x <= 1.35e-6:
		tmp = z
	elif x <= 1.9e+114:
		tmp = 2.0 * y
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e+63)
		tmp = Float64(x * 3.0);
	elseif (x <= -5.4e-13)
		tmp = z;
	elseif (x <= -3.3e-82)
		tmp = Float64(2.0 * y);
	elseif (x <= -2e-178)
		tmp = z;
	elseif (x <= -3.7e-255)
		tmp = Float64(2.0 * y);
	elseif (x <= 1.35e-6)
		tmp = z;
	elseif (x <= 1.9e+114)
		tmp = Float64(2.0 * y);
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.4e+63)
		tmp = x * 3.0;
	elseif (x <= -5.4e-13)
		tmp = z;
	elseif (x <= -3.3e-82)
		tmp = 2.0 * y;
	elseif (x <= -2e-178)
		tmp = z;
	elseif (x <= -3.7e-255)
		tmp = 2.0 * y;
	elseif (x <= 1.35e-6)
		tmp = z;
	elseif (x <= 1.9e+114)
		tmp = 2.0 * y;
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.4e+63], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, -5.4e-13], z, If[LessEqual[x, -3.3e-82], N[(2.0 * y), $MachinePrecision], If[LessEqual[x, -2e-178], z, If[LessEqual[x, -3.7e-255], N[(2.0 * y), $MachinePrecision], If[LessEqual[x, 1.35e-6], z, If[LessEqual[x, 1.9e+114], N[(2.0 * y), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.3999999999999999e63 or 1.9e114 < 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%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. count-2 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 74.6%

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

   if -3.3999999999999999e63 < x < -5.40000000000000021e-13 or -3.30000000000000022e-82 < x < -1.9999999999999999e-178 or -3.7000000000000002e-255 < x < 1.34999999999999999e-6

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 63.6%

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

   if -5.40000000000000021e-13 < x < -3.30000000000000022e-82 or -1.9999999999999999e-178 < x < -3.7000000000000002e-255 or 1.34999999999999999e-6 < x < 1.9e114

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 64.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-13}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-82}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-178}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-255}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-6}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+114}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]

Alternative 3: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z + x \cdot 3\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+31}:\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+155}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ z (* x 3.0))))
   (if (<= x -2.4e+18)
     t_0
     (if (<= x 5.2e+31)
       (+ z (* 2.0 y))
       (if (<= x 2.6e+155) (+ x (* 2.0 (+ x y))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z + (x * 3.0);
	double tmp;
	if (x <= -2.4e+18) {
		tmp = t_0;
	} else if (x <= 5.2e+31) {
		tmp = z + (2.0 * y);
	} else if (x <= 2.6e+155) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z + (x * 3.0d0)
    if (x <= (-2.4d+18)) then
        tmp = t_0
    else if (x <= 5.2d+31) then
        tmp = z + (2.0d0 * y)
    else if (x <= 2.6d+155) then
        tmp = x + (2.0d0 * (x + y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z + (x * 3.0);
	double tmp;
	if (x <= -2.4e+18) {
		tmp = t_0;
	} else if (x <= 5.2e+31) {
		tmp = z + (2.0 * y);
	} else if (x <= 2.6e+155) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z + (x * 3.0)
	tmp = 0
	if x <= -2.4e+18:
		tmp = t_0
	elif x <= 5.2e+31:
		tmp = z + (2.0 * y)
	elif x <= 2.6e+155:
		tmp = x + (2.0 * (x + y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z + Float64(x * 3.0))
	tmp = 0.0
	if (x <= -2.4e+18)
		tmp = t_0;
	elseif (x <= 5.2e+31)
		tmp = Float64(z + Float64(2.0 * y));
	elseif (x <= 2.6e+155)
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z + (x * 3.0);
	tmp = 0.0;
	if (x <= -2.4e+18)
		tmp = t_0;
	elseif (x <= 5.2e+31)
		tmp = z + (2.0 * y);
	elseif (x <= 2.6e+155)
		tmp = x + (2.0 * (x + y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+18], t$95$0, If[LessEqual[x, 5.2e+31], N[(z + N[(2.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+155], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4e18 or 2.6000000000000002e155 < 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. distribute-neg-in 99.7%

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

      5. distribute-neg-in 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub-neg 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. associate-+r+ 99.8%

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

      11. associate--l+ 99.7%

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

      12. count-2 99.7%

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

      13. *-commutative 99.7%

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

      14. fma-def 99.7%

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

      15. count-2 99.7%

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

      16. neg-mul-1 99.7%

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

      17. distribute-rgt-out-- 99.7%

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

      18. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 91.9%

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

   if -2.4e18 < x < 5.2e31

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 94.3%

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

   if 5.2e31 < x < 2.6000000000000002e155

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 95.2%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+31}:\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+155}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \]

Alternative 4: 84.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+18} \lor \neg \left(x \leq 1.62 \cdot 10^{+109}\right):\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + 2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.16e+18) (not (<= x 1.62e+109)))
   (+ z (* x 3.0))
   (+ z (* 2.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.16e+18) || !(x <= 1.62e+109)) {
		tmp = z + (x * 3.0);
	} else {
		tmp = z + (2.0 * y);
	}
	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 <= (-1.16d+18)) .or. (.not. (x <= 1.62d+109))) then
        tmp = z + (x * 3.0d0)
    else
        tmp = z + (2.0d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.16e+18) || !(x <= 1.62e+109)) {
		tmp = z + (x * 3.0);
	} else {
		tmp = z + (2.0 * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.16e+18) or not (x <= 1.62e+109):
		tmp = z + (x * 3.0)
	else:
		tmp = z + (2.0 * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.16e+18) || !(x <= 1.62e+109))
		tmp = Float64(z + Float64(x * 3.0));
	else
		tmp = Float64(z + Float64(2.0 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.16e+18) || ~((x <= 1.62e+109)))
		tmp = z + (x * 3.0);
	else
		tmp = z + (2.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.16e+18], N[Not[LessEqual[x, 1.62e+109]], $MachinePrecision]], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(z + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.16e18 or 1.62e109 < 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+ 99.8%

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

      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. distribute-neg-in 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. remove-double-neg 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. associate-+r+ 99.8%

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

      11. associate--l+ 99.8%

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

      12. count-2 99.8%

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

      13. *-commutative 99.8%

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

      14. fma-def 99.8%

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

      15. count-2 99.8%

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

      16. neg-mul-1 99.8%

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

      17. distribute-rgt-out-- 99.8%

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

      18. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 90.4%

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

   if -1.16e18 < x < 1.62e109

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 92.4%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+18} \lor \neg \left(x \leq 1.62 \cdot 10^{+109}\right):\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + 2 \cdot y\\ \end{array} \]

Alternative 5: 79.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+92}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+114}:\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.5e+92) (* x 3.0) (if (<= x 2.3e+114) (+ z (* 2.0 y)) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e+92) {
		tmp = x * 3.0;
	} else if (x <= 2.3e+114) {
		tmp = z + (2.0 * y);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-3.5d+92)) then
        tmp = x * 3.0d0
    else if (x <= 2.3d+114) then
        tmp = z + (2.0d0 * y)
    else
        tmp = x * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e+92) {
		tmp = x * 3.0;
	} else if (x <= 2.3e+114) {
		tmp = z + (2.0 * y);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.5e+92:
		tmp = x * 3.0
	elif x <= 2.3e+114:
		tmp = z + (2.0 * y)
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.5e+92)
		tmp = Float64(x * 3.0);
	elseif (x <= 2.3e+114)
		tmp = Float64(z + Float64(2.0 * y));
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.5e+92)
		tmp = x * 3.0;
	elseif (x <= 2.3e+114)
		tmp = z + (2.0 * y);
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.5e+92], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 2.3e+114], N[(z + N[(2.0 * y), $MachinePrecision]), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.49999999999999986e92 or 2.3e114 < 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%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. count-2 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 76.7%

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

   if -3.49999999999999986e92 < x < 2.3e114

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 89.6%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+92}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+114}:\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]

Alternative 6: 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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto x + \left(z + 2 \cdot \left(x + y\right)\right) \]

Alternative 7: 52.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+54}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-13}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.6e+54) (* 2.0 y) (if (<= y 1.85e-13) z (* 2.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.6e+54) {
		tmp = 2.0 * y;
	} else if (y <= 1.85e-13) {
		tmp = z;
	} else {
		tmp = 2.0 * y;
	}
	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 <= (-5.6d+54)) then
        tmp = 2.0d0 * y
    else if (y <= 1.85d-13) then
        tmp = z
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.6e+54) {
		tmp = 2.0 * y;
	} else if (y <= 1.85e-13) {
		tmp = z;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.6e+54:
		tmp = 2.0 * y
	elif y <= 1.85e-13:
		tmp = z
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.6e+54)
		tmp = Float64(2.0 * y);
	elseif (y <= 1.85e-13)
		tmp = z;
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.6e+54)
		tmp = 2.0 * y;
	elseif (y <= 1.85e-13)
		tmp = z;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.6e+54], N[(2.0 * y), $MachinePrecision], If[LessEqual[y, 1.85e-13], z, N[(2.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6000000000000003e54 or 1.84999999999999994e-13 < 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. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 60.5%

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

   if -5.6000000000000003e54 < y < 1.84999999999999994e-13

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 53.5%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+54}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-13}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]

Alternative 8: 34.1% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in z around inf 37.6%

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

5. Final simplification 37.6%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023268 
(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))