Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B

Percentage Accurate: 99.9% → 99.9%

Time: 12.3s

Alternatives: 17

Speedup: 1.0×

• 26.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * ((((y + z) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * ((((y + z) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, \left(y + \left(z + z\right)\right) + \left(y + t\right), y \cdot 5\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma x (+ (+ y (+ z z)) (+ y t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return fma(x, ((y + (z + z)) + (y + t)), (y * 5.0));
}

Julia

function code(x, y, z, t)
	return fma(x, Float64(Float64(y + Float64(z + z)) + Float64(y + t)), Float64(y * 5.0))
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y + N[(z + z), $MachinePrecision]), $MachinePrecision] + N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Step-by-step derivation

   1. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

   2. associate-+l+ 100.0%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + z\right) + \left(y + t\right)}, y \cdot 5\right) \]

   3. associate-+l+ 100.0%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(y + \left(z + z\right)\right)} + \left(y + t\right), y \cdot 5\right) \]

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, \left(y + \left(z + z\right)\right) + \left(y + t\right), y \cdot 5\right) \]
6. Add Preprocessing

Alternative 2: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, t + 2 \cdot \left(y + z\right), y \cdot 5\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma x (+ t (* 2.0 (+ y z))) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return fma(x, (t + (2.0 * (y + z))), (y * 5.0));
}

Julia

function code(x, y, z, t)
	return fma(x, Float64(t + Float64(2.0 * Float64(y + z))), Float64(y * 5.0))
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Step-by-step derivation

   1. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

   2. associate-+l+ 99.9%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

   3. +-commutative 99.9%

      \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

   4. count-2 99.9%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

3. Simplified 99.9%

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

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(x, t + 2 \cdot \left(y + z\right), y \cdot 5\right) \]
6. Add Preprocessing

Alternative 3: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+156} \lor \neg \left(x \leq 1.8 \cdot 10^{+280}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))))
   (if (<= x -3.1e+15)
     (* x (* 2.0 (+ y z)))
     (if (<= x -1.45e-62)
       t_1
       (if (<= x 1.04e-181)
         (* y 5.0)
         (if (<= x 2.45e-147)
           t_1
           (if (<= x 3.4e-48)
             (* y 5.0)
             (if (or (<= x 5.8e+156) (not (<= x 1.8e+280)))
               t_1
               (* x (+ t (* y 2.0)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -3.1e+15) {
		tmp = x * (2.0 * (y + z));
	} else if (x <= -1.45e-62) {
		tmp = t_1;
	} else if (x <= 1.04e-181) {
		tmp = y * 5.0;
	} else if (x <= 2.45e-147) {
		tmp = t_1;
	} else if (x <= 3.4e-48) {
		tmp = y * 5.0;
	} else if ((x <= 5.8e+156) || !(x <= 1.8e+280)) {
		tmp = t_1;
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    if (x <= (-3.1d+15)) then
        tmp = x * (2.0d0 * (y + z))
    else if (x <= (-1.45d-62)) then
        tmp = t_1
    else if (x <= 1.04d-181) then
        tmp = y * 5.0d0
    else if (x <= 2.45d-147) then
        tmp = t_1
    else if (x <= 3.4d-48) then
        tmp = y * 5.0d0
    else if ((x <= 5.8d+156) .or. (.not. (x <= 1.8d+280))) then
        tmp = t_1
    else
        tmp = x * (t + (y * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -3.1e+15) {
		tmp = x * (2.0 * (y + z));
	} else if (x <= -1.45e-62) {
		tmp = t_1;
	} else if (x <= 1.04e-181) {
		tmp = y * 5.0;
	} else if (x <= 2.45e-147) {
		tmp = t_1;
	} else if (x <= 3.4e-48) {
		tmp = y * 5.0;
	} else if ((x <= 5.8e+156) || !(x <= 1.8e+280)) {
		tmp = t_1;
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	tmp = 0
	if x <= -3.1e+15:
		tmp = x * (2.0 * (y + z))
	elif x <= -1.45e-62:
		tmp = t_1
	elif x <= 1.04e-181:
		tmp = y * 5.0
	elif x <= 2.45e-147:
		tmp = t_1
	elif x <= 3.4e-48:
		tmp = y * 5.0
	elif (x <= 5.8e+156) or not (x <= 1.8e+280):
		tmp = t_1
	else:
		tmp = x * (t + (y * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	tmp = 0.0
	if (x <= -3.1e+15)
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	elseif (x <= -1.45e-62)
		tmp = t_1;
	elseif (x <= 1.04e-181)
		tmp = Float64(y * 5.0);
	elseif (x <= 2.45e-147)
		tmp = t_1;
	elseif (x <= 3.4e-48)
		tmp = Float64(y * 5.0);
	elseif ((x <= 5.8e+156) || !(x <= 1.8e+280))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	tmp = 0.0;
	if (x <= -3.1e+15)
		tmp = x * (2.0 * (y + z));
	elseif (x <= -1.45e-62)
		tmp = t_1;
	elseif (x <= 1.04e-181)
		tmp = y * 5.0;
	elseif (x <= 2.45e-147)
		tmp = t_1;
	elseif (x <= 3.4e-48)
		tmp = y * 5.0;
	elseif ((x <= 5.8e+156) || ~((x <= 1.8e+280)))
		tmp = t_1;
	else
		tmp = x * (t + (y * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.1e+15], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.45e-62], t$95$1, If[LessEqual[x, 1.04e-181], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 2.45e-147], t$95$1, If[LessEqual[x, 3.4e-48], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 5.8e+156], N[Not[LessEqual[x, 1.8e+280]], $MachinePrecision]], t$95$1, N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.1e15

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 99.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 99.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 99.9%

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

   6. Taylor expanded in t around 0 78.0%

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

      1. associate-*r* 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-*r* 78.0%

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

   8. Simplified 78.0%

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

   if -3.1e15 < x < -1.44999999999999993e-62 or 1.04000000000000002e-181 < x < 2.45000000000000002e-147 or 3.40000000000000028e-48 < x < 5.80000000000000021e156 or 1.8e280 < x

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 76.9%

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

   if -1.44999999999999993e-62 < x < 1.04000000000000002e-181 or 2.45000000000000002e-147 < x < 3.40000000000000028e-48

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.7%

      \[\leadsto \color{blue}{5 \cdot y} \]

   if 5.80000000000000021e156 < x < 1.8e280

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

   6. Taylor expanded in z around 0 87.5%

      \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 87.5%

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

   8. Simplified 87.5%

      \[\leadsto \color{blue}{x \cdot \left(t + y \cdot 2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+156} \lor \neg \left(x \leq 1.8 \cdot 10^{+280}\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-62} \lor \neg \left(x \leq 1.05 \cdot 10^{-181}\right) \land \left(x \leq 1.5 \cdot 10^{-153} \lor \neg \left(x \leq 3.4 \cdot 10^{-48}\right)\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.1e+14)
   (* x (* 2.0 (+ y z)))
   (if (or (<= x -1e-62)
           (and (not (<= x 1.05e-181))
                (or (<= x 1.5e-153) (not (<= x 3.4e-48)))))
     (* x (+ t (* z 2.0)))
     (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.1e+14) {
		tmp = x * (2.0 * (y + z));
	} else if ((x <= -1e-62) || (!(x <= 1.05e-181) && ((x <= 1.5e-153) || !(x <= 3.4e-48)))) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.1d+14)) then
        tmp = x * (2.0d0 * (y + z))
    else if ((x <= (-1d-62)) .or. (.not. (x <= 1.05d-181)) .and. (x <= 1.5d-153) .or. (.not. (x <= 3.4d-48))) then
        tmp = x * (t + (z * 2.0d0))
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.1e+14) {
		tmp = x * (2.0 * (y + z));
	} else if ((x <= -1e-62) || (!(x <= 1.05e-181) && ((x <= 1.5e-153) || !(x <= 3.4e-48)))) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.1e+14:
		tmp = x * (2.0 * (y + z))
	elif (x <= -1e-62) or (not (x <= 1.05e-181) and ((x <= 1.5e-153) or not (x <= 3.4e-48))):
		tmp = x * (t + (z * 2.0))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.1e+14)
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	elseif ((x <= -1e-62) || (!(x <= 1.05e-181) && ((x <= 1.5e-153) || !(x <= 3.4e-48))))
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.1e+14)
		tmp = x * (2.0 * (y + z));
	elseif ((x <= -1e-62) || (~((x <= 1.05e-181)) && ((x <= 1.5e-153) || ~((x <= 3.4e-48)))))
		tmp = x * (t + (z * 2.0));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.1e+14], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1e-62], And[N[Not[LessEqual[x, 1.05e-181]], $MachinePrecision], Or[LessEqual[x, 1.5e-153], N[Not[LessEqual[x, 3.4e-48]], $MachinePrecision]]]], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e14

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 99.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 99.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 99.9%

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

   6. Taylor expanded in t around 0 78.0%

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

      1. associate-*r* 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-*r* 78.0%

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

   8. Simplified 78.0%

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

   if -1.1e14 < x < -1e-62 or 1.05000000000000002e-181 < x < 1.5e-153 or 3.40000000000000028e-48 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.2%

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

   if -1e-62 < x < 1.05000000000000002e-181 or 1.5e-153 < x < 3.40000000000000028e-48

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.7%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-62} \lor \neg \left(x \leq 1.05 \cdot 10^{-181}\right) \land \left(x \leq 1.5 \cdot 10^{-153} \lor \neg \left(x \leq 3.4 \cdot 10^{-48}\right)\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-47}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+82}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -2.3e+101)
     t_1
     (if (<= x -1.2e+15)
       (* 2.0 (* x y))
       (if (<= x -1.7e-62)
         t_1
         (if (<= x 1.15e-47) (* y 5.0) (if (<= x 1.9e+82) (* x t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -2.3e+101) {
		tmp = t_1;
	} else if (x <= -1.2e+15) {
		tmp = 2.0 * (x * y);
	} else if (x <= -1.7e-62) {
		tmp = t_1;
	} else if (x <= 1.15e-47) {
		tmp = y * 5.0;
	} else if (x <= 1.9e+82) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-2.3d+101)) then
        tmp = t_1
    else if (x <= (-1.2d+15)) then
        tmp = 2.0d0 * (x * y)
    else if (x <= (-1.7d-62)) then
        tmp = t_1
    else if (x <= 1.15d-47) then
        tmp = y * 5.0d0
    else if (x <= 1.9d+82) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -2.3e+101) {
		tmp = t_1;
	} else if (x <= -1.2e+15) {
		tmp = 2.0 * (x * y);
	} else if (x <= -1.7e-62) {
		tmp = t_1;
	} else if (x <= 1.15e-47) {
		tmp = y * 5.0;
	} else if (x <= 1.9e+82) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -2.3e+101:
		tmp = t_1
	elif x <= -1.2e+15:
		tmp = 2.0 * (x * y)
	elif x <= -1.7e-62:
		tmp = t_1
	elif x <= 1.15e-47:
		tmp = y * 5.0
	elif x <= 1.9e+82:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -2.3e+101)
		tmp = t_1;
	elseif (x <= -1.2e+15)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (x <= -1.7e-62)
		tmp = t_1;
	elseif (x <= 1.15e-47)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.9e+82)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -2.3e+101)
		tmp = t_1;
	elseif (x <= -1.2e+15)
		tmp = 2.0 * (x * y);
	elseif (x <= -1.7e-62)
		tmp = t_1;
	elseif (x <= 1.15e-47)
		tmp = y * 5.0;
	elseif (x <= 1.9e+82)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+101], t$95$1, If[LessEqual[x, -1.2e+15], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-62], t$95$1, If[LessEqual[x, 1.15e-47], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.9e+82], N[(x * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.3000000000000001e101 or -1.2e15 < x < -1.69999999999999994e-62 or 1.90000000000000017e82 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 48.6%

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

   if -2.3000000000000001e101 < x < -1.2e15

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 99.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 99.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 99.8%

      \[\leadsto \color{blue}{x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)} \]

   6. Taylor expanded in y around inf 54.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(2 + 5 \cdot \frac{1}{x}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 54.5%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \left(2 + 5 \cdot \frac{1}{x}\right)} \]

      2. *-commutative 54.5%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot \left(2 + 5 \cdot \frac{1}{x}\right) \]

      3. associate-*r/ 54.5%

         \[\leadsto \left(y \cdot x\right) \cdot \left(2 + \color{blue}{\frac{5 \cdot 1}{x}}\right) \]

      4. metadata-eval 54.5%

         \[\leadsto \left(y \cdot x\right) \cdot \left(2 + \frac{\color{blue}{5}}{x}\right) \]

   8. Simplified 54.5%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \left(2 + \frac{5}{x}\right)} \]

   9. Taylor expanded in x around inf 54.5%

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

   if -1.69999999999999994e-62 < x < 1.14999999999999991e-47

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.8%

      \[\leadsto \color{blue}{5 \cdot y} \]

   if 1.14999999999999991e-47 < x < 1.90000000000000017e82

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 44.3%

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

   5. Simplified 44.3%

      \[\leadsto \color{blue}{x \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+101}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-62}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-47}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+82}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-13} \lor \neg \left(x \leq 5.5 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 5 + x \cdot t\right) + 2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5e-13) (not (<= x 5.5e-17)))
   (* x (+ t (+ (* 2.0 (+ y z)) (* 5.0 (/ y x)))))
   (+ (+ (* y 5.0) (* x t)) (* 2.0 (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5e-13) || !(x <= 5.5e-17)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = ((y * 5.0) + (x * t)) + (2.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5d-13)) .or. (.not. (x <= 5.5d-17))) then
        tmp = x * (t + ((2.0d0 * (y + z)) + (5.0d0 * (y / x))))
    else
        tmp = ((y * 5.0d0) + (x * t)) + (2.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5e-13) || !(x <= 5.5e-17)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = ((y * 5.0) + (x * t)) + (2.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5e-13) or not (x <= 5.5e-17):
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))))
	else:
		tmp = ((y * 5.0) + (x * t)) + (2.0 * (x * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5e-13) || !(x <= 5.5e-17))
		tmp = Float64(x * Float64(t + Float64(Float64(2.0 * Float64(y + z)) + Float64(5.0 * Float64(y / x)))));
	else
		tmp = Float64(Float64(Float64(y * 5.0) + Float64(x * t)) + Float64(2.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5e-13) || ~((x <= 5.5e-17)))
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	else
		tmp = ((y * 5.0) + (x * t)) + (2.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5e-13], N[Not[LessEqual[x, 5.5e-17]], $MachinePrecision]], N[(x * N[(t + N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9999999999999999e-13 or 5.50000000000000001e-17 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.9%

      \[\leadsto \color{blue}{x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)} \]

   if -4.9999999999999999e-13 < x < 5.50000000000000001e-17

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 99.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 99.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(y + z\right)\right) + \left(5 \cdot y + t \cdot x\right)} \]

   6. Taylor expanded in y around 0 99.9%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot z\right)} + \left(5 \cdot y + t \cdot x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-13} \lor \neg \left(x \leq 5.5 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 5 + x \cdot t\right) + 2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 8 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 5 + x \cdot t\right) + 2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.5) (not (<= x 8e-17)))
   (* x (+ t (* 2.0 (+ y z))))
   (+ (+ (* y 5.0) (* x t)) (* 2.0 (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 8e-17)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = ((y * 5.0) + (x * t)) + (2.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.5d0)) .or. (.not. (x <= 8d-17))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = ((y * 5.0d0) + (x * t)) + (2.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 8e-17)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = ((y * 5.0) + (x * t)) + (2.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.5) or not (x <= 8e-17):
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = ((y * 5.0) + (x * t)) + (2.0 * (x * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.5) || !(x <= 8e-17))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(Float64(y * 5.0) + Float64(x * t)) + Float64(2.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.5) || ~((x <= 8e-17)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = ((y * 5.0) + (x * t)) + (2.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.5], N[Not[LessEqual[x, 8e-17]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5 or 8.00000000000000057e-17 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.0%

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

   if -2.5 < x < 8.00000000000000057e-17

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 99.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 99.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 99.9%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(y + z\right)\right) + \left(5 \cdot y + t \cdot x\right)} \]

   6. Taylor expanded in y around 0 99.5%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot z\right)} + \left(5 \cdot y + t \cdot x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 8 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 5 + x \cdot t\right) + 2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 8 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.5) (not (<= x 8e-17)))
   (* x (+ t (* 2.0 (+ y z))))
   (+ (* x (+ t (+ y (* z 2.0)))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 8e-17)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.5d0)) .or. (.not. (x <= 8d-17))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = (x * (t + (y + (z * 2.0d0)))) + (y * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 8e-17)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.5) or not (x <= 8e-17):
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.5) || !(x <= 8e-17))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(y + Float64(z * 2.0)))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.5) || ~((x <= 8e-17)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.5], N[Not[LessEqual[x, 8e-17]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(y + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5 or 8.00000000000000057e-17 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.0%

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

   if -2.5 < x < 8.00000000000000057e-17

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.5%

      \[\leadsto x \cdot \left(\left(\color{blue}{2 \cdot z} + y\right) + t\right) + y \cdot 5 \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 8 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+144}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -2.1e+81)
     t_1
     (if (<= y 3.7e+43)
       (* x (+ t (* z 2.0)))
       (if (<= y 3.2e+144) (+ (* y 5.0) (* x t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.1e+81) {
		tmp = t_1;
	} else if (y <= 3.7e+43) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 3.2e+144) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-2.1d+81)) then
        tmp = t_1
    else if (y <= 3.7d+43) then
        tmp = x * (t + (z * 2.0d0))
    else if (y <= 3.2d+144) then
        tmp = (y * 5.0d0) + (x * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.1e+81) {
		tmp = t_1;
	} else if (y <= 3.7e+43) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 3.2e+144) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -2.1e+81:
		tmp = t_1
	elif y <= 3.7e+43:
		tmp = x * (t + (z * 2.0))
	elif y <= 3.2e+144:
		tmp = (y * 5.0) + (x * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -2.1e+81)
		tmp = t_1;
	elseif (y <= 3.7e+43)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (y <= 3.2e+144)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -2.1e+81)
		tmp = t_1;
	elseif (y <= 3.7e+43)
		tmp = x * (t + (z * 2.0));
	elseif (y <= 3.2e+144)
		tmp = (y * 5.0) + (x * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+81], t$95$1, If[LessEqual[y, 3.7e+43], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+144], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0999999999999999e81 or 3.2000000000000001e144 < y

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 89.9%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   5. Simplified 89.9%

      \[\leadsto \color{blue}{y \cdot \left(5 + x \cdot 2\right)} \]

   if -2.0999999999999999e81 < y < 3.7000000000000001e43

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.5%

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

   if 3.7000000000000001e43 < y < 3.2000000000000001e144

   1. Initial program 99.8%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l+ 99.8%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) + y \cdot 5 \]

      2. +-commutative 99.8%

         \[\leadsto x \cdot \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      3. flip-+ 0.0%

         \[\leadsto x \cdot \left(\color{blue}{\frac{\left(y + z\right) \cdot \left(y + z\right) - \left(y + z\right) \cdot \left(y + z\right)}{\left(y + z\right) - \left(y + z\right)}} + t\right) + y \cdot 5 \]

      4. pow2 0.0%

         \[\leadsto x \cdot \left(\frac{\color{blue}{{\left(y + z\right)}^{2}} - \left(y + z\right) \cdot \left(y + z\right)}{\left(y + z\right) - \left(y + z\right)} + t\right) + y \cdot 5 \]

      5. pow2 0.0%

         \[\leadsto x \cdot \left(\frac{{\left(y + z\right)}^{2} - \color{blue}{{\left(y + z\right)}^{2}}}{\left(y + z\right) - \left(y + z\right)} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 0.0%

      \[\leadsto x \cdot \left(\color{blue}{\frac{{\left(y + z\right)}^{2} - {\left(y + z\right)}^{2}}{\left(y + z\right) - \left(y + z\right)}} + t\right) + y \cdot 5 \]

   6. Simplified 89.3%

      \[\leadsto x \cdot \left(\color{blue}{0} + t\right) + y \cdot 5 \]

   7. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{5 \cdot y + t \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+81}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+144}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-47}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+82}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -3.1e-62)
     t_1
     (if (<= x 1.3e-47) (* y 5.0) (if (<= x 2.95e+82) (* x t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -3.1e-62) {
		tmp = t_1;
	} else if (x <= 1.3e-47) {
		tmp = y * 5.0;
	} else if (x <= 2.95e+82) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-3.1d-62)) then
        tmp = t_1
    else if (x <= 1.3d-47) then
        tmp = y * 5.0d0
    else if (x <= 2.95d+82) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -3.1e-62) {
		tmp = t_1;
	} else if (x <= 1.3e-47) {
		tmp = y * 5.0;
	} else if (x <= 2.95e+82) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -3.1e-62:
		tmp = t_1
	elif x <= 1.3e-47:
		tmp = y * 5.0
	elif x <= 2.95e+82:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -3.1e-62)
		tmp = t_1;
	elseif (x <= 1.3e-47)
		tmp = Float64(y * 5.0);
	elseif (x <= 2.95e+82)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -3.1e-62)
		tmp = t_1;
	elseif (x <= 1.3e-47)
		tmp = y * 5.0;
	elseif (x <= 2.95e+82)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.1e-62], t$95$1, If[LessEqual[x, 1.3e-47], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 2.95e+82], N[(x * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.0999999999999999e-62 or 2.9499999999999998e82 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 44.5%

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

   if -3.0999999999999999e-62 < x < 1.3e-47

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.8%

      \[\leadsto \color{blue}{5 \cdot y} \]

   if 1.3e-47 < x < 2.9499999999999998e82

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 44.3%

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

   5. Simplified 44.3%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-62}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-47}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+82}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + \left(y \cdot 5 + x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.1e+143)
   (+ (* x (+ t (+ y (* z 2.0)))) (* y 5.0))
   (+ (* 2.0 (* x (+ y z))) (+ (* y 5.0) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.1e+143) {
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0);
	} else {
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.1d+143)) then
        tmp = (x * (t + (y + (z * 2.0d0)))) + (y * 5.0d0)
    else
        tmp = (2.0d0 * (x * (y + z))) + ((y * 5.0d0) + (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.1e+143) {
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0);
	} else {
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.1e+143:
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0)
	else:
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.1e+143)
		tmp = Float64(Float64(x * Float64(t + Float64(y + Float64(z * 2.0)))) + Float64(y * 5.0));
	else
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(Float64(y * 5.0) + Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.1e+143)
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0);
	else
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.1e+143], N[(N[(x * N[(t + N[(y + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.10000000000000038e143

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.0%

      \[\leadsto x \cdot \left(\left(\color{blue}{2 \cdot z} + y\right) + t\right) + y \cdot 5 \]

   if -5.10000000000000038e143 < t

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 99.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 99.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 98.5%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(y + z\right)\right) + \left(5 \cdot y + t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + \left(y \cdot 5 + x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-62} \lor \neg \left(x \leq 6.8 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.6e-62) (not (<= x 6.8e-17)))
   (* x (+ t (* 2.0 (+ y z))))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.6e-62) || !(x <= 6.8e-17)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.6d-62)) .or. (.not. (x <= 6.8d-17))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.6e-62) || !(x <= 6.8e-17)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.6e-62) or not (x <= 6.8e-17):
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.6e-62) || !(x <= 6.8e-17))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.6e-62) || ~((x <= 6.8e-17)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.6e-62], N[Not[LessEqual[x, 6.8e-17]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6e-62 or 6.7999999999999996e-17 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.1%

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

   if -3.6e-62 < x < 6.7999999999999996e-17

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l+ 99.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) + y \cdot 5 \]

      2. +-commutative 99.9%

         \[\leadsto x \cdot \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) + y \cdot 5 \]

      3. flip-+ 0.0%

         \[\leadsto x \cdot \left(\color{blue}{\frac{\left(y + z\right) \cdot \left(y + z\right) - \left(y + z\right) \cdot \left(y + z\right)}{\left(y + z\right) - \left(y + z\right)}} + t\right) + y \cdot 5 \]

      4. pow2 0.0%

         \[\leadsto x \cdot \left(\frac{\color{blue}{{\left(y + z\right)}^{2}} - \left(y + z\right) \cdot \left(y + z\right)}{\left(y + z\right) - \left(y + z\right)} + t\right) + y \cdot 5 \]

      5. pow2 0.0%

         \[\leadsto x \cdot \left(\frac{{\left(y + z\right)}^{2} - \color{blue}{{\left(y + z\right)}^{2}}}{\left(y + z\right) - \left(y + z\right)} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 0.0%

      \[\leadsto x \cdot \left(\color{blue}{\frac{{\left(y + z\right)}^{2} - {\left(y + z\right)}^{2}}{\left(y + z\right) - \left(y + z\right)}} + t\right) + y \cdot 5 \]

   6. Simplified 85.3%

      \[\leadsto x \cdot \left(\color{blue}{0} + t\right) + y \cdot 5 \]

   7. Taylor expanded in x around 0 85.3%

      \[\leadsto \color{blue}{5 \cdot y + t \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-62} \lor \neg \left(x \leq 6.8 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-62} \lor \neg \left(x \leq 3.7 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.6e-62) (not (<= x 3.7e-16)))
   (* x (* 2.0 (+ y z)))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.6e-62) || !(x <= 3.7e-16)) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.6d-62)) .or. (.not. (x <= 3.7d-16))) then
        tmp = x * (2.0d0 * (y + z))
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.6e-62) || !(x <= 3.7e-16)) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.6e-62) or not (x <= 3.7e-16):
		tmp = x * (2.0 * (y + z))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.6e-62) || !(x <= 3.7e-16))
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.6e-62) || ~((x <= 3.7e-16)))
		tmp = x * (2.0 * (y + z));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.6e-62], N[Not[LessEqual[x, 3.7e-16]], $MachinePrecision]], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999999e-62 or 3.7e-16 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Step-by-step derivation

      1. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(\left(\left(y + z\right) + z\right) + y\right) + t, y \cdot 5\right)} \]

      2. associate-+l+ 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t, y \cdot 5\right) \]

      3. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, \left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t, y \cdot 5\right) \]

      4. count-2 100.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \left(y + z\right)} + t, y \cdot 5\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.1%

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

   6. Taylor expanded in t around 0 68.8%

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

      1. associate-*r* 68.8%

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

      2. *-commutative 68.8%

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

      3. associate-*r* 68.8%

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

   8. Simplified 68.8%

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

   if -2.5999999999999999e-62 < x < 3.7e-16

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 64.1%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-62} \lor \neg \left(x \leq 3.7 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 78.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+81} \lor \neg \left(y \leq 620000000\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.6e+81) (not (<= y 620000000.0)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e+81) || !(y <= 620000000.0)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.6d+81)) .or. (.not. (y <= 620000000.0d0))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e+81) || !(y <= 620000000.0)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.6e+81) or not (y <= 620000000.0):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.6e+81) || !(y <= 620000000.0))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.6e+81) || ~((y <= 620000000.0)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.6e+81], N[Not[LessEqual[y, 620000000.0]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999992e81 or 6.2e8 < y

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 82.8%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   5. Simplified 82.8%

      \[\leadsto \color{blue}{y \cdot \left(5 + x \cdot 2\right)} \]

   if -2.59999999999999992e81 < y < 6.2e8

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.1%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+81} \lor \neg \left(y \leq 620000000\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ t (+ y (+ z (+ y z))))) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * (t + (y + (z + (y + z))))) + (y * 5.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (t + (y + (z + (y + z))))) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * (t + (y + (z + (y + z))))) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * (t + (y + (z + (y + z))))) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(t + Float64(y + Float64(z + Float64(y + z))))) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * (t + (y + (z + (y + z))))) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(t + N[(y + N[(z + N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) + y \cdot 5 \]
4. Add Preprocessing

Alternative 16: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-62} \lor \neg \left(x \leq 1.3 \cdot 10^{-47}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.1e-62) (not (<= x 1.3e-47))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-62) || !(x <= 1.3e-47)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.1d-62)) .or. (.not. (x <= 1.3d-47))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-62) || !(x <= 1.3e-47)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.1e-62) or not (x <= 1.3e-47):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.1e-62) || !(x <= 1.3e-47))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.1e-62) || ~((x <= 1.3e-47)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.1e-62], N[Not[LessEqual[x, 1.3e-47]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0999999999999999e-62 or 1.3e-47 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 36.8%

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

   5. Simplified 36.8%

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

   if -3.0999999999999999e-62 < x < 1.3e-47

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.8%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-62} \lor \neg \left(x \leq 1.3 \cdot 10^{-47}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* y 5.0))

C

double code(double x, double y, double z, double t) {
	return y * 5.0;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = y * 5.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return y * 5.0;
}

Python

def code(x, y, z, t):
	return y * 5.0

Julia

function code(x, y, z, t)
	return Float64(y * 5.0)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = y * 5.0;
end

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Add Preprocessing

3. Taylor expanded in x around 0 29.4%

   \[\leadsto \color{blue}{5 \cdot y} \]

4. Final simplification 29.4%

   \[\leadsto y \cdot 5 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))