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

Percentage Accurate: 99.9% → 99.9%

Time: 12.6s

Alternatives: 15

Speedup: 0.1×

• 26.8% 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 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%

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

   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. Add Preprocessing

Alternative 2: 62.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ t_2 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-89}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-246}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-246}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-242}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.55 \cdot 10^{-242}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+70} \lor \neg \left(x \leq 2 \cdot 10^{+85}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x (+ y z)))) (t_2 (* 2.0 (* x z))))
   (if (<= x -270000000000.0)
     t_1
     (if (<= x -6.3e-89)
       (* x t)
       (if (<= x -2.1e-246)
         (* y 5.0)
         (if (<= x -2e-246)
           t_2
           (if (<= x 3.5e-242)
             (* y 5.0)
             (if (<= x 3.55e-242)
               t_2
               (if (<= x 5.5e-17)
                 (* y 5.0)
                 (if (or (<= x 1.9e+70) (not (<= x 2e+85)))
                   t_1
                   (* x t)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * (y + z));
	double t_2 = 2.0 * (x * z);
	double tmp;
	if (x <= -270000000000.0) {
		tmp = t_1;
	} else if (x <= -6.3e-89) {
		tmp = x * t;
	} else if (x <= -2.1e-246) {
		tmp = y * 5.0;
	} else if (x <= -2e-246) {
		tmp = t_2;
	} else if (x <= 3.5e-242) {
		tmp = y * 5.0;
	} else if (x <= 3.55e-242) {
		tmp = t_2;
	} else if (x <= 5.5e-17) {
		tmp = y * 5.0;
	} else if ((x <= 1.9e+70) || !(x <= 2e+85)) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * (y + z))
    t_2 = 2.0d0 * (x * z)
    if (x <= (-270000000000.0d0)) then
        tmp = t_1
    else if (x <= (-6.3d-89)) then
        tmp = x * t
    else if (x <= (-2.1d-246)) then
        tmp = y * 5.0d0
    else if (x <= (-2d-246)) then
        tmp = t_2
    else if (x <= 3.5d-242) then
        tmp = y * 5.0d0
    else if (x <= 3.55d-242) then
        tmp = t_2
    else if (x <= 5.5d-17) then
        tmp = y * 5.0d0
    else if ((x <= 1.9d+70) .or. (.not. (x <= 2d+85))) then
        tmp = t_1
    else
        tmp = x * t
    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 * (y + z));
	double t_2 = 2.0 * (x * z);
	double tmp;
	if (x <= -270000000000.0) {
		tmp = t_1;
	} else if (x <= -6.3e-89) {
		tmp = x * t;
	} else if (x <= -2.1e-246) {
		tmp = y * 5.0;
	} else if (x <= -2e-246) {
		tmp = t_2;
	} else if (x <= 3.5e-242) {
		tmp = y * 5.0;
	} else if (x <= 3.55e-242) {
		tmp = t_2;
	} else if (x <= 5.5e-17) {
		tmp = y * 5.0;
	} else if ((x <= 1.9e+70) || !(x <= 2e+85)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * (y + z))
	t_2 = 2.0 * (x * z)
	tmp = 0
	if x <= -270000000000.0:
		tmp = t_1
	elif x <= -6.3e-89:
		tmp = x * t
	elif x <= -2.1e-246:
		tmp = y * 5.0
	elif x <= -2e-246:
		tmp = t_2
	elif x <= 3.5e-242:
		tmp = y * 5.0
	elif x <= 3.55e-242:
		tmp = t_2
	elif x <= 5.5e-17:
		tmp = y * 5.0
	elif (x <= 1.9e+70) or not (x <= 2e+85):
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * Float64(y + z)))
	t_2 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = t_1;
	elseif (x <= -6.3e-89)
		tmp = Float64(x * t);
	elseif (x <= -2.1e-246)
		tmp = Float64(y * 5.0);
	elseif (x <= -2e-246)
		tmp = t_2;
	elseif (x <= 3.5e-242)
		tmp = Float64(y * 5.0);
	elseif (x <= 3.55e-242)
		tmp = t_2;
	elseif (x <= 5.5e-17)
		tmp = Float64(y * 5.0);
	elseif ((x <= 1.9e+70) || !(x <= 2e+85))
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * (y + z));
	t_2 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -270000000000.0)
		tmp = t_1;
	elseif (x <= -6.3e-89)
		tmp = x * t;
	elseif (x <= -2.1e-246)
		tmp = y * 5.0;
	elseif (x <= -2e-246)
		tmp = t_2;
	elseif (x <= 3.5e-242)
		tmp = y * 5.0;
	elseif (x <= 3.55e-242)
		tmp = t_2;
	elseif (x <= 5.5e-17)
		tmp = y * 5.0;
	elseif ((x <= 1.9e+70) || ~((x <= 2e+85)))
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -270000000000.0], t$95$1, If[LessEqual[x, -6.3e-89], N[(x * t), $MachinePrecision], If[LessEqual[x, -2.1e-246], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, -2e-246], t$95$2, If[LessEqual[x, 3.5e-242], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 3.55e-242], t$95$2, If[LessEqual[x, 5.5e-17], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 1.9e+70], N[Not[LessEqual[x, 2e+85]], $MachinePrecision]], t$95$1, N[(x * t), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.7e11 or 5.50000000000000001e-17 < x < 1.8999999999999999e70 or 2e85 < 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 0 100.0%

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

   4. Taylor expanded in t around 0 76.4%

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

      1. *-commutative 76.4%

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

      2. distribute-lft-out 76.4%

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

   6. Simplified 76.4%

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

   7. Taylor expanded in x around inf 76.4%

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

      1. +-commutative 76.4%

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

   9. Simplified 76.4%

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

   if -2.7e11 < x < -6.2999999999999996e-89 or 1.8999999999999999e70 < x < 2e85

   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 t around inf 49.4%

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

   5. Simplified 49.4%

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

   if -6.2999999999999996e-89 < x < -2.09999999999999995e-246 or -1.99999999999999991e-246 < x < 3.4999999999999999e-242 or 3.54999999999999981e-242 < x < 5.50000000000000001e-17

   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 x around 0 77.9%

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

   if -2.09999999999999995e-246 < x < -1.99999999999999991e-246 or 3.4999999999999999e-242 < x < 3.54999999999999981e-242

   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 100.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-89}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-246}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-246}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-242}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.55 \cdot 10^{-242}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+70} \lor \neg \left(x \leq 2 \cdot 10^{+85}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.7 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))) (t_2 (* 2.0 (* x (+ y z)))))
   (if (<= x -4.8e+141)
     t_2
     (if (<= x -8.6e+123)
       t_1
       (if (<= x -8e+24)
         t_2
         (if (<= x -3.8e-40)
           t_1
           (if (<= x 1.05e-17)
             (* y 5.0)
             (if (<= x 6.5e+47)
               t_1
               (if (<= x 4.4e+73)
                 t_2
                 (if (<= x 3.15e+122)
                   t_1
                   (if (<= x 6.7e+137) t_2 (* 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 t_2 = 2.0 * (x * (y + z));
	double tmp;
	if (x <= -4.8e+141) {
		tmp = t_2;
	} else if (x <= -8.6e+123) {
		tmp = t_1;
	} else if (x <= -8e+24) {
		tmp = t_2;
	} else if (x <= -3.8e-40) {
		tmp = t_1;
	} else if (x <= 1.05e-17) {
		tmp = y * 5.0;
	} else if (x <= 6.5e+47) {
		tmp = t_1;
	} else if (x <= 4.4e+73) {
		tmp = t_2;
	} else if (x <= 3.15e+122) {
		tmp = t_1;
	} else if (x <= 6.7e+137) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    t_2 = 2.0d0 * (x * (y + z))
    if (x <= (-4.8d+141)) then
        tmp = t_2
    else if (x <= (-8.6d+123)) then
        tmp = t_1
    else if (x <= (-8d+24)) then
        tmp = t_2
    else if (x <= (-3.8d-40)) then
        tmp = t_1
    else if (x <= 1.05d-17) then
        tmp = y * 5.0d0
    else if (x <= 6.5d+47) then
        tmp = t_1
    else if (x <= 4.4d+73) then
        tmp = t_2
    else if (x <= 3.15d+122) then
        tmp = t_1
    else if (x <= 6.7d+137) then
        tmp = t_2
    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 t_2 = 2.0 * (x * (y + z));
	double tmp;
	if (x <= -4.8e+141) {
		tmp = t_2;
	} else if (x <= -8.6e+123) {
		tmp = t_1;
	} else if (x <= -8e+24) {
		tmp = t_2;
	} else if (x <= -3.8e-40) {
		tmp = t_1;
	} else if (x <= 1.05e-17) {
		tmp = y * 5.0;
	} else if (x <= 6.5e+47) {
		tmp = t_1;
	} else if (x <= 4.4e+73) {
		tmp = t_2;
	} else if (x <= 3.15e+122) {
		tmp = t_1;
	} else if (x <= 6.7e+137) {
		tmp = t_2;
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	t_2 = 2.0 * (x * (y + z))
	tmp = 0
	if x <= -4.8e+141:
		tmp = t_2
	elif x <= -8.6e+123:
		tmp = t_1
	elif x <= -8e+24:
		tmp = t_2
	elif x <= -3.8e-40:
		tmp = t_1
	elif x <= 1.05e-17:
		tmp = y * 5.0
	elif x <= 6.5e+47:
		tmp = t_1
	elif x <= 4.4e+73:
		tmp = t_2
	elif x <= 3.15e+122:
		tmp = t_1
	elif x <= 6.7e+137:
		tmp = t_2
	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)))
	t_2 = Float64(2.0 * Float64(x * Float64(y + z)))
	tmp = 0.0
	if (x <= -4.8e+141)
		tmp = t_2;
	elseif (x <= -8.6e+123)
		tmp = t_1;
	elseif (x <= -8e+24)
		tmp = t_2;
	elseif (x <= -3.8e-40)
		tmp = t_1;
	elseif (x <= 1.05e-17)
		tmp = Float64(y * 5.0);
	elseif (x <= 6.5e+47)
		tmp = t_1;
	elseif (x <= 4.4e+73)
		tmp = t_2;
	elseif (x <= 3.15e+122)
		tmp = t_1;
	elseif (x <= 6.7e+137)
		tmp = t_2;
	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));
	t_2 = 2.0 * (x * (y + z));
	tmp = 0.0;
	if (x <= -4.8e+141)
		tmp = t_2;
	elseif (x <= -8.6e+123)
		tmp = t_1;
	elseif (x <= -8e+24)
		tmp = t_2;
	elseif (x <= -3.8e-40)
		tmp = t_1;
	elseif (x <= 1.05e-17)
		tmp = y * 5.0;
	elseif (x <= 6.5e+47)
		tmp = t_1;
	elseif (x <= 4.4e+73)
		tmp = t_2;
	elseif (x <= 3.15e+122)
		tmp = t_1;
	elseif (x <= 6.7e+137)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+141], t$95$2, If[LessEqual[x, -8.6e+123], t$95$1, If[LessEqual[x, -8e+24], t$95$2, If[LessEqual[x, -3.8e-40], t$95$1, If[LessEqual[x, 1.05e-17], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 6.5e+47], t$95$1, If[LessEqual[x, 4.4e+73], t$95$2, If[LessEqual[x, 3.15e+122], t$95$1, If[LessEqual[x, 6.7e+137], t$95$2, N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.79999999999999995e141 or -8.59999999999999972e123 < x < -7.9999999999999999e24 or 6.49999999999999988e47 < x < 4.4e73 or 3.1500000000000001e122 < x < 6.6999999999999999e137

   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 0 100.0%

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

   4. Taylor expanded in t around 0 88.2%

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

      1. *-commutative 88.2%

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

      2. distribute-lft-out 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in x around inf 88.2%

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

      1. +-commutative 88.2%

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

   9. Simplified 88.2%

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

   if -4.79999999999999995e141 < x < -8.59999999999999972e123 or -7.9999999999999999e24 < x < -3.7999999999999999e-40 or 1.04999999999999996e-17 < x < 6.49999999999999988e47 or 4.4e73 < x < 3.1500000000000001e122

   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 88.3%

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

   if -3.7999999999999999e-40 < x < 1.04999999999999996e-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 x around 0 71.3%

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

   if 6.6999999999999999e137 < 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 0 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-out 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 78.5%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+141}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+24}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+73}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 6.7 \cdot 10^{+137}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(y \cdot 2\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-40}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 10500000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{+46}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+83}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))) (t_2 (* x (* y 2.0))))
   (if (<= x -2.3e+65)
     t_1
     (if (<= x -3.6e+37)
       t_2
       (if (<= x -3.2e-40)
         (* x t)
         (if (<= x 5.8e-17)
           (* y 5.0)
           (if (<= x 10500000.0)
             t_1
             (if (<= x 1.82e+46)
               (* x t)
               (if (<= x 5e+82)
                 t_2
                 (if (<= x 8.2e+83)
                   (* x t)
                   (if (<= x 8.4e+127) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double t_2 = x * (y * 2.0);
	double tmp;
	if (x <= -2.3e+65) {
		tmp = t_1;
	} else if (x <= -3.6e+37) {
		tmp = t_2;
	} else if (x <= -3.2e-40) {
		tmp = x * t;
	} else if (x <= 5.8e-17) {
		tmp = y * 5.0;
	} else if (x <= 10500000.0) {
		tmp = t_1;
	} else if (x <= 1.82e+46) {
		tmp = x * t;
	} else if (x <= 5e+82) {
		tmp = t_2;
	} else if (x <= 8.2e+83) {
		tmp = x * t;
	} else if (x <= 8.4e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    t_2 = x * (y * 2.0d0)
    if (x <= (-2.3d+65)) then
        tmp = t_1
    else if (x <= (-3.6d+37)) then
        tmp = t_2
    else if (x <= (-3.2d-40)) then
        tmp = x * t
    else if (x <= 5.8d-17) then
        tmp = y * 5.0d0
    else if (x <= 10500000.0d0) then
        tmp = t_1
    else if (x <= 1.82d+46) then
        tmp = x * t
    else if (x <= 5d+82) then
        tmp = t_2
    else if (x <= 8.2d+83) then
        tmp = x * t
    else if (x <= 8.4d+127) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = x * (y * 2.0);
	double tmp;
	if (x <= -2.3e+65) {
		tmp = t_1;
	} else if (x <= -3.6e+37) {
		tmp = t_2;
	} else if (x <= -3.2e-40) {
		tmp = x * t;
	} else if (x <= 5.8e-17) {
		tmp = y * 5.0;
	} else if (x <= 10500000.0) {
		tmp = t_1;
	} else if (x <= 1.82e+46) {
		tmp = x * t;
	} else if (x <= 5e+82) {
		tmp = t_2;
	} else if (x <= 8.2e+83) {
		tmp = x * t;
	} else if (x <= 8.4e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	t_2 = x * (y * 2.0)
	tmp = 0
	if x <= -2.3e+65:
		tmp = t_1
	elif x <= -3.6e+37:
		tmp = t_2
	elif x <= -3.2e-40:
		tmp = x * t
	elif x <= 5.8e-17:
		tmp = y * 5.0
	elif x <= 10500000.0:
		tmp = t_1
	elif x <= 1.82e+46:
		tmp = x * t
	elif x <= 5e+82:
		tmp = t_2
	elif x <= 8.2e+83:
		tmp = x * t
	elif x <= 8.4e+127:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	t_2 = Float64(x * Float64(y * 2.0))
	tmp = 0.0
	if (x <= -2.3e+65)
		tmp = t_1;
	elseif (x <= -3.6e+37)
		tmp = t_2;
	elseif (x <= -3.2e-40)
		tmp = Float64(x * t);
	elseif (x <= 5.8e-17)
		tmp = Float64(y * 5.0);
	elseif (x <= 10500000.0)
		tmp = t_1;
	elseif (x <= 1.82e+46)
		tmp = Float64(x * t);
	elseif (x <= 5e+82)
		tmp = t_2;
	elseif (x <= 8.2e+83)
		tmp = Float64(x * t);
	elseif (x <= 8.4e+127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	t_2 = x * (y * 2.0);
	tmp = 0.0;
	if (x <= -2.3e+65)
		tmp = t_1;
	elseif (x <= -3.6e+37)
		tmp = t_2;
	elseif (x <= -3.2e-40)
		tmp = x * t;
	elseif (x <= 5.8e-17)
		tmp = y * 5.0;
	elseif (x <= 10500000.0)
		tmp = t_1;
	elseif (x <= 1.82e+46)
		tmp = x * t;
	elseif (x <= 5e+82)
		tmp = t_2;
	elseif (x <= 8.2e+83)
		tmp = x * t;
	elseif (x <= 8.4e+127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+65], t$95$1, If[LessEqual[x, -3.6e+37], t$95$2, If[LessEqual[x, -3.2e-40], N[(x * t), $MachinePrecision], If[LessEqual[x, 5.8e-17], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 10500000.0], t$95$1, If[LessEqual[x, 1.82e+46], N[(x * t), $MachinePrecision], If[LessEqual[x, 5e+82], t$95$2, If[LessEqual[x, 8.2e+83], N[(x * t), $MachinePrecision], If[LessEqual[x, 8.4e+127], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.3e65 or 5.8000000000000006e-17 < x < 1.05e7 or 8.2000000000000002e83 < x < 8.39999999999999967e127

   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 52.1%

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

   if -2.3e65 < x < -3.59999999999999998e37 or 1.81999999999999989e46 < x < 5.00000000000000015e82 or 8.39999999999999967e127 < 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 0 100.0%

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

   4. Taylor expanded in t around 0 76.3%

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

      1. *-commutative 76.3%

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

      2. distribute-lft-out 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in x around inf 76.3%

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

      1. +-commutative 76.3%

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

   9. Simplified 76.3%

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

   10. Taylor expanded in z around 0 51.2%

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

       1. *-commutative 51.2%

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

       2. associate-*l* 51.2%

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

   12. Simplified 51.2%

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

   if -3.59999999999999998e37 < x < -3.20000000000000002e-40 or 1.05e7 < x < 1.81999999999999989e46 or 5.00000000000000015e82 < x < 8.2000000000000002e83

   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 t around inf 53.7%

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

   5. Simplified 53.7%

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

   if -3.20000000000000002e-40 < x < 5.8000000000000006e-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 x around 0 72.0%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+65}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-40}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 10500000:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{+46}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+83}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{+127}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+278}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+305}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))) (t_2 (* 2.0 (* x (+ y z)))))
   (if (<= x -4.6e+141)
     t_2
     (if (<= x -6.2e+123)
       t_1
       (if (<= x -7.8e+33)
         t_2
         (if (<= x 1.85e-16)
           (+ (* y 5.0) (* x t))
           (if (<= x 1.6e+122)
             t_1
             (if (<= x 2.2e+142)
               t_2
               (if (<= x 4.8e+278)
                 (* x (+ t (* y 2.0)))
                 (if (<= x 2.6e+305) t_2 (* x t)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = 2.0 * (x * (y + z));
	double tmp;
	if (x <= -4.6e+141) {
		tmp = t_2;
	} else if (x <= -6.2e+123) {
		tmp = t_1;
	} else if (x <= -7.8e+33) {
		tmp = t_2;
	} else if (x <= 1.85e-16) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1.6e+122) {
		tmp = t_1;
	} else if (x <= 2.2e+142) {
		tmp = t_2;
	} else if (x <= 4.8e+278) {
		tmp = x * (t + (y * 2.0));
	} else if (x <= 2.6e+305) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    t_2 = 2.0d0 * (x * (y + z))
    if (x <= (-4.6d+141)) then
        tmp = t_2
    else if (x <= (-6.2d+123)) then
        tmp = t_1
    else if (x <= (-7.8d+33)) then
        tmp = t_2
    else if (x <= 1.85d-16) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 1.6d+122) then
        tmp = t_1
    else if (x <= 2.2d+142) then
        tmp = t_2
    else if (x <= 4.8d+278) then
        tmp = x * (t + (y * 2.0d0))
    else if (x <= 2.6d+305) then
        tmp = t_2
    else
        tmp = x * t
    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 t_2 = 2.0 * (x * (y + z));
	double tmp;
	if (x <= -4.6e+141) {
		tmp = t_2;
	} else if (x <= -6.2e+123) {
		tmp = t_1;
	} else if (x <= -7.8e+33) {
		tmp = t_2;
	} else if (x <= 1.85e-16) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1.6e+122) {
		tmp = t_1;
	} else if (x <= 2.2e+142) {
		tmp = t_2;
	} else if (x <= 4.8e+278) {
		tmp = x * (t + (y * 2.0));
	} else if (x <= 2.6e+305) {
		tmp = t_2;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	t_2 = 2.0 * (x * (y + z))
	tmp = 0
	if x <= -4.6e+141:
		tmp = t_2
	elif x <= -6.2e+123:
		tmp = t_1
	elif x <= -7.8e+33:
		tmp = t_2
	elif x <= 1.85e-16:
		tmp = (y * 5.0) + (x * t)
	elif x <= 1.6e+122:
		tmp = t_1
	elif x <= 2.2e+142:
		tmp = t_2
	elif x <= 4.8e+278:
		tmp = x * (t + (y * 2.0))
	elif x <= 2.6e+305:
		tmp = t_2
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	t_2 = Float64(2.0 * Float64(x * Float64(y + z)))
	tmp = 0.0
	if (x <= -4.6e+141)
		tmp = t_2;
	elseif (x <= -6.2e+123)
		tmp = t_1;
	elseif (x <= -7.8e+33)
		tmp = t_2;
	elseif (x <= 1.85e-16)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 1.6e+122)
		tmp = t_1;
	elseif (x <= 2.2e+142)
		tmp = t_2;
	elseif (x <= 4.8e+278)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	elseif (x <= 2.6e+305)
		tmp = t_2;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	t_2 = 2.0 * (x * (y + z));
	tmp = 0.0;
	if (x <= -4.6e+141)
		tmp = t_2;
	elseif (x <= -6.2e+123)
		tmp = t_1;
	elseif (x <= -7.8e+33)
		tmp = t_2;
	elseif (x <= 1.85e-16)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 1.6e+122)
		tmp = t_1;
	elseif (x <= 2.2e+142)
		tmp = t_2;
	elseif (x <= 4.8e+278)
		tmp = x * (t + (y * 2.0));
	elseif (x <= 2.6e+305)
		tmp = t_2;
	else
		tmp = x * t;
	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]}, Block[{t$95$2 = N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.6e+141], t$95$2, If[LessEqual[x, -6.2e+123], t$95$1, If[LessEqual[x, -7.8e+33], t$95$2, If[LessEqual[x, 1.85e-16], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+122], t$95$1, If[LessEqual[x, 2.2e+142], t$95$2, If[LessEqual[x, 4.8e+278], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+305], t$95$2, N[(x * t), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.6000000000000003e141 or -6.20000000000000013e123 < x < -7.8000000000000004e33 or 1.60000000000000006e122 < x < 2.19999999999999987e142 or 4.7999999999999997e278 < x < 2.59999999999999984e305

   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 0 100.0%

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

   4. Taylor expanded in t around 0 87.4%

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

      1. *-commutative 87.4%

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

      2. distribute-lft-out 87.4%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in x around inf 87.4%

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

      1. +-commutative 87.4%

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

   9. Simplified 87.4%

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

   if -4.6000000000000003e141 < x < -6.20000000000000013e123 or 1.85e-16 < x < 1.60000000000000006e122

   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 85.6%

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

   if -7.8000000000000004e33 < x < 1.85e-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. 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 85.9%

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

   7. Taylor expanded in x around 0 85.9%

      \[\leadsto \color{blue}{5 \cdot y + t \cdot x} \]

   if 2.19999999999999987e142 < x < 4.7999999999999997e278

   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 0 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-out 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 88.5%

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

   if 2.59999999999999984e305 < 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 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+141}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+142}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+278}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+305}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ t_2 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ t_3 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -6800000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-246}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-246}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-242}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.55 \cdot 10^{-242}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3200000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0))))
        (t_2 (* 2.0 (* x (+ y z))))
        (t_3 (* 2.0 (* x z))))
   (if (<= x -6800000000000.0)
     t_2
     (if (<= x -6.3e-89)
       t_1
       (if (<= x -2.1e-246)
         (* y 5.0)
         (if (<= x -2e-246)
           t_3
           (if (<= x 3.5e-242)
             (* y 5.0)
             (if (<= x 3.55e-242)
               t_3
               (if (<= x 8.5e-16)
                 (* y 5.0)
                 (if (<= x 3200000000.0) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double t_2 = 2.0 * (x * (y + z));
	double t_3 = 2.0 * (x * z);
	double tmp;
	if (x <= -6800000000000.0) {
		tmp = t_2;
	} else if (x <= -6.3e-89) {
		tmp = t_1;
	} else if (x <= -2.1e-246) {
		tmp = y * 5.0;
	} else if (x <= -2e-246) {
		tmp = t_3;
	} else if (x <= 3.5e-242) {
		tmp = y * 5.0;
	} else if (x <= 3.55e-242) {
		tmp = t_3;
	} else if (x <= 8.5e-16) {
		tmp = y * 5.0;
	} else if (x <= 3200000000.0) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (t + (y * 2.0d0))
    t_2 = 2.0d0 * (x * (y + z))
    t_3 = 2.0d0 * (x * z)
    if (x <= (-6800000000000.0d0)) then
        tmp = t_2
    else if (x <= (-6.3d-89)) then
        tmp = t_1
    else if (x <= (-2.1d-246)) then
        tmp = y * 5.0d0
    else if (x <= (-2d-246)) then
        tmp = t_3
    else if (x <= 3.5d-242) then
        tmp = y * 5.0d0
    else if (x <= 3.55d-242) then
        tmp = t_3
    else if (x <= 8.5d-16) then
        tmp = y * 5.0d0
    else if (x <= 3200000000.0d0) then
        tmp = t_2
    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 = x * (t + (y * 2.0));
	double t_2 = 2.0 * (x * (y + z));
	double t_3 = 2.0 * (x * z);
	double tmp;
	if (x <= -6800000000000.0) {
		tmp = t_2;
	} else if (x <= -6.3e-89) {
		tmp = t_1;
	} else if (x <= -2.1e-246) {
		tmp = y * 5.0;
	} else if (x <= -2e-246) {
		tmp = t_3;
	} else if (x <= 3.5e-242) {
		tmp = y * 5.0;
	} else if (x <= 3.55e-242) {
		tmp = t_3;
	} else if (x <= 8.5e-16) {
		tmp = y * 5.0;
	} else if (x <= 3200000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	t_2 = 2.0 * (x * (y + z))
	t_3 = 2.0 * (x * z)
	tmp = 0
	if x <= -6800000000000.0:
		tmp = t_2
	elif x <= -6.3e-89:
		tmp = t_1
	elif x <= -2.1e-246:
		tmp = y * 5.0
	elif x <= -2e-246:
		tmp = t_3
	elif x <= 3.5e-242:
		tmp = y * 5.0
	elif x <= 3.55e-242:
		tmp = t_3
	elif x <= 8.5e-16:
		tmp = y * 5.0
	elif x <= 3200000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y * 2.0)))
	t_2 = Float64(2.0 * Float64(x * Float64(y + z)))
	t_3 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -6800000000000.0)
		tmp = t_2;
	elseif (x <= -6.3e-89)
		tmp = t_1;
	elseif (x <= -2.1e-246)
		tmp = Float64(y * 5.0);
	elseif (x <= -2e-246)
		tmp = t_3;
	elseif (x <= 3.5e-242)
		tmp = Float64(y * 5.0);
	elseif (x <= 3.55e-242)
		tmp = t_3;
	elseif (x <= 8.5e-16)
		tmp = Float64(y * 5.0);
	elseif (x <= 3200000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y * 2.0));
	t_2 = 2.0 * (x * (y + z));
	t_3 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -6800000000000.0)
		tmp = t_2;
	elseif (x <= -6.3e-89)
		tmp = t_1;
	elseif (x <= -2.1e-246)
		tmp = y * 5.0;
	elseif (x <= -2e-246)
		tmp = t_3;
	elseif (x <= 3.5e-242)
		tmp = y * 5.0;
	elseif (x <= 3.55e-242)
		tmp = t_3;
	elseif (x <= 8.5e-16)
		tmp = y * 5.0;
	elseif (x <= 3200000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6800000000000.0], t$95$2, If[LessEqual[x, -6.3e-89], t$95$1, If[LessEqual[x, -2.1e-246], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, -2e-246], t$95$3, If[LessEqual[x, 3.5e-242], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 3.55e-242], t$95$3, If[LessEqual[x, 8.5e-16], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 3200000000.0], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.8e12 or 8.5000000000000001e-16 < x < 3.2e9

   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 0 100.0%

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

   4. Taylor expanded in t around 0 81.9%

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

      1. *-commutative 81.9%

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

      2. distribute-lft-out 81.9%

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

   6. Simplified 81.9%

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

   7. Taylor expanded in x around inf 81.9%

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

      1. +-commutative 81.9%

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

   9. Simplified 81.9%

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

   if -6.8e12 < x < -6.2999999999999996e-89 or 3.2e9 < 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 0 100.0%

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

   4. Taylor expanded in x around inf 91.4%

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

      1. +-commutative 91.4%

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

      2. distribute-lft-out 91.4%

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

   6. Simplified 91.4%

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

   7. Taylor expanded in z around 0 64.5%

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

   if -6.2999999999999996e-89 < x < -2.09999999999999995e-246 or -1.99999999999999991e-246 < x < 3.4999999999999999e-242 or 3.54999999999999981e-242 < x < 8.5000000000000001e-16

   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 x around 0 77.9%

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

   if -2.09999999999999995e-246 < x < -1.99999999999999991e-246 or 3.4999999999999999e-242 < x < 3.54999999999999981e-242

   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 100.0%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6800000000000:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-246}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-246}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-242}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.55 \cdot 10^{-242}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3200000000:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.24 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.85 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+69} \lor \neg \left(y \leq 2 \cdot 10^{+69}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.8e+60)
     t_1
     (if (<= y -3.4e+15)
       (* x (+ t (* y 2.0)))
       (if (<= y -1.24e-26)
         t_1
         (if (<= y 4.85e+58)
           (* x (+ t (* z 2.0)))
           (if (or (<= y 1.95e+69) (not (<= y 2e+69))) t_1 (* x t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.8e+60) {
		tmp = t_1;
	} else if (y <= -3.4e+15) {
		tmp = x * (t + (y * 2.0));
	} else if (y <= -1.24e-26) {
		tmp = t_1;
	} else if (y <= 4.85e+58) {
		tmp = x * (t + (z * 2.0));
	} else if ((y <= 1.95e+69) || !(y <= 2e+69)) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.8d+60)) then
        tmp = t_1
    else if (y <= (-3.4d+15)) then
        tmp = x * (t + (y * 2.0d0))
    else if (y <= (-1.24d-26)) then
        tmp = t_1
    else if (y <= 4.85d+58) then
        tmp = x * (t + (z * 2.0d0))
    else if ((y <= 1.95d+69) .or. (.not. (y <= 2d+69))) then
        tmp = t_1
    else
        tmp = x * t
    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 <= -1.8e+60) {
		tmp = t_1;
	} else if (y <= -3.4e+15) {
		tmp = x * (t + (y * 2.0));
	} else if (y <= -1.24e-26) {
		tmp = t_1;
	} else if (y <= 4.85e+58) {
		tmp = x * (t + (z * 2.0));
	} else if ((y <= 1.95e+69) || !(y <= 2e+69)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.8e+60:
		tmp = t_1
	elif y <= -3.4e+15:
		tmp = x * (t + (y * 2.0))
	elif y <= -1.24e-26:
		tmp = t_1
	elif y <= 4.85e+58:
		tmp = x * (t + (z * 2.0))
	elif (y <= 1.95e+69) or not (y <= 2e+69):
		tmp = t_1
	else:
		tmp = x * t
	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 <= -1.8e+60)
		tmp = t_1;
	elseif (y <= -3.4e+15)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	elseif (y <= -1.24e-26)
		tmp = t_1;
	elseif (y <= 4.85e+58)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif ((y <= 1.95e+69) || !(y <= 2e+69))
		tmp = t_1;
	else
		tmp = Float64(x * t);
	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 <= -1.8e+60)
		tmp = t_1;
	elseif (y <= -3.4e+15)
		tmp = x * (t + (y * 2.0));
	elseif (y <= -1.24e-26)
		tmp = t_1;
	elseif (y <= 4.85e+58)
		tmp = x * (t + (z * 2.0));
	elseif ((y <= 1.95e+69) || ~((y <= 2e+69)))
		tmp = t_1;
	else
		tmp = x * t;
	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, -1.8e+60], t$95$1, If[LessEqual[y, -3.4e+15], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.24e-26], t$95$1, If[LessEqual[y, 4.85e+58], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.95e+69], N[Not[LessEqual[y, 2e+69]], $MachinePrecision]], t$95$1, N[(x * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.79999999999999984e60 or -3.4e15 < y < -1.2399999999999999e-26 or 4.8499999999999998e58 < y < 1.94999999999999995e69 or 2.0000000000000001e69 < 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 80.5%

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

   5. Simplified 80.5%

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

   if -1.79999999999999984e60 < y < -3.4e15

   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 0 100.0%

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

   4. Taylor expanded in x around inf 91.7%

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

      1. +-commutative 91.7%

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

      2. distribute-lft-out 91.7%

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

   6. Simplified 91.7%

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

   7. Taylor expanded in z around 0 72.4%

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

   if -1.2399999999999999e-26 < y < 4.8499999999999998e58

   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 79.7%

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

   if 1.94999999999999995e69 < y < 2.0000000000000001e69

   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 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.24 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 4.85 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+69} \lor \neg \left(y \leq 2 \cdot 10^{+69}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + x \cdot t\\ t_2 := x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{-71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-288}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* x t))) (t_2 (* x (+ t (* 2.0 (+ y z))))))
   (if (<= x -2.15e-71)
     t_2
     (if (<= x -1.2e-231)
       t_1
       (if (<= x -5.2e-288)
         (+ (* y 5.0) (* x (* z 2.0)))
         (if (<= x 1.08e-16) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double t_2 = x * (t + (2.0 * (y + z)));
	double tmp;
	if (x <= -2.15e-71) {
		tmp = t_2;
	} else if (x <= -1.2e-231) {
		tmp = t_1;
	} else if (x <= -5.2e-288) {
		tmp = (y * 5.0) + (x * (z * 2.0));
	} else if (x <= 1.08e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (y * 5.0d0) + (x * t)
    t_2 = x * (t + (2.0d0 * (y + z)))
    if (x <= (-2.15d-71)) then
        tmp = t_2
    else if (x <= (-1.2d-231)) then
        tmp = t_1
    else if (x <= (-5.2d-288)) then
        tmp = (y * 5.0d0) + (x * (z * 2.0d0))
    else if (x <= 1.08d-16) then
        tmp = t_1
    else
        tmp = t_2
    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 * t);
	double t_2 = x * (t + (2.0 * (y + z)));
	double tmp;
	if (x <= -2.15e-71) {
		tmp = t_2;
	} else if (x <= -1.2e-231) {
		tmp = t_1;
	} else if (x <= -5.2e-288) {
		tmp = (y * 5.0) + (x * (z * 2.0));
	} else if (x <= 1.08e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (x * t)
	t_2 = x * (t + (2.0 * (y + z)))
	tmp = 0
	if x <= -2.15e-71:
		tmp = t_2
	elif x <= -1.2e-231:
		tmp = t_1
	elif x <= -5.2e-288:
		tmp = (y * 5.0) + (x * (z * 2.0))
	elif x <= 1.08e-16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(x * t))
	t_2 = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))))
	tmp = 0.0
	if (x <= -2.15e-71)
		tmp = t_2;
	elseif (x <= -1.2e-231)
		tmp = t_1;
	elseif (x <= -5.2e-288)
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(z * 2.0)));
	elseif (x <= 1.08e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (x * t);
	t_2 = x * (t + (2.0 * (y + z)));
	tmp = 0.0;
	if (x <= -2.15e-71)
		tmp = t_2;
	elseif (x <= -1.2e-231)
		tmp = t_1;
	elseif (x <= -5.2e-288)
		tmp = (y * 5.0) + (x * (z * 2.0));
	elseif (x <= 1.08e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e-71], t$95$2, If[LessEqual[x, -1.2e-231], t$95$1, If[LessEqual[x, -5.2e-288], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.08e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1499999999999998e-71 or 1.08e-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 97.0%

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

   if -2.1499999999999998e-71 < x < -1.19999999999999996e-231 or -5.19999999999999979e-288 < x < 1.08e-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. 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 92.9%

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

   7. Taylor expanded in x around 0 92.9%

      \[\leadsto \color{blue}{5 \cdot y + t \cdot x} \]

   if -1.19999999999999996e-231 < x < -5.19999999999999979e-288

   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 82.3%

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

   4. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-231}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-288}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(z \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -21000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-89}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -21000000000000.0)
     t_1
     (if (<= x -6.3e-89)
       (* x t)
       (if (<= x 2.1e-16) (* y 5.0) (if (<= x 100000000.0) t_1 (* x t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -21000000000000.0) {
		tmp = t_1;
	} else if (x <= -6.3e-89) {
		tmp = x * t;
	} else if (x <= 2.1e-16) {
		tmp = y * 5.0;
	} else if (x <= 100000000.0) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-21000000000000.0d0)) then
        tmp = t_1
    else if (x <= (-6.3d-89)) then
        tmp = x * t
    else if (x <= 2.1d-16) then
        tmp = y * 5.0d0
    else if (x <= 100000000.0d0) then
        tmp = t_1
    else
        tmp = x * t
    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 <= -21000000000000.0) {
		tmp = t_1;
	} else if (x <= -6.3e-89) {
		tmp = x * t;
	} else if (x <= 2.1e-16) {
		tmp = y * 5.0;
	} else if (x <= 100000000.0) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -21000000000000.0:
		tmp = t_1
	elif x <= -6.3e-89:
		tmp = x * t
	elif x <= 2.1e-16:
		tmp = y * 5.0
	elif x <= 100000000.0:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -21000000000000.0)
		tmp = t_1;
	elseif (x <= -6.3e-89)
		tmp = Float64(x * t);
	elseif (x <= 2.1e-16)
		tmp = Float64(y * 5.0);
	elseif (x <= 100000000.0)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -21000000000000.0)
		tmp = t_1;
	elseif (x <= -6.3e-89)
		tmp = x * t;
	elseif (x <= 2.1e-16)
		tmp = y * 5.0;
	elseif (x <= 100000000.0)
		tmp = t_1;
	else
		tmp = x * t;
	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, -21000000000000.0], t$95$1, If[LessEqual[x, -6.3e-89], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.1e-16], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 100000000.0], t$95$1, N[(x * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1e13 or 2.1000000000000001e-16 < x < 1e8

   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 47.0%

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

   if -2.1e13 < x < -6.2999999999999996e-89 or 1e8 < 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 42.4%

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

   5. Simplified 42.4%

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

   if -6.2999999999999996e-89 < x < 2.1000000000000001e-16

   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 x around 0 76.5%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -21000000000000:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-89}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(t + t\_1\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-100}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(t\_1 + 5 \cdot \frac{y}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (<= x -7.8e+33)
     (* x (+ t t_1))
     (if (<= x 3.2e-100)
       (+ (* y 5.0) (* x (+ t (* z 2.0))))
       (* x (+ t (+ t_1 (* 5.0 (/ y x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (x <= -7.8e+33) {
		tmp = x * (t + t_1);
	} else if (x <= 3.2e-100) {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	} else {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	}
	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 * (y + z)
    if (x <= (-7.8d+33)) then
        tmp = x * (t + t_1)
    else if (x <= 3.2d-100) then
        tmp = (y * 5.0d0) + (x * (t + (z * 2.0d0)))
    else
        tmp = x * (t + (t_1 + (5.0d0 * (y / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (x <= -7.8e+33) {
		tmp = x * (t + t_1);
	} else if (x <= 3.2e-100) {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	} else {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if x <= -7.8e+33:
		tmp = x * (t + t_1)
	elif x <= 3.2e-100:
		tmp = (y * 5.0) + (x * (t + (z * 2.0)))
	else:
		tmp = x * (t + (t_1 + (5.0 * (y / x))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if (x <= -7.8e+33)
		tmp = Float64(x * Float64(t + t_1));
	elseif (x <= 3.2e-100)
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(z * 2.0))));
	else
		tmp = Float64(x * Float64(t + Float64(t_1 + Float64(5.0 * Float64(y / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if (x <= -7.8e+33)
		tmp = x * (t + t_1);
	elseif (x <= 3.2e-100)
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	else
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e+33], N[(x * N[(t + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-100], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(t$95$1 + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.8000000000000004e33

   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%

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

   if -7.8000000000000004e33 < x < 3.20000000000000017e-100

   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 98.7%

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

   if 3.20000000000000017e-100 < 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%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-100}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+33} \lor \neg \left(x \leq 4.1 \cdot 10^{-51}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.8e+33) (not (<= x 4.1e-51)))
   (* x (+ t (* 2.0 (+ y z))))
   (+ (* y 5.0) (* x (+ t (* z 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.8e+33) || !(x <= 4.1e-51)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (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 ((x <= (-7.8d+33)) .or. (.not. (x <= 4.1d-51))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = (y * 5.0d0) + (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 ((x <= -7.8e+33) || !(x <= 4.1e-51)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.8e+33) or not (x <= 4.1e-51):
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = (y * 5.0) + (x * (t + (z * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.8e+33) || !(x <= 4.1e-51))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(y * 5.0) + 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 ((x <= -7.8e+33) || ~((x <= 4.1e-51)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.8e+33], N[Not[LessEqual[x, 4.1e-51]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.8000000000000004e33 or 4.09999999999999973e-51 < 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 97.3%

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

   if -7.8000000000000004e33 < x < 4.09999999999999973e-51

   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 98.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+33} \lor \neg \left(x \leq 4.1 \cdot 10^{-51}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-72} \lor \neg \left(x \leq 1.75 \cdot 10^{-51}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.6e-72) (not (<= x 1.75e-51)))
   (* 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 <= -5.6e-72) || !(x <= 1.75e-51)) {
		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 <= (-5.6d-72)) .or. (.not. (x <= 1.75d-51))) 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 <= -5.6e-72) || !(x <= 1.75e-51)) {
		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 <= -5.6e-72) or not (x <= 1.75e-51):
		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 <= -5.6e-72) || !(x <= 1.75e-51))
		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 <= -5.6e-72) || ~((x <= 1.75e-51)))
		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, -5.6e-72], N[Not[LessEqual[x, 1.75e-51]], $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 < -5.5999999999999996e-72 or 1.7499999999999999e-51 < 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 94.7%

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

   if -5.5999999999999996e-72 < x < 1.7499999999999999e-51

   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. Step-by-step derivation

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      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 90.5%

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

   7. Taylor expanded in x around 0 90.5%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-72} \lor \neg \left(x \leq 1.75 \cdot 10^{-51}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x * (t + (y + (y + (z * 2.0))))) + (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 + (y + (z * 2.0d0))))) + (y * 5.0d0)
end function

Java

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

Python

def code(x, y, z, t):
	return (x * (t + (y + (y + (z * 2.0))))) + (y * 5.0)

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * (t + (y + (y + (z * 2.0))))) + (y * 5.0);
end

Wolfram

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

Derivation

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 0 100.0%

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

4. Final simplification 100.0%

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

Alternative 14: 46.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-17} \lor \neg \left(x \leq 3.2 \cdot 10^{-100}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1e-17) (not (<= x 3.2e-100))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1e-17) || !(x <= 3.2e-100)) {
		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 <= (-1d-17)) .or. (.not. (x <= 3.2d-100))) 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 <= -1e-17) || !(x <= 3.2e-100)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1e-17) or not (x <= 3.2e-100):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1e-17) || !(x <= 3.2e-100))
		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 <= -1e-17) || ~((x <= 3.2e-100)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1e-17], N[Not[LessEqual[x, 3.2e-100]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.00000000000000007e-17 or 3.20000000000000017e-100 < 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 33.9%

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

   5. Simplified 33.9%

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

   if -1.00000000000000007e-17 < x < 3.20000000000000017e-100

   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 70.6%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-17} \lor \neg \left(x \leq 3.2 \cdot 10^{-100}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.1% 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 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 x around 0 33.5%

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

4. Final simplification 33.5%

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

Reproduce

herbie shell --seed 2024107 
(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)))