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

Percentage Accurate: 99.9% → 99.9%

Time: 10.4s

Alternatives: 16

Speedup: 1.0×

• 26.2% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-define 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 46.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -0.017:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+153} \lor \neg \left(x \leq 1.42 \cdot 10^{+305}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* x 2.0))))
   (if (<= x -8.8e+55)
     t_1
     (if (<= x -0.017)
       (* x t)
       (if (<= x -2.3e-14)
         t_1
         (if (<= x 1.6e-63)
           (* y 5.0)
           (if (or (<= x 4.1e+153) (not (<= x 1.42e+305)))
             (* x t)
             (* x (* 2.0 y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x * 2.0);
	double tmp;
	if (x <= -8.8e+55) {
		tmp = t_1;
	} else if (x <= -0.017) {
		tmp = x * t;
	} else if (x <= -2.3e-14) {
		tmp = t_1;
	} else if (x <= 1.6e-63) {
		tmp = y * 5.0;
	} else if ((x <= 4.1e+153) || !(x <= 1.42e+305)) {
		tmp = x * t;
	} else {
		tmp = x * (2.0 * y);
	}
	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 = z * (x * 2.0d0)
    if (x <= (-8.8d+55)) then
        tmp = t_1
    else if (x <= (-0.017d0)) then
        tmp = x * t
    else if (x <= (-2.3d-14)) then
        tmp = t_1
    else if (x <= 1.6d-63) then
        tmp = y * 5.0d0
    else if ((x <= 4.1d+153) .or. (.not. (x <= 1.42d+305))) then
        tmp = x * t
    else
        tmp = x * (2.0d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x * 2.0);
	double tmp;
	if (x <= -8.8e+55) {
		tmp = t_1;
	} else if (x <= -0.017) {
		tmp = x * t;
	} else if (x <= -2.3e-14) {
		tmp = t_1;
	} else if (x <= 1.6e-63) {
		tmp = y * 5.0;
	} else if ((x <= 4.1e+153) || !(x <= 1.42e+305)) {
		tmp = x * t;
	} else {
		tmp = x * (2.0 * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x * 2.0)
	tmp = 0
	if x <= -8.8e+55:
		tmp = t_1
	elif x <= -0.017:
		tmp = x * t
	elif x <= -2.3e-14:
		tmp = t_1
	elif x <= 1.6e-63:
		tmp = y * 5.0
	elif (x <= 4.1e+153) or not (x <= 1.42e+305):
		tmp = x * t
	else:
		tmp = x * (2.0 * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x * 2.0))
	tmp = 0.0
	if (x <= -8.8e+55)
		tmp = t_1;
	elseif (x <= -0.017)
		tmp = Float64(x * t);
	elseif (x <= -2.3e-14)
		tmp = t_1;
	elseif (x <= 1.6e-63)
		tmp = Float64(y * 5.0);
	elseif ((x <= 4.1e+153) || !(x <= 1.42e+305))
		tmp = Float64(x * t);
	else
		tmp = Float64(x * Float64(2.0 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x * 2.0);
	tmp = 0.0;
	if (x <= -8.8e+55)
		tmp = t_1;
	elseif (x <= -0.017)
		tmp = x * t;
	elseif (x <= -2.3e-14)
		tmp = t_1;
	elseif (x <= 1.6e-63)
		tmp = y * 5.0;
	elseif ((x <= 4.1e+153) || ~((x <= 1.42e+305)))
		tmp = x * t;
	else
		tmp = x * (2.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.8e+55], t$95$1, If[LessEqual[x, -0.017], N[(x * t), $MachinePrecision], If[LessEqual[x, -2.3e-14], t$95$1, If[LessEqual[x, 1.6e-63], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 4.1e+153], N[Not[LessEqual[x, 1.42e+305]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(x * N[(2.0 * y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.80000000000000042e55 or -0.017000000000000001 < x < -2.29999999999999998e-14

   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 z around inf 53.4%

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

   5. Simplified 53.4%

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

   if -8.80000000000000042e55 < x < -0.017000000000000001 or 1.59999999999999994e-63 < x < 4.10000000000000017e153 or 1.42e305 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 46.1%

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

   5. Simplified 46.1%

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

   if -2.29999999999999998e-14 < x < 1.59999999999999994e-63

   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 59.8%

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

   if 4.10000000000000017e153 < x < 1.42e305

   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 61.3%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in x around inf 61.3%

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

   7. Taylor expanded in x around inf 61.3%

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

      1. *-commutative 61.3%

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

   9. Simplified 61.3%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -0.017:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+153} \lor \neg \left(x \leq 1.42 \cdot 10^{+305}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot y\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+196}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -0.00032:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 10^{+151} \lor \neg \left(x \leq 1.08 \cdot 10^{+304}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* 2.0 y))))
   (if (<= x -2e+196)
     (* x t)
     (if (<= x -1.1e+52)
       t_1
       (if (<= x -0.00032)
         (* x t)
         (if (<= x 8.6e-63)
           (* y 5.0)
           (if (or (<= x 1e+151) (not (<= x 1.08e+304))) (* x t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * y);
	double tmp;
	if (x <= -2e+196) {
		tmp = x * t;
	} else if (x <= -1.1e+52) {
		tmp = t_1;
	} else if (x <= -0.00032) {
		tmp = x * t;
	} else if (x <= 8.6e-63) {
		tmp = y * 5.0;
	} else if ((x <= 1e+151) || !(x <= 1.08e+304)) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (2.0d0 * y)
    if (x <= (-2d+196)) then
        tmp = x * t
    else if (x <= (-1.1d+52)) then
        tmp = t_1
    else if (x <= (-0.00032d0)) then
        tmp = x * t
    else if (x <= 8.6d-63) then
        tmp = y * 5.0d0
    else if ((x <= 1d+151) .or. (.not. (x <= 1.08d+304))) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * y);
	double tmp;
	if (x <= -2e+196) {
		tmp = x * t;
	} else if (x <= -1.1e+52) {
		tmp = t_1;
	} else if (x <= -0.00032) {
		tmp = x * t;
	} else if (x <= 8.6e-63) {
		tmp = y * 5.0;
	} else if ((x <= 1e+151) || !(x <= 1.08e+304)) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (2.0 * y)
	tmp = 0
	if x <= -2e+196:
		tmp = x * t
	elif x <= -1.1e+52:
		tmp = t_1
	elif x <= -0.00032:
		tmp = x * t
	elif x <= 8.6e-63:
		tmp = y * 5.0
	elif (x <= 1e+151) or not (x <= 1.08e+304):
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(2.0 * y))
	tmp = 0.0
	if (x <= -2e+196)
		tmp = Float64(x * t);
	elseif (x <= -1.1e+52)
		tmp = t_1;
	elseif (x <= -0.00032)
		tmp = Float64(x * t);
	elseif (x <= 8.6e-63)
		tmp = Float64(y * 5.0);
	elseif ((x <= 1e+151) || !(x <= 1.08e+304))
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (2.0 * y);
	tmp = 0.0;
	if (x <= -2e+196)
		tmp = x * t;
	elseif (x <= -1.1e+52)
		tmp = t_1;
	elseif (x <= -0.00032)
		tmp = x * t;
	elseif (x <= 8.6e-63)
		tmp = y * 5.0;
	elseif ((x <= 1e+151) || ~((x <= 1.08e+304)))
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(2.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+196], N[(x * t), $MachinePrecision], If[LessEqual[x, -1.1e+52], t$95$1, If[LessEqual[x, -0.00032], N[(x * t), $MachinePrecision], If[LessEqual[x, 8.6e-63], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 1e+151], N[Not[LessEqual[x, 1.08e+304]], $MachinePrecision]], N[(x * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.9999999999999999e196 or -1.1e52 < x < -3.20000000000000026e-4 or 8.5999999999999997e-63 < x < 1.00000000000000002e151 or 1.08000000000000004e304 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 49.4%

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

   5. Simplified 49.4%

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

   if -1.9999999999999999e196 < x < -1.1e52 or 1.00000000000000002e151 < x < 1.08000000000000004e304

   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 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in x around inf 52.8%

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

   7. Taylor expanded in x around inf 52.8%

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

      1. *-commutative 52.8%

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

   9. Simplified 52.8%

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

   if -3.20000000000000026e-4 < x < 8.5999999999999997e-63

   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 58.6%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+196}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(2 \cdot y\right)\\ \mathbf{elif}\;x \leq -0.00032:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 10^{+151} \lor \neg \left(x \leq 1.08 \cdot 10^{+304}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;x \leq -1.32 \cdot 10^{+213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -0.00028 \lor \neg \left(x \leq 1.95 \cdot 10^{-63}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 y)))))
   (if (<= x -1.32e+213)
     t_1
     (if (<= x -1.35e+56)
       (* x (* 2.0 (+ y z)))
       (if (or (<= x -0.00028) (not (<= x 1.95e-63))) t_1 (* y 5.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -1.32e+213) {
		tmp = t_1;
	} else if (x <= -1.35e+56) {
		tmp = x * (2.0 * (y + z));
	} else if ((x <= -0.00028) || !(x <= 1.95e-63)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * y))
    if (x <= (-1.32d+213)) then
        tmp = t_1
    else if (x <= (-1.35d+56)) then
        tmp = x * (2.0d0 * (y + z))
    else if ((x <= (-0.00028d0)) .or. (.not. (x <= 1.95d-63))) then
        tmp = t_1
    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 t_1 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -1.32e+213) {
		tmp = t_1;
	} else if (x <= -1.35e+56) {
		tmp = x * (2.0 * (y + z));
	} else if ((x <= -0.00028) || !(x <= 1.95e-63)) {
		tmp = t_1;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * y))
	tmp = 0
	if x <= -1.32e+213:
		tmp = t_1
	elif x <= -1.35e+56:
		tmp = x * (2.0 * (y + z))
	elif (x <= -0.00028) or not (x <= 1.95e-63):
		tmp = t_1
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (x <= -1.32e+213)
		tmp = t_1;
	elseif (x <= -1.35e+56)
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	elseif ((x <= -0.00028) || !(x <= 1.95e-63))
		tmp = t_1;
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (x <= -1.32e+213)
		tmp = t_1;
	elseif (x <= -1.35e+56)
		tmp = x * (2.0 * (y + z));
	elseif ((x <= -0.00028) || ~((x <= 1.95e-63)))
		tmp = t_1;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.32e+213], t$95$1, If[LessEqual[x, -1.35e+56], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -0.00028], N[Not[LessEqual[x, 1.95e-63]], $MachinePrecision]], t$95$1, N[(y * 5.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.32e213 or -1.35000000000000005e56 < x < -2.7999999999999998e-4 or 1.95000000000000011e-63 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 78.6%

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

   4. Taylor expanded in x around inf 74.9%

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

   if -1.32e213 < x < -1.35000000000000005e56

   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 0 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in x around inf 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*r* 81.7%

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

      3. *-commutative 81.7%

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

   8. Simplified 81.7%

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

   if -2.7999999999999998e-4 < x < 1.95000000000000011e-63

   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 58.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -0.00028 \lor \neg \left(x \leq 1.95 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \left(5 + 2 \cdot \left(x + x \cdot \frac{z}{y}\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e+130)
   (* y (+ 5.0 (* 2.0 (+ x (* x (/ z y))))))
   (if (<= y 1.35e+70)
     (* x (+ t (+ (* 2.0 (+ y z)) (* 5.0 (/ y x)))))
     (+ (* x (+ t (+ y y))) (* y 5.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e+130) {
		tmp = y * (5.0 + (2.0 * (x + (x * (z / y)))));
	} else if (y <= 1.35e+70) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (x * (t + (y + y))) + (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 (y <= (-1.15d+130)) then
        tmp = y * (5.0d0 + (2.0d0 * (x + (x * (z / y)))))
    else if (y <= 1.35d+70) then
        tmp = x * (t + ((2.0d0 * (y + z)) + (5.0d0 * (y / x))))
    else
        tmp = (x * (t + (y + y))) + (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 (y <= -1.15e+130) {
		tmp = y * (5.0 + (2.0 * (x + (x * (z / y)))));
	} else if (y <= 1.35e+70) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e+130:
		tmp = y * (5.0 + (2.0 * (x + (x * (z / y)))))
	elif y <= 1.35e+70:
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))))
	else:
		tmp = (x * (t + (y + y))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e+130)
		tmp = Float64(y * Float64(5.0 + Float64(2.0 * Float64(x + Float64(x * Float64(z / y))))));
	elseif (y <= 1.35e+70)
		tmp = Float64(x * Float64(t + Float64(Float64(2.0 * Float64(y + z)) + Float64(5.0 * Float64(y / x)))));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(y + y))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e+130)
		tmp = y * (5.0 + (2.0 * (x + (x * (z / y)))));
	elseif (y <= 1.35e+70)
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	else
		tmp = (x * (t + (y + y))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e+130], N[(y * N[(5.0 + N[(2.0 * N[(x + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+70], N[(x * N[(t + N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000011e130

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around inf 95.5%

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

      1. distribute-lft-out 95.5%

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

      2. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

   if -1.15000000000000011e130 < y < 1.35e70

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 98.7%

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

   if 1.35e70 < 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 97.7%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \left(5 + 2 \cdot \left(x + x \cdot \frac{z}{y}\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.07 \cdot 10^{-106}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -4.6e+131)
     t_1
     (if (<= y -1.07e-106)
       (+ (* y 5.0) (* x t))
       (if (<= y 2.25e+121) (* x (+ t (* 2.0 z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -4.6e+131) {
		tmp = t_1;
	} else if (y <= -1.07e-106) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 2.25e+121) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-4.6d+131)) then
        tmp = t_1
    else if (y <= (-1.07d-106)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 2.25d+121) then
        tmp = x * (t + (2.0d0 * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -4.6e+131) {
		tmp = t_1;
	} else if (y <= -1.07e-106) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 2.25e+121) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -4.6e+131:
		tmp = t_1
	elif y <= -1.07e-106:
		tmp = (y * 5.0) + (x * t)
	elif y <= 2.25e+121:
		tmp = x * (t + (2.0 * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -4.6e+131)
		tmp = t_1;
	elseif (y <= -1.07e-106)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 2.25e+121)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -4.6e+131)
		tmp = t_1;
	elseif (y <= -1.07e-106)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 2.25e+121)
		tmp = x * (t + (2.0 * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+131], t$95$1, If[LessEqual[y, -1.07e-106], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+121], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.59999999999999983e131 or 2.2500000000000002e121 < 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 94.0%

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

   5. Simplified 94.0%

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

   if -4.59999999999999983e131 < y < -1.07e-106

   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 83.1%

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

      1. +-commutative 83.1%

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

      2. distribute-lft-in 79.0%

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

      3. flip-+ 0.0%

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

      4. +-inverses 0.0%

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

      5. +-inverses 0.0%

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

   5. Applied egg-rr 0.0%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in x around 0 72.1%

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

   if -1.07e-106 < y < 2.2500000000000002e121

   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 86.2%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+131}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.07 \cdot 10^{-106}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+91} \lor \neg \left(t \leq 3.2 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.5e+91) (not (<= t 3.2e-10)))
   (+ (* x (+ t (+ y y))) (* y 5.0))
   (+ (* (+ y z) (* x 2.0)) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.5e+91) || !(t <= 3.2e-10)) {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	} else {
		tmp = ((y + z) * (x * 2.0)) + (y * 5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5.5d+91)) .or. (.not. (t <= 3.2d-10))) then
        tmp = (x * (t + (y + y))) + (y * 5.0d0)
    else
        tmp = ((y + z) * (x * 2.0d0)) + (y * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.5e+91) || !(t <= 3.2e-10)) {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	} else {
		tmp = ((y + z) * (x * 2.0)) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.5e+91) or not (t <= 3.2e-10):
		tmp = (x * (t + (y + y))) + (y * 5.0)
	else:
		tmp = ((y + z) * (x * 2.0)) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.5e+91) || !(t <= 3.2e-10))
		tmp = Float64(Float64(x * Float64(t + Float64(y + y))) + Float64(y * 5.0));
	else
		tmp = Float64(Float64(Float64(y + z) * Float64(x * 2.0)) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.5e+91) || ~((t <= 3.2e-10)))
		tmp = (x * (t + (y + y))) + (y * 5.0);
	else
		tmp = ((y + z) * (x * 2.0)) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.5e+91], N[Not[LessEqual[t, 3.2e-10]], $MachinePrecision]], N[(N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.4999999999999998e91 or 3.19999999999999981e-10 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.1%

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

   if -5.4999999999999998e91 < t < 3.19999999999999981e-10

   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 0 95.3%

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

   5. Simplified 95.3%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+91} \lor \neg \left(t \leq 3.2 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.07 \cdot 10^{-106} \lor \neg \left(y \leq 3.6 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.07e-106) (not (<= y 3.6e+70)))
   (+ (* x (+ t (+ y y))) (* y 5.0))
   (* x (+ (* 2.0 (+ y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.07e-106) || !(y <= 3.6e+70)) {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	} else {
		tmp = x * ((2.0 * (y + z)) + 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 ((y <= (-1.07d-106)) .or. (.not. (y <= 3.6d+70))) then
        tmp = (x * (t + (y + y))) + (y * 5.0d0)
    else
        tmp = x * ((2.0d0 * (y + z)) + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.07e-106) || !(y <= 3.6e+70)) {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	} else {
		tmp = x * ((2.0 * (y + z)) + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.07e-106) or not (y <= 3.6e+70):
		tmp = (x * (t + (y + y))) + (y * 5.0)
	else:
		tmp = x * ((2.0 * (y + z)) + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.07e-106) || !(y <= 3.6e+70))
		tmp = Float64(Float64(x * Float64(t + Float64(y + y))) + Float64(y * 5.0));
	else
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.07e-106) || ~((y <= 3.6e+70)))
		tmp = (x * (t + (y + y))) + (y * 5.0);
	else
		tmp = x * ((2.0 * (y + z)) + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.07e-106], N[Not[LessEqual[y, 3.6e+70]], $MachinePrecision]], N[(N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.07e-106 or 3.6e70 < 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 91.6%

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

   if -1.07e-106 < y < 3.6e70

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 90.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.07 \cdot 10^{-106} \lor \neg \left(y \leq 3.6 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 175:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 175.0)
   (+ (* x (+ t (* 2.0 z))) (* y (+ 5.0 (* x 2.0))))
   (* x (+ (* 2.0 (+ y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 175.0) {
		tmp = (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)));
	} else {
		tmp = x * ((2.0 * (y + z)) + 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 <= 175.0d0) then
        tmp = (x * (t + (2.0d0 * z))) + (y * (5.0d0 + (x * 2.0d0)))
    else
        tmp = x * ((2.0d0 * (y + z)) + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 175.0) {
		tmp = (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)));
	} else {
		tmp = x * ((2.0 * (y + z)) + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 175.0:
		tmp = (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)))
	else:
		tmp = x * ((2.0 * (y + z)) + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 175.0)
		tmp = Float64(Float64(x * Float64(t + Float64(2.0 * z))) + Float64(y * Float64(5.0 + Float64(x * 2.0))));
	else
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 175.0)
		tmp = (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)));
	else
		tmp = x * ((2.0 * (y + z)) + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 175.0], N[(N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 175

   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 98.4%

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

   if 175 < 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 100.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 175:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-12} \lor \neg \left(x \leq 9.2 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.3e-12) (not (<= x 9.2e-39)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.3e-12) || !(x <= 9.2e-39)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} 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 <= (-2.3d-12)) .or. (.not. (x <= 9.2d-39))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    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 <= -2.3e-12) || !(x <= 9.2e-39)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.3e-12) or not (x <= 9.2e-39):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.3e-12) || !(x <= 9.2e-39))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	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 <= -2.3e-12) || ~((x <= 9.2e-39)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.3e-12], N[Not[LessEqual[x, 9.2e-39]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.29999999999999989e-12 or 9.20000000000000033e-39 < x

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 97.2%

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

   if -2.29999999999999989e-12 < x < 9.20000000000000033e-39

   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 78.5%

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

      1. +-commutative 78.5%

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

      2. distribute-lft-in 78.5%

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

      3. flip-+ 0.0%

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

      4. +-inverses 0.0%

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

      5. +-inverses 0.0%

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

   5. Applied egg-rr 0.0%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in x around 0 78.5%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-12} \lor \neg \left(x \leq 9.2 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+57} \lor \neg \left(y \leq 2.5 \cdot 10^{+121}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.6e+57) (not (<= y 2.5e+121)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.6e+57) || !(y <= 2.5e+121)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.6d+57)) .or. (.not. (y <= 2.5d+121))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (2.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.6e+57) || !(y <= 2.5e+121)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.6e+57) or not (y <= 2.5e+121):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.6e+57) || !(y <= 2.5e+121))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.6e+57) || ~((y <= 2.5e+121)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.6e+57], N[Not[LessEqual[y, 2.5e+121]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6000000000000002e57 or 2.50000000000000004e121 < 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 88.0%

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

   5. Simplified 88.0%

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

   if -3.6000000000000002e57 < y < 2.50000000000000004e121

   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 82.1%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+57} \lor \neg \left(y \leq 2.5 \cdot 10^{+121}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+148} \lor \neg \left(y \leq 6 \cdot 10^{+122}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5e+148) (not (<= y 6e+122))) (* y 5.0) (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e+148) || !(y <= 6e+122)) {
		tmp = y * 5.0;
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5d+148)) .or. (.not. (y <= 6d+122))) then
        tmp = y * 5.0d0
    else
        tmp = x * (t + (2.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e+148) || !(y <= 6e+122)) {
		tmp = y * 5.0;
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5e+148) or not (y <= 6e+122):
		tmp = y * 5.0
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5e+148) || !(y <= 6e+122))
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5e+148) || ~((y <= 6e+122)))
		tmp = y * 5.0;
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5e+148], N[Not[LessEqual[y, 6e+122]], $MachinePrecision]], N[(y * 5.0), $MachinePrecision], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000024e148 or 5.99999999999999972e122 < 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 x around 0 59.0%

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

   if -5.00000000000000024e148 < y < 5.99999999999999972e122

   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 77.4%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+148} \lor \neg \left(y \leq 6 \cdot 10^{+122}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-12} \lor \neg \left(x \leq 5.4 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.45e-12) (not (<= x 5.4e-39)))
   (* x (* 2.0 (+ y z)))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.45e-12) || !(x <= 5.4e-39)) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.45d-12)) .or. (.not. (x <= 5.4d-39))) then
        tmp = x * (2.0d0 * (y + z))
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.45e-12) || !(x <= 5.4e-39)) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.45e-12) or not (x <= 5.4e-39):
		tmp = x * (2.0 * (y + z))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.45e-12) || !(x <= 5.4e-39))
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.45e-12) || ~((x <= 5.4e-39)))
		tmp = x * (2.0 * (y + z));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.45e-12], N[Not[LessEqual[x, 5.4e-39]], $MachinePrecision]], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.44999999999999986e-12 or 5.4000000000000001e-39 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in x around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-*r* 64.9%

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

      3. *-commutative 64.9%

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

   8. Simplified 64.9%

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

   if -2.44999999999999986e-12 < x < 5.4000000000000001e-39

   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 58.6%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-12} \lor \neg \left(x \leq 5.4 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 15: 48.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00028 \lor \neg \left(x \leq 4.2 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.00028) (not (<= x 4.2e-63))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.00028) || !(x <= 4.2e-63)) {
		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 <= (-0.00028d0)) .or. (.not. (x <= 4.2d-63))) 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 <= -0.00028) || !(x <= 4.2e-63)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.00028) or not (x <= 4.2e-63):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.00028) || !(x <= 4.2e-63))
		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 <= -0.00028) || ~((x <= 4.2e-63)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.00028], N[Not[LessEqual[x, 4.2e-63]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7999999999999998e-4 or 4.2e-63 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 43.4%

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

   5. Simplified 43.4%

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

   if -2.7999999999999998e-4 < x < 4.2e-63

   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 58.6%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00028 \lor \neg \left(x \leq 4.2 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.7% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 30.0%

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

4. Final simplification 30.0%

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

Reproduce

herbie shell --seed 2024102 
(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)))