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

Percentage Accurate: 99.9% → 99.9%

Time: 10.3s

Alternatives: 10

Speedup: 1.0×

• 26.3% 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-def 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. Final simplification 100.0%

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

Alternative 2: 45.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+168}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-113}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-108}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+68} \lor \neg \left(x \leq 1.8 \cdot 10^{+114}\right) \land x \leq 1.02 \cdot 10^{+239}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))))
   (if (<= x -9.6e+242)
     t_1
     (if (<= x -2.7e+168)
       (* x t)
       (if (<= x -1.12e+42)
         t_1
         (if (<= x -3.4e-113)
           (* x t)
           (if (<= x 3.5e-108)
             (* y 5.0)
             (if (or (<= x 1.85e+68)
                     (and (not (<= x 1.8e+114)) (<= x 1.02e+239)))
               (* x t)
               t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if (x <= -9.6e+242) {
		tmp = t_1;
	} else if (x <= -2.7e+168) {
		tmp = x * t;
	} else if (x <= -1.12e+42) {
		tmp = t_1;
	} else if (x <= -3.4e-113) {
		tmp = x * t;
	} else if (x <= 3.5e-108) {
		tmp = y * 5.0;
	} else if ((x <= 1.85e+68) || (!(x <= 1.8e+114) && (x <= 1.02e+239))) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    if (x <= (-9.6d+242)) then
        tmp = t_1
    else if (x <= (-2.7d+168)) then
        tmp = x * t
    else if (x <= (-1.12d+42)) then
        tmp = t_1
    else if (x <= (-3.4d-113)) then
        tmp = x * t
    else if (x <= 3.5d-108) then
        tmp = y * 5.0d0
    else if ((x <= 1.85d+68) .or. (.not. (x <= 1.8d+114)) .and. (x <= 1.02d+239)) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if (x <= -9.6e+242) {
		tmp = t_1;
	} else if (x <= -2.7e+168) {
		tmp = x * t;
	} else if (x <= -1.12e+42) {
		tmp = t_1;
	} else if (x <= -3.4e-113) {
		tmp = x * t;
	} else if (x <= 3.5e-108) {
		tmp = y * 5.0;
	} else if ((x <= 1.85e+68) || (!(x <= 1.8e+114) && (x <= 1.02e+239))) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * y)
	tmp = 0
	if x <= -9.6e+242:
		tmp = t_1
	elif x <= -2.7e+168:
		tmp = x * t
	elif x <= -1.12e+42:
		tmp = t_1
	elif x <= -3.4e-113:
		tmp = x * t
	elif x <= 3.5e-108:
		tmp = y * 5.0
	elif (x <= 1.85e+68) or (not (x <= 1.8e+114) and (x <= 1.02e+239)):
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (x <= -9.6e+242)
		tmp = t_1;
	elseif (x <= -2.7e+168)
		tmp = Float64(x * t);
	elseif (x <= -1.12e+42)
		tmp = t_1;
	elseif (x <= -3.4e-113)
		tmp = Float64(x * t);
	elseif (x <= 3.5e-108)
		tmp = Float64(y * 5.0);
	elseif ((x <= 1.85e+68) || (!(x <= 1.8e+114) && (x <= 1.02e+239)))
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * y);
	tmp = 0.0;
	if (x <= -9.6e+242)
		tmp = t_1;
	elseif (x <= -2.7e+168)
		tmp = x * t;
	elseif (x <= -1.12e+42)
		tmp = t_1;
	elseif (x <= -3.4e-113)
		tmp = x * t;
	elseif (x <= 3.5e-108)
		tmp = y * 5.0;
	elseif ((x <= 1.85e+68) || (~((x <= 1.8e+114)) && (x <= 1.02e+239)))
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.6e+242], t$95$1, If[LessEqual[x, -2.7e+168], N[(x * t), $MachinePrecision], If[LessEqual[x, -1.12e+42], t$95$1, If[LessEqual[x, -3.4e-113], N[(x * t), $MachinePrecision], If[LessEqual[x, 3.5e-108], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 1.85e+68], And[N[Not[LessEqual[x, 1.8e+114]], $MachinePrecision], LessEqual[x, 1.02e+239]]], N[(x * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.60000000000000049e242 or -2.70000000000000016e168 < x < -1.12e42 or 1.84999999999999999e68 < x < 1.8e114 or 1.02e239 < 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. Taylor expanded in y around inf 54.7%

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

   3. Taylor expanded in x around inf 54.7%

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

   if -9.60000000000000049e242 < x < -2.70000000000000016e168 or -1.12e42 < x < -3.4000000000000002e-113 or 3.4999999999999999e-108 < x < 1.84999999999999999e68 or 1.8e114 < x < 1.02e239

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 90.4%

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

   3. Taylor expanded in x around inf 83.7%

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

      1. distribute-lft-in 81.8%

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

      2. *-commutative 81.8%

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

      3. *-commutative 81.8%

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

      4. associate-*r* 81.8%

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

      5. +-commutative 81.8%

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

   5. Applied egg-rr 81.8%

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

   6. Taylor expanded in z around 0 52.6%

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

   if -3.4000000000000002e-113 < x < 3.4999999999999999e-108

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0 58.5%

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

   4. Simplified 58.5%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+242}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+168}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+42}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-113}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-108}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+68} \lor \neg \left(x \leq 1.8 \cdot 10^{+114}\right) \land x \leq 1.02 \cdot 10^{+239}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 3: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.95 \lor \neg \left(y \leq 3.1 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.95) (not (<= y 3.1e-31)))
   (+ (* y 5.0) (* x (+ y (+ y t))))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.95) || !(y <= 3.1e-31)) {
		tmp = (y * 5.0) + (x * (y + (y + t)));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-0.95d0)) .or. (.not. (y <= 3.1d-31))) then
        tmp = (y * 5.0d0) + (x * (y + (y + t)))
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.95) || !(y <= 3.1e-31)) {
		tmp = (y * 5.0) + (x * (y + (y + t)));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.95) or not (y <= 3.1e-31):
		tmp = (y * 5.0) + (x * (y + (y + t)))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.95) || !(y <= 3.1e-31))
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(y + Float64(y + t))));
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.95) || ~((y <= 3.1e-31)))
		tmp = (y * 5.0) + (x * (y + (y + t)));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.95], N[Not[LessEqual[y, 3.1e-31]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(y + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.94999999999999996 or 3.1e-31 < y

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around inf 86.4%

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

      1. associate-+l+ 86.4%

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

      2. distribute-lft-in 83.3%

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

      3. +-commutative 83.3%

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

   4. Applied egg-rr 83.3%

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

   6. Simplified 86.4%

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

   if -0.94999999999999996 < y < 3.1e-31

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 97.7%

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

   3. Taylor expanded in x around inf 89.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.95 \lor \neg \left(y \leq 3.1 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 4: 93.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+55} \lor \neg \left(y \leq 4.8 \cdot 10^{+107}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.4e+55) (not (<= y 4.8e+107)))
   (+ (* y 5.0) (* x (+ y (+ y t))))
   (+ (* y 5.0) (* x (+ t (* z 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e+55) || !(y <= 4.8e+107)) {
		tmp = (y * 5.0) + (x * (y + (y + t)));
	} 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 ((y <= (-3.4d+55)) .or. (.not. (y <= 4.8d+107))) then
        tmp = (y * 5.0d0) + (x * (y + (y + t)))
    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 ((y <= -3.4e+55) || !(y <= 4.8e+107)) {
		tmp = (y * 5.0) + (x * (y + (y + t)));
	} else {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.4e+55) or not (y <= 4.8e+107):
		tmp = (y * 5.0) + (x * (y + (y + t)))
	else:
		tmp = (y * 5.0) + (x * (t + (z * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.4e+55) || !(y <= 4.8e+107))
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(y + Float64(y + t))));
	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 ((y <= -3.4e+55) || ~((y <= 4.8e+107)))
		tmp = (y * 5.0) + (x * (y + (y + t)));
	else
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.4e+55], N[Not[LessEqual[y, 4.8e+107]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(y + N[(y + t), $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 y < -3.3999999999999998e55 or 4.8000000000000001e107 < 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. Taylor expanded in y around inf 93.6%

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

      1. associate-+l+ 93.6%

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

      2. distribute-lft-in 89.0%

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

      3. +-commutative 89.0%

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

   4. Applied egg-rr 89.0%

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

   6. Simplified 93.6%

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

   if -3.3999999999999998e55 < y < 4.8000000000000001e107

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 94.8%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+55} \lor \neg \left(y \leq 4.8 \cdot 10^{+107}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(y + \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (x * (t + (y + (z + (y + z)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + N[(z + N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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. Final simplification 100.0%

   \[\leadsto y \cdot 5 + x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) \]

Alternative 6: 43.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+167}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* x 2.0))))
   (if (<= t -5.4e+167)
     (* x t)
     (if (<= t 1.35e-170)
       t_1
       (if (<= t 2.65e-95)
         (* 2.0 (* x y))
         (if (<= t 3.6e+101) t_1 (* x t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x * 2.0);
	double tmp;
	if (t <= -5.4e+167) {
		tmp = x * t;
	} else if (t <= 1.35e-170) {
		tmp = t_1;
	} else if (t <= 2.65e-95) {
		tmp = 2.0 * (x * y);
	} else if (t <= 3.6e+101) {
		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 = z * (x * 2.0d0)
    if (t <= (-5.4d+167)) then
        tmp = x * t
    else if (t <= 1.35d-170) then
        tmp = t_1
    else if (t <= 2.65d-95) then
        tmp = 2.0d0 * (x * y)
    else if (t <= 3.6d+101) 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 = z * (x * 2.0);
	double tmp;
	if (t <= -5.4e+167) {
		tmp = x * t;
	} else if (t <= 1.35e-170) {
		tmp = t_1;
	} else if (t <= 2.65e-95) {
		tmp = 2.0 * (x * y);
	} else if (t <= 3.6e+101) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x * 2.0)
	tmp = 0
	if t <= -5.4e+167:
		tmp = x * t
	elif t <= 1.35e-170:
		tmp = t_1
	elif t <= 2.65e-95:
		tmp = 2.0 * (x * y)
	elif t <= 3.6e+101:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x * 2.0))
	tmp = 0.0
	if (t <= -5.4e+167)
		tmp = Float64(x * t);
	elseif (t <= 1.35e-170)
		tmp = t_1;
	elseif (t <= 2.65e-95)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (t <= 3.6e+101)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x * 2.0);
	tmp = 0.0;
	if (t <= -5.4e+167)
		tmp = x * t;
	elseif (t <= 1.35e-170)
		tmp = t_1;
	elseif (t <= 2.65e-95)
		tmp = 2.0 * (x * y);
	elseif (t <= 3.6e+101)
		tmp = t_1;
	else
		tmp = x * t;
	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[t, -5.4e+167], N[(x * t), $MachinePrecision], If[LessEqual[t, 1.35e-170], t$95$1, If[LessEqual[t, 2.65e-95], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+101], t$95$1, N[(x * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4000000000000001e167 or 3.60000000000000029e101 < 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. Taylor expanded in y around 0 95.1%

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

   3. Taylor expanded in x around inf 86.4%

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

      1. distribute-lft-in 81.4%

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

      2. *-commutative 81.4%

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

      3. *-commutative 81.4%

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

      4. associate-*r* 81.4%

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

      5. +-commutative 81.4%

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

   5. Applied egg-rr 81.4%

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

   6. Taylor expanded in z around 0 80.0%

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

   if -5.4000000000000001e167 < t < 1.3499999999999999e-170 or 2.6499999999999999e-95 < t < 3.60000000000000029e101

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 82.2%

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

   3. Taylor expanded in x around inf 58.7%

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

      1. distribute-lft-in 58.1%

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

      2. *-commutative 58.1%

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

      3. *-commutative 58.1%

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

      4. associate-*r* 58.1%

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

      5. +-commutative 58.1%

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

   5. Applied egg-rr 58.1%

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

   6. Taylor expanded in z around inf 50.2%

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

   8. Simplified 50.2%

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

   if 1.3499999999999999e-170 < t < 2.6499999999999999e-95

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around inf 64.3%

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

   3. Taylor expanded in x around inf 44.1%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+167}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-170}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 7: 65.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-209} \lor \neg \left(x \leq 2.9 \cdot 10^{-135}\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.7e-209) (not (<= x 2.9e-135)))
   (* x (+ t (* z 2.0)))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e-209) || !(x <= 2.9e-135)) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.7d-209)) .or. (.not. (x <= 2.9d-135))) then
        tmp = x * (t + (z * 2.0d0))
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e-209) || !(x <= 2.9e-135)) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.7e-209) or not (x <= 2.9e-135):
		tmp = x * (t + (z * 2.0))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.7e-209) || !(x <= 2.9e-135))
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.7e-209) || ~((x <= 2.9e-135)))
		tmp = x * (t + (z * 2.0));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.7e-209], N[Not[LessEqual[x, 2.9e-135]], $MachinePrecision]], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999994e-209 or 2.9000000000000002e-135 < 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. Taylor expanded in y around 0 80.5%

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

   3. Taylor expanded in x around inf 74.2%

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

   if -1.69999999999999994e-209 < x < 2.9000000000000002e-135

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0 70.5%

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

   4. Simplified 70.5%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-209} \lor \neg \left(x \leq 2.9 \cdot 10^{-135}\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 8: 78.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -780 \lor \neg \left(y \leq 6.2 \cdot 10^{+106}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -780.0) (not (<= y 6.2e+106)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -780.0) || !(y <= 6.2e+106)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-780.0d0)) .or. (.not. (y <= 6.2d+106))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -780.0) || !(y <= 6.2e+106)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -780.0) or not (y <= 6.2e+106):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -780.0) || !(y <= 6.2e+106))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -780.0) || ~((y <= 6.2e+106)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -780.0], N[Not[LessEqual[y, 6.2e+106]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -780 or 6.1999999999999999e106 < y

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around inf 79.0%

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

   if -780 < y < 6.1999999999999999e106

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in y around 0 96.3%

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

   3. Taylor expanded in x around inf 85.7%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -780 \lor \neg \left(y \leq 6.2 \cdot 10^{+106}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 9: 46.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-109} \lor \neg \left(x \leq 8.8 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.6e-109) (not (<= x 8.8e-107))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.6e-109) || !(x <= 8.8e-107)) {
		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 <= (-4.6d-109)) .or. (.not. (x <= 8.8d-107))) 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 <= -4.6e-109) || !(x <= 8.8e-107)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.6e-109) or not (x <= 8.8e-107):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.6e-109) || !(x <= 8.8e-107))
		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 <= -4.6e-109) || ~((x <= 8.8e-107)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.6e-109], N[Not[LessEqual[x, 8.8e-107]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6000000000000003e-109 or 8.8000000000000005e-107 < 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. Taylor expanded in y around 0 78.2%

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

   3. Taylor expanded in x around inf 74.3%

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

      1. distribute-lft-in 71.5%

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

      2. *-commutative 71.5%

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

      3. *-commutative 71.5%

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

      4. associate-*r* 71.5%

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

      5. +-commutative 71.5%

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

   5. Applied egg-rr 71.5%

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

   6. Taylor expanded in z around 0 39.8%

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

   if -4.6000000000000003e-109 < x < 8.8000000000000005e-107

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

   2. Taylor expanded in x around 0 58.5%

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

   4. Simplified 58.5%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-109} \lor \neg \left(x \leq 8.8 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 10: 31.4% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ x \cdot t \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x * t), $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. Taylor expanded in y around 0 84.5%

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

3. Taylor expanded in x around inf 65.7%

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

   1. distribute-lft-in 63.8%

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

   2. *-commutative 63.8%

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

   3. *-commutative 63.8%

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

   4. associate-*r* 63.8%

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

   5. +-commutative 63.8%

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

5. Applied egg-rr 63.8%

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

6. Taylor expanded in z around 0 32.8%

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

7. Final simplification 32.8%

   \[\leadsto x \cdot t \]

Reproduce

herbie shell --seed 2023308 
(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)))