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

Percentage Accurate: 99.8% → 99.8%

Time: 10.6s

Alternatives: 11

Speedup: 1.0×

• 27.5% 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: 99.8% 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: 99.8% 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. Final simplification 99.9%

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

Alternative 2: 47.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -8.6 \cdot 10^{+69}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-26}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 10^{-31}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+96}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -8.6e+69)
     (* x t)
     (if (<= x -6.8e-19)
       t_1
       (if (<= x -7e-26)
         (* x t)
         (if (<= x 1e-31) (* y 5.0) (if (<= x 2.1e+96) (* x t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -8.6e+69) {
		tmp = x * t;
	} else if (x <= -6.8e-19) {
		tmp = t_1;
	} else if (x <= -7e-26) {
		tmp = x * t;
	} else if (x <= 1e-31) {
		tmp = y * 5.0;
	} else if (x <= 2.1e+96) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-8.6d+69)) then
        tmp = x * t
    else if (x <= (-6.8d-19)) then
        tmp = t_1
    else if (x <= (-7d-26)) then
        tmp = x * t
    else if (x <= 1d-31) then
        tmp = y * 5.0d0
    else if (x <= 2.1d+96) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -8.6e+69) {
		tmp = x * t;
	} else if (x <= -6.8e-19) {
		tmp = t_1;
	} else if (x <= -7e-26) {
		tmp = x * t;
	} else if (x <= 1e-31) {
		tmp = y * 5.0;
	} else if (x <= 2.1e+96) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -8.6e+69:
		tmp = x * t
	elif x <= -6.8e-19:
		tmp = t_1
	elif x <= -7e-26:
		tmp = x * t
	elif x <= 1e-31:
		tmp = y * 5.0
	elif x <= 2.1e+96:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -8.6e+69)
		tmp = Float64(x * t);
	elseif (x <= -6.8e-19)
		tmp = t_1;
	elseif (x <= -7e-26)
		tmp = Float64(x * t);
	elseif (x <= 1e-31)
		tmp = Float64(y * 5.0);
	elseif (x <= 2.1e+96)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -8.6e+69)
		tmp = x * t;
	elseif (x <= -6.8e-19)
		tmp = t_1;
	elseif (x <= -7e-26)
		tmp = x * t;
	elseif (x <= 1e-31)
		tmp = y * 5.0;
	elseif (x <= 2.1e+96)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.6e+69], N[(x * t), $MachinePrecision], If[LessEqual[x, -6.8e-19], t$95$1, If[LessEqual[x, -7e-26], N[(x * t), $MachinePrecision], If[LessEqual[x, 1e-31], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 2.1e+96], N[(x * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.59999999999999986e69 or -6.8000000000000004e-19 < x < -6.9999999999999997e-26 or 1e-31 < x < 2.1000000000000001e96

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 54.7%

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

   5. Simplified 54.7%

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

   if -8.59999999999999986e69 < x < -6.8000000000000004e-19 or 2.1000000000000001e96 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 53.5%

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

   if -6.9999999999999997e-26 < x < 1e-31

   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 x around 0 67.1%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+69}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-19}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-26}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 10^{-31}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+96}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-95}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ (* 2.0 (+ y z)) t))))
   (if (<= x -1.05e-16)
     t_1
     (if (<= x -4.3e-113)
       (* t (+ x (* y (/ 5.0 t))))
       (if (<= x -1.56e-139)
         (* x (+ t (* 2.0 z)))
         (if (<= x 2.25e-95) (* y 5.0) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((2.0 * (y + z)) + t);
	double tmp;
	if (x <= -1.05e-16) {
		tmp = t_1;
	} else if (x <= -4.3e-113) {
		tmp = t * (x + (y * (5.0 / t)));
	} else if (x <= -1.56e-139) {
		tmp = x * (t + (2.0 * z));
	} else if (x <= 2.25e-95) {
		tmp = y * 5.0;
	} 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 + z)) + t)
    if (x <= (-1.05d-16)) then
        tmp = t_1
    else if (x <= (-4.3d-113)) then
        tmp = t * (x + (y * (5.0d0 / t)))
    else if (x <= (-1.56d-139)) then
        tmp = x * (t + (2.0d0 * z))
    else if (x <= 2.25d-95) then
        tmp = y * 5.0d0
    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 + z)) + t);
	double tmp;
	if (x <= -1.05e-16) {
		tmp = t_1;
	} else if (x <= -4.3e-113) {
		tmp = t * (x + (y * (5.0 / t)));
	} else if (x <= -1.56e-139) {
		tmp = x * (t + (2.0 * z));
	} else if (x <= 2.25e-95) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((2.0 * (y + z)) + t)
	tmp = 0
	if x <= -1.05e-16:
		tmp = t_1
	elif x <= -4.3e-113:
		tmp = t * (x + (y * (5.0 / t)))
	elif x <= -1.56e-139:
		tmp = x * (t + (2.0 * z))
	elif x <= 2.25e-95:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t))
	tmp = 0.0
	if (x <= -1.05e-16)
		tmp = t_1;
	elseif (x <= -4.3e-113)
		tmp = Float64(t * Float64(x + Float64(y * Float64(5.0 / t))));
	elseif (x <= -1.56e-139)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	elseif (x <= 2.25e-95)
		tmp = Float64(y * 5.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((2.0 * (y + z)) + t);
	tmp = 0.0;
	if (x <= -1.05e-16)
		tmp = t_1;
	elseif (x <= -4.3e-113)
		tmp = t * (x + (y * (5.0 / t)));
	elseif (x <= -1.56e-139)
		tmp = x * (t + (2.0 * z));
	elseif (x <= 2.25e-95)
		tmp = y * 5.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e-16], t$95$1, If[LessEqual[x, -4.3e-113], N[(t * N[(x + N[(y * N[(5.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.56e-139], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e-95], N[(y * 5.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.0500000000000001e-16 or 2.25e-95 < 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 96.0%

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

   if -1.0500000000000001e-16 < x < -4.3e-113

   1. Initial program 99.8%

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

      1. fma-define 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 93.1%

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

   6. Taylor expanded in x around 0 80.7%

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

      1. associate-*r/ 80.6%

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

      2. *-commutative 80.6%

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

      3. associate-/l* 80.6%

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

   8. Simplified 80.6%

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

   if -4.3e-113 < x < -1.56000000000000008e-139

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.2%

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

   if -1.56000000000000008e-139 < x < 2.25e-95

   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 x around 0 74.1%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-95}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;y \leq -5.3 \cdot 10^{+169}:\\ \;\;\;\;y \cdot 5 + x \cdot t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(t + \left(t\_1 + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (<= y -5.3e+169)
     (+ (* y 5.0) (* x t_1))
     (if (<= y 9e+70)
       (* x (+ t (+ t_1 (* 5.0 (/ y x)))))
       (+ (* y 5.0) (* x (+ t (+ y y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (y <= -5.3e+169) {
		tmp = (y * 5.0) + (x * t_1);
	} else if (y <= 9e+70) {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	} else {
		tmp = (y * 5.0) + (x * (t + (y + 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 = 2.0d0 * (y + z)
    if (y <= (-5.3d+169)) then
        tmp = (y * 5.0d0) + (x * t_1)
    else if (y <= 9d+70) then
        tmp = x * (t + (t_1 + (5.0d0 * (y / x))))
    else
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (y <= -5.3e+169) {
		tmp = (y * 5.0) + (x * t_1);
	} else if (y <= 9e+70) {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	} else {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if y <= -5.3e+169:
		tmp = (y * 5.0) + (x * t_1)
	elif y <= 9e+70:
		tmp = x * (t + (t_1 + (5.0 * (y / x))))
	else:
		tmp = (y * 5.0) + (x * (t + (y + y)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if (y <= -5.3e+169)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t_1));
	elseif (y <= 9e+70)
		tmp = Float64(x * Float64(t + Float64(t_1 + Float64(5.0 * Float64(y / x)))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if (y <= -5.3e+169)
		tmp = (y * 5.0) + (x * t_1);
	elseif (y <= 9e+70)
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	else
		tmp = (y * 5.0) + (x * (t + (y + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.3e+169], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+70], N[(x * N[(t + N[(t$95$1 + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2999999999999999e169

   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 97.2%

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

   5. Simplified 97.2%

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

   if -5.2999999999999999e169 < y < 8.9999999999999999e70

   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 98.3%

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

   if 8.9999999999999999e70 < 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 93.7%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+169}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-67}:\\ \;\;\;\;y \cdot 5 + x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t\_1 + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (<= t -2.8e+107)
     (* t (+ x (* y (/ 5.0 t))))
     (if (<= t 3.4e-67) (+ (* y 5.0) (* x t_1)) (* x (+ t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (t <= -2.8e+107) {
		tmp = t * (x + (y * (5.0 / t)));
	} else if (t <= 3.4e-67) {
		tmp = (y * 5.0) + (x * t_1);
	} else {
		tmp = x * (t_1 + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    if (t <= (-2.8d+107)) then
        tmp = t * (x + (y * (5.0d0 / t)))
    else if (t <= 3.4d-67) then
        tmp = (y * 5.0d0) + (x * t_1)
    else
        tmp = x * (t_1 + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (t <= -2.8e+107) {
		tmp = t * (x + (y * (5.0 / t)));
	} else if (t <= 3.4e-67) {
		tmp = (y * 5.0) + (x * t_1);
	} else {
		tmp = x * (t_1 + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if t <= -2.8e+107:
		tmp = t * (x + (y * (5.0 / t)))
	elif t <= 3.4e-67:
		tmp = (y * 5.0) + (x * t_1)
	else:
		tmp = x * (t_1 + t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if (t <= -2.8e+107)
		tmp = Float64(t * Float64(x + Float64(y * Float64(5.0 / t))));
	elseif (t <= 3.4e-67)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t_1));
	else
		tmp = Float64(x * Float64(t_1 + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if (t <= -2.8e+107)
		tmp = t * (x + (y * (5.0 / t)));
	elseif (t <= 3.4e-67)
		tmp = (y * 5.0) + (x * t_1);
	else
		tmp = x * (t_1 + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+107], N[(t * N[(x + N[(y * N[(5.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-67], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$1 + t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.79999999999999985e107

   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 t around inf 97.4%

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

   6. Taylor expanded in x around 0 98.1%

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

      1. associate-*r/ 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-/l* 98.1%

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

   8. Simplified 98.1%

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

   if -2.79999999999999985e107 < t < 3.4000000000000001e-67

   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 94.5%

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

   5. Simplified 94.5%

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

   if 3.4000000000000001e-67 < t

   1. Initial program 99.9%

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

      1. fma-define 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 84.9%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-67}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+106}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-66}:\\ \;\;\;\;y \cdot 5 + x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t\_1 + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (<= t -7.8e+106)
     (+ (* y 5.0) (* x (+ t (+ y y))))
     (if (<= t 9.5e-66) (+ (* y 5.0) (* x t_1)) (* x (+ t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (t <= -7.8e+106) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else if (t <= 9.5e-66) {
		tmp = (y * 5.0) + (x * t_1);
	} else {
		tmp = x * (t_1 + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    if (t <= (-7.8d+106)) then
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    else if (t <= 9.5d-66) then
        tmp = (y * 5.0d0) + (x * t_1)
    else
        tmp = x * (t_1 + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (t <= -7.8e+106) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else if (t <= 9.5e-66) {
		tmp = (y * 5.0) + (x * t_1);
	} else {
		tmp = x * (t_1 + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if t <= -7.8e+106:
		tmp = (y * 5.0) + (x * (t + (y + y)))
	elif t <= 9.5e-66:
		tmp = (y * 5.0) + (x * t_1)
	else:
		tmp = x * (t_1 + t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if (t <= -7.8e+106)
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	elseif (t <= 9.5e-66)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t_1));
	else
		tmp = Float64(x * Float64(t_1 + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if (t <= -7.8e+106)
		tmp = (y * 5.0) + (x * (t + (y + y)));
	elseif (t <= 9.5e-66)
		tmp = (y * 5.0) + (x * t_1);
	else
		tmp = x * (t_1 + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+106], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-66], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$1 + t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.79999999999999937e106

   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 98.2%

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

   if -7.79999999999999937e106 < t < 9.5000000000000004e-66

   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 94.5%

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

   5. Simplified 94.5%

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

   if 9.5000000000000004e-66 < t

   1. Initial program 99.9%

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

      1. fma-define 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 84.9%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+106}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-66}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.62 \cdot 10^{-139} \lor \neg \left(x \leq 1.1 \cdot 10^{-66}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.62e-139) (not (<= x 1.1e-66)))
   (* x (+ t (* 2.0 z)))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.62e-139) || !(x <= 1.1e-66)) {
		tmp = x * (t + (2.0 * 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 <= (-1.62d-139)) .or. (.not. (x <= 1.1d-66))) then
        tmp = x * (t + (2.0d0 * 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 <= -1.62e-139) || !(x <= 1.1e-66)) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.62e-139) or not (x <= 1.1e-66):
		tmp = x * (t + (2.0 * z))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.62e-139) || !(x <= 1.1e-66))
		tmp = Float64(x * Float64(t + Float64(2.0 * 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 <= -1.62e-139) || ~((x <= 1.1e-66)))
		tmp = x * (t + (2.0 * z));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.62e-139], N[Not[LessEqual[x, 1.1e-66]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.62000000000000001e-139 or 1.1000000000000001e-66 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.2%

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

   if -1.62000000000000001e-139 < x < 1.1000000000000001e-66

   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 x around 0 73.6%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.62 \cdot 10^{-139} \lor \neg \left(x \leq 1.1 \cdot 10^{-66}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+103} \lor \neg \left(y \leq 10^{+43}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2e+103) (not (<= y 1e+43)))
   (* 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 <= -2e+103) || !(y <= 1e+43)) {
		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 <= (-2d+103)) .or. (.not. (y <= 1d+43))) 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 <= -2e+103) || !(y <= 1e+43)) {
		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 <= -2e+103) or not (y <= 1e+43):
		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 <= -2e+103) || !(y <= 1e+43))
		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 <= -2e+103) || ~((y <= 1e+43)))
		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, -2e+103], N[Not[LessEqual[y, 1e+43]], $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 < -2e103 or 1.00000000000000001e43 < y

   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 y around inf 84.8%

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

   5. Simplified 84.8%

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

   if -2e103 < y < 1.00000000000000001e43

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.3%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+103} \lor \neg \left(y \leq 10^{+43}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.8% 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 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%

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

Alternative 10: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-40} \lor \neg \left(x \leq 8.5 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.7e-40) (not (<= x 8.5e-32))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e-40) || !(x <= 8.5e-32)) {
		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 <= (-1.7d-40)) .or. (.not. (x <= 8.5d-32))) 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 <= -1.7e-40) || !(x <= 8.5e-32)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.7e-40) or not (x <= 8.5e-32):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.7e-40) || !(x <= 8.5e-32))
		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 <= -1.7e-40) || ~((x <= 8.5e-32)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.7e-40], N[Not[LessEqual[x, 8.5e-32]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999992e-40 or 8.5000000000000003e-32 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 45.2%

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

   5. Simplified 45.2%

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

   if -1.69999999999999992e-40 < x < 8.5000000000000003e-32

   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 x around 0 67.1%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-40} \lor \neg \left(x \leq 8.5 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.5% 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 30.8%

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

4. Final simplification 30.8%

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

Reproduce

herbie shell --seed 2024078 
(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)))