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

Percentage Accurate: 99.8% → 99.9%

Time: 7.4s

Alternatives: 11

Speedup: 0.1×

• 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: 99.8% 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: 99.9% 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-def 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. Final simplification 99.9%

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

Alternative 2: 59.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-64}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+58} \lor \neg \left(x \leq 3.1 \cdot 10^{+155}\right) \land x \leq 2.1 \cdot 10^{+208}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x (+ y z)))))
   (if (<= x -3e-102)
     t_1
     (if (<= x 6e-64)
       (* y 5.0)
       (if (or (<= x 4.5e+58) (and (not (<= x 3.1e+155)) (<= x 2.1e+208)))
         (* x t)
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * (y + z));
	double tmp;
	if (x <= -3e-102) {
		tmp = t_1;
	} else if (x <= 6e-64) {
		tmp = y * 5.0;
	} else if ((x <= 4.5e+58) || (!(x <= 3.1e+155) && (x <= 2.1e+208))) {
		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 + z))
    if (x <= (-3d-102)) then
        tmp = t_1
    else if (x <= 6d-64) then
        tmp = y * 5.0d0
    else if ((x <= 4.5d+58) .or. (.not. (x <= 3.1d+155)) .and. (x <= 2.1d+208)) 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 + z));
	double tmp;
	if (x <= -3e-102) {
		tmp = t_1;
	} else if (x <= 6e-64) {
		tmp = y * 5.0;
	} else if ((x <= 4.5e+58) || (!(x <= 3.1e+155) && (x <= 2.1e+208))) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * (y + z))
	tmp = 0
	if x <= -3e-102:
		tmp = t_1
	elif x <= 6e-64:
		tmp = y * 5.0
	elif (x <= 4.5e+58) or (not (x <= 3.1e+155) and (x <= 2.1e+208)):
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * Float64(y + z)))
	tmp = 0.0
	if (x <= -3e-102)
		tmp = t_1;
	elseif (x <= 6e-64)
		tmp = Float64(y * 5.0);
	elseif ((x <= 4.5e+58) || (!(x <= 3.1e+155) && (x <= 2.1e+208)))
		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 + z));
	tmp = 0.0;
	if (x <= -3e-102)
		tmp = t_1;
	elseif (x <= 6e-64)
		tmp = y * 5.0;
	elseif ((x <= 4.5e+58) || (~((x <= 3.1e+155)) && (x <= 2.1e+208)))
		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 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e-102], t$95$1, If[LessEqual[x, 6e-64], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 4.5e+58], And[N[Not[LessEqual[x, 3.1e+155]], $MachinePrecision], LessEqual[x, 2.1e+208]]], N[(x * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3e-102 or 4.4999999999999998e58 < x < 3.09999999999999989e155 or 2.0999999999999998e208 < 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 t around 0 75.2%

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

   4. Simplified 75.2%

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

   5. Taylor expanded in x around inf 70.0%

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

   if -3e-102 < x < 6.0000000000000001e-64

   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 66.5%

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

   if 6.0000000000000001e-64 < x < 4.4999999999999998e58 or 3.09999999999999989e155 < x < 2.0999999999999998e208

   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 t around inf 60.5%

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

   4. Simplified 60.5%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-102}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-64}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+58} \lor \neg \left(x \leq 3.1 \cdot 10^{+155}\right) \land x \leq 2.1 \cdot 10^{+208}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \]

Alternative 3: 64.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+47}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+125} \lor \neg \left(y \leq 4.6 \cdot 10^{+218}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e+47)
   (* y 5.0)
   (if (<= y 3.55e+81)
     (* x (+ t (* 2.0 z)))
     (if (or (<= y 3.3e+125) (not (<= y 4.6e+218)))
       (* y 5.0)
       (* 2.0 (* x (+ y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+47) {
		tmp = y * 5.0;
	} else if (y <= 3.55e+81) {
		tmp = x * (t + (2.0 * z));
	} else if ((y <= 3.3e+125) || !(y <= 4.6e+218)) {
		tmp = y * 5.0;
	} else {
		tmp = 2.0 * (x * (y + 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 <= (-1.65d+47)) then
        tmp = y * 5.0d0
    else if (y <= 3.55d+81) then
        tmp = x * (t + (2.0d0 * z))
    else if ((y <= 3.3d+125) .or. (.not. (y <= 4.6d+218))) then
        tmp = y * 5.0d0
    else
        tmp = 2.0d0 * (x * (y + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+47) {
		tmp = y * 5.0;
	} else if (y <= 3.55e+81) {
		tmp = x * (t + (2.0 * z));
	} else if ((y <= 3.3e+125) || !(y <= 4.6e+218)) {
		tmp = y * 5.0;
	} else {
		tmp = 2.0 * (x * (y + z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e+47:
		tmp = y * 5.0
	elif y <= 3.55e+81:
		tmp = x * (t + (2.0 * z))
	elif (y <= 3.3e+125) or not (y <= 4.6e+218):
		tmp = y * 5.0
	else:
		tmp = 2.0 * (x * (y + z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e+47)
		tmp = Float64(y * 5.0);
	elseif (y <= 3.55e+81)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	elseif ((y <= 3.3e+125) || !(y <= 4.6e+218))
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(2.0 * Float64(x * Float64(y + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e+47)
		tmp = y * 5.0;
	elseif (y <= 3.55e+81)
		tmp = x * (t + (2.0 * z));
	elseif ((y <= 3.3e+125) || ~((y <= 4.6e+218)))
		tmp = y * 5.0;
	else
		tmp = 2.0 * (x * (y + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e+47], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, 3.55e+81], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.3e+125], N[Not[LessEqual[y, 4.6e+218]], $MachinePrecision]], N[(y * 5.0), $MachinePrecision], N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e47 or 3.54999999999999984e81 < y < 3.30000000000000005e125 or 4.6000000000000002e218 < 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. Taylor expanded in x around 0 63.2%

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

   if -1.65e47 < y < 3.54999999999999984e81

   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 81.8%

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

   if 3.30000000000000005e125 < y < 4.6000000000000002e218

   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 t around 0 85.7%

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

   4. Simplified 85.7%

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

   5. Taylor expanded in x around inf 63.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+47}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+125} \lor \neg \left(y \leq 4.6 \cdot 10^{+218}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \]

Alternative 4: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -65 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -65.0) (not (<= x 2.0)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* x (+ t (* 2.0 z))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -65.0) || !(x <= 2.0)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (x * (t + (2.0 * z))) + (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 <= (-65.0d0)) .or. (.not. (x <= 2.0d0))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (x * (t + (2.0d0 * z))) + (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 <= -65.0) || !(x <= 2.0)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (x * (t + (2.0 * z))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -65.0) or not (x <= 2.0):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (x * (t + (2.0 * z))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -65.0) || !(x <= 2.0))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(2.0 * z))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -65.0) || ~((x <= 2.0)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (x * (t + (2.0 * z))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -65.0], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -65 or 2 < 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-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%

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

      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. Taylor expanded in x around inf 98.9%

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

   if -65 < x < 2

   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 0 98.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -65 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \end{array} \]

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(t + N[(y + N[(y + N[(2.0 * 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. Taylor expanded in y around 0 99.9%

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

3. Final simplification 99.9%

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

Alternative 6: 46.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+151}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-64}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+209}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -2.4e+151)
     (* 2.0 (* x y))
     (if (<= x -2.8e-102)
       t_1
       (if (<= x 4.5e-64) (* y 5.0) (if (<= x 1.15e+209) (* x t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -2.4e+151) {
		tmp = 2.0 * (x * y);
	} else if (x <= -2.8e-102) {
		tmp = t_1;
	} else if (x <= 4.5e-64) {
		tmp = y * 5.0;
	} else if (x <= 1.15e+209) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-2.4d+151)) then
        tmp = 2.0d0 * (x * y)
    else if (x <= (-2.8d-102)) then
        tmp = t_1
    else if (x <= 4.5d-64) then
        tmp = y * 5.0d0
    else if (x <= 1.15d+209) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -2.4e+151) {
		tmp = 2.0 * (x * y);
	} else if (x <= -2.8e-102) {
		tmp = t_1;
	} else if (x <= 4.5e-64) {
		tmp = y * 5.0;
	} else if (x <= 1.15e+209) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -2.4e+151:
		tmp = 2.0 * (x * y)
	elif x <= -2.8e-102:
		tmp = t_1
	elif x <= 4.5e-64:
		tmp = y * 5.0
	elif x <= 1.15e+209:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -2.4e+151)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (x <= -2.8e-102)
		tmp = t_1;
	elseif (x <= 4.5e-64)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.15e+209)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -2.4e+151)
		tmp = 2.0 * (x * y);
	elseif (x <= -2.8e-102)
		tmp = t_1;
	elseif (x <= 4.5e-64)
		tmp = y * 5.0;
	elseif (x <= 1.15e+209)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+151], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.8e-102], t$95$1, If[LessEqual[x, 4.5e-64], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.15e+209], N[(x * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4000000000000001e151

   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 t around 0 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in x around inf 70.0%

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

   6. Taylor expanded in y around inf 44.1%

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

   if -2.4000000000000001e151 < x < -2.80000000000000013e-102 or 1.15000000000000005e209 < 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 z around inf 56.0%

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

   if -2.80000000000000013e-102 < x < 4.5000000000000001e-64

   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 66.5%

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

   if 4.5000000000000001e-64 < x < 1.15000000000000005e209

   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 t around inf 53.4%

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

   4. Simplified 53.4%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+151}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-102}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-64}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+209}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 7: 88.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-102} \lor \neg \left(x \leq 2.2 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3e-102) (not (<= x 2.2e-26)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* x t) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3e-102) || !(x <= 2.2e-26)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (x * t) + (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 <= (-3d-102)) .or. (.not. (x <= 2.2d-26))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (x * t) + (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 <= -3e-102) || !(x <= 2.2e-26)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (x * t) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3e-102) or not (x <= 2.2e-26):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (x * t) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3e-102) || !(x <= 2.2e-26))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(x * t) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3e-102) || ~((x <= 2.2e-26)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (x * t) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3e-102], N[Not[LessEqual[x, 2.2e-26]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3e-102 or 2.2000000000000001e-26 < 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-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%

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

      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. Taylor expanded in x around inf 93.2%

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

   if -3e-102 < x < 2.2000000000000001e-26

   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 0 99.9%

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

   3. Taylor expanded in t around inf 84.5%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-102} \lor \neg \left(x \leq 2.2 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \end{array} \]

Alternative 8: 79.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+44} \lor \neg \left(y \leq 3.2 \cdot 10^{+50}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.5e+44) (not (<= y 3.2e+50)))
   (* 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 <= -8.5e+44) || !(y <= 3.2e+50)) {
		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 <= (-8.5d+44)) .or. (.not. (y <= 3.2d+50))) 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 <= -8.5e+44) || !(y <= 3.2e+50)) {
		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 <= -8.5e+44) or not (y <= 3.2e+50):
		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 <= -8.5e+44) || !(y <= 3.2e+50))
		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 <= -8.5e+44) || ~((y <= 3.2e+50)))
		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, -8.5e+44], N[Not[LessEqual[y, 3.2e+50]], $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 < -8.5e44 or 3.19999999999999983e50 < 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 85.9%

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

   4. Simplified 85.9%

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

   if -8.5e44 < y < 3.19999999999999983e50

   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 82.9%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+44} \lor \neg \left(y \leq 3.2 \cdot 10^{+50}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]

Alternative 9: 47.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-45} \lor \neg \left(x \leq 6 \cdot 10^{-64}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3e-45) (not (<= x 6e-64))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3e-45) || !(x <= 6e-64)) {
		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 <= (-3d-45)) .or. (.not. (x <= 6d-64))) 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 <= -3e-45) || !(x <= 6e-64)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3e-45) or not (x <= 6e-64):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3e-45) || !(x <= 6e-64))
		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 <= -3e-45) || ~((x <= 6e-64)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3e-45], N[Not[LessEqual[x, 6e-64]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000011e-45 or 6.0000000000000001e-64 < 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 t around inf 39.2%

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

   4. Simplified 39.2%

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

   if -3.00000000000000011e-45 < x < 6.0000000000000001e-64

   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 61.9%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-45} \lor \neg \left(x \leq 6 \cdot 10^{-64}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 10: 47.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -65:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-64}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -65.0) (* 2.0 (* x y)) (if (<= x 2.8e-64) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -65.0) {
		tmp = 2.0 * (x * y);
	} else if (x <= 2.8e-64) {
		tmp = y * 5.0;
	} 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) :: tmp
    if (x <= (-65.0d0)) then
        tmp = 2.0d0 * (x * y)
    else if (x <= 2.8d-64) then
        tmp = y * 5.0d0
    else
        tmp = 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 <= -65.0) {
		tmp = 2.0 * (x * y);
	} else if (x <= 2.8e-64) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -65.0:
		tmp = 2.0 * (x * y)
	elif x <= 2.8e-64:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -65.0)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (x <= 2.8e-64)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -65.0)
		tmp = 2.0 * (x * y);
	elseif (x <= 2.8e-64)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -65.0], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e-64], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -65

   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 t around 0 76.1%

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

   4. Simplified 76.1%

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

   5. Taylor expanded in x around inf 73.9%

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

   6. Taylor expanded in y around inf 34.9%

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

   if -65 < x < 2.80000000000000004e-64

   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 59.1%

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

   if 2.80000000000000004e-64 < 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 t around inf 47.9%

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

   4. Simplified 47.9%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -65:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-64}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 11: 30.3% 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. Taylor expanded in x around 0 31.3%

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

3. Final simplification 31.3%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023314 
(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)))