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

Percentage Accurate: 99.9% → 99.9%

Time: 11.0s

Alternatives: 12

Speedup: 1.0×

• 26.5% 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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-define 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

5. 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: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot z\right)\\ t_2 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-97}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+26} \lor \neg \left(x \leq 1.7 \cdot 10^{+109}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 z)))) (t_2 (* x (+ t (* 2.0 y)))))
   (if (<= x -3.9e+117)
     t_2
     (if (<= x -1.4e+17)
       t_1
       (if (<= x -5.1e-14)
         t_2
         (if (<= x 3e-97)
           (* y 5.0)
           (if (or (<= x 6e+26) (not (<= x 1.7e+109))) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -3.9e+117) {
		tmp = t_2;
	} else if (x <= -1.4e+17) {
		tmp = t_1;
	} else if (x <= -5.1e-14) {
		tmp = t_2;
	} else if (x <= 3e-97) {
		tmp = y * 5.0;
	} else if ((x <= 6e+26) || !(x <= 1.7e+109)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * z))
    t_2 = x * (t + (2.0d0 * y))
    if (x <= (-3.9d+117)) then
        tmp = t_2
    else if (x <= (-1.4d+17)) then
        tmp = t_1
    else if (x <= (-5.1d-14)) then
        tmp = t_2
    else if (x <= 3d-97) then
        tmp = y * 5.0d0
    else if ((x <= 6d+26) .or. (.not. (x <= 1.7d+109))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -3.9e+117) {
		tmp = t_2;
	} else if (x <= -1.4e+17) {
		tmp = t_1;
	} else if (x <= -5.1e-14) {
		tmp = t_2;
	} else if (x <= 3e-97) {
		tmp = y * 5.0;
	} else if ((x <= 6e+26) || !(x <= 1.7e+109)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * z))
	t_2 = x * (t + (2.0 * y))
	tmp = 0
	if x <= -3.9e+117:
		tmp = t_2
	elif x <= -1.4e+17:
		tmp = t_1
	elif x <= -5.1e-14:
		tmp = t_2
	elif x <= 3e-97:
		tmp = y * 5.0
	elif (x <= 6e+26) or not (x <= 1.7e+109):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * z)))
	t_2 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (x <= -3.9e+117)
		tmp = t_2;
	elseif (x <= -1.4e+17)
		tmp = t_1;
	elseif (x <= -5.1e-14)
		tmp = t_2;
	elseif (x <= 3e-97)
		tmp = Float64(y * 5.0);
	elseif ((x <= 6e+26) || !(x <= 1.7e+109))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * z));
	t_2 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (x <= -3.9e+117)
		tmp = t_2;
	elseif (x <= -1.4e+17)
		tmp = t_1;
	elseif (x <= -5.1e-14)
		tmp = t_2;
	elseif (x <= 3e-97)
		tmp = y * 5.0;
	elseif ((x <= 6e+26) || ~((x <= 1.7e+109)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e+117], t$95$2, If[LessEqual[x, -1.4e+17], t$95$1, If[LessEqual[x, -5.1e-14], t$95$2, If[LessEqual[x, 3e-97], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 6e+26], N[Not[LessEqual[x, 1.7e+109]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.8999999999999999e117 or -1.4e17 < x < -5.0999999999999997e-14 or 5.99999999999999994e26 < x < 1.70000000000000003e109

   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 74.3%

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

   4. Taylor expanded in x around inf 71.7%

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

   if -3.8999999999999999e117 < x < -1.4e17 or 3.00000000000000024e-97 < x < 5.99999999999999994e26 or 1.70000000000000003e109 < 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 77.6%

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

   if -5.0999999999999997e-14 < x < 3.00000000000000024e-97

   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 73.7%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-97}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+26} \lor \neg \left(x \leq 1.7 \cdot 10^{+109}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+268}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+57}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-97}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+48}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -2.15e+268)
     (* x t)
     (if (<= x -4.7e+141)
       t_1
       (if (<= x -2.25e+57)
         (* x t)
         (if (<= x -6.5e-9)
           t_1
           (if (<= x 4.1e-97) (* y 5.0) (if (<= x 5e+48) (* 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 <= -2.15e+268) {
		tmp = x * t;
	} else if (x <= -4.7e+141) {
		tmp = t_1;
	} else if (x <= -2.25e+57) {
		tmp = x * t;
	} else if (x <= -6.5e-9) {
		tmp = t_1;
	} else if (x <= 4.1e-97) {
		tmp = y * 5.0;
	} else if (x <= 5e+48) {
		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 <= (-2.15d+268)) then
        tmp = x * t
    else if (x <= (-4.7d+141)) then
        tmp = t_1
    else if (x <= (-2.25d+57)) then
        tmp = x * t
    else if (x <= (-6.5d-9)) then
        tmp = t_1
    else if (x <= 4.1d-97) then
        tmp = y * 5.0d0
    else if (x <= 5d+48) 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 <= -2.15e+268) {
		tmp = x * t;
	} else if (x <= -4.7e+141) {
		tmp = t_1;
	} else if (x <= -2.25e+57) {
		tmp = x * t;
	} else if (x <= -6.5e-9) {
		tmp = t_1;
	} else if (x <= 4.1e-97) {
		tmp = y * 5.0;
	} else if (x <= 5e+48) {
		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 <= -2.15e+268:
		tmp = x * t
	elif x <= -4.7e+141:
		tmp = t_1
	elif x <= -2.25e+57:
		tmp = x * t
	elif x <= -6.5e-9:
		tmp = t_1
	elif x <= 4.1e-97:
		tmp = y * 5.0
	elif x <= 5e+48:
		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 <= -2.15e+268)
		tmp = Float64(x * t);
	elseif (x <= -4.7e+141)
		tmp = t_1;
	elseif (x <= -2.25e+57)
		tmp = Float64(x * t);
	elseif (x <= -6.5e-9)
		tmp = t_1;
	elseif (x <= 4.1e-97)
		tmp = Float64(y * 5.0);
	elseif (x <= 5e+48)
		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 <= -2.15e+268)
		tmp = x * t;
	elseif (x <= -4.7e+141)
		tmp = t_1;
	elseif (x <= -2.25e+57)
		tmp = x * t;
	elseif (x <= -6.5e-9)
		tmp = t_1;
	elseif (x <= 4.1e-97)
		tmp = y * 5.0;
	elseif (x <= 5e+48)
		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, -2.15e+268], N[(x * t), $MachinePrecision], If[LessEqual[x, -4.7e+141], t$95$1, If[LessEqual[x, -2.25e+57], N[(x * t), $MachinePrecision], If[LessEqual[x, -6.5e-9], t$95$1, If[LessEqual[x, 4.1e-97], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 5e+48], N[(x * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.14999999999999985e268 or -4.69999999999999979e141 < x < -2.24999999999999998e57 or 4.09999999999999993e-97 < x < 4.99999999999999973e48

   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 54.0%

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

   5. Simplified 54.0%

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

   if -2.14999999999999985e268 < x < -4.69999999999999979e141 or -2.24999999999999998e57 < x < -6.5000000000000003e-9 or 4.99999999999999973e48 < 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 47.4%

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

   if -6.5000000000000003e-9 < x < 4.09999999999999993e-97

   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 73.0%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+268}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{+141}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+57}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-97}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+48}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := y \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+55}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-97}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+48}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))) (t_2 (* y (* x 2.0))))
   (if (<= x -2.5e+117)
     t_2
     (if (<= x -2.05e+55)
       (* x t)
       (if (<= x -4e+34)
         t_2
         (if (<= x -3.2e-8)
           t_1
           (if (<= x 1.15e-97) (* y 5.0) (if (<= x 5e+48) (* x t) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double t_2 = y * (x * 2.0);
	double tmp;
	if (x <= -2.5e+117) {
		tmp = t_2;
	} else if (x <= -2.05e+55) {
		tmp = x * t;
	} else if (x <= -4e+34) {
		tmp = t_2;
	} else if (x <= -3.2e-8) {
		tmp = t_1;
	} else if (x <= 1.15e-97) {
		tmp = y * 5.0;
	} else if (x <= 5e+48) {
		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) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    t_2 = y * (x * 2.0d0)
    if (x <= (-2.5d+117)) then
        tmp = t_2
    else if (x <= (-2.05d+55)) then
        tmp = x * t
    else if (x <= (-4d+34)) then
        tmp = t_2
    else if (x <= (-3.2d-8)) then
        tmp = t_1
    else if (x <= 1.15d-97) then
        tmp = y * 5.0d0
    else if (x <= 5d+48) 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 t_2 = y * (x * 2.0);
	double tmp;
	if (x <= -2.5e+117) {
		tmp = t_2;
	} else if (x <= -2.05e+55) {
		tmp = x * t;
	} else if (x <= -4e+34) {
		tmp = t_2;
	} else if (x <= -3.2e-8) {
		tmp = t_1;
	} else if (x <= 1.15e-97) {
		tmp = y * 5.0;
	} else if (x <= 5e+48) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	t_2 = y * (x * 2.0)
	tmp = 0
	if x <= -2.5e+117:
		tmp = t_2
	elif x <= -2.05e+55:
		tmp = x * t
	elif x <= -4e+34:
		tmp = t_2
	elif x <= -3.2e-8:
		tmp = t_1
	elif x <= 1.15e-97:
		tmp = y * 5.0
	elif x <= 5e+48:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	t_2 = Float64(y * Float64(x * 2.0))
	tmp = 0.0
	if (x <= -2.5e+117)
		tmp = t_2;
	elseif (x <= -2.05e+55)
		tmp = Float64(x * t);
	elseif (x <= -4e+34)
		tmp = t_2;
	elseif (x <= -3.2e-8)
		tmp = t_1;
	elseif (x <= 1.15e-97)
		tmp = Float64(y * 5.0);
	elseif (x <= 5e+48)
		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);
	t_2 = y * (x * 2.0);
	tmp = 0.0;
	if (x <= -2.5e+117)
		tmp = t_2;
	elseif (x <= -2.05e+55)
		tmp = x * t;
	elseif (x <= -4e+34)
		tmp = t_2;
	elseif (x <= -3.2e-8)
		tmp = t_1;
	elseif (x <= 1.15e-97)
		tmp = y * 5.0;
	elseif (x <= 5e+48)
		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]}, Block[{t$95$2 = N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+117], t$95$2, If[LessEqual[x, -2.05e+55], N[(x * t), $MachinePrecision], If[LessEqual[x, -4e+34], t$95$2, If[LessEqual[x, -3.2e-8], t$95$1, If[LessEqual[x, 1.15e-97], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 5e+48], N[(x * t), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.49999999999999992e117 or -2.04999999999999991e55 < x < -3.99999999999999978e34

   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 74.4%

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

   4. Taylor expanded in x around inf 74.4%

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

   5. Taylor expanded in t around 0 53.3%

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

      1. associate-*r* 53.3%

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

      2. *-commutative 53.3%

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

   7. Simplified 53.3%

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

   if -2.49999999999999992e117 < x < -2.04999999999999991e55 or 1.14999999999999997e-97 < x < 4.99999999999999973e48

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 53.0%

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

   5. Simplified 53.0%

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

   if -3.99999999999999978e34 < x < -3.2000000000000002e-8 or 4.99999999999999973e48 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 46.9%

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

   if -3.2000000000000002e-8 < x < 1.14999999999999997e-97

   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 73.0%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+55}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-97}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+48}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.92 \lor \neg \left(x \leq 3.3 \cdot 10^{-97}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.92) (not (<= x 3.3e-97)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* x (+ t (+ y y))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.92) || !(x <= 3.3e-97)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.92d0)) .or. (.not. (x <= 3.3d-97))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (x * (t + (y + y))) + (y * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.92) || !(x <= 3.3e-97)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.92) or not (x <= 3.3e-97):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (x * (t + (y + y))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.92) || !(x <= 3.3e-97))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(y + y))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.92) || ~((x <= 3.3e-97)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (x * (t + (y + y))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.92], N[Not[LessEqual[x, 3.3e-97]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9199999999999999 or 3.3000000000000001e-97 < x

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.8%

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

   if -1.9199999999999999 < x < 3.3000000000000001e-97

   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 90.1%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.92 \lor \neg \left(x \leq 3.3 \cdot 10^{-97}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+44} \lor \neg \left(z \leq 1.12 \cdot 10^{-27}\right):\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.2e+44) (not (<= z 1.12e-27)))
   (+ (* (+ y z) (* x 2.0)) (* y 5.0))
   (+ (* x (+ t (+ y y))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.2e+44) || !(z <= 1.12e-27)) {
		tmp = ((y + z) * (x * 2.0)) + (y * 5.0);
	} else {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.2d+44)) .or. (.not. (z <= 1.12d-27))) then
        tmp = ((y + z) * (x * 2.0d0)) + (y * 5.0d0)
    else
        tmp = (x * (t + (y + y))) + (y * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.2e+44) || !(z <= 1.12e-27)) {
		tmp = ((y + z) * (x * 2.0)) + (y * 5.0);
	} else {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.2e+44) or not (z <= 1.12e-27):
		tmp = ((y + z) * (x * 2.0)) + (y * 5.0)
	else:
		tmp = (x * (t + (y + y))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.2e+44) || !(z <= 1.12e-27))
		tmp = Float64(Float64(Float64(y + z) * Float64(x * 2.0)) + Float64(y * 5.0));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(y + y))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.2e+44) || ~((z <= 1.12e-27)))
		tmp = ((y + z) * (x * 2.0)) + (y * 5.0);
	else
		tmp = (x * (t + (y + y))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.2e+44], N[Not[LessEqual[z, 1.12e-27]], $MachinePrecision]], N[(N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000007e44 or 1.1199999999999999e-27 < z

   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 91.6%

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

   5. Simplified 91.6%

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

   if -1.20000000000000007e44 < z < 1.1199999999999999e-27

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 97.7%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+44} \lor \neg \left(z \leq 1.12 \cdot 10^{-27}\right):\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-7} \lor \neg \left(x \leq 4.1 \cdot 10^{-97}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.5e-7) (not (<= x 4.1e-97)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.5e-7) || !(x <= 4.1e-97)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.5d-7)) .or. (.not. (x <= 4.1d-97))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.5e-7) || !(x <= 4.1e-97)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.5e-7) or not (x <= 4.1e-97):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.5e-7) || !(x <= 4.1e-97))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.5e-7) || ~((x <= 4.1e-97)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.5e-7], N[Not[LessEqual[x, 4.1e-97]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4999999999999998e-7 or 4.09999999999999993e-97 < x

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.2%

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

   if -4.4999999999999998e-7 < x < 4.09999999999999993e-97

   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 y around 0 99.8%

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

   6. Taylor expanded in z around 0 90.8%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-7} \lor \neg \left(x \leq 4.1 \cdot 10^{-97}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.1 \cdot 10^{-13} \lor \neg \left(x \leq 4.1 \cdot 10^{-97}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.1e-13) (not (<= x 4.1e-97)))
   (* x (+ t (* 2.0 y)))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.1e-13) || !(x <= 4.1e-97)) {
		tmp = x * (t + (2.0 * y));
	} 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 <= (-7.1d-13)) .or. (.not. (x <= 4.1d-97))) then
        tmp = x * (t + (2.0d0 * y))
    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 <= -7.1e-13) || !(x <= 4.1e-97)) {
		tmp = x * (t + (2.0 * y));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.1e-13) or not (x <= 4.1e-97):
		tmp = x * (t + (2.0 * y))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.1e-13) || !(x <= 4.1e-97))
		tmp = Float64(x * Float64(t + Float64(2.0 * y)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.1e-13) || ~((x <= 4.1e-97)))
		tmp = x * (t + (2.0 * y));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.1e-13], N[Not[LessEqual[x, 4.1e-97]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.1e-13 or 4.09999999999999993e-97 < 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 inf 68.4%

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

   4. Taylor expanded in x around inf 65.7%

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

   if -7.1e-13 < x < 4.09999999999999993e-97

   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 73.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.1 \cdot 10^{-13} \lor \neg \left(x \leq 4.1 \cdot 10^{-97}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-6} \lor \neg \left(y \leq 7.8 \cdot 10^{+50}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.8e-6) (not (<= y 7.8e+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 <= -8.8e-6) || !(y <= 7.8e+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 <= (-8.8d-6)) .or. (.not. (y <= 7.8d+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 <= -8.8e-6) || !(y <= 7.8e+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 <= -8.8e-6) or not (y <= 7.8e+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 <= -8.8e-6) || !(y <= 7.8e+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 <= -8.8e-6) || ~((y <= 7.8e+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, -8.8e-6], N[Not[LessEqual[y, 7.8e+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 < -8.8000000000000004e-6 or 7.79999999999999935e50 < 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 84.6%

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

   5. Simplified 84.6%

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

   if -8.8000000000000004e-6 < y < 7.79999999999999935e50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 80.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-6} \lor \neg \left(y \leq 7.8 \cdot 10^{+50}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 11: 47.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-13} \lor \neg \left(x \leq 2.9 \cdot 10^{-99}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7e-13) (not (<= x 2.9e-99))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7e-13) || !(x <= 2.9e-99)) {
		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 <= (-7d-13)) .or. (.not. (x <= 2.9d-99))) 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 <= -7e-13) || !(x <= 2.9e-99)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7e-13) or not (x <= 2.9e-99):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7e-13) || !(x <= 2.9e-99))
		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 <= -7e-13) || ~((x <= 2.9e-99)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7e-13], N[Not[LessEqual[x, 2.9e-99]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.0000000000000005e-13 or 2.89999999999999985e-99 < 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 34.9%

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

   5. Simplified 34.9%

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

   if -7.0000000000000005e-13 < x < 2.89999999999999985e-99

   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 73.7%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-13} \lor \neg \left(x \leq 2.9 \cdot 10^{-99}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.1% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 33.0%

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

4. Final simplification 33.0%

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

Reproduce

herbie shell --seed 2024045 
(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)))