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

Percentage Accurate: 99.9% → 99.9%

Time: 10.6s

Alternatives: 15

Speedup: 1.0×

• 25.9% 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: 42.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-228}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq -3.95 \cdot 10^{-289}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-295}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-58}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+103}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* x 2.0))))
   (if (<= z -1.6e+141)
     t_1
     (if (<= z -2.3e-228)
       (* x t)
       (if (<= z -3.95e-289)
         (* y 5.0)
         (if (<= z 3.6e-295)
           (* x t)
           (if (<= z 3.6e-120)
             (* y (* x 2.0))
             (if (<= z 2.6e-58)
               (* x t)
               (if (<= z 2.3e-17)
                 (* y 5.0)
                 (if (<= z 2.8e+103) (* x t) t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x * 2.0);
	double tmp;
	if (z <= -1.6e+141) {
		tmp = t_1;
	} else if (z <= -2.3e-228) {
		tmp = x * t;
	} else if (z <= -3.95e-289) {
		tmp = y * 5.0;
	} else if (z <= 3.6e-295) {
		tmp = x * t;
	} else if (z <= 3.6e-120) {
		tmp = y * (x * 2.0);
	} else if (z <= 2.6e-58) {
		tmp = x * t;
	} else if (z <= 2.3e-17) {
		tmp = y * 5.0;
	} else if (z <= 2.8e+103) {
		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 = z * (x * 2.0d0)
    if (z <= (-1.6d+141)) then
        tmp = t_1
    else if (z <= (-2.3d-228)) then
        tmp = x * t
    else if (z <= (-3.95d-289)) then
        tmp = y * 5.0d0
    else if (z <= 3.6d-295) then
        tmp = x * t
    else if (z <= 3.6d-120) then
        tmp = y * (x * 2.0d0)
    else if (z <= 2.6d-58) then
        tmp = x * t
    else if (z <= 2.3d-17) then
        tmp = y * 5.0d0
    else if (z <= 2.8d+103) 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 = z * (x * 2.0);
	double tmp;
	if (z <= -1.6e+141) {
		tmp = t_1;
	} else if (z <= -2.3e-228) {
		tmp = x * t;
	} else if (z <= -3.95e-289) {
		tmp = y * 5.0;
	} else if (z <= 3.6e-295) {
		tmp = x * t;
	} else if (z <= 3.6e-120) {
		tmp = y * (x * 2.0);
	} else if (z <= 2.6e-58) {
		tmp = x * t;
	} else if (z <= 2.3e-17) {
		tmp = y * 5.0;
	} else if (z <= 2.8e+103) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x * 2.0)
	tmp = 0
	if z <= -1.6e+141:
		tmp = t_1
	elif z <= -2.3e-228:
		tmp = x * t
	elif z <= -3.95e-289:
		tmp = y * 5.0
	elif z <= 3.6e-295:
		tmp = x * t
	elif z <= 3.6e-120:
		tmp = y * (x * 2.0)
	elif z <= 2.6e-58:
		tmp = x * t
	elif z <= 2.3e-17:
		tmp = y * 5.0
	elif z <= 2.8e+103:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x * 2.0))
	tmp = 0.0
	if (z <= -1.6e+141)
		tmp = t_1;
	elseif (z <= -2.3e-228)
		tmp = Float64(x * t);
	elseif (z <= -3.95e-289)
		tmp = Float64(y * 5.0);
	elseif (z <= 3.6e-295)
		tmp = Float64(x * t);
	elseif (z <= 3.6e-120)
		tmp = Float64(y * Float64(x * 2.0));
	elseif (z <= 2.6e-58)
		tmp = Float64(x * t);
	elseif (z <= 2.3e-17)
		tmp = Float64(y * 5.0);
	elseif (z <= 2.8e+103)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x * 2.0);
	tmp = 0.0;
	if (z <= -1.6e+141)
		tmp = t_1;
	elseif (z <= -2.3e-228)
		tmp = x * t;
	elseif (z <= -3.95e-289)
		tmp = y * 5.0;
	elseif (z <= 3.6e-295)
		tmp = x * t;
	elseif (z <= 3.6e-120)
		tmp = y * (x * 2.0);
	elseif (z <= 2.6e-58)
		tmp = x * t;
	elseif (z <= 2.3e-17)
		tmp = y * 5.0;
	elseif (z <= 2.8e+103)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+141], t$95$1, If[LessEqual[z, -2.3e-228], N[(x * t), $MachinePrecision], If[LessEqual[z, -3.95e-289], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, 3.6e-295], N[(x * t), $MachinePrecision], If[LessEqual[z, 3.6e-120], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-58], N[(x * t), $MachinePrecision], If[LessEqual[z, 2.3e-17], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, 2.8e+103], N[(x * t), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.60000000000000009e141 or 2.80000000000000008e103 < z

   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 76.4%

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

   5. Simplified 76.4%

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

   if -1.60000000000000009e141 < z < -2.2999999999999999e-228 or -3.9499999999999999e-289 < z < 3.6000000000000001e-295 or 3.6000000000000003e-120 < z < 2.60000000000000007e-58 or 2.30000000000000009e-17 < z < 2.80000000000000008e103

   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 54.6%

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

   5. Simplified 54.6%

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

   if -2.2999999999999999e-228 < z < -3.9499999999999999e-289 or 2.60000000000000007e-58 < z < 2.30000000000000009e-17

   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 x around 0 71.1%

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

   if 3.6000000000000001e-295 < z < 3.6000000000000003e-120

   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 0 99.9%

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

   4. Taylor expanded in x around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. *-commutative 70.9%

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

      3. associate-*r* 70.9%

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

   6. Simplified 70.9%

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

   7. Taylor expanded in y around inf 49.2%

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

      1. associate-*r* 49.2%

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

      2. *-commutative 49.2%

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

      3. *-commutative 49.2%

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

   9. Simplified 49.2%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-228}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq -3.95 \cdot 10^{-289}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-295}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-58}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+103}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+57}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1250000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-87}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-92}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+128} \lor \neg \left(x \leq 1.28 \cdot 10^{+181}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x 2.0))))
   (if (<= x -7.6e+202)
     t_1
     (if (<= x -2.3e+57)
       (* x t)
       (if (<= x -1250000000000.0)
         t_1
         (if (<= x -3.9e-87)
           (* x t)
           (if (<= x 3.8e-92)
             (* y 5.0)
             (if (or (<= x 6.4e+128) (not (<= x 1.28e+181)))
               (* x t)
               t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * 2.0);
	double tmp;
	if (x <= -7.6e+202) {
		tmp = t_1;
	} else if (x <= -2.3e+57) {
		tmp = x * t;
	} else if (x <= -1250000000000.0) {
		tmp = t_1;
	} else if (x <= -3.9e-87) {
		tmp = x * t;
	} else if (x <= 3.8e-92) {
		tmp = y * 5.0;
	} else if ((x <= 6.4e+128) || !(x <= 1.28e+181)) {
		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 = y * (x * 2.0d0)
    if (x <= (-7.6d+202)) then
        tmp = t_1
    else if (x <= (-2.3d+57)) then
        tmp = x * t
    else if (x <= (-1250000000000.0d0)) then
        tmp = t_1
    else if (x <= (-3.9d-87)) then
        tmp = x * t
    else if (x <= 3.8d-92) then
        tmp = y * 5.0d0
    else if ((x <= 6.4d+128) .or. (.not. (x <= 1.28d+181))) 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 = y * (x * 2.0);
	double tmp;
	if (x <= -7.6e+202) {
		tmp = t_1;
	} else if (x <= -2.3e+57) {
		tmp = x * t;
	} else if (x <= -1250000000000.0) {
		tmp = t_1;
	} else if (x <= -3.9e-87) {
		tmp = x * t;
	} else if (x <= 3.8e-92) {
		tmp = y * 5.0;
	} else if ((x <= 6.4e+128) || !(x <= 1.28e+181)) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * 2.0)
	tmp = 0
	if x <= -7.6e+202:
		tmp = t_1
	elif x <= -2.3e+57:
		tmp = x * t
	elif x <= -1250000000000.0:
		tmp = t_1
	elif x <= -3.9e-87:
		tmp = x * t
	elif x <= 3.8e-92:
		tmp = y * 5.0
	elif (x <= 6.4e+128) or not (x <= 1.28e+181):
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * 2.0))
	tmp = 0.0
	if (x <= -7.6e+202)
		tmp = t_1;
	elseif (x <= -2.3e+57)
		tmp = Float64(x * t);
	elseif (x <= -1250000000000.0)
		tmp = t_1;
	elseif (x <= -3.9e-87)
		tmp = Float64(x * t);
	elseif (x <= 3.8e-92)
		tmp = Float64(y * 5.0);
	elseif ((x <= 6.4e+128) || !(x <= 1.28e+181))
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * 2.0);
	tmp = 0.0;
	if (x <= -7.6e+202)
		tmp = t_1;
	elseif (x <= -2.3e+57)
		tmp = x * t;
	elseif (x <= -1250000000000.0)
		tmp = t_1;
	elseif (x <= -3.9e-87)
		tmp = x * t;
	elseif (x <= 3.8e-92)
		tmp = y * 5.0;
	elseif ((x <= 6.4e+128) || ~((x <= 1.28e+181)))
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.6e+202], t$95$1, If[LessEqual[x, -2.3e+57], N[(x * t), $MachinePrecision], If[LessEqual[x, -1250000000000.0], t$95$1, If[LessEqual[x, -3.9e-87], N[(x * t), $MachinePrecision], If[LessEqual[x, 3.8e-92], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 6.4e+128], N[Not[LessEqual[x, 1.28e+181]], $MachinePrecision]], N[(x * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.6000000000000001e202 or -2.2999999999999999e57 < x < -1.25e12 or 6.39999999999999971e128 < x < 1.27999999999999997e181

   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 88.6%

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

   4. Taylor expanded in x around inf 88.0%

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

      1. *-commutative 88.0%

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

      2. *-commutative 88.0%

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

      3. associate-*r* 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in y around inf 58.1%

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

      1. associate-*r* 58.1%

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

      2. *-commutative 58.1%

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

      3. *-commutative 58.1%

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

   9. Simplified 58.1%

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

   if -7.6000000000000001e202 < x < -2.2999999999999999e57 or -1.25e12 < x < -3.8999999999999998e-87 or 3.8000000000000001e-92 < x < 6.39999999999999971e128 or 1.27999999999999997e181 < 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 51.0%

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

   5. Simplified 51.0%

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

   if -3.8999999999999998e-87 < x < 3.8000000000000001e-92

   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 63.8%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+202}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+57}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1250000000000:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-87}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-92}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+128} \lor \neg \left(x \leq 1.28 \cdot 10^{+181}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot z\right)\\ t_2 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;x \leq -2900000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-141}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+147} \lor \neg \left(x \leq 6 \cdot 10^{+255}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -2900000000000.0)
     t_2
     (if (<= x -1.3e-87)
       t_1
       (if (<= x 1.22e-141)
         (* y 5.0)
         (if (or (<= x 2.2e+147) (not (<= x 6e+255))) 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 <= -2900000000000.0) {
		tmp = t_2;
	} else if (x <= -1.3e-87) {
		tmp = t_1;
	} else if (x <= 1.22e-141) {
		tmp = y * 5.0;
	} else if ((x <= 2.2e+147) || !(x <= 6e+255)) {
		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 <= (-2900000000000.0d0)) then
        tmp = t_2
    else if (x <= (-1.3d-87)) then
        tmp = t_1
    else if (x <= 1.22d-141) then
        tmp = y * 5.0d0
    else if ((x <= 2.2d+147) .or. (.not. (x <= 6d+255))) 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 <= -2900000000000.0) {
		tmp = t_2;
	} else if (x <= -1.3e-87) {
		tmp = t_1;
	} else if (x <= 1.22e-141) {
		tmp = y * 5.0;
	} else if ((x <= 2.2e+147) || !(x <= 6e+255)) {
		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 <= -2900000000000.0:
		tmp = t_2
	elif x <= -1.3e-87:
		tmp = t_1
	elif x <= 1.22e-141:
		tmp = y * 5.0
	elif (x <= 2.2e+147) or not (x <= 6e+255):
		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 <= -2900000000000.0)
		tmp = t_2;
	elseif (x <= -1.3e-87)
		tmp = t_1;
	elseif (x <= 1.22e-141)
		tmp = Float64(y * 5.0);
	elseif ((x <= 2.2e+147) || !(x <= 6e+255))
		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 <= -2900000000000.0)
		tmp = t_2;
	elseif (x <= -1.3e-87)
		tmp = t_1;
	elseif (x <= 1.22e-141)
		tmp = y * 5.0;
	elseif ((x <= 2.2e+147) || ~((x <= 6e+255)))
		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, -2900000000000.0], t$95$2, If[LessEqual[x, -1.3e-87], t$95$1, If[LessEqual[x, 1.22e-141], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 2.2e+147], N[Not[LessEqual[x, 6e+255]], $MachinePrecision]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9e12 or 2.2000000000000002e147 < x < 6.00000000000000035e255

   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 99.7%

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

   6. Taylor expanded in z around 0 80.5%

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

   if -2.9e12 < x < -1.30000000000000001e-87 or 1.22e-141 < x < 2.2000000000000002e147 or 6.00000000000000035e255 < 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 78.8%

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

   if -1.30000000000000001e-87 < x < 1.22e-141

   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 67.5%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2900000000000:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-141}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+147} \lor \neg \left(x \leq 6 \cdot 10^{+255}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;y \leq -400000000000 \lor \neg \left(y \leq 1.95 \cdot 10^{-19}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.7e+89)
     t_1
     (if (<= y -4.6e+33)
       (* x (+ t (* 2.0 y)))
       (if (or (<= y -400000000000.0) (not (<= y 1.95e-19)))
         t_1
         (* x (+ t (* 2.0 z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.7e+89) {
		tmp = t_1;
	} else if (y <= -4.6e+33) {
		tmp = x * (t + (2.0 * y));
	} else if ((y <= -400000000000.0) || !(y <= 1.95e-19)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.7d+89)) then
        tmp = t_1
    else if (y <= (-4.6d+33)) then
        tmp = x * (t + (2.0d0 * y))
    else if ((y <= (-400000000000.0d0)) .or. (.not. (y <= 1.95d-19))) then
        tmp = t_1
    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 t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.7e+89) {
		tmp = t_1;
	} else if (y <= -4.6e+33) {
		tmp = x * (t + (2.0 * y));
	} else if ((y <= -400000000000.0) || !(y <= 1.95e-19)) {
		tmp = t_1;
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.7e+89:
		tmp = t_1
	elif y <= -4.6e+33:
		tmp = x * (t + (2.0 * y))
	elif (y <= -400000000000.0) or not (y <= 1.95e-19):
		tmp = t_1
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -1.7e+89)
		tmp = t_1;
	elseif (y <= -4.6e+33)
		tmp = Float64(x * Float64(t + Float64(2.0 * y)));
	elseif ((y <= -400000000000.0) || !(y <= 1.95e-19))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -1.7e+89)
		tmp = t_1;
	elseif (y <= -4.6e+33)
		tmp = x * (t + (2.0 * y));
	elseif ((y <= -400000000000.0) || ~((y <= 1.95e-19)))
		tmp = t_1;
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+89], t$95$1, If[LessEqual[y, -4.6e+33], N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -400000000000.0], N[Not[LessEqual[y, 1.95e-19]], $MachinePrecision]], t$95$1, N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7000000000000001e89 or -4.60000000000000021e33 < y < -4e11 or 1.94999999999999998e-19 < 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 78.2%

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

   5. Simplified 78.2%

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

   if -1.7000000000000001e89 < y < -4.60000000000000021e33

   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 78.2%

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

   6. Taylor expanded in z around 0 78.2%

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

   if -4e11 < y < 1.94999999999999998e-19

   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 83.6%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;y \leq -400000000000 \lor \neg \left(y \leq 1.95 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ t_2 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;z \leq -2.95 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-229}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-286}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 4.65 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* x 2.0))) (t_2 (* x (+ t (* 2.0 y)))))
   (if (<= z -2.95e+141)
     t_1
     (if (<= z -9.5e-229)
       t_2
       (if (<= z -7.8e-286) (* y 5.0) (if (<= z 4.65e+114) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x * 2.0);
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (z <= -2.95e+141) {
		tmp = t_1;
	} else if (z <= -9.5e-229) {
		tmp = t_2;
	} else if (z <= -7.8e-286) {
		tmp = y * 5.0;
	} else if (z <= 4.65e+114) {
		tmp = t_2;
	} 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 = z * (x * 2.0d0)
    t_2 = x * (t + (2.0d0 * y))
    if (z <= (-2.95d+141)) then
        tmp = t_1
    else if (z <= (-9.5d-229)) then
        tmp = t_2
    else if (z <= (-7.8d-286)) then
        tmp = y * 5.0d0
    else if (z <= 4.65d+114) then
        tmp = t_2
    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 = z * (x * 2.0);
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (z <= -2.95e+141) {
		tmp = t_1;
	} else if (z <= -9.5e-229) {
		tmp = t_2;
	} else if (z <= -7.8e-286) {
		tmp = y * 5.0;
	} else if (z <= 4.65e+114) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x * 2.0)
	t_2 = x * (t + (2.0 * y))
	tmp = 0
	if z <= -2.95e+141:
		tmp = t_1
	elif z <= -9.5e-229:
		tmp = t_2
	elif z <= -7.8e-286:
		tmp = y * 5.0
	elif z <= 4.65e+114:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x * 2.0))
	t_2 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (z <= -2.95e+141)
		tmp = t_1;
	elseif (z <= -9.5e-229)
		tmp = t_2;
	elseif (z <= -7.8e-286)
		tmp = Float64(y * 5.0);
	elseif (z <= 4.65e+114)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x * 2.0);
	t_2 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (z <= -2.95e+141)
		tmp = t_1;
	elseif (z <= -9.5e-229)
		tmp = t_2;
	elseif (z <= -7.8e-286)
		tmp = y * 5.0;
	elseif (z <= 4.65e+114)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.95e+141], t$95$1, If[LessEqual[z, -9.5e-229], t$95$2, If[LessEqual[z, -7.8e-286], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, 4.65e+114], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.95000000000000014e141 or 4.6500000000000001e114 < z

   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 77.4%

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

   5. Simplified 77.4%

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

   if -2.95000000000000014e141 < z < -9.4999999999999997e-229 or -7.7999999999999999e-286 < z < 4.6500000000000001e114

   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 72.7%

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

   6. Taylor expanded in z around 0 65.9%

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

   if -9.4999999999999997e-229 < z < -7.7999999999999999e-286

   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 x around 0 80.3%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-286}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 4.65 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-16} \lor \neg \left(x \leq 1.1 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.3e-16) (not (<= x 1.1e-10)))
   (* x (+ t (+ (* 2.0 (+ y z)) (* 5.0 (/ y x)))))
   (+ (* x (+ t (* 2.0 z))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e-16) || !(x <= 1.1e-10)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} 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 <= (-4.3d-16)) .or. (.not. (x <= 1.1d-10))) then
        tmp = x * (t + ((2.0d0 * (y + z)) + (5.0d0 * (y / x))))
    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 <= -4.3e-16) || !(x <= 1.1e-10)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (x * (t + (2.0 * z))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.3e-16) or not (x <= 1.1e-10):
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))))
	else:
		tmp = (x * (t + (2.0 * z))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.3e-16) || !(x <= 1.1e-10))
		tmp = Float64(x * Float64(t + Float64(Float64(2.0 * Float64(y + z)) + Float64(5.0 * Float64(y / x)))));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(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 <= -4.3e-16) || ~((x <= 1.1e-10)))
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	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, -4.3e-16], N[Not[LessEqual[x, 1.1e-10]], $MachinePrecision]], N[(x * N[(t + N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2999999999999999e-16 or 1.09999999999999995e-10 < x

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

   if -4.2999999999999999e-16 < x < 1.09999999999999995e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.6%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-16} \lor \neg \left(x \leq 1.1 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{if}\;x \leq -7.3 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ (* 2.0 (+ y z)) t))))
   (if (<= x -7.3e-34)
     t_1
     (if (<= x 7e-280)
       (+ (* y 5.0) (* x t))
       (if (<= x 7.5e-117) (+ (* y 5.0) (* 2.0 (* x z))) 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 <= -7.3e-34) {
		tmp = t_1;
	} else if (x <= 7e-280) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 7.5e-117) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((2.0d0 * (y + z)) + t)
    if (x <= (-7.3d-34)) then
        tmp = t_1
    else if (x <= 7d-280) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 7.5d-117) then
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((2.0 * (y + z)) + t);
	double tmp;
	if (x <= -7.3e-34) {
		tmp = t_1;
	} else if (x <= 7e-280) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 7.5e-117) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} 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 <= -7.3e-34:
		tmp = t_1
	elif x <= 7e-280:
		tmp = (y * 5.0) + (x * t)
	elif x <= 7.5e-117:
		tmp = (y * 5.0) + (2.0 * (x * z))
	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 <= -7.3e-34)
		tmp = t_1;
	elseif (x <= 7e-280)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 7.5e-117)
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	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 <= -7.3e-34)
		tmp = t_1;
	elseif (x <= 7e-280)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 7.5e-117)
		tmp = (y * 5.0) + (2.0 * (x * z));
	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, -7.3e-34], t$95$1, If[LessEqual[x, 7e-280], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-117], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.29999999999999996e-34 or 7.50000000000000066e-117 < 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 95.0%

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

   if -7.29999999999999996e-34 < x < 7.0000000000000002e-280

   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 99.9%

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

   4. Taylor expanded in z around 0 90.9%

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

   if 7.0000000000000002e-280 < x < 7.50000000000000066e-117

   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 99.9%

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

   4. Taylor expanded in t around 0 86.8%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.3 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-46}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -4e+147)
     t_1
     (if (<= y -1.4e-46)
       (+ (* y 5.0) (* x t))
       (if (<= y 1.6e-18) (* x (+ t (* 2.0 z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -4e+147) {
		tmp = t_1;
	} else if (y <= -1.4e-46) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1.6e-18) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-4d+147)) then
        tmp = t_1
    else if (y <= (-1.4d-46)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 1.6d-18) then
        tmp = x * (t + (2.0d0 * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -4e+147) {
		tmp = t_1;
	} else if (y <= -1.4e-46) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1.6e-18) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -4e+147:
		tmp = t_1
	elif y <= -1.4e-46:
		tmp = (y * 5.0) + (x * t)
	elif y <= 1.6e-18:
		tmp = x * (t + (2.0 * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -4e+147)
		tmp = t_1;
	elseif (y <= -1.4e-46)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 1.6e-18)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -4e+147)
		tmp = t_1;
	elseif (y <= -1.4e-46)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 1.6e-18)
		tmp = x * (t + (2.0 * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+147], t$95$1, If[LessEqual[y, -1.4e-46], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-18], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999999e147 or 1.6e-18 < 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 79.8%

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

   5. Simplified 79.8%

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

   if -3.9999999999999999e147 < y < -1.3999999999999999e-46

   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 84.4%

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

   4. Taylor expanded in z around 0 75.0%

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

   if -1.3999999999999999e-46 < y < 1.6e-18

   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 87.1%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+147}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-46}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -650000000000 \lor \neg \left(x \leq 2.5\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -650000000000.0) (not (<= x 2.5)))
   (* 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 <= -650000000000.0) || !(x <= 2.5)) {
		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 <= (-650000000000.0d0)) .or. (.not. (x <= 2.5d0))) 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 <= -650000000000.0) || !(x <= 2.5)) {
		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 <= -650000000000.0) or not (x <= 2.5):
		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 <= -650000000000.0) || !(x <= 2.5))
		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 <= -650000000000.0) || ~((x <= 2.5)))
		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, -650000000000.0], N[Not[LessEqual[x, 2.5]], $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 < -6.5e11 or 2.5 < 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 99.8%

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

   if -6.5e11 < x < 2.5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 98.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -650000000000 \lor \neg \left(x \leq 2.5\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-34} \lor \neg \left(x \leq 3.8 \cdot 10^{-92}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.9e-34) (not (<= x 3.8e-92)))
   (* 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 <= -3.9e-34) || !(x <= 3.8e-92)) {
		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 <= (-3.9d-34)) .or. (.not. (x <= 3.8d-92))) 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 <= -3.9e-34) || !(x <= 3.8e-92)) {
		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 <= -3.9e-34) or not (x <= 3.8e-92):
		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 <= -3.9e-34) || !(x <= 3.8e-92))
		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 <= -3.9e-34) || ~((x <= 3.8e-92)))
		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, -3.9e-34], N[Not[LessEqual[x, 3.8e-92]], $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 < -3.89999999999999991e-34 or 3.8000000000000001e-92 < 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 96.2%

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

   if -3.89999999999999991e-34 < x < 3.8000000000000001e-92

   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 99.9%

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

   4. Taylor expanded in z around 0 83.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-34} \lor \neg \left(x \leq 3.8 \cdot 10^{-92}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (2.0d0 * z))) + (y * (5.0d0 + (x * 2.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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 y around 0 96.8%

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

4. Final simplification 96.8%

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

Alternative 13: 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 14: 46.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-87} \lor \neg \left(x \leq 1.9 \cdot 10^{-93}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.6e-87) (not (<= x 1.9e-93))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.6e-87) || !(x <= 1.9e-93)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.6d-87)) .or. (.not. (x <= 1.9d-93))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.6e-87) || !(x <= 1.9e-93)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.6e-87) or not (x <= 1.9e-93):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.6e-87) || !(x <= 1.9e-93))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.6e-87) || ~((x <= 1.9e-93)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.6e-87], N[Not[LessEqual[x, 1.9e-93]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6000000000000003e-87 or 1.8999999999999999e-93 < 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 43.5%

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

   5. Simplified 43.5%

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

   if -4.6000000000000003e-87 < x < 1.8999999999999999e-93

   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 63.8%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-87} \lor \neg \left(x \leq 1.9 \cdot 10^{-93}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.7% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 27.7%

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

4. Final simplification 27.7%

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

Reproduce

herbie shell --seed 2024082 
(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)))