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

Percentage Accurate: 99.9% → 99.9%

Time: 11.2s

Alternatives: 16

Speedup: 1.0×

• 26.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% 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: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-26} \lor \neg \left(y \leq 5.6 \cdot 10^{-25}\right) \land \left(y \leq 4.5 \cdot 10^{+20} \lor \neg \left(y \leq 2.7 \cdot 10^{+90}\right)\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2e-26)
         (and (not (<= y 5.6e-25)) (or (<= y 4.5e+20) (not (<= y 2.7e+90)))))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-26) || (!(y <= 5.6e-25) && ((y <= 4.5e+20) || !(y <= 2.7e+90)))) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2d-26)) .or. (.not. (y <= 5.6d-25)) .and. (y <= 4.5d+20) .or. (.not. (y <= 2.7d+90))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (2.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-26) || (!(y <= 5.6e-25) && ((y <= 4.5e+20) || !(y <= 2.7e+90)))) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2e-26) or (not (y <= 5.6e-25) and ((y <= 4.5e+20) or not (y <= 2.7e+90))):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2e-26) || (!(y <= 5.6e-25) && ((y <= 4.5e+20) || !(y <= 2.7e+90))))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2e-26) || (~((y <= 5.6e-25)) && ((y <= 4.5e+20) || ~((y <= 2.7e+90)))))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2e-26], And[N[Not[LessEqual[y, 5.6e-25]], $MachinePrecision], Or[LessEqual[y, 4.5e+20], N[Not[LessEqual[y, 2.7e+90]], $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 < -2.0000000000000001e-26 or 5.59999999999999976e-25 < y < 4.5e20 or 2.7e90 < 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 84.1%

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

   5. Simplified 84.1%

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

   if -2.0000000000000001e-26 < y < 5.59999999999999976e-25 or 4.5e20 < y < 2.7e90

   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 86.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-26} \lor \neg \left(y \leq 5.6 \cdot 10^{-25}\right) \land \left(y \leq 4.5 \cdot 10^{+20} \lor \neg \left(y \leq 2.7 \cdot 10^{+90}\right)\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot z\right)\\ t_2 := x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -5500000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-67}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 z)))) (t_2 (* x (* 2.0 (+ y z)))))
   (if (<= x -5500000000.0)
     t_2
     (if (<= x -2.3e-133)
       t_1
       (if (<= x 2.2e-67) (* y 5.0) (if (<= x 1.7e+173) 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 * (2.0 * (y + z));
	double tmp;
	if (x <= -5500000000.0) {
		tmp = t_2;
	} else if (x <= -2.3e-133) {
		tmp = t_1;
	} else if (x <= 2.2e-67) {
		tmp = y * 5.0;
	} else if (x <= 1.7e+173) {
		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 * (2.0d0 * (y + z))
    if (x <= (-5500000000.0d0)) then
        tmp = t_2
    else if (x <= (-2.3d-133)) then
        tmp = t_1
    else if (x <= 2.2d-67) then
        tmp = y * 5.0d0
    else if (x <= 1.7d+173) 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 * (2.0 * (y + z));
	double tmp;
	if (x <= -5500000000.0) {
		tmp = t_2;
	} else if (x <= -2.3e-133) {
		tmp = t_1;
	} else if (x <= 2.2e-67) {
		tmp = y * 5.0;
	} else if (x <= 1.7e+173) {
		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 * (2.0 * (y + z))
	tmp = 0
	if x <= -5500000000.0:
		tmp = t_2
	elif x <= -2.3e-133:
		tmp = t_1
	elif x <= 2.2e-67:
		tmp = y * 5.0
	elif x <= 1.7e+173:
		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(2.0 * Float64(y + z)))
	tmp = 0.0
	if (x <= -5500000000.0)
		tmp = t_2;
	elseif (x <= -2.3e-133)
		tmp = t_1;
	elseif (x <= 2.2e-67)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.7e+173)
		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 * (2.0 * (y + z));
	tmp = 0.0;
	if (x <= -5500000000.0)
		tmp = t_2;
	elseif (x <= -2.3e-133)
		tmp = t_1;
	elseif (x <= 2.2e-67)
		tmp = y * 5.0;
	elseif (x <= 1.7e+173)
		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[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5500000000.0], t$95$2, If[LessEqual[x, -2.3e-133], t$95$1, If[LessEqual[x, 2.2e-67], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.7e+173], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5e9 or 1.70000000000000011e173 < 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 0 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in x around inf 82.6%

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

      1. associate-*r* 82.6%

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

      2. *-commutative 82.6%

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

      3. associate-*r* 82.6%

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

   8. Simplified 82.6%

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

   if -5.5e9 < x < -2.3e-133 or 2.2000000000000001e-67 < x < 1.70000000000000011e173

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.2%

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

   if -2.3e-133 < x < 2.2000000000000001e-67

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 67.5%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5500000000:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-133}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-67}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -2.3e-26)
     t_1
     (if (<= y 2.1e+15)
       (* x (+ (* 2.0 (+ y z)) t))
       (if (<= y 2.8e+77)
         (* t (+ x (* y (/ 5.0 t))))
         (if (<= y 2.8e+90) (* 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 <= -2.3e-26) {
		tmp = t_1;
	} else if (y <= 2.1e+15) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else if (y <= 2.8e+77) {
		tmp = t * (x + (y * (5.0 / t)));
	} else if (y <= 2.8e+90) {
		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 <= (-2.3d-26)) then
        tmp = t_1
    else if (y <= 2.1d+15) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else if (y <= 2.8d+77) then
        tmp = t * (x + (y * (5.0d0 / t)))
    else if (y <= 2.8d+90) 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 <= -2.3e-26) {
		tmp = t_1;
	} else if (y <= 2.1e+15) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else if (y <= 2.8e+77) {
		tmp = t * (x + (y * (5.0 / t)));
	} else if (y <= 2.8e+90) {
		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 <= -2.3e-26:
		tmp = t_1
	elif y <= 2.1e+15:
		tmp = x * ((2.0 * (y + z)) + t)
	elif y <= 2.8e+77:
		tmp = t * (x + (y * (5.0 / t)))
	elif y <= 2.8e+90:
		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 <= -2.3e-26)
		tmp = t_1;
	elseif (y <= 2.1e+15)
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	elseif (y <= 2.8e+77)
		tmp = Float64(t * Float64(x + Float64(y * Float64(5.0 / t))));
	elseif (y <= 2.8e+90)
		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 <= -2.3e-26)
		tmp = t_1;
	elseif (y <= 2.1e+15)
		tmp = x * ((2.0 * (y + z)) + t);
	elseif (y <= 2.8e+77)
		tmp = t * (x + (y * (5.0 / t)));
	elseif (y <= 2.8e+90)
		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, -2.3e-26], t$95$1, If[LessEqual[y, 2.1e+15], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+77], N[(t * N[(x + N[(y * N[(5.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+90], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.30000000000000009e-26 or 2.8e90 < 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 85.5%

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

   5. Simplified 85.5%

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

   if -2.30000000000000009e-26 < y < 2.1e15

   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 89.5%

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

   if 2.1e15 < y < 2.8e77

   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 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 82.6%

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

   6. Taylor expanded in x around 0 82.6%

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

      1. associate-*r/ 82.9%

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

      2. *-commutative 82.9%

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

      3. associate-/l* 82.8%

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

   8. Simplified 82.8%

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

   if 2.8e77 < y < 2.8e90

   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 0 100.0%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+204}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* x 2.0))))
   (if (<= x -1.02e+48)
     (* y (* x 2.0))
     (if (<= x -1.75e-125)
       t_1
       (if (<= x 3.4e-56) (* y 5.0) (if (<= x 1.08e+204) (* 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 (x <= -1.02e+48) {
		tmp = y * (x * 2.0);
	} else if (x <= -1.75e-125) {
		tmp = t_1;
	} else if (x <= 3.4e-56) {
		tmp = y * 5.0;
	} else if (x <= 1.08e+204) {
		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 (x <= (-1.02d+48)) then
        tmp = y * (x * 2.0d0)
    else if (x <= (-1.75d-125)) then
        tmp = t_1
    else if (x <= 3.4d-56) then
        tmp = y * 5.0d0
    else if (x <= 1.08d+204) 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 (x <= -1.02e+48) {
		tmp = y * (x * 2.0);
	} else if (x <= -1.75e-125) {
		tmp = t_1;
	} else if (x <= 3.4e-56) {
		tmp = y * 5.0;
	} else if (x <= 1.08e+204) {
		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 x <= -1.02e+48:
		tmp = y * (x * 2.0)
	elif x <= -1.75e-125:
		tmp = t_1
	elif x <= 3.4e-56:
		tmp = y * 5.0
	elif x <= 1.08e+204:
		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 (x <= -1.02e+48)
		tmp = Float64(y * Float64(x * 2.0));
	elseif (x <= -1.75e-125)
		tmp = t_1;
	elseif (x <= 3.4e-56)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.08e+204)
		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 (x <= -1.02e+48)
		tmp = y * (x * 2.0);
	elseif (x <= -1.75e-125)
		tmp = t_1;
	elseif (x <= 3.4e-56)
		tmp = y * 5.0;
	elseif (x <= 1.08e+204)
		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[x, -1.02e+48], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.75e-125], t$95$1, If[LessEqual[x, 3.4e-56], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.08e+204], N[(x * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.02e48

   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%

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

   6. Taylor expanded in z around 0 74.3%

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

   7. Taylor expanded in t around 0 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-*l* 54.2%

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

      3. *-commutative 54.2%

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

      4. associate-*r* 54.2%

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

   9. Simplified 54.2%

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

   if -1.02e48 < x < -1.74999999999999999e-125 or 1.08e204 < 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 55.9%

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

   5. Simplified 55.9%

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

   if -1.74999999999999999e-125 < x < 3.39999999999999982e-56

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 67.5%

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

   if 3.39999999999999982e-56 < x < 1.08e204

   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 39.8%

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

   5. Simplified 39.8%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+204}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+83}:\\ \;\;\;\;x \cdot t\_1 + y \cdot 5\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(t + \left(t\_1 + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (<= y -1.05e+83)
     (+ (* x t_1) (* y 5.0))
     (if (<= y 1.05e+87)
       (* x (+ t (+ t_1 (* 5.0 (/ y x)))))
       (+ (* x (+ t (+ y y))) (* y 5.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (y <= -1.05e+83) {
		tmp = (x * t_1) + (y * 5.0);
	} else if (y <= 1.05e+87) {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    if (y <= (-1.05d+83)) then
        tmp = (x * t_1) + (y * 5.0d0)
    else if (y <= 1.05d+87) then
        tmp = x * (t + (t_1 + (5.0d0 * (y / x))))
    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 t_1 = 2.0 * (y + z);
	double tmp;
	if (y <= -1.05e+83) {
		tmp = (x * t_1) + (y * 5.0);
	} else if (y <= 1.05e+87) {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	} else {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if y <= -1.05e+83:
		tmp = (x * t_1) + (y * 5.0)
	elif y <= 1.05e+87:
		tmp = x * (t + (t_1 + (5.0 * (y / x))))
	else:
		tmp = (x * (t + (y + y))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if (y <= -1.05e+83)
		tmp = Float64(Float64(x * t_1) + Float64(y * 5.0));
	elseif (y <= 1.05e+87)
		tmp = Float64(x * Float64(t + Float64(t_1 + Float64(5.0 * Float64(y / x)))));
	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)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if (y <= -1.05e+83)
		tmp = (x * t_1) + (y * 5.0);
	elseif (y <= 1.05e+87)
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	else
		tmp = (x * (t + (y + y))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+83], N[(N[(x * t$95$1), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+87], N[(x * N[(t + N[(t$95$1 + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05000000000000001e83

   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 95.9%

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

   5. Simplified 95.9%

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

   if -1.05000000000000001e83 < y < 1.05e87

   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 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 99.3%

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

   if 1.05e87 < 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 97.6%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -2.3e-26)
     t_1
     (if (<= y 1.1e-25)
       (* x (+ t (* 2.0 z)))
       (if (<= y 8.2e+93) (* t (+ x (* y (/ 5.0 t)))) 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 <= -2.3e-26) {
		tmp = t_1;
	} else if (y <= 1.1e-25) {
		tmp = x * (t + (2.0 * z));
	} else if (y <= 8.2e+93) {
		tmp = t * (x + (y * (5.0 / 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 * (5.0d0 + (x * 2.0d0))
    if (y <= (-2.3d-26)) then
        tmp = t_1
    else if (y <= 1.1d-25) then
        tmp = x * (t + (2.0d0 * z))
    else if (y <= 8.2d+93) then
        tmp = t * (x + (y * (5.0d0 / 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 * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.3e-26) {
		tmp = t_1;
	} else if (y <= 1.1e-25) {
		tmp = x * (t + (2.0 * z));
	} else if (y <= 8.2e+93) {
		tmp = t * (x + (y * (5.0 / t)));
	} 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 <= -2.3e-26:
		tmp = t_1
	elif y <= 1.1e-25:
		tmp = x * (t + (2.0 * z))
	elif y <= 8.2e+93:
		tmp = t * (x + (y * (5.0 / t)))
	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 <= -2.3e-26)
		tmp = t_1;
	elseif (y <= 1.1e-25)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	elseif (y <= 8.2e+93)
		tmp = Float64(t * Float64(x + Float64(y * Float64(5.0 / t))));
	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 <= -2.3e-26)
		tmp = t_1;
	elseif (y <= 1.1e-25)
		tmp = x * (t + (2.0 * z));
	elseif (y <= 8.2e+93)
		tmp = t * (x + (y * (5.0 / t)));
	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, -2.3e-26], t$95$1, If[LessEqual[y, 1.1e-25], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+93], N[(t * N[(x + N[(y * N[(5.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.30000000000000009e-26 or 8.2000000000000002e93 < 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 85.5%

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

   5. Simplified 85.5%

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

   if -2.30000000000000009e-26 < y < 1.1000000000000001e-25

   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 89.8%

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

   if 1.1000000000000001e-25 < y < 8.2000000000000002e93

   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 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 78.4%

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

   6. Taylor expanded in x around 0 70.0%

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

      1. associate-*r/ 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-/l* 70.2%

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

   8. Simplified 70.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(t\_1 + t\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+167}:\\ \;\;\;\;x \cdot t\_1 + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (<= t -5.4e+103)
     (* x (+ t_1 t))
     (if (<= t 4.5e+167)
       (+ (* x t_1) (* y 5.0))
       (* t (+ x (* y (/ 5.0 t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (t <= -5.4e+103) {
		tmp = x * (t_1 + t);
	} else if (t <= 4.5e+167) {
		tmp = (x * t_1) + (y * 5.0);
	} else {
		tmp = t * (x + (y * (5.0 / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    if (t <= (-5.4d+103)) then
        tmp = x * (t_1 + t)
    else if (t <= 4.5d+167) then
        tmp = (x * t_1) + (y * 5.0d0)
    else
        tmp = t * (x + (y * (5.0d0 / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (t <= -5.4e+103) {
		tmp = x * (t_1 + t);
	} else if (t <= 4.5e+167) {
		tmp = (x * t_1) + (y * 5.0);
	} else {
		tmp = t * (x + (y * (5.0 / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if t <= -5.4e+103:
		tmp = x * (t_1 + t)
	elif t <= 4.5e+167:
		tmp = (x * t_1) + (y * 5.0)
	else:
		tmp = t * (x + (y * (5.0 / t)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if (t <= -5.4e+103)
		tmp = Float64(x * Float64(t_1 + t));
	elseif (t <= 4.5e+167)
		tmp = Float64(Float64(x * t_1) + Float64(y * 5.0));
	else
		tmp = Float64(t * Float64(x + Float64(y * Float64(5.0 / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if (t <= -5.4e+103)
		tmp = x * (t_1 + t);
	elseif (t <= 4.5e+167)
		tmp = (x * t_1) + (y * 5.0);
	else
		tmp = t * (x + (y * (5.0 / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e+103], N[(x * N[(t$95$1 + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+167], N[(N[(x * t$95$1), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(x + N[(y * N[(5.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.39999999999999985e103

   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 92.6%

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

   if -5.39999999999999985e103 < t < 4.4999999999999999e167

   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 93.6%

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

   5. Simplified 93.6%

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

   if 4.4999999999999999e167 < t

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 95.6%

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

   6. Taylor expanded in x around 0 92.0%

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

      1. associate-*r/ 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-/l* 92.0%

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

   8. Simplified 92.0%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(t\_1 + t\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+137}:\\ \;\;\;\;x \cdot t\_1 + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (<= t -2.15e+104)
     (* x (+ t_1 t))
     (if (<= t 2.6e+137)
       (+ (* x t_1) (* y 5.0))
       (+ (* x (+ t (+ y y))) (* y 5.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (t <= -2.15e+104) {
		tmp = x * (t_1 + t);
	} else if (t <= 2.6e+137) {
		tmp = (x * t_1) + (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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    if (t <= (-2.15d+104)) then
        tmp = x * (t_1 + t)
    else if (t <= 2.6d+137) then
        tmp = (x * t_1) + (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 t_1 = 2.0 * (y + z);
	double tmp;
	if (t <= -2.15e+104) {
		tmp = x * (t_1 + t);
	} else if (t <= 2.6e+137) {
		tmp = (x * t_1) + (y * 5.0);
	} else {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if t <= -2.15e+104:
		tmp = x * (t_1 + t)
	elif t <= 2.6e+137:
		tmp = (x * t_1) + (y * 5.0)
	else:
		tmp = (x * (t + (y + y))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if (t <= -2.15e+104)
		tmp = Float64(x * Float64(t_1 + t));
	elseif (t <= 2.6e+137)
		tmp = Float64(Float64(x * t_1) + 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)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if (t <= -2.15e+104)
		tmp = x * (t_1 + t);
	elseif (t <= 2.6e+137)
		tmp = (x * t_1) + (y * 5.0);
	else
		tmp = (x * (t + (y + y))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e+104], N[(x * N[(t$95$1 + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+137], N[(N[(x * t$95$1), $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 3 regimes

2. if t < -2.1500000000000001e104

   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 92.6%

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

   if -2.1500000000000001e104 < t < 2.5999999999999999e137

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 94.2%

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

   5. Simplified 94.2%

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

   if 2.5999999999999999e137 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 93.2%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -16000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+155}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x 2.0))))
   (if (<= x -16000000.0)
     t_1
     (if (<= x 2.9e-55) (* y 5.0) (if (<= x 6.2e+155) (* 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 <= -16000000.0) {
		tmp = t_1;
	} else if (x <= 2.9e-55) {
		tmp = y * 5.0;
	} else if (x <= 6.2e+155) {
		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 <= (-16000000.0d0)) then
        tmp = t_1
    else if (x <= 2.9d-55) then
        tmp = y * 5.0d0
    else if (x <= 6.2d+155) 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 <= -16000000.0) {
		tmp = t_1;
	} else if (x <= 2.9e-55) {
		tmp = y * 5.0;
	} else if (x <= 6.2e+155) {
		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 <= -16000000.0:
		tmp = t_1
	elif x <= 2.9e-55:
		tmp = y * 5.0
	elif x <= 6.2e+155:
		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 <= -16000000.0)
		tmp = t_1;
	elseif (x <= 2.9e-55)
		tmp = Float64(y * 5.0);
	elseif (x <= 6.2e+155)
		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 <= -16000000.0)
		tmp = t_1;
	elseif (x <= 2.9e-55)
		tmp = y * 5.0;
	elseif (x <= 6.2e+155)
		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, -16000000.0], t$95$1, If[LessEqual[x, 2.9e-55], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 6.2e+155], N[(x * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6e7 or 6.19999999999999978e155 < 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%

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

   6. Taylor expanded in z around 0 67.8%

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

   7. Taylor expanded in t around 0 48.4%

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

      1. *-commutative 48.4%

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

      2. associate-*l* 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-*r* 48.4%

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

   9. Simplified 48.4%

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

   if -1.6e7 < x < 2.9e-55

   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 55.2%

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

   if 2.9e-55 < x < 6.19999999999999978e155

   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 40.5%

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

   5. Simplified 40.5%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16000000:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+155}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1e+160)
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* x (+ t (* 2.0 z))) (* y (+ 5.0 (* x 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1e+160) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1d+160)) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (x * (t + (2.0d0 * z))) + (y * (5.0d0 + (x * 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1e+160) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1e+160:
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1e+160)
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(2.0 * z))) + Float64(y * Float64(5.0 + Float64(x * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1e+160)
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (x * (t + (2.0 * z))) + (y * (5.0 + (x * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1e+160], 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 * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.00000000000000001e160

   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%

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

   if -1.00000000000000001e160 < 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 y around 0 98.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right) + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-125} \lor \neg \left(x \leq 3.3 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + \frac{x \cdot t}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.6e-125) (not (<= x 3.3e-9)))
   (* x (+ (* 2.0 (+ y z)) t))
   (* y (+ 5.0 (/ (* x t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e-125) || !(x <= 3.3e-9)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = y * (5.0 + ((x * t) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.6d-125)) .or. (.not. (x <= 3.3d-9))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = y * (5.0d0 + ((x * t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e-125) || !(x <= 3.3e-9)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = y * (5.0 + ((x * t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.6e-125) or not (x <= 3.3e-9):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = y * (5.0 + ((x * t) / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.6e-125) || !(x <= 3.3e-9))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(y * Float64(5.0 + Float64(Float64(x * t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.6e-125) || ~((x <= 3.3e-9)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = y * (5.0 + ((x * t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.6e-125], N[Not[LessEqual[x, 3.3e-9]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(y * N[(5.0 + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5999999999999999e-125 or 3.30000000000000018e-9 < 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 93.3%

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

   if -1.5999999999999999e-125 < x < 3.30000000000000018e-9

   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 96.5%

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

   4. Taylor expanded in z around 0 77.3%

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

   5. Taylor expanded in t around inf 76.9%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-125} \lor \neg \left(x \leq 3.3 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + \frac{x \cdot t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-134} \lor \neg \left(x \leq 5.3 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.7e-134) (not (<= x 5.3e-9)))
   (* x (* 2.0 (+ y z)))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.7e-134) || !(x <= 5.3e-9)) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.7d-134)) .or. (.not. (x <= 5.3d-9))) then
        tmp = x * (2.0d0 * (y + z))
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.7e-134) || !(x <= 5.3e-9)) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.7e-134) or not (x <= 5.3e-9):
		tmp = x * (2.0 * (y + z))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.7e-134) || !(x <= 5.3e-9))
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.7e-134) || ~((x <= 5.3e-9)))
		tmp = x * (2.0 * (y + z));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.7e-134], N[Not[LessEqual[x, 5.3e-9]], $MachinePrecision]], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6999999999999998e-134 or 5.30000000000000031e-9 < 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 0 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in x around inf 70.0%

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

      1. associate-*r* 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*r* 70.0%

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

   8. Simplified 70.0%

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

   if -2.6999999999999998e-134 < x < 5.30000000000000031e-9

   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 66.8%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-134} \lor \neg \left(x \leq 5.3 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 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 15: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-121} \lor \neg \left(x \leq 1.12 \cdot 10^{-54}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9.5e-121) (not (<= x 1.12e-54))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.5e-121) || !(x <= 1.12e-54)) {
		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 <= (-9.5d-121)) .or. (.not. (x <= 1.12d-54))) 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 <= -9.5e-121) || !(x <= 1.12e-54)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9.5e-121) or not (x <= 1.12e-54):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9.5e-121) || !(x <= 1.12e-54))
		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 <= -9.5e-121) || ~((x <= 1.12e-54)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9.5e-121], N[Not[LessEqual[x, 1.12e-54]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4999999999999994e-121 or 1.11999999999999994e-54 < 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 30.3%

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

   5. Simplified 30.3%

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

   if -9.4999999999999994e-121 < x < 1.11999999999999994e-54

   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 66.8%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-121} \lor \neg \left(x \leq 1.12 \cdot 10^{-54}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.1% 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 27.2%

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

4. Final simplification 27.2%

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

Reproduce

herbie shell --seed 2024066 
(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)))