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

Percentage Accurate: 99.9% → 99.9%

Time: 11.0s

Alternatives: 14

Speedup: 1.0×

• 27.1% 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 100.0%

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

   1. fma-def 100.0%

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

   2. associate-+l+ 100.0%

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

   3. +-commutative 100.0%

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

   4. count-2 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 46.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1.28 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-97}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-12}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))) (t_2 (* 2.0 (* x y))))
   (if (<= x -1.28e+187)
     t_1
     (if (<= x -2.8e+57)
       t_2
       (if (<= x -9.2e-97)
         (* x t)
         (if (<= x 2.85e-12) (* y 5.0) (if (<= x 1.08e+82) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (x <= -1.28e+187) {
		tmp = t_1;
	} else if (x <= -2.8e+57) {
		tmp = t_2;
	} else if (x <= -9.2e-97) {
		tmp = x * t;
	} else if (x <= 2.85e-12) {
		tmp = y * 5.0;
	} else if (x <= 1.08e+82) {
		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 = 2.0d0 * (x * z)
    t_2 = 2.0d0 * (x * y)
    if (x <= (-1.28d+187)) then
        tmp = t_1
    else if (x <= (-2.8d+57)) then
        tmp = t_2
    else if (x <= (-9.2d-97)) then
        tmp = x * t
    else if (x <= 2.85d-12) then
        tmp = y * 5.0d0
    else if (x <= 1.08d+82) 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 = 2.0 * (x * z);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (x <= -1.28e+187) {
		tmp = t_1;
	} else if (x <= -2.8e+57) {
		tmp = t_2;
	} else if (x <= -9.2e-97) {
		tmp = x * t;
	} else if (x <= 2.85e-12) {
		tmp = y * 5.0;
	} else if (x <= 1.08e+82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if x <= -1.28e+187:
		tmp = t_1
	elif x <= -2.8e+57:
		tmp = t_2
	elif x <= -9.2e-97:
		tmp = x * t
	elif x <= 2.85e-12:
		tmp = y * 5.0
	elif x <= 1.08e+82:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (x <= -1.28e+187)
		tmp = t_1;
	elseif (x <= -2.8e+57)
		tmp = t_2;
	elseif (x <= -9.2e-97)
		tmp = Float64(x * t);
	elseif (x <= 2.85e-12)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.08e+82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (x <= -1.28e+187)
		tmp = t_1;
	elseif (x <= -2.8e+57)
		tmp = t_2;
	elseif (x <= -9.2e-97)
		tmp = x * t;
	elseif (x <= 2.85e-12)
		tmp = y * 5.0;
	elseif (x <= 1.08e+82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.28e+187], t$95$1, If[LessEqual[x, -2.8e+57], t$95$2, If[LessEqual[x, -9.2e-97], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.85e-12], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.08e+82], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.28e187 or 2.8500000000000002e-12 < x < 1.08e82

   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 60.8%

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

   if -1.28e187 < x < -2.8e57 or 1.08e82 < 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 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in x around inf 78.7%

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

   7. Taylor expanded in y around inf 50.5%

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

      1. *-commutative 50.5%

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

   9. Simplified 50.5%

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

   if -2.8e57 < x < -9.19999999999999976e-97

   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 42.0%

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

   5. Simplified 42.0%

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

   if -9.19999999999999976e-97 < x < 2.8500000000000002e-12

   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 67.2%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{+187}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+57}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-97}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-12}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{+26}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq -3400 \lor \neg \left(y \leq 1.08 \cdot 10^{-48}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -3.1e+134)
     t_1
     (if (<= y -2.55e+26)
       (+ (* y 5.0) (* x t))
       (if (or (<= y -3400.0) (not (<= y 1.08e-48)))
         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 <= -3.1e+134) {
		tmp = t_1;
	} else if (y <= -2.55e+26) {
		tmp = (y * 5.0) + (x * t);
	} else if ((y <= -3400.0) || !(y <= 1.08e-48)) {
		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 <= (-3.1d+134)) then
        tmp = t_1
    else if (y <= (-2.55d+26)) then
        tmp = (y * 5.0d0) + (x * t)
    else if ((y <= (-3400.0d0)) .or. (.not. (y <= 1.08d-48))) 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 <= -3.1e+134) {
		tmp = t_1;
	} else if (y <= -2.55e+26) {
		tmp = (y * 5.0) + (x * t);
	} else if ((y <= -3400.0) || !(y <= 1.08e-48)) {
		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 <= -3.1e+134:
		tmp = t_1
	elif y <= -2.55e+26:
		tmp = (y * 5.0) + (x * t)
	elif (y <= -3400.0) or not (y <= 1.08e-48):
		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 <= -3.1e+134)
		tmp = t_1;
	elseif (y <= -2.55e+26)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif ((y <= -3400.0) || !(y <= 1.08e-48))
		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 <= -3.1e+134)
		tmp = t_1;
	elseif (y <= -2.55e+26)
		tmp = (y * 5.0) + (x * t);
	elseif ((y <= -3400.0) || ~((y <= 1.08e-48)))
		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, -3.1e+134], t$95$1, If[LessEqual[y, -2.55e+26], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3400.0], N[Not[LessEqual[y, 1.08e-48]], $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 < -3.09999999999999982e134 or -2.5499999999999999e26 < y < -3400 or 1.08e-48 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.1%

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

   5. Simplified 80.1%

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

   if -3.09999999999999982e134 < y < -2.5499999999999999e26

   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 89.6%

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

      1. distribute-lft-in 85.9%

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

      2. count-2 85.9%

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

      3. *-commutative 85.9%

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

      4. +-commutative 85.9%

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

      5. *-commutative 85.9%

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

      6. count-2 85.9%

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

      7. flip-+ 0.0%

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

      8. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{\color{blue}{0}}{y - y}\right) + y \cdot 5 \]

      9. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{0}{\color{blue}{0}}\right) + y \cdot 5 \]

   5. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\left(x \cdot t + x \cdot \frac{0}{0}\right)} + y \cdot 5 \]

   7. Simplified 82.8%

      \[\leadsto \color{blue}{x \cdot \left(t + 0\right)} + y \cdot 5 \]

   8. Taylor expanded in x around 0 82.8%

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

   if -3400 < y < 1.08e-48

   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 88.5%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{+26}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq -3400 \lor \neg \left(y \leq 1.08 \cdot 10^{-48}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ t_2 := x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+192}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-14}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x (+ y z)))) (t_2 (* x (+ t (* 2.0 z)))))
   (if (<= x -6.5e+192)
     t_2
     (if (<= x -4e+53)
       t_1
       (if (<= x -6.2e-98) t_2 (if (<= x 3e-14) (* y 5.0) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * (y + z));
	double t_2 = x * (t + (2.0 * z));
	double tmp;
	if (x <= -6.5e+192) {
		tmp = t_2;
	} else if (x <= -4e+53) {
		tmp = t_1;
	} else if (x <= -6.2e-98) {
		tmp = t_2;
	} else if (x <= 3e-14) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * (y + z))
    t_2 = x * (t + (2.0d0 * z))
    if (x <= (-6.5d+192)) then
        tmp = t_2
    else if (x <= (-4d+53)) then
        tmp = t_1
    else if (x <= (-6.2d-98)) then
        tmp = t_2
    else if (x <= 3d-14) then
        tmp = y * 5.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * (y + z));
	double t_2 = x * (t + (2.0 * z));
	double tmp;
	if (x <= -6.5e+192) {
		tmp = t_2;
	} else if (x <= -4e+53) {
		tmp = t_1;
	} else if (x <= -6.2e-98) {
		tmp = t_2;
	} else if (x <= 3e-14) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * (y + z))
	t_2 = x * (t + (2.0 * z))
	tmp = 0
	if x <= -6.5e+192:
		tmp = t_2
	elif x <= -4e+53:
		tmp = t_1
	elif x <= -6.2e-98:
		tmp = t_2
	elif x <= 3e-14:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * Float64(y + z)))
	t_2 = Float64(x * Float64(t + Float64(2.0 * z)))
	tmp = 0.0
	if (x <= -6.5e+192)
		tmp = t_2;
	elseif (x <= -4e+53)
		tmp = t_1;
	elseif (x <= -6.2e-98)
		tmp = t_2;
	elseif (x <= 3e-14)
		tmp = Float64(y * 5.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * (y + z));
	t_2 = x * (t + (2.0 * z));
	tmp = 0.0;
	if (x <= -6.5e+192)
		tmp = t_2;
	elseif (x <= -4e+53)
		tmp = t_1;
	elseif (x <= -6.2e-98)
		tmp = t_2;
	elseif (x <= 3e-14)
		tmp = y * 5.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.5e+192], t$95$2, If[LessEqual[x, -4e+53], t$95$1, If[LessEqual[x, -6.2e-98], t$95$2, If[LessEqual[x, 3e-14], N[(y * 5.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.50000000000000033e192 or -4e53 < x < -6.2e-98

   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 79.2%

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

   if -6.50000000000000033e192 < x < -4e53 or 2.9999999999999998e-14 < 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 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in x around inf 81.3%

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

   if -6.2e-98 < x < 2.9999999999999998e-14

   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 67.2%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+53}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-14}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ t_2 := x \cdot \left(t\_1 + t\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-248}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 26000:\\ \;\;\;\;x \cdot t\_1 + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))) (t_2 (* x (+ t_1 t))))
   (if (<= x -1.25e-51)
     t_2
     (if (<= x -2.45e-248)
       (+ (* y 5.0) (* x t))
       (if (<= x 26000.0) (+ (* x t_1) (* y 5.0)) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double t_2 = x * (t_1 + t);
	double tmp;
	if (x <= -1.25e-51) {
		tmp = t_2;
	} else if (x <= -2.45e-248) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 26000.0) {
		tmp = (x * t_1) + (y * 5.0);
	} 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 = 2.0d0 * (y + z)
    t_2 = x * (t_1 + t)
    if (x <= (-1.25d-51)) then
        tmp = t_2
    else if (x <= (-2.45d-248)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 26000.0d0) then
        tmp = (x * t_1) + (y * 5.0d0)
    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 = 2.0 * (y + z);
	double t_2 = x * (t_1 + t);
	double tmp;
	if (x <= -1.25e-51) {
		tmp = t_2;
	} else if (x <= -2.45e-248) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 26000.0) {
		tmp = (x * t_1) + (y * 5.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	t_2 = x * (t_1 + t)
	tmp = 0
	if x <= -1.25e-51:
		tmp = t_2
	elif x <= -2.45e-248:
		tmp = (y * 5.0) + (x * t)
	elif x <= 26000.0:
		tmp = (x * t_1) + (y * 5.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	t_2 = Float64(x * Float64(t_1 + t))
	tmp = 0.0
	if (x <= -1.25e-51)
		tmp = t_2;
	elseif (x <= -2.45e-248)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 26000.0)
		tmp = Float64(Float64(x * t_1) + Float64(y * 5.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	t_2 = x * (t_1 + t);
	tmp = 0.0;
	if (x <= -1.25e-51)
		tmp = t_2;
	elseif (x <= -2.45e-248)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 26000.0)
		tmp = (x * t_1) + (y * 5.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t$95$1 + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e-51], t$95$2, If[LessEqual[x, -2.45e-248], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 26000.0], N[(N[(x * t$95$1), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25000000000000001e-51 or 26000 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 98.0%

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

   if -1.25000000000000001e-51 < x < -2.4499999999999998e-248

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 85.9%

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

      1. distribute-lft-in 85.9%

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

      2. count-2 85.9%

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

      3. *-commutative 85.9%

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

      4. +-commutative 85.9%

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

      5. *-commutative 85.9%

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

      6. count-2 85.9%

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

      7. flip-+ 0.0%

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

      8. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{\color{blue}{0}}{y - y}\right) + y \cdot 5 \]

      9. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{0}{\color{blue}{0}}\right) + y \cdot 5 \]

   5. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\left(x \cdot t + x \cdot \frac{0}{0}\right)} + y \cdot 5 \]

   7. Simplified 85.9%

      \[\leadsto \color{blue}{x \cdot \left(t + 0\right)} + y \cdot 5 \]

   8. Taylor expanded in x around 0 85.9%

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

   if -2.4499999999999998e-248 < x < 26000

   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 t around 0 89.5%

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

   5. Simplified 89.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-248}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 26000:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-95}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-11}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x (+ y z)))))
   (if (<= x -4.5e-50)
     t_1
     (if (<= x -6e-95) (* x t) (if (<= x 1.02e-11) (* y 5.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * (y + z));
	double tmp;
	if (x <= -4.5e-50) {
		tmp = t_1;
	} else if (x <= -6e-95) {
		tmp = x * t;
	} else if (x <= 1.02e-11) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * (y + z))
    if (x <= (-4.5d-50)) then
        tmp = t_1
    else if (x <= (-6d-95)) then
        tmp = x * t
    else if (x <= 1.02d-11) then
        tmp = y * 5.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * (y + z));
	double tmp;
	if (x <= -4.5e-50) {
		tmp = t_1;
	} else if (x <= -6e-95) {
		tmp = x * t;
	} else if (x <= 1.02e-11) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * (y + z))
	tmp = 0
	if x <= -4.5e-50:
		tmp = t_1
	elif x <= -6e-95:
		tmp = x * t
	elif x <= 1.02e-11:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * Float64(y + z)))
	tmp = 0.0
	if (x <= -4.5e-50)
		tmp = t_1;
	elseif (x <= -6e-95)
		tmp = Float64(x * t);
	elseif (x <= 1.02e-11)
		tmp = Float64(y * 5.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * (y + z));
	tmp = 0.0;
	if (x <= -4.5e-50)
		tmp = t_1;
	elseif (x <= -6e-95)
		tmp = x * t;
	elseif (x <= 1.02e-11)
		tmp = y * 5.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e-50], t$95$1, If[LessEqual[x, -6e-95], N[(x * t), $MachinePrecision], If[LessEqual[x, 1.02e-11], N[(y * 5.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.49999999999999962e-50 or 1.01999999999999994e-11 < 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 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in x around inf 75.9%

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

   if -4.49999999999999962e-50 < x < -6e-95

   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 60.8%

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

   5. Simplified 60.8%

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

   if -6e-95 < x < 1.01999999999999994e-11

   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 67.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-50}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-95}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-11}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+26} \lor \neg \left(t \leq 0.00075\right):\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.9e+26) (not (<= t 0.00075)))
   (+ (* x (+ t (+ y y))) (* y 5.0))
   (+ (* x (* 2.0 (+ y z))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.9e+26) || !(t <= 0.00075)) {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	} else {
		tmp = (x * (2.0 * (y + 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 ((t <= (-1.9d+26)) .or. (.not. (t <= 0.00075d0))) then
        tmp = (x * (t + (y + y))) + (y * 5.0d0)
    else
        tmp = (x * (2.0d0 * (y + 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 ((t <= -1.9e+26) || !(t <= 0.00075)) {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	} else {
		tmp = (x * (2.0 * (y + z))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.9e+26) or not (t <= 0.00075):
		tmp = (x * (t + (y + y))) + (y * 5.0)
	else:
		tmp = (x * (2.0 * (y + z))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.9e+26) || !(t <= 0.00075))
		tmp = Float64(Float64(x * Float64(t + Float64(y + y))) + Float64(y * 5.0));
	else
		tmp = Float64(Float64(x * Float64(2.0 * Float64(y + z))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.9e+26) || ~((t <= 0.00075)))
		tmp = (x * (t + (y + y))) + (y * 5.0);
	else
		tmp = (x * (2.0 * (y + z))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.9e+26], N[Not[LessEqual[t, 0.00075]], $MachinePrecision]], N[(N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9000000000000001e26 or 7.5000000000000002e-4 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 91.2%

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

   if -1.9000000000000001e26 < t < 7.5000000000000002e-4

   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 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+26} \lor \neg \left(t \leq 0.00075\right):\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-96}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-10}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -3.5e-53)
     t_1
     (if (<= x -8e-96) (* x t) (if (<= x 2.85e-10) (* y 5.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -3.5e-53) {
		tmp = t_1;
	} else if (x <= -8e-96) {
		tmp = x * t;
	} else if (x <= 2.85e-10) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-3.5d-53)) then
        tmp = t_1
    else if (x <= (-8d-96)) then
        tmp = x * t
    else if (x <= 2.85d-10) then
        tmp = y * 5.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -3.5e-53) {
		tmp = t_1;
	} else if (x <= -8e-96) {
		tmp = x * t;
	} else if (x <= 2.85e-10) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -3.5e-53:
		tmp = t_1
	elif x <= -8e-96:
		tmp = x * t
	elif x <= 2.85e-10:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -3.5e-53)
		tmp = t_1;
	elseif (x <= -8e-96)
		tmp = Float64(x * t);
	elseif (x <= 2.85e-10)
		tmp = Float64(y * 5.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -3.5e-53)
		tmp = t_1;
	elseif (x <= -8e-96)
		tmp = x * t;
	elseif (x <= 2.85e-10)
		tmp = y * 5.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e-53], t$95$1, If[LessEqual[x, -8e-96], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.85e-10], N[(y * 5.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.49999999999999993e-53 or 2.84999999999999998e-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. Add Preprocessing

   3. Taylor expanded in z around inf 44.8%

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

   if -3.49999999999999993e-53 < x < -7.9999999999999993e-96

   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 60.8%

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

   5. Simplified 60.8%

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

   if -7.9999999999999993e-96 < x < 2.84999999999999998e-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 x around 0 67.2%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-96}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-10}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-54} \lor \neg \left(x \leq 1.38 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.35e-54) (not (<= x 1.38e-14)))
   (* 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 <= -2.35e-54) || !(x <= 1.38e-14)) {
		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 <= (-2.35d-54)) .or. (.not. (x <= 1.38d-14))) 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 <= -2.35e-54) || !(x <= 1.38e-14)) {
		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 <= -2.35e-54) or not (x <= 1.38e-14):
		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 <= -2.35e-54) || !(x <= 1.38e-14))
		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 <= -2.35e-54) || ~((x <= 1.38e-14)))
		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, -2.35e-54], N[Not[LessEqual[x, 1.38e-14]], $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 < -2.35e-54 or 1.38000000000000002e-14 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.0%

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

   if -2.35e-54 < x < 1.38000000000000002e-14

   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 83.1%

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

      1. distribute-lft-in 83.1%

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

      2. count-2 83.1%

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

      3. *-commutative 83.1%

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

      4. +-commutative 83.1%

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

      5. *-commutative 83.1%

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

      6. count-2 83.1%

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

      7. flip-+ 0.0%

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

      8. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{\color{blue}{0}}{y - y}\right) + y \cdot 5 \]

      9. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{0}{\color{blue}{0}}\right) + y \cdot 5 \]

   5. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\left(x \cdot t + x \cdot \frac{0}{0}\right)} + y \cdot 5 \]

   7. Simplified 83.1%

      \[\leadsto \color{blue}{x \cdot \left(t + 0\right)} + y \cdot 5 \]

   8. Taylor expanded in x around 0 83.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-54} \lor \neg \left(x \leq 1.38 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -12000 \lor \neg \left(y \leq 1.08 \cdot 10^{-48}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -12000.0) (not (<= y 1.08e-48)))
   (* 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 <= -12000.0) || !(y <= 1.08e-48)) {
		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 <= (-12000.0d0)) .or. (.not. (y <= 1.08d-48))) 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 <= -12000.0) || !(y <= 1.08e-48)) {
		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 <= -12000.0) or not (y <= 1.08e-48):
		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 <= -12000.0) || !(y <= 1.08e-48))
		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 <= -12000.0) || ~((y <= 1.08e-48)))
		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, -12000.0], N[Not[LessEqual[y, 1.08e-48]], $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 < -12000 or 1.08e-48 < 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 76.4%

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

   5. Simplified 76.4%

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

   if -12000 < y < 1.08e-48

   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 88.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12000 \lor \neg \left(y \leq 1.08 \cdot 10^{-48}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-13}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6e-95)
   (* x (+ t (* 2.0 y)))
   (if (<= x 6e-13) (* y 5.0) (* 2.0 (* x (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e-95) {
		tmp = x * (t + (2.0 * y));
	} else if (x <= 6e-13) {
		tmp = y * 5.0;
	} else {
		tmp = 2.0 * (x * (y + z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6d-95)) then
        tmp = x * (t + (2.0d0 * y))
    else if (x <= 6d-13) then
        tmp = y * 5.0d0
    else
        tmp = 2.0d0 * (x * (y + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e-95) {
		tmp = x * (t + (2.0 * y));
	} else if (x <= 6e-13) {
		tmp = y * 5.0;
	} else {
		tmp = 2.0 * (x * (y + z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6e-95:
		tmp = x * (t + (2.0 * y))
	elif x <= 6e-13:
		tmp = y * 5.0
	else:
		tmp = 2.0 * (x * (y + z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6e-95)
		tmp = Float64(x * Float64(t + Float64(2.0 * y)));
	elseif (x <= 6e-13)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(2.0 * Float64(x * Float64(y + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6e-95)
		tmp = x * (t + (2.0 * y));
	elseif (x <= 6e-13)
		tmp = y * 5.0;
	else
		tmp = 2.0 * (x * (y + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6e-95], N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-13], N[(y * 5.0), $MachinePrecision], N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6e-95

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.6%

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

   4. Taylor expanded in x around inf 65.2%

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

   if -6e-95 < x < 5.99999999999999968e-13

   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 67.2%

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

   if 5.99999999999999968e-13 < 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 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in x around inf 81.4%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-13}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 100.0%

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

3. Final simplification 100.0%

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

Alternative 13: 47.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-95} \lor \neg \left(x \leq 3.7 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4e-95) (not (<= x 3.7e-26))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e-95) || !(x <= 3.7e-26)) {
		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 <= (-4d-95)) .or. (.not. (x <= 3.7d-26))) 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 <= -4e-95) || !(x <= 3.7e-26)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4e-95) or not (x <= 3.7e-26):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4e-95) || !(x <= 3.7e-26))
		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 <= -4e-95) || ~((x <= 3.7e-26)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4e-95], N[Not[LessEqual[x, 3.7e-26]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999996e-95 or 3.6999999999999999e-26 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 31.2%

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

   5. Simplified 31.2%

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

   if -3.99999999999999996e-95 < x < 3.6999999999999999e-26

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 67.8%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-95} \lor \neg \left(x \leq 3.7 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.6% 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 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 27.6%

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

4. Final simplification 27.6%

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

Reproduce

herbie shell --seed 2024096 
(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)))