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

Percentage Accurate: 99.9% → 99.7%

Time: 9.6s

Alternatives: 14

Speedup: 1.0×

• 26.6% 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: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+155} \lor \neg \left(x \leq 2 \cdot 10^{+50}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2e+155) (not (<= x 2e+50)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* 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 ((x <= -2e+155) || !(x <= 2e+50)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * (5.0 + (x * 2.0))) + (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 ((x <= (-2d+155)) .or. (.not. (x <= 2d+50))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * (5.0d0 + (x * 2.0d0))) + (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 ((x <= -2e+155) || !(x <= 2e+50)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * (5.0 + (x * 2.0))) + (x * (t + (2.0 * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2e+155) or not (x <= 2e+50):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * (5.0 + (x * 2.0))) + (x * (t + (2.0 * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2e+155) || !(x <= 2e+50))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * Float64(5.0 + Float64(x * 2.0))) + 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 ((x <= -2e+155) || ~((x <= 2e+50)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * (5.0 + (x * 2.0))) + (x * (t + (2.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2e+155], N[Not[LessEqual[x, 2e+50]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.00000000000000001e155 or 2.0000000000000002e50 < 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 100.0%

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

   if -2.00000000000000001e155 < x < 2.0000000000000002e50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+155} \lor \neg \left(x \leq 2 \cdot 10^{+50}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-def 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
4. 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 3: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ t_2 := y \cdot 5 + x \cdot t_1\\ t_3 := x \cdot \left(t_1 + t\right)\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{+22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.24 \cdot 10^{-231}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1350000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z)))
        (t_2 (+ (* y 5.0) (* x t_1)))
        (t_3 (* x (+ t_1 t))))
   (if (<= x -1.22e+22)
     t_3
     (if (<= x -4.8e-152)
       t_2
       (if (<= x -1.24e-231)
         (+ (* y 5.0) (* x t))
         (if (<= x 1350000.0) t_2 t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double t_2 = (y * 5.0) + (x * t_1);
	double t_3 = x * (t_1 + t);
	double tmp;
	if (x <= -1.22e+22) {
		tmp = t_3;
	} else if (x <= -4.8e-152) {
		tmp = t_2;
	} else if (x <= -1.24e-231) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1350000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    t_2 = (y * 5.0d0) + (x * t_1)
    t_3 = x * (t_1 + t)
    if (x <= (-1.22d+22)) then
        tmp = t_3
    else if (x <= (-4.8d-152)) then
        tmp = t_2
    else if (x <= (-1.24d-231)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 1350000.0d0) then
        tmp = t_2
    else
        tmp = t_3
    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 = (y * 5.0) + (x * t_1);
	double t_3 = x * (t_1 + t);
	double tmp;
	if (x <= -1.22e+22) {
		tmp = t_3;
	} else if (x <= -4.8e-152) {
		tmp = t_2;
	} else if (x <= -1.24e-231) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1350000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	t_2 = (y * 5.0) + (x * t_1)
	t_3 = x * (t_1 + t)
	tmp = 0
	if x <= -1.22e+22:
		tmp = t_3
	elif x <= -4.8e-152:
		tmp = t_2
	elif x <= -1.24e-231:
		tmp = (y * 5.0) + (x * t)
	elif x <= 1350000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	t_2 = Float64(Float64(y * 5.0) + Float64(x * t_1))
	t_3 = Float64(x * Float64(t_1 + t))
	tmp = 0.0
	if (x <= -1.22e+22)
		tmp = t_3;
	elseif (x <= -4.8e-152)
		tmp = t_2;
	elseif (x <= -1.24e-231)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 1350000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	t_2 = (y * 5.0) + (x * t_1);
	t_3 = x * (t_1 + t);
	tmp = 0.0;
	if (x <= -1.22e+22)
		tmp = t_3;
	elseif (x <= -4.8e-152)
		tmp = t_2;
	elseif (x <= -1.24e-231)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 1350000.0)
		tmp = t_2;
	else
		tmp = t_3;
	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[(N[(y * 5.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(t$95$1 + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.22e+22], t$95$3, If[LessEqual[x, -4.8e-152], t$95$2, If[LessEqual[x, -1.24e-231], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1350000.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.22e22 or 1.35e6 < 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 100.0%

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

   if -1.22e22 < x < -4.8e-152 or -1.24e-231 < x < 1.35e6

   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 86.2%

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

   5. Simplified 86.2%

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

   if -4.8e-152 < x < -1.24e-231

   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. Step-by-step derivation

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. flip-+ 0.0%

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

      4. pow2 0.0%

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

      5. pow2 0.0%

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

   4. Applied egg-rr 0.0%

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

   6. Simplified 98.1%

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

   7. Taylor expanded in x around 0 98.1%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-152}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -1.24 \cdot 10^{-231}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1350000:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1750000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+53}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+60}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1750000000.0)
     t_1
     (if (<= y 4.8e-61)
       (* x (+ t (* 2.0 z)))
       (if (<= y 1.9e+53)
         (+ (* y 5.0) (* x t))
         (if (<= y 2.4e+60) (* (+ y z) (* x 2.0)) 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 <= -1750000000.0) {
		tmp = t_1;
	} else if (y <= 4.8e-61) {
		tmp = x * (t + (2.0 * z));
	} else if (y <= 1.9e+53) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 2.4e+60) {
		tmp = (y + z) * (x * 2.0);
	} 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 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1750000000.0d0)) then
        tmp = t_1
    else if (y <= 4.8d-61) then
        tmp = x * (t + (2.0d0 * z))
    else if (y <= 1.9d+53) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 2.4d+60) then
        tmp = (y + z) * (x * 2.0d0)
    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 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1750000000.0) {
		tmp = t_1;
	} else if (y <= 4.8e-61) {
		tmp = x * (t + (2.0 * z));
	} else if (y <= 1.9e+53) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 2.4e+60) {
		tmp = (y + z) * (x * 2.0);
	} 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 <= -1750000000.0:
		tmp = t_1
	elif y <= 4.8e-61:
		tmp = x * (t + (2.0 * z))
	elif y <= 1.9e+53:
		tmp = (y * 5.0) + (x * t)
	elif y <= 2.4e+60:
		tmp = (y + z) * (x * 2.0)
	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 <= -1750000000.0)
		tmp = t_1;
	elseif (y <= 4.8e-61)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	elseif (y <= 1.9e+53)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 2.4e+60)
		tmp = Float64(Float64(y + z) * Float64(x * 2.0));
	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 <= -1750000000.0)
		tmp = t_1;
	elseif (y <= 4.8e-61)
		tmp = x * (t + (2.0 * z));
	elseif (y <= 1.9e+53)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 2.4e+60)
		tmp = (y + z) * (x * 2.0);
	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, -1750000000.0], t$95$1, If[LessEqual[y, 4.8e-61], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+53], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+60], N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.75e9 or 2.4e60 < 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 81.6%

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

   if -1.75e9 < y < 4.8000000000000002e-61

   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 82.0%

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

   5. Simplified 82.0%

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

   if 4.8000000000000002e-61 < y < 1.89999999999999999e53

   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. Step-by-step derivation

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. flip-+ 0.0%

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

      4. pow2 0.0%

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

      5. pow2 0.0%

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

   4. Applied egg-rr 0.0%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in x around 0 67.1%

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

   if 1.89999999999999999e53 < y < 2.4e60

   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 100.0%

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

   6. Taylor expanded in t around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1750000000:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+53}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+60}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -175000 \lor \neg \left(x \leq 2.8 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -175000.0) (not (<= x 2.8e-7)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x (+ t (* 2.0 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -175000.0) || !(x <= 2.8e-7)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (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 ((x <= (-175000.0d0)) .or. (.not. (x <= 2.8d-7))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (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 ((x <= -175000.0) || !(x <= 2.8e-7)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (2.0 * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -175000.0) or not (x <= 2.8e-7):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * (t + (2.0 * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -175000.0) || !(x <= 2.8e-7))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + 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 ((x <= -175000.0) || ~((x <= 2.8e-7)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * (t + (2.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -175000.0], N[Not[LessEqual[x, 2.8e-7]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -175000 or 2.80000000000000019e-7 < 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 98.5%

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

   if -175000 < x < 2.80000000000000019e-7

   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 98.8%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -175000 \lor \neg \left(x \leq 2.8 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (x * (t + (y + (z + (y + z)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 7: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{+145}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-7} \lor \neg \left(x \leq 2.85 \cdot 10^{-52}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -3.9e+238)
     t_1
     (if (<= x -6.7e+145)
       (* x t)
       (if (or (<= x -1e-7) (not (<= x 2.85e-52))) t_1 (* y 5.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -3.9e+238) {
		tmp = t_1;
	} else if (x <= -6.7e+145) {
		tmp = x * t;
	} else if ((x <= -1e-7) || !(x <= 2.85e-52)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-3.9d+238)) then
        tmp = t_1
    else if (x <= (-6.7d+145)) then
        tmp = x * t
    else if ((x <= (-1d-7)) .or. (.not. (x <= 2.85d-52))) then
        tmp = t_1
    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 t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -3.9e+238) {
		tmp = t_1;
	} else if (x <= -6.7e+145) {
		tmp = x * t;
	} else if ((x <= -1e-7) || !(x <= 2.85e-52)) {
		tmp = t_1;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -3.9e+238:
		tmp = t_1
	elif x <= -6.7e+145:
		tmp = x * t
	elif (x <= -1e-7) or not (x <= 2.85e-52):
		tmp = t_1
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -3.9e+238)
		tmp = t_1;
	elseif (x <= -6.7e+145)
		tmp = Float64(x * t);
	elseif ((x <= -1e-7) || !(x <= 2.85e-52))
		tmp = t_1;
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -3.9e+238)
		tmp = t_1;
	elseif (x <= -6.7e+145)
		tmp = x * t;
	elseif ((x <= -1e-7) || ~((x <= 2.85e-52)))
		tmp = t_1;
	else
		tmp = y * 5.0;
	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, -3.9e+238], t$95$1, If[LessEqual[x, -6.7e+145], N[(x * t), $MachinePrecision], If[Or[LessEqual[x, -1e-7], N[Not[LessEqual[x, 2.85e-52]], $MachinePrecision]], t$95$1, N[(y * 5.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.89999999999999993e238 or -6.6999999999999996e145 < x < -9.9999999999999995e-8 or 2.8499999999999999e-52 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 43.5%

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

   5. Simplified 43.5%

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

   if -3.89999999999999993e238 < x < -6.6999999999999996e145

   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 53.5%

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

   5. Simplified 53.5%

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

   if -9.9999999999999995e-8 < x < 2.8499999999999999e-52

   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 65.6%

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

   5. Simplified 65.6%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+238}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{+145}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-7} \lor \neg \left(x \leq 2.85 \cdot 10^{-52}\right):\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-6} \lor \neg \left(x \leq 1.1 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.2e-6) (not (<= x 1.1e-52)))
   (* 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 <= -5.2e-6) || !(x <= 1.1e-52)) {
		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 <= (-5.2d-6)) .or. (.not. (x <= 1.1d-52))) 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 <= -5.2e-6) || !(x <= 1.1e-52)) {
		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 <= -5.2e-6) or not (x <= 1.1e-52):
		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 <= -5.2e-6) || !(x <= 1.1e-52))
		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 <= -5.2e-6) || ~((x <= 1.1e-52)))
		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, -5.2e-6], N[Not[LessEqual[x, 1.1e-52]], $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 < -5.20000000000000019e-6 or 1.10000000000000005e-52 < 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 96.0%

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

   if -5.20000000000000019e-6 < x < 1.10000000000000005e-52

   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. Step-by-step derivation

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. flip-+ 0.0%

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

      4. pow2 0.0%

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

      5. pow2 0.0%

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

   4. Applied egg-rr 0.0%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in x around 0 81.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-6} \lor \neg \left(x \leq 1.1 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-44} \lor \neg \left(x \leq 3.7 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.35e-44) (not (<= x 3.7e-9)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* 2.0 (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.35e-44) || !(x <= 3.7e-9)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (2.0 * (x * 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 <= (-1.35d-44)) .or. (.not. (x <= 3.7d-9))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.35e-44) || !(x <= 3.7e-9)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (2.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.35e-44) or not (x <= 3.7e-9):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (2.0 * (x * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.35e-44) || !(x <= 3.7e-9))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.35e-44) || ~((x <= 3.7e-9)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (2.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.35e-44], N[Not[LessEqual[x, 3.7e-9]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e-44 or 3.7e-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-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 97.3%

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

   if -1.35e-44 < x < 3.7e-9

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.5%

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

   4. Taylor expanded in t around 0 83.1%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-44} \lor \neg \left(x \leq 3.7 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -175000:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-52}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -3.9e+183)
     t_1
     (if (<= x -175000.0) (* y (* x 2.0)) (if (<= x 4.5e-52) (* 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 <= -3.9e+183) {
		tmp = t_1;
	} else if (x <= -175000.0) {
		tmp = y * (x * 2.0);
	} else if (x <= 4.5e-52) {
		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 <= (-3.9d+183)) then
        tmp = t_1
    else if (x <= (-175000.0d0)) then
        tmp = y * (x * 2.0d0)
    else if (x <= 4.5d-52) 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 <= -3.9e+183) {
		tmp = t_1;
	} else if (x <= -175000.0) {
		tmp = y * (x * 2.0);
	} else if (x <= 4.5e-52) {
		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 <= -3.9e+183:
		tmp = t_1
	elif x <= -175000.0:
		tmp = y * (x * 2.0)
	elif x <= 4.5e-52:
		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 <= -3.9e+183)
		tmp = t_1;
	elseif (x <= -175000.0)
		tmp = Float64(y * Float64(x * 2.0));
	elseif (x <= 4.5e-52)
		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 <= -3.9e+183)
		tmp = t_1;
	elseif (x <= -175000.0)
		tmp = y * (x * 2.0);
	elseif (x <= 4.5e-52)
		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, -3.9e+183], t$95$1, If[LessEqual[x, -175000.0], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e-52], N[(y * 5.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.8999999999999999e183 or 4.5e-52 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 46.7%

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

   5. Simplified 46.7%

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

   if -3.8999999999999999e183 < x < -175000

   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 57.6%

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

   4. Taylor expanded in x around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. *-commutative 54.9%

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

      3. associate-*r* 54.9%

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

   6. Simplified 54.9%

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

   if -175000 < x < 4.5e-52

   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 65.0%

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

   5. Simplified 65.0%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+183}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -175000:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-52}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+47} \lor \neg \left(y \leq 8.2 \cdot 10^{+149}\right):\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.2e+47) (not (<= y 8.2e+149)))
   (* y (* x 2.0))
   (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e+47) || !(y <= 8.2e+149)) {
		tmp = y * (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 <= (-6.2d+47)) .or. (.not. (y <= 8.2d+149))) then
        tmp = y * (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 <= -6.2e+47) || !(y <= 8.2e+149)) {
		tmp = y * (x * 2.0);
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.2e+47) or not (y <= 8.2e+149):
		tmp = y * (x * 2.0)
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.2e+47) || !(y <= 8.2e+149))
		tmp = Float64(y * 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 <= -6.2e+47) || ~((y <= 8.2e+149)))
		tmp = y * (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, -6.2e+47], N[Not[LessEqual[y, 8.2e+149]], $MachinePrecision]], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000001e47 or 8.1999999999999992e149 < 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 88.7%

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

   4. Taylor expanded in x around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. *-commutative 53.0%

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

      3. associate-*r* 53.0%

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

   6. Simplified 53.0%

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

   if -6.2000000000000001e47 < y < 8.1999999999999992e149

   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 71.6%

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

   5. Simplified 71.6%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+47} \lor \neg \left(y \leq 8.2 \cdot 10^{+149}\right):\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1700000000 \lor \neg \left(y \leq 7 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1700000000.0) (not (<= y 7e+41)))
   (* 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 <= -1700000000.0) || !(y <= 7e+41)) {
		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 <= (-1700000000.0d0)) .or. (.not. (y <= 7d+41))) 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 <= -1700000000.0) || !(y <= 7e+41)) {
		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 <= -1700000000.0) or not (y <= 7e+41):
		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 <= -1700000000.0) || !(y <= 7e+41))
		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 <= -1700000000.0) || ~((y <= 7e+41)))
		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, -1700000000.0], N[Not[LessEqual[y, 7e+41]], $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 < -1.7e9 or 6.9999999999999998e41 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.7%

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

   if -1.7e9 < y < 6.9999999999999998e41

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.4%

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

   5. Simplified 77.4%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1700000000 \lor \neg \left(y \leq 7 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-32} \lor \neg \left(x \leq 6 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.5e-32) (not (<= x 6e-8))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.5e-32) || !(x <= 6e-8)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.5d-32)) .or. (.not. (x <= 6d-8))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.5e-32) || !(x <= 6e-8)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.5e-32) or not (x <= 6e-8):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.5e-32) || !(x <= 6e-8))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.5e-32) || ~((x <= 6e-8)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.5e-32], N[Not[LessEqual[x, 6e-8]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.50000000000000005e-32 or 5.99999999999999946e-8 < 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 32.7%

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

   5. Simplified 32.7%

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

   if -4.50000000000000005e-32 < x < 5.99999999999999946e-8

   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 64.3%

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

   5. Simplified 64.3%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-32} \lor \neg \left(x \leq 6 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.2% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ x \cdot t \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x * t), $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 t around inf 26.4%

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

5. Simplified 26.4%

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

6. Final simplification 26.4%

   \[\leadsto x \cdot t \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(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)))