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

Percentage Accurate: 99.9% → 99.9%

Time: 15.1s

Alternatives: 15

Speedup: 1.0×

• 25.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-define 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+212} \lor \neg \left(x \leq 1.95 \cdot 10^{+235}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 y)))))
   (if (<= x -1.7e-12)
     t_1
     (if (<= x 6.2e-48)
       (* y 5.0)
       (if (or (<= x 1.25e+212) (not (<= x 1.95e+235)))
         t_1
         (* z (* x 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -1.7e-12) {
		tmp = t_1;
	} else if (x <= 6.2e-48) {
		tmp = y * 5.0;
	} else if ((x <= 1.25e+212) || !(x <= 1.95e+235)) {
		tmp = t_1;
	} else {
		tmp = z * (x * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * y))
    if (x <= (-1.7d-12)) then
        tmp = t_1
    else if (x <= 6.2d-48) then
        tmp = y * 5.0d0
    else if ((x <= 1.25d+212) .or. (.not. (x <= 1.95d+235))) then
        tmp = t_1
    else
        tmp = z * (x * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -1.7e-12) {
		tmp = t_1;
	} else if (x <= 6.2e-48) {
		tmp = y * 5.0;
	} else if ((x <= 1.25e+212) || !(x <= 1.95e+235)) {
		tmp = t_1;
	} else {
		tmp = z * (x * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * y))
	tmp = 0
	if x <= -1.7e-12:
		tmp = t_1
	elif x <= 6.2e-48:
		tmp = y * 5.0
	elif (x <= 1.25e+212) or not (x <= 1.95e+235):
		tmp = t_1
	else:
		tmp = z * (x * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (x <= -1.7e-12)
		tmp = t_1;
	elseif (x <= 6.2e-48)
		tmp = Float64(y * 5.0);
	elseif ((x <= 1.25e+212) || !(x <= 1.95e+235))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (x <= -1.7e-12)
		tmp = t_1;
	elseif (x <= 6.2e-48)
		tmp = y * 5.0;
	elseif ((x <= 1.25e+212) || ~((x <= 1.95e+235)))
		tmp = t_1;
	else
		tmp = z * (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e-12], t$95$1, If[LessEqual[x, 6.2e-48], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 1.25e+212], N[Not[LessEqual[x, 1.95e+235]], $MachinePrecision]], t$95$1, N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7e-12 or 6.20000000000000033e-48 < x < 1.24999999999999998e212 or 1.9500000000000001e235 < x

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.6%

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

   6. Taylor expanded in z around 0 76.4%

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

   if -1.7e-12 < x < 6.20000000000000033e-48

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 63.8%

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

   if 1.24999999999999998e212 < x < 1.9500000000000001e235

   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 86.1%

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

   5. Simplified 86.1%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+212} \lor \neg \left(x \leq 1.95 \cdot 10^{+235}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot z\right)\\ t_2 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+212}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 z)))) (t_2 (* x (+ t (* 2.0 y)))))
   (if (<= x -8e+41)
     t_2
     (if (<= x -2.8e-101)
       t_1
       (if (<= x 5.5e-48) (* y 5.0) (if (<= x 1.25e+212) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -8e+41) {
		tmp = t_2;
	} else if (x <= -2.8e-101) {
		tmp = t_1;
	} else if (x <= 5.5e-48) {
		tmp = y * 5.0;
	} else if (x <= 1.25e+212) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * z))
    t_2 = x * (t + (2.0d0 * y))
    if (x <= (-8d+41)) then
        tmp = t_2
    else if (x <= (-2.8d-101)) then
        tmp = t_1
    else if (x <= 5.5d-48) then
        tmp = y * 5.0d0
    else if (x <= 1.25d+212) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (x <= -8e+41) {
		tmp = t_2;
	} else if (x <= -2.8e-101) {
		tmp = t_1;
	} else if (x <= 5.5e-48) {
		tmp = y * 5.0;
	} else if (x <= 1.25e+212) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * z))
	t_2 = x * (t + (2.0 * y))
	tmp = 0
	if x <= -8e+41:
		tmp = t_2
	elif x <= -2.8e-101:
		tmp = t_1
	elif x <= 5.5e-48:
		tmp = y * 5.0
	elif x <= 1.25e+212:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * z)))
	t_2 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (x <= -8e+41)
		tmp = t_2;
	elseif (x <= -2.8e-101)
		tmp = t_1;
	elseif (x <= 5.5e-48)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.25e+212)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * z));
	t_2 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (x <= -8e+41)
		tmp = t_2;
	elseif (x <= -2.8e-101)
		tmp = t_1;
	elseif (x <= 5.5e-48)
		tmp = y * 5.0;
	elseif (x <= 1.25e+212)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+41], t$95$2, If[LessEqual[x, -2.8e-101], t$95$1, If[LessEqual[x, 5.5e-48], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.25e+212], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.00000000000000005e41 or 5.50000000000000047e-48 < x < 1.24999999999999998e212

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.5%

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

   6. Taylor expanded in z around 0 77.8%

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

   if -8.00000000000000005e41 < x < -2.79999999999999989e-101 or 1.24999999999999998e212 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.0%

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

   if -2.79999999999999989e-101 < x < 5.50000000000000047e-48

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 68.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+211} \lor \neg \left(x \leq 2.55 \cdot 10^{+238}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.02e-8)
   (* y (* x 2.0))
   (if (<= x 8.5e-48)
     (* y 5.0)
     (if (or (<= x 5.2e+211) (not (<= x 2.55e+238)))
       (* x t)
       (* z (* x 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.02e-8) {
		tmp = y * (x * 2.0);
	} else if (x <= 8.5e-48) {
		tmp = y * 5.0;
	} else if ((x <= 5.2e+211) || !(x <= 2.55e+238)) {
		tmp = x * t;
	} else {
		tmp = z * (x * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.02d-8)) then
        tmp = y * (x * 2.0d0)
    else if (x <= 8.5d-48) then
        tmp = y * 5.0d0
    else if ((x <= 5.2d+211) .or. (.not. (x <= 2.55d+238))) then
        tmp = x * t
    else
        tmp = z * (x * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.02e-8) {
		tmp = y * (x * 2.0);
	} else if (x <= 8.5e-48) {
		tmp = y * 5.0;
	} else if ((x <= 5.2e+211) || !(x <= 2.55e+238)) {
		tmp = x * t;
	} else {
		tmp = z * (x * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.02e-8:
		tmp = y * (x * 2.0)
	elif x <= 8.5e-48:
		tmp = y * 5.0
	elif (x <= 5.2e+211) or not (x <= 2.55e+238):
		tmp = x * t
	else:
		tmp = z * (x * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.02e-8)
		tmp = Float64(y * Float64(x * 2.0));
	elseif (x <= 8.5e-48)
		tmp = Float64(y * 5.0);
	elseif ((x <= 5.2e+211) || !(x <= 2.55e+238))
		tmp = Float64(x * t);
	else
		tmp = Float64(z * Float64(x * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.02e-8)
		tmp = y * (x * 2.0);
	elseif (x <= 8.5e-48)
		tmp = y * 5.0;
	elseif ((x <= 5.2e+211) || ~((x <= 2.55e+238)))
		tmp = x * t;
	else
		tmp = z * (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.02e-8], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-48], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 5.2e+211], N[Not[LessEqual[x, 2.55e+238]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.02000000000000003e-8

   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 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in x around inf 48.1%

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

      1. *-commutative 48.1%

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

      2. *-commutative 48.1%

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

      3. associate-*r* 48.1%

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

   8. Simplified 48.1%

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

   if -1.02000000000000003e-8 < x < 8.5000000000000004e-48

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 63.3%

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

   if 8.5000000000000004e-48 < x < 5.1999999999999997e211 or 2.5500000000000001e238 < 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 45.1%

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

   5. Simplified 45.1%

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

   if 5.1999999999999997e211 < x < 2.5500000000000001e238

   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 86.1%

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

   5. Simplified 86.1%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+211} \lor \neg \left(x \leq 2.55 \cdot 10^{+238}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+168} \lor \neg \left(y \leq 9 \cdot 10^{+77}\right):\\ \;\;\;\;y \cdot 5 + x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(t\_1 + 5 \cdot \frac{y}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (or (<= y -3.1e+168) (not (<= y 9e+77)))
     (+ (* y 5.0) (* x t_1))
     (* x (+ t (+ t_1 (* 5.0 (/ y x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if ((y <= -3.1e+168) || !(y <= 9e+77)) {
		tmp = (y * 5.0) + (x * t_1);
	} else {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    if ((y <= (-3.1d+168)) .or. (.not. (y <= 9d+77))) then
        tmp = (y * 5.0d0) + (x * t_1)
    else
        tmp = x * (t + (t_1 + (5.0d0 * (y / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if ((y <= -3.1e+168) || !(y <= 9e+77)) {
		tmp = (y * 5.0) + (x * t_1);
	} else {
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if (y <= -3.1e+168) or not (y <= 9e+77):
		tmp = (y * 5.0) + (x * t_1)
	else:
		tmp = x * (t + (t_1 + (5.0 * (y / x))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if ((y <= -3.1e+168) || !(y <= 9e+77))
		tmp = Float64(Float64(y * 5.0) + Float64(x * t_1));
	else
		tmp = Float64(x * Float64(t + Float64(t_1 + Float64(5.0 * Float64(y / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if ((y <= -3.1e+168) || ~((y <= 9e+77)))
		tmp = (y * 5.0) + (x * t_1);
	else
		tmp = x * (t + (t_1 + (5.0 * (y / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -3.1e+168], N[Not[LessEqual[y, 9e+77]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(t$95$1 + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.09999999999999996e168 or 9.00000000000000049e77 < 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 t around 0 96.5%

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

   5. Simplified 96.5%

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

   if -3.09999999999999996e168 < y < 9.00000000000000049e77

   1. Initial program 99.9%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.3%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+168} \lor \neg \left(y \leq 9 \cdot 10^{+77}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+27}:\\ \;\;\;\;y \cdot 5 + x \cdot t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+27}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(t\_1 + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (<= z -9.6e+27)
     (+ (* y 5.0) (* x t_1))
     (if (<= z 3.1e+27)
       (+ (* y 5.0) (* x (+ t (+ y y))))
       (if (<= z 3.1e+159) (* x (+ t_1 t)) (+ (* y 5.0) (* x (* 2.0 z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if (z <= -9.6e+27) {
		tmp = (y * 5.0) + (x * t_1);
	} else if (z <= 3.1e+27) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else if (z <= 3.1e+159) {
		tmp = x * (t_1 + t);
	} else {
		tmp = (y * 5.0) + (x * (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 = 2.0d0 * (y + z)
    if (z <= (-9.6d+27)) then
        tmp = (y * 5.0d0) + (x * t_1)
    else if (z <= 3.1d+27) then
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    else if (z <= 3.1d+159) then
        tmp = x * (t_1 + t)
    else
        tmp = (y * 5.0d0) + (x * (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 = 2.0 * (y + z);
	double tmp;
	if (z <= -9.6e+27) {
		tmp = (y * 5.0) + (x * t_1);
	} else if (z <= 3.1e+27) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else if (z <= 3.1e+159) {
		tmp = x * (t_1 + t);
	} else {
		tmp = (y * 5.0) + (x * (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if z <= -9.6e+27:
		tmp = (y * 5.0) + (x * t_1)
	elif z <= 3.1e+27:
		tmp = (y * 5.0) + (x * (t + (y + y)))
	elif z <= 3.1e+159:
		tmp = x * (t_1 + t)
	else:
		tmp = (y * 5.0) + (x * (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if (z <= -9.6e+27)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t_1));
	elseif (z <= 3.1e+27)
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	elseif (z <= 3.1e+159)
		tmp = Float64(x * Float64(t_1 + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(2.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if (z <= -9.6e+27)
		tmp = (y * 5.0) + (x * t_1);
	elseif (z <= 3.1e+27)
		tmp = (y * 5.0) + (x * (t + (y + y)));
	elseif (z <= 3.1e+159)
		tmp = x * (t_1 + t);
	else
		tmp = (y * 5.0) + (x * (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+27], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+27], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+159], N[(x * N[(t$95$1 + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.59999999999999991e27

   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 89.7%

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

   5. Simplified 89.7%

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

   if -9.59999999999999991e27 < z < 3.09999999999999996e27

   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 95.6%

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

   if 3.09999999999999996e27 < z < 3.0999999999999998e159

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 87.0%

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

   if 3.0999999999999998e159 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in y around 0 93.6%

      \[\leadsto x \cdot \left(2 \cdot \color{blue}{z}\right) + y \cdot 5 \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+27}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+27}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ t_2 := x \cdot \left(t\_1 + t\right)\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-194}:\\ \;\;\;\;y \cdot 5 + x \cdot t\_1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))) (t_2 (* x (+ t_1 t))))
   (if (<= x -4.6e-12)
     t_2
     (if (<= x -4.5e-194)
       (+ (* y 5.0) (* x t_1))
       (if (<= x 7.8e-48) (+ (* y 5.0) (* x t)) 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 <= -4.6e-12) {
		tmp = t_2;
	} else if (x <= -4.5e-194) {
		tmp = (y * 5.0) + (x * t_1);
	} else if (x <= 7.8e-48) {
		tmp = (y * 5.0) + (x * t);
	} 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 <= (-4.6d-12)) then
        tmp = t_2
    else if (x <= (-4.5d-194)) then
        tmp = (y * 5.0d0) + (x * t_1)
    else if (x <= 7.8d-48) then
        tmp = (y * 5.0d0) + (x * t)
    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 <= -4.6e-12) {
		tmp = t_2;
	} else if (x <= -4.5e-194) {
		tmp = (y * 5.0) + (x * t_1);
	} else if (x <= 7.8e-48) {
		tmp = (y * 5.0) + (x * t);
	} 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 <= -4.6e-12:
		tmp = t_2
	elif x <= -4.5e-194:
		tmp = (y * 5.0) + (x * t_1)
	elif x <= 7.8e-48:
		tmp = (y * 5.0) + (x * t)
	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 <= -4.6e-12)
		tmp = t_2;
	elseif (x <= -4.5e-194)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t_1));
	elseif (x <= 7.8e-48)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	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 <= -4.6e-12)
		tmp = t_2;
	elseif (x <= -4.5e-194)
		tmp = (y * 5.0) + (x * t_1);
	elseif (x <= 7.8e-48)
		tmp = (y * 5.0) + (x * t);
	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, -4.6e-12], t$95$2, If[LessEqual[x, -4.5e-194], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e-48], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.59999999999999979e-12 or 7.800000000000001e-48 < x

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.6%

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

   if -4.59999999999999979e-12 < x < -4.4999999999999999e-194

   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 88.6%

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

   5. Simplified 88.6%

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

   if -4.4999999999999999e-194 < x < 7.800000000000001e-48

   1. Initial program 99.8%

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

      1. fma-define 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 65.5%

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

   6. Taylor expanded in t around inf 62.8%

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

   7. Taylor expanded in x around 0 71.2%

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

      1. associate-*r/ 71.4%

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

      2. *-commutative 71.4%

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

      3. associate-/l* 71.3%

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

   9. Simplified 71.3%

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

   10. Taylor expanded in t around 0 89.1%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-194}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-194}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot z\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ (* 2.0 (+ y z)) t))))
   (if (<= x -1.65e-12)
     t_1
     (if (<= x -1.2e-194)
       (+ (* y 5.0) (* x (* 2.0 z)))
       (if (<= x 9e-48) (+ (* y 5.0) (* x t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((2.0 * (y + z)) + t);
	double tmp;
	if (x <= -1.65e-12) {
		tmp = t_1;
	} else if (x <= -1.2e-194) {
		tmp = (y * 5.0) + (x * (2.0 * z));
	} else if (x <= 9e-48) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((2.0d0 * (y + z)) + t)
    if (x <= (-1.65d-12)) then
        tmp = t_1
    else if (x <= (-1.2d-194)) then
        tmp = (y * 5.0d0) + (x * (2.0d0 * z))
    else if (x <= 9d-48) then
        tmp = (y * 5.0d0) + (x * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((2.0 * (y + z)) + t);
	double tmp;
	if (x <= -1.65e-12) {
		tmp = t_1;
	} else if (x <= -1.2e-194) {
		tmp = (y * 5.0) + (x * (2.0 * z));
	} else if (x <= 9e-48) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((2.0 * (y + z)) + t)
	tmp = 0
	if x <= -1.65e-12:
		tmp = t_1
	elif x <= -1.2e-194:
		tmp = (y * 5.0) + (x * (2.0 * z))
	elif x <= 9e-48:
		tmp = (y * 5.0) + (x * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t))
	tmp = 0.0
	if (x <= -1.65e-12)
		tmp = t_1;
	elseif (x <= -1.2e-194)
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(2.0 * z)));
	elseif (x <= 9e-48)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((2.0 * (y + z)) + t);
	tmp = 0.0;
	if (x <= -1.65e-12)
		tmp = t_1;
	elseif (x <= -1.2e-194)
		tmp = (y * 5.0) + (x * (2.0 * z));
	elseif (x <= 9e-48)
		tmp = (y * 5.0) + (x * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e-12], t$95$1, If[LessEqual[x, -1.2e-194], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-48], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e-12 or 8.99999999999999977e-48 < x

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.6%

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

   if -1.65e-12 < x < -1.2e-194

   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 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in y around 0 88.5%

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

   if -1.2e-194 < x < 8.99999999999999977e-48

   1. Initial program 99.8%

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

      1. fma-define 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 65.5%

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

   6. Taylor expanded in t around inf 62.8%

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

   7. Taylor expanded in x around 0 71.2%

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

      1. associate-*r/ 71.4%

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

      2. *-commutative 71.4%

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

      3. associate-/l* 71.3%

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

   9. Simplified 71.3%

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

   10. Taylor expanded in t around 0 89.1%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-194}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot z\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+37} \lor \neg \left(y \leq 6.6 \cdot 10^{+77}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(5 \cdot \frac{y}{x} + 2 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.6e+37) (not (<= y 6.6e+77)))
   (+ (* y 5.0) (* x (* 2.0 (+ y z))))
   (* x (+ t (+ (* 5.0 (/ y x)) (* 2.0 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.6e+37) || !(y <= 6.6e+77)) {
		tmp = (y * 5.0) + (x * (2.0 * (y + z)));
	} else {
		tmp = x * (t + ((5.0 * (y / x)) + (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 <= (-6.6d+37)) .or. (.not. (y <= 6.6d+77))) then
        tmp = (y * 5.0d0) + (x * (2.0d0 * (y + z)))
    else
        tmp = x * (t + ((5.0d0 * (y / x)) + (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 <= -6.6e+37) || !(y <= 6.6e+77)) {
		tmp = (y * 5.0) + (x * (2.0 * (y + z)));
	} else {
		tmp = x * (t + ((5.0 * (y / x)) + (2.0 * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.6e+37) or not (y <= 6.6e+77):
		tmp = (y * 5.0) + (x * (2.0 * (y + z)))
	else:
		tmp = x * (t + ((5.0 * (y / x)) + (2.0 * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.6e+37) || !(y <= 6.6e+77))
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(x * Float64(t + Float64(Float64(5.0 * Float64(y / x)) + Float64(2.0 * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.6e+37) || ~((y <= 6.6e+77)))
		tmp = (y * 5.0) + (x * (2.0 * (y + z)));
	else
		tmp = x * (t + ((5.0 * (y / x)) + (2.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.6e+37], N[Not[LessEqual[y, 6.6e+77]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.6000000000000002e37 or 6.5999999999999996e77 < 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 t around 0 94.9%

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

   5. Simplified 94.9%

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

   if -6.6000000000000002e37 < y < 6.5999999999999996e77

   1. Initial program 99.9%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.9%

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

   6. Taylor expanded in y around 0 92.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+37} \lor \neg \left(y \leq 6.6 \cdot 10^{+77}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(5 \cdot \frac{y}{x} + 2 \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-51} \lor \neg \left(x \leq 7 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.4e-51) (not (<= x 7e-48)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.4e-51) || !(x <= 7e-48)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.4d-51)) .or. (.not. (x <= 7d-48))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.4e-51) || !(x <= 7e-48)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.4e-51) or not (x <= 7e-48):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.4e-51) || !(x <= 7e-48))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.4e-51) || ~((x <= 7e-48)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.4e-51], N[Not[LessEqual[x, 7e-48]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.40000000000000003e-51 or 6.99999999999999982e-48 < x

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.1%

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

   if -3.40000000000000003e-51 < x < 6.99999999999999982e-48

   1. Initial program 99.8%

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

      1. fma-define 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 72.5%

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

   6. Taylor expanded in t around inf 63.9%

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

   7. Taylor expanded in x around 0 66.7%

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

      1. associate-*r/ 66.8%

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

      2. *-commutative 66.8%

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

      3. associate-/l* 66.7%

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

   9. Simplified 66.7%

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

   10. Taylor expanded in t around 0 82.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-51} \lor \neg \left(x \leq 7 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+21} \lor \neg \left(y \leq 7.8 \cdot 10^{+77}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.55e+21) (not (<= y 7.8e+77)))
   (* 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 <= -1.55e+21) || !(y <= 7.8e+77)) {
		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 <= (-1.55d+21)) .or. (.not. (y <= 7.8d+77))) 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 <= -1.55e+21) || !(y <= 7.8e+77)) {
		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 <= -1.55e+21) or not (y <= 7.8e+77):
		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 <= -1.55e+21) || !(y <= 7.8e+77))
		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 <= -1.55e+21) || ~((y <= 7.8e+77)))
		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, -1.55e+21], N[Not[LessEqual[y, 7.8e+77]], $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 < -1.55e21 or 7.7999999999999995e77 < 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 83.1%

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

   5. Simplified 83.1%

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

   if -1.55e21 < y < 7.7999999999999995e77

   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 78.6%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+21} \lor \neg \left(y \leq 7.8 \cdot 10^{+77}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 13: 47.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-12} \lor \neg \left(x \leq 6.5 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.6e-12) (not (<= x 6.5e-48))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-12) || !(x <= 6.5e-48)) {
		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 <= (-7.6d-12)) .or. (.not. (x <= 6.5d-48))) 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 <= -7.6e-12) || !(x <= 6.5e-48)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.6e-12) or not (x <= 6.5e-48):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.6e-12) || !(x <= 6.5e-48))
		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 <= -7.6e-12) || ~((x <= 6.5e-48)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.6e-12], N[Not[LessEqual[x, 6.5e-48]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.59999999999999993e-12 or 6.5e-48 < 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 39.0%

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

   5. Simplified 39.0%

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

   if -7.59999999999999993e-12 < x < 6.5e-48

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 63.8%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-12} \lor \neg \left(x \leq 6.5 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.02e-8) (* y (* x 2.0)) (if (<= x 4.8e-48) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.02e-8) {
		tmp = y * (x * 2.0);
	} else if (x <= 4.8e-48) {
		tmp = y * 5.0;
	} else {
		tmp = 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 <= (-1.02d-8)) then
        tmp = y * (x * 2.0d0)
    else if (x <= 4.8d-48) then
        tmp = y * 5.0d0
    else
        tmp = 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 <= -1.02e-8) {
		tmp = y * (x * 2.0);
	} else if (x <= 4.8e-48) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.02e-8:
		tmp = y * (x * 2.0)
	elif x <= 4.8e-48:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.02e-8)
		tmp = Float64(y * Float64(x * 2.0));
	elseif (x <= 4.8e-48)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.02e-8)
		tmp = y * (x * 2.0);
	elseif (x <= 4.8e-48)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.02e-8], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e-48], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02000000000000003e-8

   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 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in x around inf 48.1%

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

      1. *-commutative 48.1%

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

      2. *-commutative 48.1%

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

      3. associate-*r* 48.1%

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

   8. Simplified 48.1%

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

   if -1.02000000000000003e-8 < x < 4.8e-48

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 63.3%

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

   if 4.8e-48 < 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 42.0%

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

   5. Simplified 42.0%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-48}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.5% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 28.9%

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

4. Final simplification 28.9%

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

Reproduce

herbie shell --seed 2024110 
(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)))