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

Percentage Accurate: 99.9% → 99.9%

Time: 10.4s

Alternatives: 16

Speedup: 1.0×

• 26.8% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

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

   3. associate-+l+ 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. fma-def 100.0%

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

   2. associate-+l+ 100.0%

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

   3. +-commutative 100.0%

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

   4. count-2 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 3: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -240000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-24}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+101} \lor \neg \left(x \leq 8.5 \cdot 10^{+186}\right) \land x \leq 8.5 \cdot 10^{+304}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))))
   (if (<= x -240000000000.0)
     t_1
     (if (<= x -1.4e-163)
       (* x (+ t (* z 2.0)))
       (if (<= x 8e-24)
         (* y 5.0)
         (if (or (<= x 2.55e+101) (and (not (<= x 8.5e+186)) (<= x 8.5e+304)))
           (* x (* 2.0 (+ y z)))
           t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -240000000000.0) {
		tmp = t_1;
	} else if (x <= -1.4e-163) {
		tmp = x * (t + (z * 2.0));
	} else if (x <= 8e-24) {
		tmp = y * 5.0;
	} else if ((x <= 2.55e+101) || (!(x <= 8.5e+186) && (x <= 8.5e+304))) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (y * 2.0d0))
    if (x <= (-240000000000.0d0)) then
        tmp = t_1
    else if (x <= (-1.4d-163)) then
        tmp = x * (t + (z * 2.0d0))
    else if (x <= 8d-24) then
        tmp = y * 5.0d0
    else if ((x <= 2.55d+101) .or. (.not. (x <= 8.5d+186)) .and. (x <= 8.5d+304)) then
        tmp = x * (2.0d0 * (y + z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -240000000000.0) {
		tmp = t_1;
	} else if (x <= -1.4e-163) {
		tmp = x * (t + (z * 2.0));
	} else if (x <= 8e-24) {
		tmp = y * 5.0;
	} else if ((x <= 2.55e+101) || (!(x <= 8.5e+186) && (x <= 8.5e+304))) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	tmp = 0
	if x <= -240000000000.0:
		tmp = t_1
	elif x <= -1.4e-163:
		tmp = x * (t + (z * 2.0))
	elif x <= 8e-24:
		tmp = y * 5.0
	elif (x <= 2.55e+101) or (not (x <= 8.5e+186) and (x <= 8.5e+304)):
		tmp = x * (2.0 * (y + z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y * 2.0)))
	tmp = 0.0
	if (x <= -240000000000.0)
		tmp = t_1;
	elseif (x <= -1.4e-163)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (x <= 8e-24)
		tmp = Float64(y * 5.0);
	elseif ((x <= 2.55e+101) || (!(x <= 8.5e+186) && (x <= 8.5e+304)))
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y * 2.0));
	tmp = 0.0;
	if (x <= -240000000000.0)
		tmp = t_1;
	elseif (x <= -1.4e-163)
		tmp = x * (t + (z * 2.0));
	elseif (x <= 8e-24)
		tmp = y * 5.0;
	elseif ((x <= 2.55e+101) || (~((x <= 8.5e+186)) && (x <= 8.5e+304)))
		tmp = x * (2.0 * (y + z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -240000000000.0], t$95$1, If[LessEqual[x, -1.4e-163], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-24], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 2.55e+101], And[N[Not[LessEqual[x, 8.5e+186]], $MachinePrecision], LessEqual[x, 8.5e+304]]], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4e11 or 2.54999999999999997e101 < x < 8.4999999999999999e186 or 8.5000000000000005e304 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.3%

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

   4. Taylor expanded in z around 0 84.4%

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

   5. Taylor expanded in x around inf 86.7%

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

   if -2.4e11 < x < -1.4e-163

   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 62.1%

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

   if -1.4e-163 < x < 7.99999999999999939e-24

   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 66.6%

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

   if 7.99999999999999939e-24 < x < 2.54999999999999997e101 or 8.4999999999999999e186 < x < 8.5000000000000005e304

   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 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in x around inf 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-*r* 81.3%

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

      3. *-commutative 81.3%

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

   8. Simplified 81.3%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -240000000000:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-24}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+101} \lor \neg \left(x \leq 8.5 \cdot 10^{+186}\right) \land x \leq 8.5 \cdot 10^{+304}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+101} \lor \neg \left(x \leq 1.2 \cdot 10^{+184}\right) \land x \leq 1.75 \cdot 10^{+305}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))))
   (if (<= x -200.0)
     t_1
     (if (<= x 5.6e-27)
       (* y 5.0)
       (if (or (<= x 1.15e+101) (and (not (<= x 1.2e+184)) (<= x 1.75e+305)))
         (* x (* 2.0 (+ y z)))
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -200.0) {
		tmp = t_1;
	} else if (x <= 5.6e-27) {
		tmp = y * 5.0;
	} else if ((x <= 1.15e+101) || (!(x <= 1.2e+184) && (x <= 1.75e+305))) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (y * 2.0d0))
    if (x <= (-200.0d0)) then
        tmp = t_1
    else if (x <= 5.6d-27) then
        tmp = y * 5.0d0
    else if ((x <= 1.15d+101) .or. (.not. (x <= 1.2d+184)) .and. (x <= 1.75d+305)) then
        tmp = x * (2.0d0 * (y + z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -200.0) {
		tmp = t_1;
	} else if (x <= 5.6e-27) {
		tmp = y * 5.0;
	} else if ((x <= 1.15e+101) || (!(x <= 1.2e+184) && (x <= 1.75e+305))) {
		tmp = x * (2.0 * (y + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	tmp = 0
	if x <= -200.0:
		tmp = t_1
	elif x <= 5.6e-27:
		tmp = y * 5.0
	elif (x <= 1.15e+101) or (not (x <= 1.2e+184) and (x <= 1.75e+305)):
		tmp = x * (2.0 * (y + z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y * 2.0)))
	tmp = 0.0
	if (x <= -200.0)
		tmp = t_1;
	elseif (x <= 5.6e-27)
		tmp = Float64(y * 5.0);
	elseif ((x <= 1.15e+101) || (!(x <= 1.2e+184) && (x <= 1.75e+305)))
		tmp = Float64(x * Float64(2.0 * Float64(y + z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y * 2.0));
	tmp = 0.0;
	if (x <= -200.0)
		tmp = t_1;
	elseif (x <= 5.6e-27)
		tmp = y * 5.0;
	elseif ((x <= 1.15e+101) || (~((x <= 1.2e+184)) && (x <= 1.75e+305)))
		tmp = x * (2.0 * (y + z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -200.0], t$95$1, If[LessEqual[x, 5.6e-27], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 1.15e+101], And[N[Not[LessEqual[x, 1.2e+184]], $MachinePrecision], LessEqual[x, 1.75e+305]]], N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -200 or 1.1500000000000001e101 < x < 1.19999999999999998e184 or 1.75e305 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.3%

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

   4. Taylor expanded in z around 0 84.4%

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

   5. Taylor expanded in x around inf 86.7%

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

   if -200 < x < 5.5999999999999999e-27

   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 58.5%

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

   if 5.5999999999999999e-27 < x < 1.1500000000000001e101 or 1.19999999999999998e184 < x < 1.75e305

   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 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in x around inf 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-*r* 81.3%

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

      3. *-commutative 81.3%

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

   8. Simplified 81.3%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -200:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+101} \lor \neg \left(x \leq 1.2 \cdot 10^{+184}\right) \land x \leq 1.75 \cdot 10^{+305}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+101}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-79} \lor \neg \left(x \leq 2.7 \cdot 10^{-25}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* 2.0 (+ y z)))))
   (if (<= x -5.5e+221)
     t_1
     (if (<= x -5.4e+101)
       (* x t)
       (if (or (<= x -1.8e-79) (not (<= x 2.7e-25))) t_1 (* y 5.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -5.5e+221) {
		tmp = t_1;
	} else if (x <= -5.4e+101) {
		tmp = x * t;
	} else if ((x <= -1.8e-79) || !(x <= 2.7e-25)) {
		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 = x * (2.0d0 * (y + z))
    if (x <= (-5.5d+221)) then
        tmp = t_1
    else if (x <= (-5.4d+101)) then
        tmp = x * t
    else if ((x <= (-1.8d-79)) .or. (.not. (x <= 2.7d-25))) 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 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -5.5e+221) {
		tmp = t_1;
	} else if (x <= -5.4e+101) {
		tmp = x * t;
	} else if ((x <= -1.8e-79) || !(x <= 2.7e-25)) {
		tmp = t_1;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (2.0 * (y + z))
	tmp = 0
	if x <= -5.5e+221:
		tmp = t_1
	elif x <= -5.4e+101:
		tmp = x * t
	elif (x <= -1.8e-79) or not (x <= 2.7e-25):
		tmp = t_1
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(2.0 * Float64(y + z)))
	tmp = 0.0
	if (x <= -5.5e+221)
		tmp = t_1;
	elseif (x <= -5.4e+101)
		tmp = Float64(x * t);
	elseif ((x <= -1.8e-79) || !(x <= 2.7e-25))
		tmp = t_1;
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (2.0 * (y + z));
	tmp = 0.0;
	if (x <= -5.5e+221)
		tmp = t_1;
	elseif (x <= -5.4e+101)
		tmp = x * t;
	elseif ((x <= -1.8e-79) || ~((x <= 2.7e-25)))
		tmp = t_1;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e+221], t$95$1, If[LessEqual[x, -5.4e+101], N[(x * t), $MachinePrecision], If[Or[LessEqual[x, -1.8e-79], N[Not[LessEqual[x, 2.7e-25]], $MachinePrecision]], t$95$1, N[(y * 5.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5000000000000003e221 or -5.40000000000000012e101 < x < -1.8000000000000001e-79 or 2.70000000000000016e-25 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in x around inf 72.3%

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

      1. *-commutative 72.3%

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

      2. associate-*r* 72.3%

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

      3. *-commutative 72.3%

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

   8. Simplified 72.3%

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

   if -5.5000000000000003e221 < x < -5.40000000000000012e101

   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 73.2%

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

   5. Simplified 73.2%

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

   if -1.8000000000000001e-79 < x < 2.70000000000000016e-25

   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 61.5%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+221}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+101}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-79} \lor \neg \left(x \leq 2.7 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + x \cdot t\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* x t))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -4.3e+114)
     t_2
     (if (<= y -1.12e-7)
       t_1
       (if (<= y 2.2e-14)
         (* x (+ t (* z 2.0)))
         (if (<= y 7.6e+62) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -4.3e+114) {
		tmp = t_2;
	} else if (y <= -1.12e-7) {
		tmp = t_1;
	} else if (y <= 2.2e-14) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 7.6e+62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * 5.0d0) + (x * t)
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-4.3d+114)) then
        tmp = t_2
    else if (y <= (-1.12d-7)) then
        tmp = t_1
    else if (y <= 2.2d-14) then
        tmp = x * (t + (z * 2.0d0))
    else if (y <= 7.6d+62) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -4.3e+114) {
		tmp = t_2;
	} else if (y <= -1.12e-7) {
		tmp = t_1;
	} else if (y <= 2.2e-14) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 7.6e+62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (x * t)
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -4.3e+114:
		tmp = t_2
	elif y <= -1.12e-7:
		tmp = t_1
	elif y <= 2.2e-14:
		tmp = x * (t + (z * 2.0))
	elif y <= 7.6e+62:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(x * t))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -4.3e+114)
		tmp = t_2;
	elseif (y <= -1.12e-7)
		tmp = t_1;
	elseif (y <= 2.2e-14)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (y <= 7.6e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (x * t);
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -4.3e+114)
		tmp = t_2;
	elseif (y <= -1.12e-7)
		tmp = t_1;
	elseif (y <= 2.2e-14)
		tmp = x * (t + (z * 2.0));
	elseif (y <= 7.6e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+114], t$95$2, If[LessEqual[y, -1.12e-7], t$95$1, If[LessEqual[y, 2.2e-14], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e+62], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3000000000000001e114 or 7.59999999999999967e62 < 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 93.7%

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

   5. Simplified 93.7%

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

   if -4.3000000000000001e114 < y < -1.12e-7 or 2.2000000000000001e-14 < y < 7.59999999999999967e62

   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 70.5%

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

   7. Taylor expanded in x around 0 70.5%

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

   if -1.12e-7 < y < 2.2000000000000001e-14

   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 82.2%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-7}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+62}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+101}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-23}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+101}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x 2.0))))
   (if (<= x -5.2e+101)
     (* x t)
     (if (<= x -200.0)
       t_1
       (if (<= x 9.6e-23)
         (* y 5.0)
         (if (<= x 1.95e+101) (* 2.0 (* x z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * 2.0);
	double tmp;
	if (x <= -5.2e+101) {
		tmp = x * t;
	} else if (x <= -200.0) {
		tmp = t_1;
	} else if (x <= 9.6e-23) {
		tmp = y * 5.0;
	} else if (x <= 1.95e+101) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * 2.0d0)
    if (x <= (-5.2d+101)) then
        tmp = x * t
    else if (x <= (-200.0d0)) then
        tmp = t_1
    else if (x <= 9.6d-23) then
        tmp = y * 5.0d0
    else if (x <= 1.95d+101) then
        tmp = 2.0d0 * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x * 2.0);
	double tmp;
	if (x <= -5.2e+101) {
		tmp = x * t;
	} else if (x <= -200.0) {
		tmp = t_1;
	} else if (x <= 9.6e-23) {
		tmp = y * 5.0;
	} else if (x <= 1.95e+101) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * 2.0)
	tmp = 0
	if x <= -5.2e+101:
		tmp = x * t
	elif x <= -200.0:
		tmp = t_1
	elif x <= 9.6e-23:
		tmp = y * 5.0
	elif x <= 1.95e+101:
		tmp = 2.0 * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * 2.0))
	tmp = 0.0
	if (x <= -5.2e+101)
		tmp = Float64(x * t);
	elseif (x <= -200.0)
		tmp = t_1;
	elseif (x <= 9.6e-23)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.95e+101)
		tmp = Float64(2.0 * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * 2.0);
	tmp = 0.0;
	if (x <= -5.2e+101)
		tmp = x * t;
	elseif (x <= -200.0)
		tmp = t_1;
	elseif (x <= 9.6e-23)
		tmp = y * 5.0;
	elseif (x <= 1.95e+101)
		tmp = 2.0 * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+101], N[(x * t), $MachinePrecision], If[LessEqual[x, -200.0], t$95$1, If[LessEqual[x, 9.6e-23], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.95e+101], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.2e101

   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 61.4%

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

   5. Simplified 61.4%

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

   if -5.2e101 < x < -200 or 1.95e101 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around 0 80.0%

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

   5. Taylor expanded in x around inf 79.9%

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

   6. Taylor expanded in t around 0 51.5%

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

      1. *-commutative 51.5%

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

      2. *-commutative 51.5%

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

      3. associate-*r* 51.5%

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

   8. Simplified 51.5%

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

   if -200 < x < 9.59999999999999986e-23

   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 58.5%

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

   if 9.59999999999999986e-23 < x < 1.95e101

   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 50.0%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+101}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -200:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-23}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+101}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-56} \lor \neg \left(y \leq 5.5 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9e-56) (not (<= y 5.5e-17)))
   (+ (* y (+ 5.0 (* x 2.0))) (* x t))
   (* x (+ t (* 2.0 (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e-56) || !(y <= 5.5e-17)) {
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	} else {
		tmp = x * (t + (2.0 * (y + z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9d-56)) .or. (.not. (y <= 5.5d-17))) then
        tmp = (y * (5.0d0 + (x * 2.0d0))) + (x * t)
    else
        tmp = x * (t + (2.0d0 * (y + z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e-56) || !(y <= 5.5e-17)) {
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	} else {
		tmp = x * (t + (2.0 * (y + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9e-56) or not (y <= 5.5e-17):
		tmp = (y * (5.0 + (x * 2.0))) + (x * t)
	else:
		tmp = x * (t + (2.0 * (y + z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9e-56) || !(y <= 5.5e-17))
		tmp = Float64(Float64(y * Float64(5.0 + Float64(x * 2.0))) + Float64(x * t));
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9e-56) || ~((y <= 5.5e-17)))
		tmp = (y * (5.0 + (x * 2.0))) + (x * t);
	else
		tmp = x * (t + (2.0 * (y + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9e-56], N[Not[LessEqual[y, 5.5e-17]], $MachinePrecision]], N[(N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.0000000000000001e-56 or 5.50000000000000001e-17 < 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 0 97.9%

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

   4. Taylor expanded in z around 0 87.7%

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

   if -9.0000000000000001e-56 < y < 5.50000000000000001e-17

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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 88.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-56} \lor \neg \left(y \leq 5.5 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+32} \lor \neg \left(x \leq 65000000000000\right):\\ \;\;\;\;x \cdot \left(t + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\_1 + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (or (<= x -1.1e+32) (not (<= x 65000000000000.0)))
     (* x (+ t t_1))
     (+ (* x t_1) (* y 5.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if ((x <= -1.1e+32) || !(x <= 65000000000000.0)) {
		tmp = x * (t + t_1);
	} else {
		tmp = (x * t_1) + (y * 5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    if ((x <= (-1.1d+32)) .or. (.not. (x <= 65000000000000.0d0))) then
        tmp = x * (t + t_1)
    else
        tmp = (x * t_1) + (y * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if ((x <= -1.1e+32) || !(x <= 65000000000000.0)) {
		tmp = x * (t + t_1);
	} else {
		tmp = (x * t_1) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if (x <= -1.1e+32) or not (x <= 65000000000000.0):
		tmp = x * (t + t_1)
	else:
		tmp = (x * t_1) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if ((x <= -1.1e+32) || !(x <= 65000000000000.0))
		tmp = Float64(x * Float64(t + t_1));
	else
		tmp = Float64(Float64(x * t_1) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if ((x <= -1.1e+32) || ~((x <= 65000000000000.0)))
		tmp = x * (t + t_1);
	else
		tmp = (x * t_1) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.1e+32], N[Not[LessEqual[x, 65000000000000.0]], $MachinePrecision]], N[(x * N[(t + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x * t$95$1), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e32 or 6.5e13 < 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 -1.1e32 < x < 6.5e13

   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 85.3%

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

   5. Simplified 85.3%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+32} \lor \neg \left(x \leq 65000000000000\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -200:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-24}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+101}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -200.0)
   (* x t)
   (if (<= x 1.18e-24)
     (* y 5.0)
     (if (<= x 1.55e+101) (* 2.0 (* x z)) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -200.0) {
		tmp = x * t;
	} else if (x <= 1.18e-24) {
		tmp = y * 5.0;
	} else if (x <= 1.55e+101) {
		tmp = 2.0 * (x * z);
	} 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 <= (-200.0d0)) then
        tmp = x * t
    else if (x <= 1.18d-24) then
        tmp = y * 5.0d0
    else if (x <= 1.55d+101) then
        tmp = 2.0d0 * (x * z)
    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 <= -200.0) {
		tmp = x * t;
	} else if (x <= 1.18e-24) {
		tmp = y * 5.0;
	} else if (x <= 1.55e+101) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -200.0:
		tmp = x * t
	elif x <= 1.18e-24:
		tmp = y * 5.0
	elif x <= 1.55e+101:
		tmp = 2.0 * (x * z)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -200.0)
		tmp = Float64(x * t);
	elseif (x <= 1.18e-24)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.55e+101)
		tmp = Float64(2.0 * Float64(x * z));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -200.0)
		tmp = x * t;
	elseif (x <= 1.18e-24)
		tmp = y * 5.0;
	elseif (x <= 1.55e+101)
		tmp = 2.0 * (x * z);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -200.0], N[(x * t), $MachinePrecision], If[LessEqual[x, 1.18e-24], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.55e+101], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -200 or 1.55e101 < 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 46.6%

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

   5. Simplified 46.6%

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

   if -200 < x < 1.18e-24

   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 58.5%

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

   if 1.18e-24 < x < 1.55e101

   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 50.0%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -200:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-24}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+101}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-79} \lor \neg \left(x \leq 4.5 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.45e-79) (not (<= x 4.5e-28)))
   (* x (+ t (* 2.0 (+ y z))))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.45e-79) || !(x <= 4.5e-28)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.45d-79)) .or. (.not. (x <= 4.5d-28))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.45e-79) || !(x <= 4.5e-28)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.45e-79) or not (x <= 4.5e-28):
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.45e-79) || !(x <= 4.5e-28))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.45e-79) || ~((x <= 4.5e-28)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.45e-79], N[Not[LessEqual[x, 4.5e-28]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.45e-79 or 4.4999999999999998e-28 < 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 94.4%

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

   if -2.45e-79 < x < 4.4999999999999998e-28

   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 77.7%

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

   7. Taylor expanded in x around 0 77.7%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-79} \lor \neg \left(x \leq 4.5 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+116} \lor \neg \left(y \leq 260000000\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1e+116) (not (<= y 260000000.0)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e+116) || !(y <= 260000000.0)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 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 ((y <= (-1d+116)) .or. (.not. (y <= 260000000.0d0))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e+116) || !(y <= 260000000.0)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1e+116) or not (y <= 260000000.0):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1e+116) || !(y <= 260000000.0))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1e+116) || ~((y <= 260000000.0)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1e+116], N[Not[LessEqual[y, 260000000.0]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000002e116 or 2.6e8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 87.2%

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

   5. Simplified 87.2%

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

   if -1.00000000000000002e116 < y < 2.6e8

   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 75.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+116} \lor \neg \left(y \leq 260000000\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (t + (z * 2.0d0))) + (y * (5.0d0 + (x * 2.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 98.8%

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

4. Final simplification 98.8%

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

Alternative 14: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 15: 47.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -200 \lor \neg \left(x \leq 50000000000000\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -200.0) (not (<= x 50000000000000.0))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -200.0) || !(x <= 50000000000000.0)) {
		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 <= (-200.0d0)) .or. (.not. (x <= 50000000000000.0d0))) 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 <= -200.0) || !(x <= 50000000000000.0)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -200.0) or not (x <= 50000000000000.0):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -200.0) || !(x <= 50000000000000.0))
		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 <= -200.0) || ~((x <= 50000000000000.0)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -200.0], N[Not[LessEqual[x, 50000000000000.0]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -200 or 5e13 < 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 42.5%

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

   5. Simplified 42.5%

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

   if -200 < x < 5e13

   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 56.1%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -200 \lor \neg \left(x \leq 50000000000000\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.2% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 29.1%

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

4. Final simplification 29.1%

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

Reproduce

herbie shell --seed 2024029 
(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)))