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

Percentage Accurate: 99.9% → 99.9%

Time: 10.1s

Alternatives: 12

Speedup: 1.0×

• 27.3% 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-def 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 47.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := y \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{+184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-25}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-21}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+242}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+293}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))) (t_2 (* y (* x 2.0))))
   (if (<= x -2.5e+250)
     t_1
     (if (<= x -3.05e+184)
       t_2
       (if (<= x -8.5e+95)
         t_1
         (if (<= x -2.3e-25)
           (* x t)
           (if (<= x 1.15e-21)
             (* y 5.0)
             (if (<= x 7.5e+242) (* x t) (if (<= x 1.05e+293) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double t_2 = y * (x * 2.0);
	double tmp;
	if (x <= -2.5e+250) {
		tmp = t_1;
	} else if (x <= -3.05e+184) {
		tmp = t_2;
	} else if (x <= -8.5e+95) {
		tmp = t_1;
	} else if (x <= -2.3e-25) {
		tmp = x * t;
	} else if (x <= 1.15e-21) {
		tmp = y * 5.0;
	} else if (x <= 7.5e+242) {
		tmp = x * t;
	} else if (x <= 1.05e+293) {
		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 = 2.0d0 * (x * z)
    t_2 = y * (x * 2.0d0)
    if (x <= (-2.5d+250)) then
        tmp = t_1
    else if (x <= (-3.05d+184)) then
        tmp = t_2
    else if (x <= (-8.5d+95)) then
        tmp = t_1
    else if (x <= (-2.3d-25)) then
        tmp = x * t
    else if (x <= 1.15d-21) then
        tmp = y * 5.0d0
    else if (x <= 7.5d+242) then
        tmp = x * t
    else if (x <= 1.05d+293) 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 = 2.0 * (x * z);
	double t_2 = y * (x * 2.0);
	double tmp;
	if (x <= -2.5e+250) {
		tmp = t_1;
	} else if (x <= -3.05e+184) {
		tmp = t_2;
	} else if (x <= -8.5e+95) {
		tmp = t_1;
	} else if (x <= -2.3e-25) {
		tmp = x * t;
	} else if (x <= 1.15e-21) {
		tmp = y * 5.0;
	} else if (x <= 7.5e+242) {
		tmp = x * t;
	} else if (x <= 1.05e+293) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	t_2 = y * (x * 2.0)
	tmp = 0
	if x <= -2.5e+250:
		tmp = t_1
	elif x <= -3.05e+184:
		tmp = t_2
	elif x <= -8.5e+95:
		tmp = t_1
	elif x <= -2.3e-25:
		tmp = x * t
	elif x <= 1.15e-21:
		tmp = y * 5.0
	elif x <= 7.5e+242:
		tmp = x * t
	elif x <= 1.05e+293:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	t_2 = Float64(y * Float64(x * 2.0))
	tmp = 0.0
	if (x <= -2.5e+250)
		tmp = t_1;
	elseif (x <= -3.05e+184)
		tmp = t_2;
	elseif (x <= -8.5e+95)
		tmp = t_1;
	elseif (x <= -2.3e-25)
		tmp = Float64(x * t);
	elseif (x <= 1.15e-21)
		tmp = Float64(y * 5.0);
	elseif (x <= 7.5e+242)
		tmp = Float64(x * t);
	elseif (x <= 1.05e+293)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	t_2 = y * (x * 2.0);
	tmp = 0.0;
	if (x <= -2.5e+250)
		tmp = t_1;
	elseif (x <= -3.05e+184)
		tmp = t_2;
	elseif (x <= -8.5e+95)
		tmp = t_1;
	elseif (x <= -2.3e-25)
		tmp = x * t;
	elseif (x <= 1.15e-21)
		tmp = y * 5.0;
	elseif (x <= 7.5e+242)
		tmp = x * t;
	elseif (x <= 1.05e+293)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+250], t$95$1, If[LessEqual[x, -3.05e+184], t$95$2, If[LessEqual[x, -8.5e+95], t$95$1, If[LessEqual[x, -2.3e-25], N[(x * t), $MachinePrecision], If[LessEqual[x, 1.15e-21], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 7.5e+242], N[(x * t), $MachinePrecision], If[LessEqual[x, 1.05e+293], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.5000000000000001e250 or -3.05000000000000004e184 < x < -8.5000000000000002e95 or 1.05e293 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 61.6%

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

   if -2.5000000000000001e250 < x < -3.05000000000000004e184 or 7.49999999999999961e242 < x < 1.05e293

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

   6. Taylor expanded in y around inf 68.6%

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

      1. *-commutative 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-*r* 68.6%

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

   8. Simplified 68.6%

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

   if -8.5000000000000002e95 < x < -2.2999999999999999e-25 or 1.15e-21 < x < 7.49999999999999961e242

   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 49.9%

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

   5. Simplified 49.9%

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

   if -2.2999999999999999e-25 < x < 1.15e-21

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 64.3%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+250}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+95}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-25}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-21}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+242}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+293}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-98} \lor \neg \left(x \leq 2.7 \cdot 10^{-29}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 z)))))
   (if (<= x -5e+209)
     t_1
     (if (<= x -1.2e+185)
       (* y (* x 2.0))
       (if (or (<= x -5e-98) (not (<= x 2.7e-29))) t_1 (* y 5.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double tmp;
	if (x <= -5e+209) {
		tmp = t_1;
	} else if (x <= -1.2e+185) {
		tmp = y * (x * 2.0);
	} else if ((x <= -5e-98) || !(x <= 2.7e-29)) {
		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 * (t + (2.0d0 * z))
    if (x <= (-5d+209)) then
        tmp = t_1
    else if (x <= (-1.2d+185)) then
        tmp = y * (x * 2.0d0)
    else if ((x <= (-5d-98)) .or. (.not. (x <= 2.7d-29))) 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 * (t + (2.0 * z));
	double tmp;
	if (x <= -5e+209) {
		tmp = t_1;
	} else if (x <= -1.2e+185) {
		tmp = y * (x * 2.0);
	} else if ((x <= -5e-98) || !(x <= 2.7e-29)) {
		tmp = t_1;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * z))
	tmp = 0
	if x <= -5e+209:
		tmp = t_1
	elif x <= -1.2e+185:
		tmp = y * (x * 2.0)
	elif (x <= -5e-98) or not (x <= 2.7e-29):
		tmp = t_1
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * z)))
	tmp = 0.0
	if (x <= -5e+209)
		tmp = t_1;
	elseif (x <= -1.2e+185)
		tmp = Float64(y * Float64(x * 2.0));
	elseif ((x <= -5e-98) || !(x <= 2.7e-29))
		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 * (t + (2.0 * z));
	tmp = 0.0;
	if (x <= -5e+209)
		tmp = t_1;
	elseif (x <= -1.2e+185)
		tmp = y * (x * 2.0);
	elseif ((x <= -5e-98) || ~((x <= 2.7e-29)))
		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[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+209], t$95$1, If[LessEqual[x, -1.2e+185], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5e-98], N[Not[LessEqual[x, 2.7e-29]], $MachinePrecision]], t$95$1, N[(y * 5.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.99999999999999964e209 or -1.19999999999999995e185 < x < -5.00000000000000018e-98 or 2.70000000000000023e-29 < 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 74.5%

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

   if -4.99999999999999964e209 < x < -1.19999999999999995e185

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

   8. Simplified 100.0%

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

   if -5.00000000000000018e-98 < x < 2.70000000000000023e-29

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 67.6%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+209}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-98} \lor \neg \left(x \leq 2.7 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ t_2 := x \cdot \left(t\_1 + t\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-278}:\\ \;\;\;\;x \cdot t\_1 + y \cdot 5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))) (t_2 (* x (+ t_1 t))))
   (if (<= x -1.7e-24)
     t_2
     (if (<= x 1.1e-278)
       (+ (* x t_1) (* y 5.0))
       (if (<= x 1.4e-29) (+ (* x (+ t (+ y y))) (* y 5.0)) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double t_2 = x * (t_1 + t);
	double tmp;
	if (x <= -1.7e-24) {
		tmp = t_2;
	} else if (x <= 1.1e-278) {
		tmp = (x * t_1) + (y * 5.0);
	} else if (x <= 1.4e-29) {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    t_2 = x * (t_1 + t)
    if (x <= (-1.7d-24)) then
        tmp = t_2
    else if (x <= 1.1d-278) then
        tmp = (x * t_1) + (y * 5.0d0)
    else if (x <= 1.4d-29) then
        tmp = (x * (t + (y + y))) + (y * 5.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double t_2 = x * (t_1 + t);
	double tmp;
	if (x <= -1.7e-24) {
		tmp = t_2;
	} else if (x <= 1.1e-278) {
		tmp = (x * t_1) + (y * 5.0);
	} else if (x <= 1.4e-29) {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	t_2 = x * (t_1 + t)
	tmp = 0
	if x <= -1.7e-24:
		tmp = t_2
	elif x <= 1.1e-278:
		tmp = (x * t_1) + (y * 5.0)
	elif x <= 1.4e-29:
		tmp = (x * (t + (y + y))) + (y * 5.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	t_2 = Float64(x * Float64(t_1 + t))
	tmp = 0.0
	if (x <= -1.7e-24)
		tmp = t_2;
	elseif (x <= 1.1e-278)
		tmp = Float64(Float64(x * t_1) + Float64(y * 5.0));
	elseif (x <= 1.4e-29)
		tmp = Float64(Float64(x * Float64(t + Float64(y + y))) + Float64(y * 5.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	t_2 = x * (t_1 + t);
	tmp = 0.0;
	if (x <= -1.7e-24)
		tmp = t_2;
	elseif (x <= 1.1e-278)
		tmp = (x * t_1) + (y * 5.0);
	elseif (x <= 1.4e-29)
		tmp = (x * (t + (y + y))) + (y * 5.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t$95$1 + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e-24], t$95$2, If[LessEqual[x, 1.1e-278], N[(N[(x * t$95$1), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e-29], N[(N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.69999999999999996e-24 or 1.4000000000000001e-29 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.9%

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

   if -1.69999999999999996e-24 < x < 1.1e-278

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 89.4%

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

   5. Simplified 89.4%

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

   if 1.1e-278 < x < 1.4000000000000001e-29

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 88.4%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-93} \lor \neg \left(x \leq 3 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.15e+185)
   (* x (+ t (* 2.0 y)))
   (if (or (<= x -1.9e-93) (not (<= x 3e-30)))
     (* x (+ t (* 2.0 z)))
     (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e+185) {
		tmp = x * (t + (2.0 * y));
	} else if ((x <= -1.9e-93) || !(x <= 3e-30)) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.15d+185)) then
        tmp = x * (t + (2.0d0 * y))
    else if ((x <= (-1.9d-93)) .or. (.not. (x <= 3d-30))) then
        tmp = x * (t + (2.0d0 * z))
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e+185) {
		tmp = x * (t + (2.0 * y));
	} else if ((x <= -1.9e-93) || !(x <= 3e-30)) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.15e+185:
		tmp = x * (t + (2.0 * y))
	elif (x <= -1.9e-93) or not (x <= 3e-30):
		tmp = x * (t + (2.0 * z))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.15e+185)
		tmp = Float64(x * Float64(t + Float64(2.0 * y)));
	elseif ((x <= -1.9e-93) || !(x <= 3e-30))
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.15e+185)
		tmp = x * (t + (2.0 * y));
	elseif ((x <= -1.9e-93) || ~((x <= 3e-30)))
		tmp = x * (t + (2.0 * z));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.15e+185], N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.9e-93], N[Not[LessEqual[x, 3e-30]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1500000000000001e185

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

   6. Taylor expanded in z around 0 76.6%

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

      1. *-commutative 76.6%

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

   8. Simplified 76.6%

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

   if -1.1500000000000001e185 < x < -1.8999999999999999e-93 or 2.9999999999999999e-30 < 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 74.0%

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

   if -1.8999999999999999e-93 < x < 2.9999999999999999e-30

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 67.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-93} \lor \neg \left(x \leq 3 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{-25} \lor \neg \left(x \leq 2.8 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(t\_1 + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\_1 + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (or (<= x -1.85e-25) (not (<= x 2.8e-24)))
     (* x (+ t_1 t))
     (+ (* 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 <= -1.85e-25) || !(x <= 2.8e-24)) {
		tmp = x * (t_1 + t);
	} 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 <= (-1.85d-25)) .or. (.not. (x <= 2.8d-24))) then
        tmp = x * (t_1 + t)
    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 <= -1.85e-25) || !(x <= 2.8e-24)) {
		tmp = x * (t_1 + t);
	} 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 <= -1.85e-25) or not (x <= 2.8e-24):
		tmp = x * (t_1 + t)
	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 <= -1.85e-25) || !(x <= 2.8e-24))
		tmp = Float64(x * Float64(t_1 + t));
	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 <= -1.85e-25) || ~((x <= 2.8e-24)))
		tmp = x * (t_1 + t);
	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, -1.85e-25], N[Not[LessEqual[x, 2.8e-24]], $MachinePrecision]], N[(x * N[(t$95$1 + t), $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 < -1.85000000000000004e-25 or 2.8000000000000002e-24 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 98.5%

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

   if -1.85000000000000004e-25 < x < 2.8000000000000002e-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 t around 0 82.7%

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

   5. Simplified 82.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-25} \lor \neg \left(x \leq 2.8 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-94} \lor \neg \left(x \leq 3.1 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.3e-94) (not (<= x 3.1e-30)))
   (* x (+ (* 2.0 (+ y z)) t))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.3e-94) || !(x <= 3.1e-30)) {
		tmp = x * ((2.0 * (y + z)) + 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 <= (-3.3d-94)) .or. (.not. (x <= 3.1d-30))) then
        tmp = x * ((2.0d0 * (y + z)) + 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 <= -3.3e-94) || !(x <= 3.1e-30)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.3e-94) or not (x <= 3.1e-30):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.3e-94) || !(x <= 3.1e-30))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + 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 <= -3.3e-94) || ~((x <= 3.1e-30)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.3e-94], N[Not[LessEqual[x, 3.1e-30]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3000000000000001e-94 or 3.09999999999999991e-30 < 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 95.6%

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

   if -3.3000000000000001e-94 < x < 3.09999999999999991e-30

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 67.6%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-94} \lor \neg \left(x \leq 3.1 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+97}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-26} \lor \neg \left(x \leq 1.15 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.55e+97)
   (* 2.0 (* x z))
   (if (or (<= x -1.8e-26) (not (<= x 1.15e-21))) (* x t) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e+97) {
		tmp = 2.0 * (x * z);
	} else if ((x <= -1.8e-26) || !(x <= 1.15e-21)) {
		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 <= (-1.55d+97)) then
        tmp = 2.0d0 * (x * z)
    else if ((x <= (-1.8d-26)) .or. (.not. (x <= 1.15d-21))) 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 <= -1.55e+97) {
		tmp = 2.0 * (x * z);
	} else if ((x <= -1.8e-26) || !(x <= 1.15e-21)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.55e+97:
		tmp = 2.0 * (x * z)
	elif (x <= -1.8e-26) or not (x <= 1.15e-21):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.55e+97)
		tmp = Float64(2.0 * Float64(x * z));
	elseif ((x <= -1.8e-26) || !(x <= 1.15e-21))
		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 <= -1.55e+97)
		tmp = 2.0 * (x * z);
	elseif ((x <= -1.8e-26) || ~((x <= 1.15e-21)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.55e+97], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.8e-26], N[Not[LessEqual[x, 1.15e-21]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.54999999999999991e97

   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 46.9%

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

   if -1.54999999999999991e97 < x < -1.8000000000000001e-26 or 1.15e-21 < 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 46.8%

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

   5. Simplified 46.8%

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

   if -1.8000000000000001e-26 < x < 1.15e-21

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 64.3%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+97}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-26} \lor \neg \left(x \leq 1.15 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+84} \lor \neg \left(y \leq 1.2 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.85e+84) (not (<= y 1.2e+46)))
   (* 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 <= -1.85e+84) || !(y <= 1.2e+46)) {
		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 <= (-1.85d+84)) .or. (.not. (y <= 1.2d+46))) 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 <= -1.85e+84) || !(y <= 1.2e+46)) {
		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 <= -1.85e+84) or not (y <= 1.2e+46):
		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 <= -1.85e+84) || !(y <= 1.2e+46))
		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 <= -1.85e+84) || ~((y <= 1.2e+46)))
		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, -1.85e+84], N[Not[LessEqual[y, 1.2e+46]], $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 < -1.85e84 or 1.20000000000000004e46 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 84.3%

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

   5. Simplified 84.3%

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

   if -1.85e84 < y < 1.20000000000000004e46

   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 80.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+84} \lor \neg \left(y \leq 1.2 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 11: 47.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-26} \lor \neg \left(x \leq 4.2 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.3e-26) (not (<= x 4.2e-20))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e-26) || !(x <= 4.2e-20)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.3d-26)) .or. (.not. (x <= 4.2d-20))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e-26) || !(x <= 4.2e-20)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.3e-26) or not (x <= 4.2e-20):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.3e-26) || !(x <= 4.2e-20))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.3e-26) || ~((x <= 4.2e-20)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.3e-26], N[Not[LessEqual[x, 4.2e-20]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.29999999999999988e-26 or 4.1999999999999998e-20 < 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 41.0%

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

   5. Simplified 41.0%

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

   if -4.29999999999999988e-26 < x < 4.1999999999999998e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 64.3%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-26} \lor \neg \left(x \leq 4.2 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 29.4%

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

4. Final simplification 29.4%

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

Reproduce

herbie shell --seed 2024031 
(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)))