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

Percentage Accurate: 99.9% → 99.9%

Time: 12.7s

Alternatives: 15

Speedup: 1.0×

• 26.2% 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: 53.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ t_2 := y \cdot \left(x + 5\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-122}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-217}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* x 2.0))) (t_2 (* y (+ x 5.0))))
   (if (<= y -5e+86)
     t_2
     (if (<= y -2.9e-122)
       (* x t)
       (if (<= y 1.08e-302)
         t_1
         (if (<= y 3.8e-217)
           (* x t)
           (if (<= y 6.3e-74)
             t_1
             (if (<= y 8e-52) (* x t) (if (<= y 1.45e-22) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x * 2.0);
	double t_2 = y * (x + 5.0);
	double tmp;
	if (y <= -5e+86) {
		tmp = t_2;
	} else if (y <= -2.9e-122) {
		tmp = x * t;
	} else if (y <= 1.08e-302) {
		tmp = t_1;
	} else if (y <= 3.8e-217) {
		tmp = x * t;
	} else if (y <= 6.3e-74) {
		tmp = t_1;
	} else if (y <= 8e-52) {
		tmp = x * t;
	} else if (y <= 1.45e-22) {
		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 = z * (x * 2.0d0)
    t_2 = y * (x + 5.0d0)
    if (y <= (-5d+86)) then
        tmp = t_2
    else if (y <= (-2.9d-122)) then
        tmp = x * t
    else if (y <= 1.08d-302) then
        tmp = t_1
    else if (y <= 3.8d-217) then
        tmp = x * t
    else if (y <= 6.3d-74) then
        tmp = t_1
    else if (y <= 8d-52) then
        tmp = x * t
    else if (y <= 1.45d-22) 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 = z * (x * 2.0);
	double t_2 = y * (x + 5.0);
	double tmp;
	if (y <= -5e+86) {
		tmp = t_2;
	} else if (y <= -2.9e-122) {
		tmp = x * t;
	} else if (y <= 1.08e-302) {
		tmp = t_1;
	} else if (y <= 3.8e-217) {
		tmp = x * t;
	} else if (y <= 6.3e-74) {
		tmp = t_1;
	} else if (y <= 8e-52) {
		tmp = x * t;
	} else if (y <= 1.45e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x * 2.0)
	t_2 = y * (x + 5.0)
	tmp = 0
	if y <= -5e+86:
		tmp = t_2
	elif y <= -2.9e-122:
		tmp = x * t
	elif y <= 1.08e-302:
		tmp = t_1
	elif y <= 3.8e-217:
		tmp = x * t
	elif y <= 6.3e-74:
		tmp = t_1
	elif y <= 8e-52:
		tmp = x * t
	elif y <= 1.45e-22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x * 2.0))
	t_2 = Float64(y * Float64(x + 5.0))
	tmp = 0.0
	if (y <= -5e+86)
		tmp = t_2;
	elseif (y <= -2.9e-122)
		tmp = Float64(x * t);
	elseif (y <= 1.08e-302)
		tmp = t_1;
	elseif (y <= 3.8e-217)
		tmp = Float64(x * t);
	elseif (y <= 6.3e-74)
		tmp = t_1;
	elseif (y <= 8e-52)
		tmp = Float64(x * t);
	elseif (y <= 1.45e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x * 2.0);
	t_2 = y * (x + 5.0);
	tmp = 0.0;
	if (y <= -5e+86)
		tmp = t_2;
	elseif (y <= -2.9e-122)
		tmp = x * t;
	elseif (y <= 1.08e-302)
		tmp = t_1;
	elseif (y <= 3.8e-217)
		tmp = x * t;
	elseif (y <= 6.3e-74)
		tmp = t_1;
	elseif (y <= 8e-52)
		tmp = x * t;
	elseif (y <= 1.45e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+86], t$95$2, If[LessEqual[y, -2.9e-122], N[(x * t), $MachinePrecision], If[LessEqual[y, 1.08e-302], t$95$1, If[LessEqual[y, 3.8e-217], N[(x * t), $MachinePrecision], If[LessEqual[y, 6.3e-74], t$95$1, If[LessEqual[y, 8e-52], N[(x * t), $MachinePrecision], If[LessEqual[y, 1.45e-22], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999998e86 or 1.4500000000000001e-22 < 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. Step-by-step derivation

      1. associate-+r+ 99.9%

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

      2. add-cube-cbrt 99.7%

         \[\leadsto x \cdot \left(\left(\color{blue}{\left(\sqrt[3]{y + \left(z + z\right)} \cdot \sqrt[3]{y + \left(z + z\right)}\right) \cdot \sqrt[3]{y + \left(z + z\right)}} + y\right) + t\right) + y \cdot 5 \]

      3. pow3 99.7%

         \[\leadsto x \cdot \left(\left(\color{blue}{{\left(\sqrt[3]{y + \left(z + z\right)}\right)}^{3}} + y\right) + t\right) + y \cdot 5 \]

      4. +-commutative 99.7%

         \[\leadsto x \cdot \left(\left({\left(\sqrt[3]{\color{blue}{\left(z + z\right) + y}}\right)}^{3} + y\right) + t\right) + y \cdot 5 \]

      5. count-2 99.7%

         \[\leadsto x \cdot \left(\left({\left(\sqrt[3]{\color{blue}{2 \cdot z} + y}\right)}^{3} + y\right) + t\right) + y \cdot 5 \]

      6. fma-def 99.7%

         \[\leadsto x \cdot \left(\left({\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(2, z, y\right)}}\right)}^{3} + y\right) + t\right) + y \cdot 5 \]

   4. Applied egg-rr 99.7%

      \[\leadsto x \cdot \left(\left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(2, z, y\right)}\right)}^{3}} + y\right) + t\right) + y \cdot 5 \]

   5. Taylor expanded in y around inf 71.9%

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

      1. +-commutative 71.9%

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

   7. Simplified 71.9%

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

   if -4.9999999999999998e86 < y < -2.9000000000000002e-122 or 1.07999999999999994e-302 < y < 3.79999999999999987e-217 or 6.30000000000000003e-74 < y < 8.0000000000000001e-52

   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 t around inf 55.6%

      \[\leadsto \color{blue}{t \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 55.6%

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

   6. Simplified 55.6%

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

   if -2.9000000000000002e-122 < y < 1.07999999999999994e-302 or 3.79999999999999987e-217 < y < 6.30000000000000003e-74 or 8.0000000000000001e-52 < y < 1.4500000000000001e-22

   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 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in z around inf 58.8%

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

      1. associate-*r* 58.8%

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

      2. *-commutative 58.8%

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

   8. Simplified 58.8%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-122}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-217}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{-74}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + x \cdot t\\ t_2 := x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-252}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* x t))) (t_2 (* x (+ t (* 2.0 (+ y z))))))
   (if (<= x -2.1e-76)
     t_2
     (if (<= x -9.5e-169)
       t_1
       (if (<= x 1.3e-252)
         (+ (* y 5.0) (* 2.0 (* x z)))
         (if (<= x 8.5e-162) 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 = x * (t + (2.0 * (y + z)));
	double tmp;
	if (x <= -2.1e-76) {
		tmp = t_2;
	} else if (x <= -9.5e-169) {
		tmp = t_1;
	} else if (x <= 1.3e-252) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else if (x <= 8.5e-162) {
		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 = x * (t + (2.0d0 * (y + z)))
    if (x <= (-2.1d-76)) then
        tmp = t_2
    else if (x <= (-9.5d-169)) then
        tmp = t_1
    else if (x <= 1.3d-252) then
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    else if (x <= 8.5d-162) 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 = x * (t + (2.0 * (y + z)));
	double tmp;
	if (x <= -2.1e-76) {
		tmp = t_2;
	} else if (x <= -9.5e-169) {
		tmp = t_1;
	} else if (x <= 1.3e-252) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else if (x <= 8.5e-162) {
		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 = x * (t + (2.0 * (y + z)))
	tmp = 0
	if x <= -2.1e-76:
		tmp = t_2
	elif x <= -9.5e-169:
		tmp = t_1
	elif x <= 1.3e-252:
		tmp = (y * 5.0) + (2.0 * (x * z))
	elif x <= 8.5e-162:
		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(x * Float64(t + Float64(2.0 * Float64(y + z))))
	tmp = 0.0
	if (x <= -2.1e-76)
		tmp = t_2;
	elseif (x <= -9.5e-169)
		tmp = t_1;
	elseif (x <= 1.3e-252)
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	elseif (x <= 8.5e-162)
		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 = x * (t + (2.0 * (y + z)));
	tmp = 0.0;
	if (x <= -2.1e-76)
		tmp = t_2;
	elseif (x <= -9.5e-169)
		tmp = t_1;
	elseif (x <= 1.3e-252)
		tmp = (y * 5.0) + (2.0 * (x * z));
	elseif (x <= 8.5e-162)
		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[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e-76], t$95$2, If[LessEqual[x, -9.5e-169], t$95$1, If[LessEqual[x, 1.3e-252], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-162], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.09999999999999992e-76 or 8.49999999999999955e-162 < x

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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. Taylor expanded in x around inf 93.6%

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

   if -2.09999999999999992e-76 < x < -9.5000000000000001e-169 or 1.3e-252 < x < 8.49999999999999955e-162

   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 85.5%

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

   5. Simplified 85.5%

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

   if -9.5000000000000001e-169 < x < 1.3e-252

   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 83.5%

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

   5. Simplified 83.5%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-169}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-252}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-162}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-8}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-104}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-161}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* 2.0 (+ y z)))))
   (if (<= x -2.5e+24)
     t_1
     (if (<= x -2.9e-8)
       (* x t)
       (if (<= x -1.35e-104)
         (* z (* x 2.0))
         (if (<= x 1.05e-161) (* y 5.0) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -2.5e+24) {
		tmp = t_1;
	} else if (x <= -2.9e-8) {
		tmp = x * t;
	} else if (x <= -1.35e-104) {
		tmp = z * (x * 2.0);
	} else if (x <= 1.05e-161) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (2.0d0 * (y + z))
    if (x <= (-2.5d+24)) then
        tmp = t_1
    else if (x <= (-2.9d-8)) then
        tmp = x * t
    else if (x <= (-1.35d-104)) then
        tmp = z * (x * 2.0d0)
    else if (x <= 1.05d-161) then
        tmp = y * 5.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -2.5e+24) {
		tmp = t_1;
	} else if (x <= -2.9e-8) {
		tmp = x * t;
	} else if (x <= -1.35e-104) {
		tmp = z * (x * 2.0);
	} else if (x <= 1.05e-161) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (2.0 * (y + z))
	tmp = 0
	if x <= -2.5e+24:
		tmp = t_1
	elif x <= -2.9e-8:
		tmp = x * t
	elif x <= -1.35e-104:
		tmp = z * (x * 2.0)
	elif x <= 1.05e-161:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(2.0 * Float64(y + z)))
	tmp = 0.0
	if (x <= -2.5e+24)
		tmp = t_1;
	elseif (x <= -2.9e-8)
		tmp = Float64(x * t);
	elseif (x <= -1.35e-104)
		tmp = Float64(z * Float64(x * 2.0));
	elseif (x <= 1.05e-161)
		tmp = Float64(y * 5.0);
	else
		tmp = t_1;
	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 <= -2.5e+24)
		tmp = t_1;
	elseif (x <= -2.9e-8)
		tmp = x * t;
	elseif (x <= -1.35e-104)
		tmp = z * (x * 2.0);
	elseif (x <= 1.05e-161)
		tmp = y * 5.0;
	else
		tmp = t_1;
	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, -2.5e+24], t$95$1, If[LessEqual[x, -2.9e-8], N[(x * t), $MachinePrecision], If[LessEqual[x, -1.35e-104], N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-161], N[(y * 5.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.50000000000000023e24 or 1.05e-161 < 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 95.9%

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

   6. Taylor expanded in t around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. +-commutative 69.6%

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

      3. associate-*r* 69.6%

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

      4. *-commutative 69.6%

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

      5. +-commutative 69.6%

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

   8. Simplified 69.6%

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

   if -2.50000000000000023e24 < x < -2.9000000000000002e-8

   1. Initial program 99.6%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   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 t around inf 75.6%

      \[\leadsto \color{blue}{t \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 75.6%

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

   6. Simplified 75.6%

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

   if -2.9000000000000002e-8 < x < -1.3499999999999999e-104

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in z around inf 58.7%

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

      1. associate-*r* 58.7%

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

      2. *-commutative 58.7%

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

   8. Simplified 58.7%

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

   if -1.3499999999999999e-104 < x < 1.05e-161

   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 57.7%

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

   5. Simplified 57.7%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-8}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-104}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-161}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+86} \lor \neg \left(y \leq 1.95 \cdot 10^{-46}\right):\\ \;\;\;\;y \cdot 5 + x \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))))
   (if (or (<= y -5e+86) (not (<= y 1.95e-46)))
     (+ (* y 5.0) (* x t_1))
     (* x (+ t t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double tmp;
	if ((y <= -5e+86) || !(y <= 1.95e-46)) {
		tmp = (y * 5.0) + (x * t_1);
	} else {
		tmp = x * (t + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (y + z)
    if ((y <= (-5d+86)) .or. (.not. (y <= 1.95d-46))) then
        tmp = (y * 5.0d0) + (x * t_1)
    else
        tmp = x * (t + 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 * (y + z);
	double tmp;
	if ((y <= -5e+86) || !(y <= 1.95e-46)) {
		tmp = (y * 5.0) + (x * t_1);
	} else {
		tmp = x * (t + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	tmp = 0
	if (y <= -5e+86) or not (y <= 1.95e-46):
		tmp = (y * 5.0) + (x * t_1)
	else:
		tmp = x * (t + t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	tmp = 0.0
	if ((y <= -5e+86) || !(y <= 1.95e-46))
		tmp = Float64(Float64(y * 5.0) + Float64(x * t_1));
	else
		tmp = Float64(x * Float64(t + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	tmp = 0.0;
	if ((y <= -5e+86) || ~((y <= 1.95e-46)))
		tmp = (y * 5.0) + (x * t_1);
	else
		tmp = x * (t + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -5e+86], N[Not[LessEqual[y, 1.95e-46]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999998e86 or 1.9500000000000001e-46 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 94.3%

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

   5. Simplified 94.3%

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

   if -4.9999999999999998e86 < y < 1.9500000000000001e-46

   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 87.0%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+86} \lor \neg \left(y \leq 1.95 \cdot 10^{-46}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+41} \lor \neg \left(x \leq 2.5\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.1e+41) (not (<= x 2.5)))
   (* x (+ t (* 2.0 (+ y z))))
   (+ (* y 5.0) (* x (+ t (* z 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e+41) || !(x <= 2.5)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (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 ((x <= (-3.1d+41)) .or. (.not. (x <= 2.5d0))) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = (y * 5.0d0) + (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 ((x <= -3.1e+41) || !(x <= 2.5)) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.1e+41) or not (x <= 2.5):
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = (y * 5.0) + (x * (t + (z * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.1e+41) || !(x <= 2.5))
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(y * 5.0) + 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 ((x <= -3.1e+41) || ~((x <= 2.5)))
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.1e+41], N[Not[LessEqual[x, 2.5]], $MachinePrecision]], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1e41 or 2.5 < x

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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. Taylor expanded in x around inf 99.9%

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

   if -3.1e41 < x < 2.5

   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 98.7%

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

   5. Simplified 98.7%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+41} \lor \neg \left(x \leq 2.5\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right) + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4e+99)
   (* x (+ t (* 2.0 (+ y z))))
   (+ (* x (+ t (* z 2.0))) (* y (+ 5.0 (* x 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e+99) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (x * (t + (z * 2.0))) + (y * (5.0 + (x * 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4d+99)) then
        tmp = x * (t + (2.0d0 * (y + z)))
    else
        tmp = (x * (t + (z * 2.0d0))) + (y * (5.0d0 + (x * 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e+99) {
		tmp = x * (t + (2.0 * (y + z)));
	} else {
		tmp = (x * (t + (z * 2.0))) + (y * (5.0 + (x * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4e+99:
		tmp = x * (t + (2.0 * (y + z)))
	else:
		tmp = (x * (t + (z * 2.0))) + (y * (5.0 + (x * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4e+99)
		tmp = Float64(x * Float64(t + Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(z * 2.0))) + Float64(y * Float64(5.0 + Float64(x * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4e+99)
		tmp = x * (t + (2.0 * (y + z)));
	else
		tmp = (x * (t + (z * 2.0))) + (y * (5.0 + (x * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4e+99], N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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. Split input into 2 regimes

2. if x < -3.9999999999999999e99

   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 -3.9999999999999999e99 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right) + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-86} \lor \neg \left(x \leq 1.8 \cdot 10^{-164}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.5e-86) (not (<= x 1.8e-164)))
   (* 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 <= -3.5e-86) || !(x <= 1.8e-164)) {
		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 <= (-3.5d-86)) .or. (.not. (x <= 1.8d-164))) 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 <= -3.5e-86) || !(x <= 1.8e-164)) {
		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 <= -3.5e-86) or not (x <= 1.8e-164):
		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 <= -3.5e-86) || !(x <= 1.8e-164))
		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 <= -3.5e-86) || ~((x <= 1.8e-164)))
		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, -3.5e-86], N[Not[LessEqual[x, 1.8e-164]], $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 < -3.50000000000000021e-86 or 1.79999999999999997e-164 < x

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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. Taylor expanded in x around inf 93.6%

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

   if -3.50000000000000021e-86 < x < 1.79999999999999997e-164

   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 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-86} \lor \neg \left(x \leq 1.8 \cdot 10^{-164}\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+86} \lor \neg \left(y \leq 2.8 \cdot 10^{+89}\right):\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5e+86) (not (<= y 2.8e+89)))
   (* y (+ x 5.0))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e+86) || !(y <= 2.8e+89)) {
		tmp = y * (x + 5.0);
	} 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 <= (-5d+86)) .or. (.not. (y <= 2.8d+89))) then
        tmp = y * (x + 5.0d0)
    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 <= -5e+86) || !(y <= 2.8e+89)) {
		tmp = y * (x + 5.0);
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5e+86) or not (y <= 2.8e+89):
		tmp = y * (x + 5.0)
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5e+86) || !(y <= 2.8e+89))
		tmp = Float64(y * Float64(x + 5.0));
	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 <= -5e+86) || ~((y <= 2.8e+89)))
		tmp = y * (x + 5.0);
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5e+86], N[Not[LessEqual[y, 2.8e+89]], $MachinePrecision]], N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999998e86 or 2.7999999999999998e89 < 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. Step-by-step derivation

      1. associate-+r+ 99.9%

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

      2. add-cube-cbrt 99.7%

         \[\leadsto x \cdot \left(\left(\color{blue}{\left(\sqrt[3]{y + \left(z + z\right)} \cdot \sqrt[3]{y + \left(z + z\right)}\right) \cdot \sqrt[3]{y + \left(z + z\right)}} + y\right) + t\right) + y \cdot 5 \]

      3. pow3 99.7%

         \[\leadsto x \cdot \left(\left(\color{blue}{{\left(\sqrt[3]{y + \left(z + z\right)}\right)}^{3}} + y\right) + t\right) + y \cdot 5 \]

      4. +-commutative 99.7%

         \[\leadsto x \cdot \left(\left({\left(\sqrt[3]{\color{blue}{\left(z + z\right) + y}}\right)}^{3} + y\right) + t\right) + y \cdot 5 \]

      5. count-2 99.7%

         \[\leadsto x \cdot \left(\left({\left(\sqrt[3]{\color{blue}{2 \cdot z} + y}\right)}^{3} + y\right) + t\right) + y \cdot 5 \]

      6. fma-def 99.7%

         \[\leadsto x \cdot \left(\left({\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(2, z, y\right)}}\right)}^{3} + y\right) + t\right) + y \cdot 5 \]

   4. Applied egg-rr 99.7%

      \[\leadsto x \cdot \left(\left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(2, z, y\right)}\right)}^{3}} + y\right) + t\right) + y \cdot 5 \]

   5. Taylor expanded in y around inf 78.4%

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

      1. +-commutative 78.4%

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

   7. Simplified 78.4%

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

   if -4.9999999999999998e86 < y < 2.7999999999999998e89

   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 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in x around inf 80.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+86} \lor \neg \left(y \leq 2.8 \cdot 10^{+89}\right):\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+86} \lor \neg \left(y \leq 2.3 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.5e+86) (not (<= y 2.3e-19)))
   (* 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 <= -5.5e+86) || !(y <= 2.3e-19)) {
		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 <= (-5.5d+86)) .or. (.not. (y <= 2.3d-19))) 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 <= -5.5e+86) || !(y <= 2.3e-19)) {
		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 <= -5.5e+86) or not (y <= 2.3e-19):
		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 <= -5.5e+86) || !(y <= 2.3e-19))
		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 <= -5.5e+86) || ~((y <= 2.3e-19)))
		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, -5.5e+86], N[Not[LessEqual[y, 2.3e-19]], $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 < -5.5000000000000002e86 or 2.2999999999999998e-19 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.8%

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

   if -5.5000000000000002e86 < y < 2.2999999999999998e-19

   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 96.0%

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

   5. Simplified 96.0%

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

   6. Taylor expanded in x around inf 83.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+86} \lor \neg \left(y \leq 2.3 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+86} \lor \neg \left(y \leq 1.38 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7e+86) (not (<= y 1.38e-58))) (* y (+ x 5.0)) (* x t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e+86) || !(y <= 1.38e-58)) {
		tmp = y * (x + 5.0);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7d+86)) .or. (.not. (y <= 1.38d-58))) then
        tmp = y * (x + 5.0d0)
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e+86) || !(y <= 1.38e-58)) {
		tmp = y * (x + 5.0);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7e+86) or not (y <= 1.38e-58):
		tmp = y * (x + 5.0)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7e+86) || !(y <= 1.38e-58))
		tmp = Float64(y * Float64(x + 5.0));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7e+86) || ~((y <= 1.38e-58)))
		tmp = y * (x + 5.0);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7e+86], N[Not[LessEqual[y, 1.38e-58]], $MachinePrecision]], N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.00000000000000038e86 or 1.37999999999999996e-58 < 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. Step-by-step derivation

      1. associate-+r+ 99.9%

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

      2. add-cube-cbrt 99.6%

         \[\leadsto x \cdot \left(\left(\color{blue}{\left(\sqrt[3]{y + \left(z + z\right)} \cdot \sqrt[3]{y + \left(z + z\right)}\right) \cdot \sqrt[3]{y + \left(z + z\right)}} + y\right) + t\right) + y \cdot 5 \]

      3. pow3 99.6%

         \[\leadsto x \cdot \left(\left(\color{blue}{{\left(\sqrt[3]{y + \left(z + z\right)}\right)}^{3}} + y\right) + t\right) + y \cdot 5 \]

      4. +-commutative 99.6%

         \[\leadsto x \cdot \left(\left({\left(\sqrt[3]{\color{blue}{\left(z + z\right) + y}}\right)}^{3} + y\right) + t\right) + y \cdot 5 \]

      5. count-2 99.6%

         \[\leadsto x \cdot \left(\left({\left(\sqrt[3]{\color{blue}{2 \cdot z} + y}\right)}^{3} + y\right) + t\right) + y \cdot 5 \]

      6. fma-def 99.6%

         \[\leadsto x \cdot \left(\left({\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(2, z, y\right)}}\right)}^{3} + y\right) + t\right) + y \cdot 5 \]

   4. Applied egg-rr 99.6%

      \[\leadsto x \cdot \left(\left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(2, z, y\right)}\right)}^{3}} + y\right) + t\right) + y \cdot 5 \]

   5. Taylor expanded in y around inf 68.1%

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

      1. +-commutative 68.1%

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

   7. Simplified 68.1%

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

   if -7.00000000000000038e86 < y < 1.37999999999999996e-58

   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 t around inf 43.7%

      \[\leadsto \color{blue}{t \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 43.7%

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

   6. Simplified 43.7%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+86} \lor \neg \left(y \leq 1.38 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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%

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

Alternative 14: 42.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+86} \lor \neg \left(y \leq 2.1 \cdot 10^{+75}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8e+86) (not (<= y 2.1e+75))) (* y 5.0) (* x t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e+86) || !(y <= 2.1e+75)) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-8d+86)) .or. (.not. (y <= 2.1d+75))) then
        tmp = y * 5.0d0
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e+86) || !(y <= 2.1e+75)) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8e+86) or not (y <= 2.1e+75):
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8e+86) || !(y <= 2.1e+75))
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8e+86) || ~((y <= 2.1e+75)))
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8e+86], N[Not[LessEqual[y, 2.1e+75]], $MachinePrecision]], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.0000000000000001e86 or 2.09999999999999999e75 < 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 x around 0 45.7%

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

   5. Simplified 45.7%

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

   if -8.0000000000000001e86 < y < 2.09999999999999999e75

   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. Taylor expanded in t around inf 41.8%

      \[\leadsto \color{blue}{t \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 41.8%

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

   6. Simplified 41.8%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+86} \lor \neg \left(y \leq 2.1 \cdot 10^{+75}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.4% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 96.1%

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

4. Taylor expanded in t around inf 30.6%

   \[\leadsto \color{blue}{t \cdot x} \]
5. Step-by-step derivation

   1. *-commutative 30.6%

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

6. Simplified 30.6%

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

7. Final simplification 30.6%

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

Reproduce

herbie shell --seed 2024020 
(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)))