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

Percentage Accurate: 99.9% → 99.9%

Time: 10.5s

Alternatives: 15

Speedup: 1.0×

• 26.4% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-define 100.0%

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

   3. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \color{blue}{\left(1 \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)}\right) \]

   4. *-un-lft-identity 100.0%

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

   5. associate-+l+ 100.0%

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

   6. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

   7. +-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

   8. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

   9. distribute-rgt-out 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

   10. metadata-eval 100.0%

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

4. Applied egg-rr 100.0%

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

Alternative 2: 78.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+67}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 10^{+83}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -2.4e+65)
     t_1
     (if (<= y -9.4e+32)
       (* x (+ t (* y 2.0)))
       (if (<= y -8.5e+14)
         t_1
         (if (<= y 5.9e-6)
           (* x (+ t (* z 2.0)))
           (if (<= y 2e+67)
             (+ (* y 5.0) (* x t))
             (if (<= y 1e+83) (* x (* (+ y z) 2.0)) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.4e+65) {
		tmp = t_1;
	} else if (y <= -9.4e+32) {
		tmp = x * (t + (y * 2.0));
	} else if (y <= -8.5e+14) {
		tmp = t_1;
	} else if (y <= 5.9e-6) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 2e+67) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1e+83) {
		tmp = x * ((y + z) * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-2.4d+65)) then
        tmp = t_1
    else if (y <= (-9.4d+32)) then
        tmp = x * (t + (y * 2.0d0))
    else if (y <= (-8.5d+14)) then
        tmp = t_1
    else if (y <= 5.9d-6) then
        tmp = x * (t + (z * 2.0d0))
    else if (y <= 2d+67) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 1d+83) then
        tmp = x * ((y + z) * 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.4e+65) {
		tmp = t_1;
	} else if (y <= -9.4e+32) {
		tmp = x * (t + (y * 2.0));
	} else if (y <= -8.5e+14) {
		tmp = t_1;
	} else if (y <= 5.9e-6) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 2e+67) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1e+83) {
		tmp = x * ((y + z) * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -2.4e+65:
		tmp = t_1
	elif y <= -9.4e+32:
		tmp = x * (t + (y * 2.0))
	elif y <= -8.5e+14:
		tmp = t_1
	elif y <= 5.9e-6:
		tmp = x * (t + (z * 2.0))
	elif y <= 2e+67:
		tmp = (y * 5.0) + (x * t)
	elif y <= 1e+83:
		tmp = x * ((y + z) * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -2.4e+65)
		tmp = t_1;
	elseif (y <= -9.4e+32)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	elseif (y <= -8.5e+14)
		tmp = t_1;
	elseif (y <= 5.9e-6)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (y <= 2e+67)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 1e+83)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -2.4e+65)
		tmp = t_1;
	elseif (y <= -9.4e+32)
		tmp = x * (t + (y * 2.0));
	elseif (y <= -8.5e+14)
		tmp = t_1;
	elseif (y <= 5.9e-6)
		tmp = x * (t + (z * 2.0));
	elseif (y <= 2e+67)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 1e+83)
		tmp = x * ((y + z) * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+65], t$95$1, If[LessEqual[y, -9.4e+32], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e+14], t$95$1, If[LessEqual[y, 5.9e-6], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+67], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+83], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.4000000000000002e65 or -9.40000000000000047e32 < y < -8.5e14 or 1.00000000000000003e83 < y

   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 y around inf 87.1%

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

   5. Simplified 87.1%

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

   if -2.4000000000000002e65 < y < -9.40000000000000047e32

   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 inf 100.0%

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

   4. Taylor expanded in z around 0 78.0%

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

   if -8.5e14 < y < 5.90000000000000026e-6

   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 83.9%

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

   if 5.90000000000000026e-6 < y < 1.99999999999999997e67

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

   4. Taylor expanded in z around 0 80.7%

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

   if 1.99999999999999997e67 < y < 1.00000000000000003e83

   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 inf 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. distribute-lft-in 100.0%

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

      2. +-commutative 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+67}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 10^{+83}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -38000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* 2.0 (* x z)))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -3.5e+134)
     t_2
     (if (<= y -5.5e+45)
       t_1
       (if (<= y -38000000000000.0)
         t_2
         (if (<= y 7.6e-164)
           (* x (+ t (* z 2.0)))
           (if (<= y 2e+152) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (2.0 * (x * z));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -3.5e+134) {
		tmp = t_2;
	} else if (y <= -5.5e+45) {
		tmp = t_1;
	} else if (y <= -38000000000000.0) {
		tmp = t_2;
	} else if (y <= 7.6e-164) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 2e+152) {
		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) + (2.0d0 * (x * z))
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-3.5d+134)) then
        tmp = t_2
    else if (y <= (-5.5d+45)) then
        tmp = t_1
    else if (y <= (-38000000000000.0d0)) then
        tmp = t_2
    else if (y <= 7.6d-164) then
        tmp = x * (t + (z * 2.0d0))
    else if (y <= 2d+152) 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) + (2.0 * (x * z));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -3.5e+134) {
		tmp = t_2;
	} else if (y <= -5.5e+45) {
		tmp = t_1;
	} else if (y <= -38000000000000.0) {
		tmp = t_2;
	} else if (y <= 7.6e-164) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 2e+152) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (2.0 * (x * z))
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -3.5e+134:
		tmp = t_2
	elif y <= -5.5e+45:
		tmp = t_1
	elif y <= -38000000000000.0:
		tmp = t_2
	elif y <= 7.6e-164:
		tmp = x * (t + (z * 2.0))
	elif y <= 2e+152:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -3.5e+134)
		tmp = t_2;
	elseif (y <= -5.5e+45)
		tmp = t_1;
	elseif (y <= -38000000000000.0)
		tmp = t_2;
	elseif (y <= 7.6e-164)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (y <= 2e+152)
		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) + (2.0 * (x * z));
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -3.5e+134)
		tmp = t_2;
	elseif (y <= -5.5e+45)
		tmp = t_1;
	elseif (y <= -38000000000000.0)
		tmp = t_2;
	elseif (y <= 7.6e-164)
		tmp = x * (t + (z * 2.0));
	elseif (y <= 2e+152)
		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[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+134], t$95$2, If[LessEqual[y, -5.5e+45], t$95$1, If[LessEqual[y, -38000000000000.0], t$95$2, If[LessEqual[y, 7.6e-164], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+152], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.50000000000000003e134 or -5.5000000000000001e45 < y < -3.8e13 or 2.0000000000000001e152 < 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 91.1%

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

   5. Simplified 91.1%

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

   if -3.50000000000000003e134 < y < -5.5000000000000001e45 or 7.59999999999999979e-164 < y < 2.0000000000000001e152

   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 89.0%

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

   4. Taylor expanded in t around 0 77.2%

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

   if -3.8e13 < y < 7.59999999999999979e-164

   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 88.5%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+45}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -38000000000000:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+152}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ t_2 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+195}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-120}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))) (t_2 (* x (* (+ y z) 2.0))))
   (if (<= x -8e+195)
     t_2
     (if (<= x -2.2e+135)
       t_1
       (if (<= x -1.22e-61)
         t_2
         (if (<= x 3.6e-120) (* y 5.0) (if (<= x 2.4e+38) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double t_2 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -8e+195) {
		tmp = t_2;
	} else if (x <= -2.2e+135) {
		tmp = t_1;
	} else if (x <= -1.22e-61) {
		tmp = t_2;
	} else if (x <= 3.6e-120) {
		tmp = y * 5.0;
	} else if (x <= 2.4e+38) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (y * 2.0d0))
    t_2 = x * ((y + z) * 2.0d0)
    if (x <= (-8d+195)) then
        tmp = t_2
    else if (x <= (-2.2d+135)) then
        tmp = t_1
    else if (x <= (-1.22d-61)) then
        tmp = t_2
    else if (x <= 3.6d-120) then
        tmp = y * 5.0d0
    else if (x <= 2.4d+38) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double t_2 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -8e+195) {
		tmp = t_2;
	} else if (x <= -2.2e+135) {
		tmp = t_1;
	} else if (x <= -1.22e-61) {
		tmp = t_2;
	} else if (x <= 3.6e-120) {
		tmp = y * 5.0;
	} else if (x <= 2.4e+38) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	t_2 = x * ((y + z) * 2.0)
	tmp = 0
	if x <= -8e+195:
		tmp = t_2
	elif x <= -2.2e+135:
		tmp = t_1
	elif x <= -1.22e-61:
		tmp = t_2
	elif x <= 3.6e-120:
		tmp = y * 5.0
	elif x <= 2.4e+38:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y * 2.0)))
	t_2 = Float64(x * Float64(Float64(y + z) * 2.0))
	tmp = 0.0
	if (x <= -8e+195)
		tmp = t_2;
	elseif (x <= -2.2e+135)
		tmp = t_1;
	elseif (x <= -1.22e-61)
		tmp = t_2;
	elseif (x <= 3.6e-120)
		tmp = Float64(y * 5.0);
	elseif (x <= 2.4e+38)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y * 2.0));
	t_2 = x * ((y + z) * 2.0);
	tmp = 0.0;
	if (x <= -8e+195)
		tmp = t_2;
	elseif (x <= -2.2e+135)
		tmp = t_1;
	elseif (x <= -1.22e-61)
		tmp = t_2;
	elseif (x <= 3.6e-120)
		tmp = y * 5.0;
	elseif (x <= 2.4e+38)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+195], t$95$2, If[LessEqual[x, -2.2e+135], t$95$1, If[LessEqual[x, -1.22e-61], t$95$2, If[LessEqual[x, 3.6e-120], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 2.4e+38], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.99999999999999982e195 or -2.1999999999999999e135 < x < -1.22e-61 or 3.6000000000000003e-120 < x < 2.40000000000000017e38

   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 inf 89.7%

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

   4. Taylor expanded in t around 0 69.8%

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

      1. distribute-lft-in 69.8%

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

      2. +-commutative 69.8%

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

   6. Simplified 69.8%

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

   if -7.99999999999999982e195 < x < -2.1999999999999999e135 or 2.40000000000000017e38 < 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 x around inf 100.0%

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

   4. Taylor expanded in z around 0 81.0%

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

   if -1.22e-61 < x < 3.6000000000000003e-120

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 64.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+195}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-120}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot 2\right)\\ t_2 := z \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -6.9 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-121}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+184}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y 2.0))) (t_2 (* z (* x 2.0))))
   (if (<= x -6.9e+152)
     t_1
     (if (<= x -3.3e-58)
       t_2
       (if (<= x 2.8e-121)
         (* y 5.0)
         (if (<= x 6.3e+38) t_2 (if (<= x 2.1e+184) (* x t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * 2.0);
	double t_2 = z * (x * 2.0);
	double tmp;
	if (x <= -6.9e+152) {
		tmp = t_1;
	} else if (x <= -3.3e-58) {
		tmp = t_2;
	} else if (x <= 2.8e-121) {
		tmp = y * 5.0;
	} else if (x <= 6.3e+38) {
		tmp = t_2;
	} else if (x <= 2.1e+184) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * 2.0d0)
    t_2 = z * (x * 2.0d0)
    if (x <= (-6.9d+152)) then
        tmp = t_1
    else if (x <= (-3.3d-58)) then
        tmp = t_2
    else if (x <= 2.8d-121) then
        tmp = y * 5.0d0
    else if (x <= 6.3d+38) then
        tmp = t_2
    else if (x <= 2.1d+184) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y * 2.0);
	double t_2 = z * (x * 2.0);
	double tmp;
	if (x <= -6.9e+152) {
		tmp = t_1;
	} else if (x <= -3.3e-58) {
		tmp = t_2;
	} else if (x <= 2.8e-121) {
		tmp = y * 5.0;
	} else if (x <= 6.3e+38) {
		tmp = t_2;
	} else if (x <= 2.1e+184) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * 2.0)
	t_2 = z * (x * 2.0)
	tmp = 0
	if x <= -6.9e+152:
		tmp = t_1
	elif x <= -3.3e-58:
		tmp = t_2
	elif x <= 2.8e-121:
		tmp = y * 5.0
	elif x <= 6.3e+38:
		tmp = t_2
	elif x <= 2.1e+184:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y * 2.0))
	t_2 = Float64(z * Float64(x * 2.0))
	tmp = 0.0
	if (x <= -6.9e+152)
		tmp = t_1;
	elseif (x <= -3.3e-58)
		tmp = t_2;
	elseif (x <= 2.8e-121)
		tmp = Float64(y * 5.0);
	elseif (x <= 6.3e+38)
		tmp = t_2;
	elseif (x <= 2.1e+184)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y * 2.0);
	t_2 = z * (x * 2.0);
	tmp = 0.0;
	if (x <= -6.9e+152)
		tmp = t_1;
	elseif (x <= -3.3e-58)
		tmp = t_2;
	elseif (x <= 2.8e-121)
		tmp = y * 5.0;
	elseif (x <= 6.3e+38)
		tmp = t_2;
	elseif (x <= 2.1e+184)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.9e+152], t$95$1, If[LessEqual[x, -3.3e-58], t$95$2, If[LessEqual[x, 2.8e-121], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 6.3e+38], t$95$2, If[LessEqual[x, 2.1e+184], N[(x * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.9e152 or 2.1e184 < 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 x around inf 100.0%

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

   4. Taylor expanded in y around inf 55.1%

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

      1. associate-*r* 55.1%

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

      2. *-commutative 55.1%

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

      3. associate-*r* 55.1%

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

   6. Simplified 55.1%

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

   if -6.9e152 < x < -3.30000000000000026e-58 or 2.8000000000000001e-121 < x < 6.30000000000000003e38

   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 52.0%

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

   5. Simplified 52.0%

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

   if -3.30000000000000026e-58 < x < 2.8000000000000001e-121

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 64.9%

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

   if 6.30000000000000003e38 < x < 2.1e184

   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 60.0%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.9 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-121}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+184}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+15} \lor \neg \left(y \leq 2.2 \cdot 10^{-9}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.08e+64)
     t_1
     (if (<= y -1.62e+32)
       (* x (+ t (* y 2.0)))
       (if (or (<= y -5.8e+15) (not (<= y 2.2e-9)))
         t_1
         (* x (+ t (* z 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.08e+64) {
		tmp = t_1;
	} else if (y <= -1.62e+32) {
		tmp = x * (t + (y * 2.0));
	} else if ((y <= -5.8e+15) || !(y <= 2.2e-9)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.08d+64)) then
        tmp = t_1
    else if (y <= (-1.62d+32)) then
        tmp = x * (t + (y * 2.0d0))
    else if ((y <= (-5.8d+15)) .or. (.not. (y <= 2.2d-9))) then
        tmp = t_1
    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 t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.08e+64) {
		tmp = t_1;
	} else if (y <= -1.62e+32) {
		tmp = x * (t + (y * 2.0));
	} else if ((y <= -5.8e+15) || !(y <= 2.2e-9)) {
		tmp = t_1;
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.08e+64:
		tmp = t_1
	elif y <= -1.62e+32:
		tmp = x * (t + (y * 2.0))
	elif (y <= -5.8e+15) or not (y <= 2.2e-9):
		tmp = t_1
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -1.08e+64)
		tmp = t_1;
	elseif (y <= -1.62e+32)
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	elseif ((y <= -5.8e+15) || !(y <= 2.2e-9))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -1.08e+64)
		tmp = t_1;
	elseif (y <= -1.62e+32)
		tmp = x * (t + (y * 2.0));
	elseif ((y <= -5.8e+15) || ~((y <= 2.2e-9)))
		tmp = t_1;
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.08e+64], t$95$1, If[LessEqual[y, -1.62e+32], N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.8e+15], N[Not[LessEqual[y, 2.2e-9]], $MachinePrecision]], t$95$1, N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.08000000000000007e64 or -1.62e32 < y < -5.8e15 or 2.1999999999999998e-9 < 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 82.4%

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

   5. Simplified 82.4%

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

   if -1.08000000000000007e64 < y < -1.62e32

   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 inf 100.0%

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

   4. Taylor expanded in z around 0 78.0%

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

   if -5.8e15 < y < 2.1999999999999998e-9

   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 83.9%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+15} \lor \neg \left(y \leq 2.2 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-120}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+39} \lor \neg \left(x \leq 10^{+137}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* (+ y z) 2.0))))
   (if (<= x -1.3e-56)
     t_1
     (if (<= x 4e-120)
       (* y 5.0)
       (if (or (<= x 2.05e+39) (not (<= x 1e+137))) t_1 (* x t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -1.3e-56) {
		tmp = t_1;
	} else if (x <= 4e-120) {
		tmp = y * 5.0;
	} else if ((x <= 2.05e+39) || !(x <= 1e+137)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + z) * 2.0d0)
    if (x <= (-1.3d-56)) then
        tmp = t_1
    else if (x <= 4d-120) then
        tmp = y * 5.0d0
    else if ((x <= 2.05d+39) .or. (.not. (x <= 1d+137))) then
        tmp = t_1
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + z) * 2.0);
	double tmp;
	if (x <= -1.3e-56) {
		tmp = t_1;
	} else if (x <= 4e-120) {
		tmp = y * 5.0;
	} else if ((x <= 2.05e+39) || !(x <= 1e+137)) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + z) * 2.0)
	tmp = 0
	if x <= -1.3e-56:
		tmp = t_1
	elif x <= 4e-120:
		tmp = y * 5.0
	elif (x <= 2.05e+39) or not (x <= 1e+137):
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + z) * 2.0))
	tmp = 0.0
	if (x <= -1.3e-56)
		tmp = t_1;
	elseif (x <= 4e-120)
		tmp = Float64(y * 5.0);
	elseif ((x <= 2.05e+39) || !(x <= 1e+137))
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + z) * 2.0);
	tmp = 0.0;
	if (x <= -1.3e-56)
		tmp = t_1;
	elseif (x <= 4e-120)
		tmp = y * 5.0;
	elseif ((x <= 2.05e+39) || ~((x <= 1e+137)))
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e-56], t$95$1, If[LessEqual[x, 4e-120], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 2.05e+39], N[Not[LessEqual[x, 1e+137]], $MachinePrecision]], t$95$1, N[(x * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.29999999999999998e-56 or 3.99999999999999991e-120 < x < 2.05000000000000002e39 or 1e137 < 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 x around inf 93.5%

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

   4. Taylor expanded in t around 0 70.6%

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

      1. distribute-lft-in 70.6%

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

      2. +-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -1.29999999999999998e-56 < x < 3.99999999999999991e-120

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 64.9%

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

   if 2.05000000000000002e39 < x < 1e137

   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 62.2%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-120}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+39} \lor \neg \left(x \leq 10^{+137}\right):\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-120}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))))
   (if (<= x -8.5e+184)
     (* x (* (+ y z) 2.0))
     (if (<= x -1.2e-148)
       t_1
       (if (<= x 1.65e-120)
         (* y 5.0)
         (if (<= x 3.9e+257) t_1 (* x (+ t (* y 2.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -8.5e+184) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= -1.2e-148) {
		tmp = t_1;
	} else if (x <= 1.65e-120) {
		tmp = y * 5.0;
	} else if (x <= 3.9e+257) {
		tmp = t_1;
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    if (x <= (-8.5d+184)) then
        tmp = x * ((y + z) * 2.0d0)
    else if (x <= (-1.2d-148)) then
        tmp = t_1
    else if (x <= 1.65d-120) then
        tmp = y * 5.0d0
    else if (x <= 3.9d+257) then
        tmp = t_1
    else
        tmp = x * (t + (y * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double tmp;
	if (x <= -8.5e+184) {
		tmp = x * ((y + z) * 2.0);
	} else if (x <= -1.2e-148) {
		tmp = t_1;
	} else if (x <= 1.65e-120) {
		tmp = y * 5.0;
	} else if (x <= 3.9e+257) {
		tmp = t_1;
	} else {
		tmp = x * (t + (y * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	tmp = 0
	if x <= -8.5e+184:
		tmp = x * ((y + z) * 2.0)
	elif x <= -1.2e-148:
		tmp = t_1
	elif x <= 1.65e-120:
		tmp = y * 5.0
	elif x <= 3.9e+257:
		tmp = t_1
	else:
		tmp = x * (t + (y * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	tmp = 0.0
	if (x <= -8.5e+184)
		tmp = Float64(x * Float64(Float64(y + z) * 2.0));
	elseif (x <= -1.2e-148)
		tmp = t_1;
	elseif (x <= 1.65e-120)
		tmp = Float64(y * 5.0);
	elseif (x <= 3.9e+257)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t + Float64(y * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	tmp = 0.0;
	if (x <= -8.5e+184)
		tmp = x * ((y + z) * 2.0);
	elseif (x <= -1.2e-148)
		tmp = t_1;
	elseif (x <= 1.65e-120)
		tmp = y * 5.0;
	elseif (x <= 3.9e+257)
		tmp = t_1;
	else
		tmp = x * (t + (y * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e+184], N[(x * N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.2e-148], t$95$1, If[LessEqual[x, 1.65e-120], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 3.9e+257], t$95$1, N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.50000000000000043e184

   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 inf 100.0%

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

   4. Taylor expanded in t around 0 95.0%

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

      1. distribute-lft-in 95.0%

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

      2. +-commutative 95.0%

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

   6. Simplified 95.0%

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

   if -8.50000000000000043e184 < x < -1.2000000000000001e-148 or 1.64999999999999984e-120 < x < 3.90000000000000005e257

   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 73.2%

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

   if -1.2000000000000001e-148 < x < 1.64999999999999984e-120

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 69.9%

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

   if 3.90000000000000005e257 < 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 x around inf 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(\left(y + z\right) \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-120}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+257}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot 2\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-9}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-46}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+184}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y 2.0))))
   (if (<= x -4.8e+189)
     t_1
     (if (<= x -1.25e-9)
       (* x t)
       (if (<= x 2.75e-46) (* y 5.0) (if (<= x 1.55e+184) (* x t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * 2.0);
	double tmp;
	if (x <= -4.8e+189) {
		tmp = t_1;
	} else if (x <= -1.25e-9) {
		tmp = x * t;
	} else if (x <= 2.75e-46) {
		tmp = y * 5.0;
	} else if (x <= 1.55e+184) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * 2.0d0)
    if (x <= (-4.8d+189)) then
        tmp = t_1
    else if (x <= (-1.25d-9)) then
        tmp = x * t
    else if (x <= 2.75d-46) then
        tmp = y * 5.0d0
    else if (x <= 1.55d+184) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y * 2.0);
	double tmp;
	if (x <= -4.8e+189) {
		tmp = t_1;
	} else if (x <= -1.25e-9) {
		tmp = x * t;
	} else if (x <= 2.75e-46) {
		tmp = y * 5.0;
	} else if (x <= 1.55e+184) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * 2.0)
	tmp = 0
	if x <= -4.8e+189:
		tmp = t_1
	elif x <= -1.25e-9:
		tmp = x * t
	elif x <= 2.75e-46:
		tmp = y * 5.0
	elif x <= 1.55e+184:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y * 2.0))
	tmp = 0.0
	if (x <= -4.8e+189)
		tmp = t_1;
	elseif (x <= -1.25e-9)
		tmp = Float64(x * t);
	elseif (x <= 2.75e-46)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.55e+184)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y * 2.0);
	tmp = 0.0;
	if (x <= -4.8e+189)
		tmp = t_1;
	elseif (x <= -1.25e-9)
		tmp = x * t;
	elseif (x <= 2.75e-46)
		tmp = y * 5.0;
	elseif (x <= 1.55e+184)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+189], t$95$1, If[LessEqual[x, -1.25e-9], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.75e-46], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.55e+184], N[(x * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8000000000000001e189 or 1.5499999999999999e184 < 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 x around inf 100.0%

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

   4. Taylor expanded in y around inf 56.8%

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

      1. associate-*r* 56.8%

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

      2. *-commutative 56.8%

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

      3. associate-*r* 56.8%

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

   6. Simplified 56.8%

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

   if -4.8000000000000001e189 < x < -1.25e-9 or 2.74999999999999992e-46 < x < 1.5499999999999999e184

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 42.3%

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

   if -1.25e-9 < x < 2.74999999999999992e-46

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 58.4%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-9}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-46}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+184}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -25500000000 \lor \neg \left(x \leq 2.5\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(z \cdot 2\right) + x \cdot t\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -25500000000.0) (not (<= x 2.5)))
   (* x (+ t (+ (* y 2.0) (* z 2.0))))
   (+ (+ (* x (* z 2.0)) (* x t)) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -25500000000.0) || !(x <= 2.5)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} else {
		tmp = ((x * (z * 2.0)) + (x * t)) + (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 <= (-25500000000.0d0)) .or. (.not. (x <= 2.5d0))) then
        tmp = x * (t + ((y * 2.0d0) + (z * 2.0d0)))
    else
        tmp = ((x * (z * 2.0d0)) + (x * t)) + (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 <= -25500000000.0) || !(x <= 2.5)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} else {
		tmp = ((x * (z * 2.0)) + (x * t)) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -25500000000.0) or not (x <= 2.5):
		tmp = x * (t + ((y * 2.0) + (z * 2.0)))
	else:
		tmp = ((x * (z * 2.0)) + (x * t)) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -25500000000.0) || !(x <= 2.5))
		tmp = Float64(x * Float64(t + Float64(Float64(y * 2.0) + Float64(z * 2.0))));
	else
		tmp = Float64(Float64(Float64(x * Float64(z * 2.0)) + Float64(x * t)) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -25500000000.0) || ~((x <= 2.5)))
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	else
		tmp = ((x * (z * 2.0)) + (x * t)) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -25500000000.0], N[Not[LessEqual[x, 2.5]], $MachinePrecision]], N[(x * N[(t + N[(N[(y * 2.0), $MachinePrecision] + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.55e10 or 2.5 < 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 x around inf 99.5%

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

   if -2.55e10 < x < 2.5

   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 y around 0 99.3%

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

      1. distribute-lft-in 99.3%

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

      2. *-commutative 99.3%

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

   5. Applied egg-rr 99.3%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -25500000000 \lor \neg \left(x \leq 2.5\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(z \cdot 2\right) + x \cdot t\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -25500000000 \lor \neg \left(x \leq 2.5\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -25500000000.0) (not (<= x 2.5)))
   (* x (+ t (+ (* y 2.0) (* z 2.0))))
   (+ (* y 5.0) (* x (+ t (* z 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -25500000000.0) || !(x <= 2.5)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} 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 <= (-25500000000.0d0)) .or. (.not. (x <= 2.5d0))) then
        tmp = x * (t + ((y * 2.0d0) + (z * 2.0d0)))
    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 <= -25500000000.0) || !(x <= 2.5)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -25500000000.0) or not (x <= 2.5):
		tmp = x * (t + ((y * 2.0) + (z * 2.0)))
	else:
		tmp = (y * 5.0) + (x * (t + (z * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -25500000000.0) || !(x <= 2.5))
		tmp = Float64(x * Float64(t + Float64(Float64(y * 2.0) + Float64(z * 2.0))));
	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 <= -25500000000.0) || ~((x <= 2.5)))
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	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, -25500000000.0], N[Not[LessEqual[x, 2.5]], $MachinePrecision]], N[(x * N[(t + N[(N[(y * 2.0), $MachinePrecision] + N[(z * 2.0), $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 < -2.55e10 or 2.5 < 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 x around inf 99.5%

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

   if -2.55e10 < x < 2.5

   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 y around 0 99.3%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -25500000000 \lor \neg \left(x \leq 2.5\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.35 \cdot 10^{-69} \lor \neg \left(x \leq 1.65 \cdot 10^{-120}\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.35e-69) (not (<= x 1.65e-120)))
   (* x (+ t (+ (* y 2.0) (* z 2.0))))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.35e-69) || !(x <= 1.65e-120)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} 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 <= (-4.35d-69)) .or. (.not. (x <= 1.65d-120))) then
        tmp = x * (t + ((y * 2.0d0) + (z * 2.0d0)))
    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 <= -4.35e-69) || !(x <= 1.65e-120)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.35e-69) or not (x <= 1.65e-120):
		tmp = x * (t + ((y * 2.0) + (z * 2.0)))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.35e-69) || !(x <= 1.65e-120))
		tmp = Float64(x * Float64(t + Float64(Float64(y * 2.0) + Float64(z * 2.0))));
	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 <= -4.35e-69) || ~((x <= 1.65e-120)))
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.35e-69], N[Not[LessEqual[x, 1.65e-120]], $MachinePrecision]], N[(x * N[(t + N[(N[(y * 2.0), $MachinePrecision] + N[(z * 2.0), $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 < -4.34999999999999976e-69 or 1.64999999999999984e-120 < 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 x around inf 94.2%

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

   if -4.34999999999999976e-69 < x < 1.64999999999999984e-120

   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 y around 0 99.8%

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

   4. Taylor expanded in z around 0 86.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.35 \cdot 10^{-69} \lor \neg \left(x \leq 1.65 \cdot 10^{-120}\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 14: 41.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -24000000000 \lor \neg \left(y \leq 3.9 \cdot 10^{-141}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -24000000000.0) (not (<= y 3.9e-141))) (* y 5.0) (* x t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -24000000000.0) || !(y <= 3.9e-141)) {
		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 <= (-24000000000.0d0)) .or. (.not. (y <= 3.9d-141))) 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 <= -24000000000.0) || !(y <= 3.9e-141)) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -24000000000.0) or not (y <= 3.9e-141):
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -24000000000.0) || !(y <= 3.9e-141))
		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 <= -24000000000.0) || ~((y <= 3.9e-141)))
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -24000000000.0], N[Not[LessEqual[y, 3.9e-141]], $MachinePrecision]], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e10 or 3.8999999999999997e-141 < 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 47.5%

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

   if -2.4e10 < y < 3.8999999999999997e-141

   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 48.3%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -24000000000 \lor \neg \left(y \leq 3.9 \cdot 10^{-141}\right):\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.0% 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 30.4%

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

4. Final simplification 30.4%

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

Reproduce

herbie shell --seed 2024085 
(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)))