AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1

Percentage Accurate: 61.6% → 87.6%

Time: 13.1s

Alternatives: 12

Speedup: 0.6×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
}

Python

def code(x, y, z, t, a, b):
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]

Initial Program: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
}

Python

def code(x, y, z, t, a, b):
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+241}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+241))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+241)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+241)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+241):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+241))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+241)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+241]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.0000000000000001e241 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 70.3%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e241

   1. Initial program 99.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+241}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 58.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(y + t\right) \cdot a - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+26}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-138}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-207}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-274}:\\ \;\;\;\;z \cdot \frac{1}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (* (+ y t) a) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (<= y -3.2e+26)
     t_3
     (if (<= y -4.3e-51)
       t_2
       (if (<= y -5.6e-138)
         (* z (/ (+ x y) t_1))
         (if (<= y -3.1e-207)
           a
           (if (<= y 8.4e-274)
             (* z (/ 1.0 (/ (+ t (+ x y)) (+ x y))))
             (if (<= y 2.5e-25) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((y + t) * a) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -3.2e+26) {
		tmp = t_3;
	} else if (y <= -4.3e-51) {
		tmp = t_2;
	} else if (y <= -5.6e-138) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -3.1e-207) {
		tmp = a;
	} else if (y <= 8.4e-274) {
		tmp = z * (1.0 / ((t + (x + y)) / (x + y)));
	} else if (y <= 2.5e-25) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (((y + t) * a) - (y * b)) / t_1
    t_3 = (z + a) - b
    if (y <= (-3.2d+26)) then
        tmp = t_3
    else if (y <= (-4.3d-51)) then
        tmp = t_2
    else if (y <= (-5.6d-138)) then
        tmp = z * ((x + y) / t_1)
    else if (y <= (-3.1d-207)) then
        tmp = a
    else if (y <= 8.4d-274) then
        tmp = z * (1.0d0 / ((t + (x + y)) / (x + y)))
    else if (y <= 2.5d-25) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((y + t) * a) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -3.2e+26) {
		tmp = t_3;
	} else if (y <= -4.3e-51) {
		tmp = t_2;
	} else if (y <= -5.6e-138) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -3.1e-207) {
		tmp = a;
	} else if (y <= 8.4e-274) {
		tmp = z * (1.0 / ((t + (x + y)) / (x + y)));
	} else if (y <= 2.5e-25) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((y + t) * a) - (y * b)) / t_1
	t_3 = (z + a) - b
	tmp = 0
	if y <= -3.2e+26:
		tmp = t_3
	elif y <= -4.3e-51:
		tmp = t_2
	elif y <= -5.6e-138:
		tmp = z * ((x + y) / t_1)
	elif y <= -3.1e-207:
		tmp = a
	elif y <= 8.4e-274:
		tmp = z * (1.0 / ((t + (x + y)) / (x + y)))
	elif y <= 2.5e-25:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.2e+26)
		tmp = t_3;
	elseif (y <= -4.3e-51)
		tmp = t_2;
	elseif (y <= -5.6e-138)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	elseif (y <= -3.1e-207)
		tmp = a;
	elseif (y <= 8.4e-274)
		tmp = Float64(z * Float64(1.0 / Float64(Float64(t + Float64(x + y)) / Float64(x + y))));
	elseif (y <= 2.5e-25)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((y + t) * a) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.2e+26)
		tmp = t_3;
	elseif (y <= -4.3e-51)
		tmp = t_2;
	elseif (y <= -5.6e-138)
		tmp = z * ((x + y) / t_1);
	elseif (y <= -3.1e-207)
		tmp = a;
	elseif (y <= 8.4e-274)
		tmp = z * (1.0 / ((t + (x + y)) / (x + y)));
	elseif (y <= 2.5e-25)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.2e+26], t$95$3, If[LessEqual[y, -4.3e-51], t$95$2, If[LessEqual[y, -5.6e-138], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.1e-207], a, If[LessEqual[y, 8.4e-274], N[(z * N[(1.0 / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-25], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.20000000000000029e26 or 2.49999999999999981e-25 < y

   1. Initial program 47.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.3%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -3.20000000000000029e26 < y < -4.2999999999999997e-51 or 8.39999999999999977e-274 < y < 2.49999999999999981e-25

   1. Initial program 83.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 61.8%

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

      1. *-commutative 61.8%

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

   5. Simplified 61.8%

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

   if -4.2999999999999997e-51 < y < -5.60000000000000002e-138

   1. Initial program 91.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.6%

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

      1. associate-/l* 75.8%

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

      2. +-commutative 75.8%

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

      3. associate-+r+ 75.8%

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

   5. Simplified 75.8%

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

   if -5.60000000000000002e-138 < y < -3.1000000000000001e-207

   1. Initial program 67.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.7%

      \[\leadsto \color{blue}{a} \]

   if -3.1000000000000001e-207 < y < 8.39999999999999977e-274

   1. Initial program 66.8%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 40.3%

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

      1. associate-/l* 55.6%

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

      2. +-commutative 55.6%

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

      3. associate-+r+ 55.6%

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

   5. Simplified 55.6%

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

      1. clear-num 55.7%

         \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{\left(t + x\right) + y}{y + x}}} \]

      2. inv-pow 55.7%

         \[\leadsto z \cdot \color{blue}{{\left(\frac{\left(t + x\right) + y}{y + x}\right)}^{-1}} \]

      3. associate-+l+ 55.7%

         \[\leadsto z \cdot {\left(\frac{\color{blue}{t + \left(x + y\right)}}{y + x}\right)}^{-1} \]

      4. +-commutative 55.7%

         \[\leadsto z \cdot {\left(\frac{t + \color{blue}{\left(y + x\right)}}{y + x}\right)}^{-1} \]

   7. Applied egg-rr 55.7%

      \[\leadsto z \cdot \color{blue}{{\left(\frac{t + \left(y + x\right)}{y + x}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 55.7%

         \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{t + \left(y + x\right)}{y + x}}} \]

   9. Simplified 55.7%

      \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{t + \left(y + x\right)}{y + x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+26}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-51}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-138}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-207}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-274}:\\ \;\;\;\;z \cdot \frac{1}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z \cdot \left(x + y\right)\\ t_3 := y + \left(x + t\right)\\ t_4 := a \cdot \frac{y + t}{t\_3}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+156}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq -3500000:\\ \;\;\;\;z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{t\_2}\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 0.19:\\ \;\;\;\;\frac{t\_2 - y \cdot b}{t\_3}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (* z (+ x y)))
        (t_3 (+ y (+ x t)))
        (t_4 (* a (/ (+ y t) t_3))))
   (if (<= a -1.2e+156)
     t_4
     (if (<= a -3500000.0)
       (* z (+ 1.0 (/ (* y (- a b)) t_2)))
       (if (<= a -1.2e-174)
         t_1
         (if (<= a 0.19)
           (/ (- t_2 (* y b)) t_3)
           (if (<= a 1.5e+96) t_1 t_4)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z * (x + y);
	double t_3 = y + (x + t);
	double t_4 = a * ((y + t) / t_3);
	double tmp;
	if (a <= -1.2e+156) {
		tmp = t_4;
	} else if (a <= -3500000.0) {
		tmp = z * (1.0 + ((y * (a - b)) / t_2));
	} else if (a <= -1.2e-174) {
		tmp = t_1;
	} else if (a <= 0.19) {
		tmp = (t_2 - (y * b)) / t_3;
	} else if (a <= 1.5e+96) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z * (x + y)
    t_3 = y + (x + t)
    t_4 = a * ((y + t) / t_3)
    if (a <= (-1.2d+156)) then
        tmp = t_4
    else if (a <= (-3500000.0d0)) then
        tmp = z * (1.0d0 + ((y * (a - b)) / t_2))
    else if (a <= (-1.2d-174)) then
        tmp = t_1
    else if (a <= 0.19d0) then
        tmp = (t_2 - (y * b)) / t_3
    else if (a <= 1.5d+96) then
        tmp = t_1
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z * (x + y);
	double t_3 = y + (x + t);
	double t_4 = a * ((y + t) / t_3);
	double tmp;
	if (a <= -1.2e+156) {
		tmp = t_4;
	} else if (a <= -3500000.0) {
		tmp = z * (1.0 + ((y * (a - b)) / t_2));
	} else if (a <= -1.2e-174) {
		tmp = t_1;
	} else if (a <= 0.19) {
		tmp = (t_2 - (y * b)) / t_3;
	} else if (a <= 1.5e+96) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z * (x + y)
	t_3 = y + (x + t)
	t_4 = a * ((y + t) / t_3)
	tmp = 0
	if a <= -1.2e+156:
		tmp = t_4
	elif a <= -3500000.0:
		tmp = z * (1.0 + ((y * (a - b)) / t_2))
	elif a <= -1.2e-174:
		tmp = t_1
	elif a <= 0.19:
		tmp = (t_2 - (y * b)) / t_3
	elif a <= 1.5e+96:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z * Float64(x + y))
	t_3 = Float64(y + Float64(x + t))
	t_4 = Float64(a * Float64(Float64(y + t) / t_3))
	tmp = 0.0
	if (a <= -1.2e+156)
		tmp = t_4;
	elseif (a <= -3500000.0)
		tmp = Float64(z * Float64(1.0 + Float64(Float64(y * Float64(a - b)) / t_2)));
	elseif (a <= -1.2e-174)
		tmp = t_1;
	elseif (a <= 0.19)
		tmp = Float64(Float64(t_2 - Float64(y * b)) / t_3);
	elseif (a <= 1.5e+96)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = z * (x + y);
	t_3 = y + (x + t);
	t_4 = a * ((y + t) / t_3);
	tmp = 0.0;
	if (a <= -1.2e+156)
		tmp = t_4;
	elseif (a <= -3500000.0)
		tmp = z * (1.0 + ((y * (a - b)) / t_2));
	elseif (a <= -1.2e-174)
		tmp = t_1;
	elseif (a <= 0.19)
		tmp = (t_2 - (y * b)) / t_3;
	elseif (a <= 1.5e+96)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(y + t), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e+156], t$95$4, If[LessEqual[a, -3500000.0], N[(z * N[(1.0 + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.2e-174], t$95$1, If[LessEqual[a, 0.19], N[(N[(t$95$2 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[a, 1.5e+96], t$95$1, t$95$4]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.2000000000000001e156 or 1.5e96 < a

   1. Initial program 37.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 27.7%

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

      1. associate-/l* 76.4%

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

      2. associate-+r+ 76.4%

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

   5. Simplified 76.4%

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

   if -1.2000000000000001e156 < a < -3.5e6

   1. Initial program 87.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf 95.7%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 95.7%

         \[\leadsto \color{blue}{-z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)} \]

      2. distribute-rgt-neg-in 95.7%

         \[\leadsto \color{blue}{z \cdot \left(-\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)} \]

      3. mul-1-neg 95.7%

         \[\leadsto z \cdot \left(-\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \color{blue}{\left(-\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right)\right) \]

      4. unsub-neg 95.7%

         \[\leadsto z \cdot \left(-\color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} - \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right) \]

   5. Simplified 95.7%

      \[\leadsto \color{blue}{z \cdot \left(-\left(\frac{\left(-x\right) - y}{\left(t + x\right) + y} - \frac{\frac{a \cdot \left(t + y\right) - y \cdot b}{\left(t + x\right) + y}}{z}\right)\right)} \]

   6. Taylor expanded in t around 0 78.7%

      \[\leadsto \color{blue}{z \cdot \left(\left(1 + \frac{a \cdot y}{z \cdot \left(x + y\right)}\right) - \frac{b \cdot y}{z \cdot \left(x + y\right)}\right)} \]
   7. Step-by-step derivation

      1. associate--l+ 78.7%

         \[\leadsto z \cdot \color{blue}{\left(1 + \left(\frac{a \cdot y}{z \cdot \left(x + y\right)} - \frac{b \cdot y}{z \cdot \left(x + y\right)}\right)\right)} \]

      2. div-sub 78.7%

         \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a \cdot y - b \cdot y}{z \cdot \left(x + y\right)}}\right) \]

      3. distribute-rgt-out-- 78.7%

         \[\leadsto z \cdot \left(1 + \frac{\color{blue}{y \cdot \left(a - b\right)}}{z \cdot \left(x + y\right)}\right) \]

      4. *-commutative 78.7%

         \[\leadsto z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{\color{blue}{\left(x + y\right) \cdot z}}\right) \]

      5. +-commutative 78.7%

         \[\leadsto z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{\color{blue}{\left(y + x\right)} \cdot z}\right) \]

   8. Simplified 78.7%

      \[\leadsto \color{blue}{z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{\left(y + x\right) \cdot z}\right)} \]

   if -3.5e6 < a < -1.2e-174 or 0.19 < a < 1.5e96

   1. Initial program 59.1%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 61.4%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -1.2e-174 < a < 0.19

   1. Initial program 78.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 68.5%

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

      1. +-commutative 68.5%

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

      2. *-commutative 68.5%

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

   5. Simplified 68.5%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+156}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -3500000:\\ \;\;\;\;z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{z \cdot \left(x + y\right)}\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-174}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 0.19:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+96}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{t\_1}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{a}{z} \cdot \frac{t}{x + t}\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)))
   (if (<= y -6.5e+26)
     t_2
     (if (<= y -8.6e-44)
       (/ (- (* (+ y t) a) (* y b)) t_1)
       (if (<= y 1.65e-187)
         (* z (+ (/ x (+ x t)) (* (/ a z) (/ t (+ x t)))))
         (if (<= y 5.6e-20) (/ (- (* z (+ x y)) (* y b)) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.5e+26) {
		tmp = t_2;
	} else if (y <= -8.6e-44) {
		tmp = (((y + t) * a) - (y * b)) / t_1;
	} else if (y <= 1.65e-187) {
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))));
	} else if (y <= 5.6e-20) {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (z + a) - b
    if (y <= (-6.5d+26)) then
        tmp = t_2
    else if (y <= (-8.6d-44)) then
        tmp = (((y + t) * a) - (y * b)) / t_1
    else if (y <= 1.65d-187) then
        tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))))
    else if (y <= 5.6d-20) then
        tmp = ((z * (x + y)) - (y * b)) / 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 a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.5e+26) {
		tmp = t_2;
	} else if (y <= -8.6e-44) {
		tmp = (((y + t) * a) - (y * b)) / t_1;
	} else if (y <= 1.65e-187) {
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))));
	} else if (y <= 5.6e-20) {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -6.5e+26:
		tmp = t_2
	elif y <= -8.6e-44:
		tmp = (((y + t) * a) - (y * b)) / t_1
	elif y <= 1.65e-187:
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))))
	elif y <= 5.6e-20:
		tmp = ((z * (x + y)) - (y * b)) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6.5e+26)
		tmp = t_2;
	elseif (y <= -8.6e-44)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / t_1);
	elseif (y <= 1.65e-187)
		tmp = Float64(z * Float64(Float64(x / Float64(x + t)) + Float64(Float64(a / z) * Float64(t / Float64(x + t)))));
	elseif (y <= 5.6e-20)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6.5e+26)
		tmp = t_2;
	elseif (y <= -8.6e-44)
		tmp = (((y + t) * a) - (y * b)) / t_1;
	elseif (y <= 1.65e-187)
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))));
	elseif (y <= 5.6e-20)
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.5e+26], t$95$2, If[LessEqual[y, -8.6e-44], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 1.65e-187], N[(z * N[(N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(a / z), $MachinePrecision] * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-20], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.50000000000000022e26 or 5.6000000000000005e-20 < y

   1. Initial program 47.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.3%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -6.50000000000000022e26 < y < -8.60000000000000027e-44

   1. Initial program 76.1%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 76.0%

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

      1. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   if -8.60000000000000027e-44 < y < 1.65e-187

   1. Initial program 75.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf 80.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 80.2%

         \[\leadsto \color{blue}{-z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)} \]

      2. distribute-rgt-neg-in 80.2%

         \[\leadsto \color{blue}{z \cdot \left(-\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)} \]

      3. mul-1-neg 80.2%

         \[\leadsto z \cdot \left(-\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \color{blue}{\left(-\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right)\right) \]

      4. unsub-neg 80.2%

         \[\leadsto z \cdot \left(-\color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} - \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right) \]

   5. Simplified 80.2%

      \[\leadsto \color{blue}{z \cdot \left(-\left(\frac{\left(-x\right) - y}{\left(t + x\right) + y} - \frac{\frac{a \cdot \left(t + y\right) - y \cdot b}{\left(t + x\right) + y}}{z}\right)\right)} \]

   6. Taylor expanded in b around inf 63.9%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{y}{t + \left(x + y\right)} + \frac{z \cdot \left(\frac{a \cdot \left(t + y\right)}{z \cdot \left(t + \left(x + y\right)\right)} - -1 \cdot \frac{x + y}{t + \left(x + y\right)}\right)}{b}\right)} \]
   7. Step-by-step derivation

      1. fma-define 63.9%

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

      2. +-commutative 63.9%

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

      3. associate-/l* 61.3%

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

   8. Simplified 70.2%

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

   9. Taylor expanded in y around 0 71.7%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t + x} + \frac{a \cdot t}{z \cdot \left(t + x\right)}\right)} \]
   10. Step-by-step derivation

       1. +-commutative 71.7%

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

       2. times-frac 79.4%

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

       3. +-commutative 79.4%

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

   11. Simplified 79.4%

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

   if 1.65e-187 < y < 5.6000000000000005e-20

   1. Initial program 85.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 67.8%

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

      1. +-commutative 67.8%

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

      2. *-commutative 67.8%

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

   5. Simplified 67.8%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+26}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{a}{z} \cdot \frac{t}{x + t}\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+135}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-116}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+120}:\\ \;\;\;\;z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{z \cdot \left(x + y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4e+135)
   (* a (/ t (+ x t)))
   (if (<= t -2.1e-116)
     (- (+ z a) b)
     (if (<= t 6.8e+120)
       (* z (+ 1.0 (/ (* y (- a b)) (* z (+ x y)))))
       (* a (/ (+ y t) (+ y (+ x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4e+135) {
		tmp = a * (t / (x + t));
	} else if (t <= -2.1e-116) {
		tmp = (z + a) - b;
	} else if (t <= 6.8e+120) {
		tmp = z * (1.0 + ((y * (a - b)) / (z * (x + y))));
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4d+135)) then
        tmp = a * (t / (x + t))
    else if (t <= (-2.1d-116)) then
        tmp = (z + a) - b
    else if (t <= 6.8d+120) then
        tmp = z * (1.0d0 + ((y * (a - b)) / (z * (x + y))))
    else
        tmp = a * ((y + t) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4e+135) {
		tmp = a * (t / (x + t));
	} else if (t <= -2.1e-116) {
		tmp = (z + a) - b;
	} else if (t <= 6.8e+120) {
		tmp = z * (1.0 + ((y * (a - b)) / (z * (x + y))));
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4e+135:
		tmp = a * (t / (x + t))
	elif t <= -2.1e-116:
		tmp = (z + a) - b
	elif t <= 6.8e+120:
		tmp = z * (1.0 + ((y * (a - b)) / (z * (x + y))))
	else:
		tmp = a * ((y + t) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4e+135)
		tmp = Float64(a * Float64(t / Float64(x + t)));
	elseif (t <= -2.1e-116)
		tmp = Float64(Float64(z + a) - b);
	elseif (t <= 6.8e+120)
		tmp = Float64(z * Float64(1.0 + Float64(Float64(y * Float64(a - b)) / Float64(z * Float64(x + y)))));
	else
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4e+135)
		tmp = a * (t / (x + t));
	elseif (t <= -2.1e-116)
		tmp = (z + a) - b;
	elseif (t <= 6.8e+120)
		tmp = z * (1.0 + ((y * (a - b)) / (z * (x + y))));
	else
		tmp = a * ((y + t) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4e+135], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.1e-116], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 6.8e+120], N[(z * N[(1.0 + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.99999999999999985e135

   1. Initial program 52.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 35.5%

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

      1. *-commutative 35.5%

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

   5. Simplified 35.5%

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

   6. Taylor expanded in y around 0 26.9%

      \[\leadsto \color{blue}{\frac{a \cdot t}{t + x}} \]
   7. Step-by-step derivation

      1. associate-/l* 60.1%

         \[\leadsto \color{blue}{a \cdot \frac{t}{t + x}} \]

      2. +-commutative 60.1%

         \[\leadsto a \cdot \frac{t}{\color{blue}{x + t}} \]

   8. Simplified 60.1%

      \[\leadsto \color{blue}{a \cdot \frac{t}{x + t}} \]

   if -3.99999999999999985e135 < t < -2.0999999999999999e-116

   1. Initial program 60.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 56.8%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -2.0999999999999999e-116 < t < 6.79999999999999998e120

   1. Initial program 73.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf 80.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 80.3%

         \[\leadsto \color{blue}{-z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)} \]

      2. distribute-rgt-neg-in 80.3%

         \[\leadsto \color{blue}{z \cdot \left(-\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)} \]

      3. mul-1-neg 80.3%

         \[\leadsto z \cdot \left(-\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \color{blue}{\left(-\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right)\right) \]

      4. unsub-neg 80.3%

         \[\leadsto z \cdot \left(-\color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} - \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right) \]

   5. Simplified 80.3%

      \[\leadsto \color{blue}{z \cdot \left(-\left(\frac{\left(-x\right) - y}{\left(t + x\right) + y} - \frac{\frac{a \cdot \left(t + y\right) - y \cdot b}{\left(t + x\right) + y}}{z}\right)\right)} \]

   6. Taylor expanded in t around 0 71.2%

      \[\leadsto \color{blue}{z \cdot \left(\left(1 + \frac{a \cdot y}{z \cdot \left(x + y\right)}\right) - \frac{b \cdot y}{z \cdot \left(x + y\right)}\right)} \]
   7. Step-by-step derivation

      1. associate--l+ 71.2%

         \[\leadsto z \cdot \color{blue}{\left(1 + \left(\frac{a \cdot y}{z \cdot \left(x + y\right)} - \frac{b \cdot y}{z \cdot \left(x + y\right)}\right)\right)} \]

      2. div-sub 71.3%

         \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a \cdot y - b \cdot y}{z \cdot \left(x + y\right)}}\right) \]

      3. distribute-rgt-out-- 71.3%

         \[\leadsto z \cdot \left(1 + \frac{\color{blue}{y \cdot \left(a - b\right)}}{z \cdot \left(x + y\right)}\right) \]

      4. *-commutative 71.3%

         \[\leadsto z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{\color{blue}{\left(x + y\right) \cdot z}}\right) \]

      5. +-commutative 71.3%

         \[\leadsto z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{\color{blue}{\left(y + x\right)} \cdot z}\right) \]

   8. Simplified 71.3%

      \[\leadsto \color{blue}{z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{\left(y + x\right) \cdot z}\right)} \]

   if 6.79999999999999998e120 < t

   1. Initial program 35.3%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 21.3%

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

      1. associate-/l* 49.4%

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

      2. associate-+r+ 49.4%

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

   5. Simplified 49.4%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+135}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-116}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+120}:\\ \;\;\;\;z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{z \cdot \left(x + y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+97}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+31}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+119}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.2e+97)
   z
   (if (<= x -6.5e+31)
     a
     (if (<= x -4.2e-57) z (if (<= x 2.9e+119) (- a b) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.2e+97) {
		tmp = z;
	} else if (x <= -6.5e+31) {
		tmp = a;
	} else if (x <= -4.2e-57) {
		tmp = z;
	} else if (x <= 2.9e+119) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.2d+97)) then
        tmp = z
    else if (x <= (-6.5d+31)) then
        tmp = a
    else if (x <= (-4.2d-57)) then
        tmp = z
    else if (x <= 2.9d+119) then
        tmp = a - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.2e+97) {
		tmp = z;
	} else if (x <= -6.5e+31) {
		tmp = a;
	} else if (x <= -4.2e-57) {
		tmp = z;
	} else if (x <= 2.9e+119) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.2e+97:
		tmp = z
	elif x <= -6.5e+31:
		tmp = a
	elif x <= -4.2e-57:
		tmp = z
	elif x <= 2.9e+119:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.2e+97)
		tmp = z;
	elseif (x <= -6.5e+31)
		tmp = a;
	elseif (x <= -4.2e-57)
		tmp = z;
	elseif (x <= 2.9e+119)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.2e+97)
		tmp = z;
	elseif (x <= -6.5e+31)
		tmp = a;
	elseif (x <= -4.2e-57)
		tmp = z;
	elseif (x <= 2.9e+119)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.2e+97], z, If[LessEqual[x, -6.5e+31], a, If[LessEqual[x, -4.2e-57], z, If[LessEqual[x, 2.9e+119], N[(a - b), $MachinePrecision], z]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2000000000000001e97 or -6.5000000000000004e31 < x < -4.1999999999999999e-57 or 2.90000000000000007e119 < x

   1. Initial program 54.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 52.1%

      \[\leadsto \color{blue}{z} \]

   if -2.2000000000000001e97 < x < -6.5000000000000004e31

   1. Initial program 47.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 67.6%

      \[\leadsto \color{blue}{a} \]

   if -4.1999999999999999e-57 < x < 2.90000000000000007e119

   1. Initial program 68.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 52.4%

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

      1. *-commutative 52.4%

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

   5. Simplified 52.4%

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

   6. Taylor expanded in y around inf 52.0%

      \[\leadsto \color{blue}{a - b} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 58.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+45} \lor \neg \left(x \leq 2.4 \cdot 10^{+123}\right):\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -4.9e+45) (not (<= x 2.4e+123)))
   (* z (/ (+ x y) (+ y (+ x t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -4.9e+45) || !(x <= 2.4e+123)) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-4.9d+45)) .or. (.not. (x <= 2.4d+123))) then
        tmp = z * ((x + y) / (y + (x + t)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -4.9e+45) || !(x <= 2.4e+123)) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -4.9e+45) or not (x <= 2.4e+123):
		tmp = z * ((x + y) / (y + (x + t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -4.9e+45) || !(x <= 2.4e+123))
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -4.9e+45) || ~((x <= 2.4e+123)))
		tmp = z * ((x + y) / (y + (x + t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -4.9e+45], N[Not[LessEqual[x, 2.4e+123]], $MachinePrecision]], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9000000000000002e45 or 2.39999999999999989e123 < x

   1. Initial program 51.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 33.0%

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

      1. associate-/l* 60.0%

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

      2. +-commutative 60.0%

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

      3. associate-+r+ 60.0%

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

   5. Simplified 60.0%

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

   if -4.9000000000000002e45 < x < 2.39999999999999989e123

   1. Initial program 67.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.2%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+45} \lor \neg \left(x \leq 2.4 \cdot 10^{+123}\right):\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+107} \lor \neg \left(x \leq 3.7 \cdot 10^{+154}\right):\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.4e+107) (not (<= x 3.7e+154)))
   (- z (/ (* y b) x))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.4e+107) || !(x <= 3.7e+154)) {
		tmp = z - ((y * b) / x);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.4d+107)) .or. (.not. (x <= 3.7d+154))) then
        tmp = z - ((y * b) / x)
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.4e+107) || !(x <= 3.7e+154)) {
		tmp = z - ((y * b) / x);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.4e+107) or not (x <= 3.7e+154):
		tmp = z - ((y * b) / x)
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.4e+107) || !(x <= 3.7e+154))
		tmp = Float64(z - Float64(Float64(y * b) / x));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.4e+107) || ~((x <= 3.7e+154)))
		tmp = z - ((y * b) / x);
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.4e+107], N[Not[LessEqual[x, 3.7e+154]], $MachinePrecision]], N[(z - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999992e107 or 3.69999999999999994e154 < x

   1. Initial program 53.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 42.2%

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

      1. +-commutative 42.2%

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

      2. *-commutative 42.2%

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

   5. Simplified 42.2%

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

   6. Taylor expanded in t around 0 42.2%

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

   7. Taylor expanded in x around inf 60.8%

      \[\leadsto \color{blue}{z + -1 \cdot \frac{b \cdot y}{x}} \]
   8. Step-by-step derivation

      1. mul-1-neg 60.8%

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

      2. distribute-frac-neg2 60.8%

         \[\leadsto z + \color{blue}{\frac{b \cdot y}{-x}} \]

   9. Simplified 60.8%

      \[\leadsto \color{blue}{z + \frac{b \cdot y}{-x}} \]

   if -1.39999999999999992e107 < x < 3.69999999999999994e154

   1. Initial program 65.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 63.6%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+107} \lor \neg \left(x \leq 3.7 \cdot 10^{+154}\right):\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+135}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+156}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.75e+135) z (if (<= x 4.8e+156) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.75e+135) {
		tmp = z;
	} else if (x <= 4.8e+156) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.75d+135)) then
        tmp = z
    else if (x <= 4.8d+156) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.75e+135) {
		tmp = z;
	} else if (x <= 4.8e+156) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.75e+135:
		tmp = z
	elif x <= 4.8e+156:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.75e+135)
		tmp = z;
	elseif (x <= 4.8e+156)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.75e+135)
		tmp = z;
	elseif (x <= 4.8e+156)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.75e+135], z, If[LessEqual[x, 4.8e+156], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7500000000000001e135 or 4.8000000000000002e156 < x

   1. Initial program 57.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.0%

      \[\leadsto \color{blue}{z} \]

   if -1.7500000000000001e135 < x < 4.8000000000000002e156

   1. Initial program 63.8%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.2%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+135}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+156}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+75} \lor \neg \left(z \leq 7.6 \cdot 10^{+142}\right):\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.1e+75) (not (<= z 7.6e+142))) (- z b) (- a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.1e+75) || !(z <= 7.6e+142)) {
		tmp = z - b;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.1d+75)) .or. (.not. (z <= 7.6d+142))) then
        tmp = z - b
    else
        tmp = a - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.1e+75) || !(z <= 7.6e+142)) {
		tmp = z - b;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.1e+75) or not (z <= 7.6e+142):
		tmp = z - b
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.1e+75) || !(z <= 7.6e+142))
		tmp = Float64(z - b);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.1e+75) || ~((z <= 7.6e+142)))
		tmp = z - b;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.1e+75], N[Not[LessEqual[z, 7.6e+142]], $MachinePrecision]], N[(z - b), $MachinePrecision], N[(a - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0999999999999998e75 or 7.59999999999999979e142 < z

   1. Initial program 39.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 34.5%

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

      1. +-commutative 34.5%

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

      2. *-commutative 34.5%

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

   5. Simplified 34.5%

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

   6. Taylor expanded in y around inf 58.0%

      \[\leadsto \color{blue}{z - b} \]

   if -4.0999999999999998e75 < z < 7.59999999999999979e142

   1. Initial program 73.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 53.3%

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

      1. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in y around inf 46.5%

      \[\leadsto \color{blue}{a - b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+75} \lor \neg \left(z \leq 7.6 \cdot 10^{+142}\right):\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+76}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+142}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -9.4e+76) z (if (<= z 7.5e+142) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.4e+76) {
		tmp = z;
	} else if (z <= 7.5e+142) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-9.4d+76)) then
        tmp = z
    else if (z <= 7.5d+142) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.4e+76) {
		tmp = z;
	} else if (z <= 7.5e+142) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -9.4e+76:
		tmp = z
	elif z <= 7.5e+142:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -9.4e+76)
		tmp = z;
	elseif (z <= 7.5e+142)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -9.4e+76)
		tmp = z;
	elseif (z <= 7.5e+142)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -9.4e+76], z, If[LessEqual[z, 7.5e+142], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4000000000000006e76 or 7.5000000000000002e142 < z

   1. Initial program 39.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 55.6%

      \[\leadsto \color{blue}{z} \]

   if -9.4000000000000006e76 < z < 7.5000000000000002e142

   1. Initial program 73.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 42.4%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 32.2% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 62.2%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
2. Add Preprocessing

3. Taylor expanded in t around inf 34.9%

   \[\leadsto \color{blue}{a} \]
4. Add Preprocessing

Developer target: 82.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t\_2}{t\_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t\_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t\_1}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
        (t_3 (/ t_2 t_1))
        (t_4 (- (+ z a) b)))
   (if (< t_3 -3.5813117084150564e+153)
     t_4
     (if (< t_3 1.2285964308315609e+82) (/ 1.0 (/ t_1 t_2)) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
    t_3 = t_2 / t_1
    t_4 = (z + a) - b
    if (t_3 < (-3.5813117084150564d+153)) then
        tmp = t_4
    else if (t_3 < 1.2285964308315609d+82) then
        tmp = 1.0d0 / (t_1 / t_2)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
	t_3 = t_2 / t_1
	t_4 = (z + a) - b
	tmp = 0
	if t_3 < -3.5813117084150564e+153:
		tmp = t_4
	elif t_3 < 1.2285964308315609e+82:
		tmp = 1.0 / (t_1 / t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	t_3 = t_2 / t_1;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = 1.0 / (t_1 / t_2);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Less[t$95$3, -3.5813117084150564e+153], t$95$4, If[Less[t$95$3, 1.2285964308315609e+82], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Reproduce

herbie shell --seed 2024101 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1.0 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b)))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))