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

Percentage Accurate: 60.5% → 87.5%

Time: 13.1s

Alternatives: 12

Speedup: 0.8×

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: 60.5% 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: 87.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 4 \cdot 10^{+251}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_1\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 4e+251)))
     (- (+ z a) b)
     (/ (- (fma (+ x y) z t_1) (* y b)) (+ x (+ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = ((((x + y) * z) + t_1) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 4e+251)) {
		tmp = (z + a) - b;
	} else {
		tmp = (fma((x + y), z, t_1) - (y * b)) / (x + (y + t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 4e+251))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(fma(Float64(x + y), z, t_1) - Float64(y * b)) / Float64(x + Float64(y + t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 4e+251]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

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 4.0000000000000002e251 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.9%

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

   3. Taylor expanded in y around inf 76.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000002e251

   1. Initial program 99.0%

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

      1. fma-define 99.0%

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

      2. +-commutative 99.0%

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

      3. associate-+l+ 99.0%

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

      4. +-commutative 99.0%

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

   3. Simplified 99.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+251}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, a \cdot \left(y + t\right)\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+251}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+251))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+251)) {
		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 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+251)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+251):
		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(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+251))
		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 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+251)))
		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[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $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, 4e+251]], $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 4.0000000000000002e251 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.9%

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

   3. Taylor expanded in y around inf 76.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000002e251

   1. Initial program 99.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+251}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(\frac{a}{b} + \frac{z}{b}\right) - \frac{y}{x + \left(y + t\right)}\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-187}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + a \cdot \left(y + t\right)}{\left(x + y\right) + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ (/ a b) (/ z b)) (/ y (+ x (+ y t)))))))
   (if (<= b -9.2e-64)
     t_1
     (if (<= b 3.4e-187)
       (- (+ z a) b)
       (if (<= b 2.6e-78)
         (/ (+ (* (+ x y) z) (* a (+ y t))) (+ (+ x y) t))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (((a / b) + (z / b)) - (y / (x + (y + t))));
	double tmp;
	if (b <= -9.2e-64) {
		tmp = t_1;
	} else if (b <= 3.4e-187) {
		tmp = (z + a) - b;
	} else if (b <= 2.6e-78) {
		tmp = (((x + y) * z) + (a * (y + t))) / ((x + y) + t);
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = b * (((a / b) + (z / b)) - (y / (x + (y + t))))
    if (b <= (-9.2d-64)) then
        tmp = t_1
    else if (b <= 3.4d-187) then
        tmp = (z + a) - b
    else if (b <= 2.6d-78) then
        tmp = (((x + y) * z) + (a * (y + t))) / ((x + y) + 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 a, double b) {
	double t_1 = b * (((a / b) + (z / b)) - (y / (x + (y + t))));
	double tmp;
	if (b <= -9.2e-64) {
		tmp = t_1;
	} else if (b <= 3.4e-187) {
		tmp = (z + a) - b;
	} else if (b <= 2.6e-78) {
		tmp = (((x + y) * z) + (a * (y + t))) / ((x + y) + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (((a / b) + (z / b)) - (y / (x + (y + t))))
	tmp = 0
	if b <= -9.2e-64:
		tmp = t_1
	elif b <= 3.4e-187:
		tmp = (z + a) - b
	elif b <= 2.6e-78:
		tmp = (((x + y) * z) + (a * (y + t))) / ((x + y) + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(Float64(a / b) + Float64(z / b)) - Float64(y / Float64(x + Float64(y + t)))))
	tmp = 0.0
	if (b <= -9.2e-64)
		tmp = t_1;
	elseif (b <= 3.4e-187)
		tmp = Float64(Float64(z + a) - b);
	elseif (b <= 2.6e-78)
		tmp = Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) / Float64(Float64(x + y) + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (((a / b) + (z / b)) - (y / (x + (y + t))));
	tmp = 0.0;
	if (b <= -9.2e-64)
		tmp = t_1;
	elseif (b <= 3.4e-187)
		tmp = (z + a) - b;
	elseif (b <= 2.6e-78)
		tmp = (((x + y) * z) + (a * (y + t))) / ((x + y) + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(N[(a / b), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e-64], t$95$1, If[LessEqual[b, 3.4e-187], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[b, 2.6e-78], N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.2000000000000006e-64 or 2.6000000000000001e-78 < b

   1. Initial program 60.5%

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

   3. Taylor expanded in b around inf 57.0%

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

      1. +-commutative 57.0%

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

      2. mul-1-neg 57.0%

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

      3. unsub-neg 57.0%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in y around inf 75.0%

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

   if -9.2000000000000006e-64 < b < 3.4000000000000001e-187

   1. Initial program 55.2%

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

   3. Taylor expanded in y around inf 72.9%

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

   if 3.4000000000000001e-187 < b < 2.6000000000000001e-78

   1. Initial program 83.8%

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

   3. Taylor expanded in b around 0 83.8%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{-64}:\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} + \frac{z}{b}\right) - \frac{y}{x + \left(y + t\right)}\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-187}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + a \cdot \left(y + t\right)}{\left(x + y\right) + t}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} + \frac{z}{b}\right) - \frac{y}{x + \left(y + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{-63} \lor \neg \left(b \leq 4.4 \cdot 10^{-85}\right):\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} + \frac{z}{b}\right) - \frac{y}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.95e-63) (not (<= b 4.4e-85)))
   (* b (- (+ (/ a b) (/ z b)) (/ y (+ x (+ y t)))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.95e-63) || !(b <= 4.4e-85)) {
		tmp = b * (((a / b) + (z / b)) - (y / (x + (y + 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 ((b <= (-1.95d-63)) .or. (.not. (b <= 4.4d-85))) then
        tmp = b * (((a / b) + (z / b)) - (y / (x + (y + 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 ((b <= -1.95e-63) || !(b <= 4.4e-85)) {
		tmp = b * (((a / b) + (z / b)) - (y / (x + (y + t))));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.95e-63) or not (b <= 4.4e-85):
		tmp = b * (((a / b) + (z / b)) - (y / (x + (y + t))))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.95e-63) || !(b <= 4.4e-85))
		tmp = Float64(b * Float64(Float64(Float64(a / b) + Float64(z / b)) - Float64(y / Float64(x + Float64(y + 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 ((b <= -1.95e-63) || ~((b <= 4.4e-85)))
		tmp = b * (((a / b) + (z / b)) - (y / (x + (y + t))));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.95e-63], N[Not[LessEqual[b, 4.4e-85]], $MachinePrecision]], N[(b * N[(N[(N[(a / b), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.95000000000000011e-63 or 4.4e-85 < b

   1. Initial program 61.0%

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

   3. Taylor expanded in b around inf 57.5%

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

      1. +-commutative 57.5%

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

      2. mul-1-neg 57.5%

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

      3. unsub-neg 57.5%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in y around inf 74.1%

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

   if -1.95000000000000011e-63 < b < 4.4e-85

   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 71.3%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{-63} \lor \neg \left(b \leq 4.4 \cdot 10^{-85}\right):\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} + \frac{z}{b}\right) - \frac{y}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-114}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= z -2.9e-127)
     t_1
     (if (<= z 1e-114)
       (/ (- (* a (+ y t)) (* y b)) (+ y (+ x t)))
       (if (<= z 7.6e+160) t_1 (* z (/ (+ x y) (+ x (+ y t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (z <= -2.9e-127) {
		tmp = t_1;
	} else if (z <= 1e-114) {
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	} else if (z <= 7.6e+160) {
		tmp = t_1;
	} else {
		tmp = z * ((x + y) / (x + (y + 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) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (z <= (-2.9d-127)) then
        tmp = t_1
    else if (z <= 1d-114) then
        tmp = ((a * (y + t)) - (y * b)) / (y + (x + t))
    else if (z <= 7.6d+160) then
        tmp = t_1
    else
        tmp = z * ((x + y) / (x + (y + 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 t_1 = (z + a) - b;
	double tmp;
	if (z <= -2.9e-127) {
		tmp = t_1;
	} else if (z <= 1e-114) {
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	} else if (z <= 7.6e+160) {
		tmp = t_1;
	} else {
		tmp = z * ((x + y) / (x + (y + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if z <= -2.9e-127:
		tmp = t_1
	elif z <= 1e-114:
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t))
	elif z <= 7.6e+160:
		tmp = t_1
	else:
		tmp = z * ((x + y) / (x + (y + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (z <= -2.9e-127)
		tmp = t_1;
	elseif (z <= 1e-114)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (z <= 7.6e+160)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(x + Float64(y + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (z <= -2.9e-127)
		tmp = t_1;
	elseif (z <= 1e-114)
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	elseif (z <= 7.6e+160)
		tmp = t_1;
	else
		tmp = z * ((x + y) / (x + (y + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[z, -2.9e-127], t$95$1, If[LessEqual[z, 1e-114], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+160], t$95$1, N[(z * N[(N[(x + y), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e-127 or 1.0000000000000001e-114 < z < 7.60000000000000024e160

   1. Initial program 53.5%

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

   3. Taylor expanded in y around inf 65.2%

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

   if -2.9e-127 < z < 1.0000000000000001e-114

   1. Initial program 78.1%

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

   3. Taylor expanded in z around 0 71.5%

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

      1. +-commutative 71.5%

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

      2. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   if 7.60000000000000024e160 < z

   1. Initial program 46.9%

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

   3. Taylor expanded in z around inf 31.3%

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

      1. associate-/l* 75.1%

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

      2. +-commutative 75.1%

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

      3. +-commutative 75.1%

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

      4. associate-+r+ 75.1%

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

   5. Simplified 75.1%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-127}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 10^{-114}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+160}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+130}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7e+74)
   (* z (/ (+ x y) (+ x (+ y t))))
   (if (<= x 9.2e+130) (- (+ z a) b) (+ z (* t (- (/ a x) (/ z x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7e+74) {
		tmp = z * ((x + y) / (x + (y + t)));
	} else if (x <= 9.2e+130) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (t * ((a / x) - (z / x)));
	}
	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 <= (-7d+74)) then
        tmp = z * ((x + y) / (x + (y + t)))
    else if (x <= 9.2d+130) then
        tmp = (z + a) - b
    else
        tmp = z + (t * ((a / x) - (z / x)))
    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 <= -7e+74) {
		tmp = z * ((x + y) / (x + (y + t)));
	} else if (x <= 9.2e+130) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (t * ((a / x) - (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7e+74:
		tmp = z * ((x + y) / (x + (y + t)))
	elif x <= 9.2e+130:
		tmp = (z + a) - b
	else:
		tmp = z + (t * ((a / x) - (z / x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7e+74)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(x + Float64(y + t))));
	elseif (x <= 9.2e+130)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + Float64(t * Float64(Float64(a / x) - Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7e+74)
		tmp = z * ((x + y) / (x + (y + t)));
	elseif (x <= 9.2e+130)
		tmp = (z + a) - b;
	else
		tmp = z + (t * ((a / x) - (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7e+74], N[(z * N[(N[(x + y), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e+130], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(t * N[(N[(a / x), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.00000000000000029e74

   1. Initial program 35.1%

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

   3. Taylor expanded in z around inf 20.3%

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

      1. associate-/l* 68.6%

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

      2. +-commutative 68.6%

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

      3. +-commutative 68.6%

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

      4. associate-+r+ 68.6%

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

   5. Simplified 68.6%

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

   if -7.00000000000000029e74 < x < 9.20000000000000085e130

   1. Initial program 68.0%

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

   3. Taylor expanded in y around inf 65.0%

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

   if 9.20000000000000085e130 < 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 54.0%

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

   4. Taylor expanded in y around 0 40.1%

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

   5. Taylor expanded in t around 0 69.4%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+130}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+128}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.4e+74)
   (* z (/ (+ x y) (+ x (+ y t))))
   (if (<= x 4.2e+128) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.4e+74) {
		tmp = z * ((x + y) / (x + (y + t)));
	} else if (x <= 4.2e+128) {
		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 <= (-7.4d+74)) then
        tmp = z * ((x + y) / (x + (y + t)))
    else if (x <= 4.2d+128) 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 <= -7.4e+74) {
		tmp = z * ((x + y) / (x + (y + t)));
	} else if (x <= 4.2e+128) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.4e+74:
		tmp = z * ((x + y) / (x + (y + t)))
	elif x <= 4.2e+128:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.4e+74)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(x + Float64(y + t))));
	elseif (x <= 4.2e+128)
		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 <= -7.4e+74)
		tmp = z * ((x + y) / (x + (y + t)));
	elseif (x <= 4.2e+128)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.4e+74], N[(z * N[(N[(x + y), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+128], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 3 regimes

2. if x < -7.4000000000000002e74

   1. Initial program 35.1%

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

   3. Taylor expanded in z around inf 20.3%

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

      1. associate-/l* 68.6%

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

      2. +-commutative 68.6%

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

      3. +-commutative 68.6%

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

      4. associate-+r+ 68.6%

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

   5. Simplified 68.6%

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

   if -7.4000000000000002e74 < x < 4.1999999999999999e128

   1. Initial program 68.0%

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

   3. Taylor expanded in y around inf 65.0%

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

   if 4.1999999999999999e128 < 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 59.8%

      \[\leadsto \color{blue}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+128}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+131}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.8e+74) (* x (/ z (+ x t))) (if (<= x 2e+131) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.8e+74) {
		tmp = x * (z / (x + t));
	} else if (x <= 2e+131) {
		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 <= (-6.8d+74)) then
        tmp = x * (z / (x + t))
    else if (x <= 2d+131) 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 <= -6.8e+74) {
		tmp = x * (z / (x + t));
	} else if (x <= 2e+131) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.8e+74:
		tmp = x * (z / (x + t))
	elif x <= 2e+131:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.8e+74)
		tmp = Float64(x * Float64(z / Float64(x + t)));
	elseif (x <= 2e+131)
		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 <= -6.8e+74)
		tmp = x * (z / (x + t));
	elseif (x <= 2e+131)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.8e+74], N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+131], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 3 regimes

2. if x < -6.7999999999999998e74

   1. Initial program 35.1%

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

   3. Taylor expanded in x around inf 35.4%

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

   4. Taylor expanded in y around 0 20.0%

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

   5. Taylor expanded in z around inf 20.4%

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

      1. associate-/l* 66.0%

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

   7. Simplified 66.0%

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

   if -6.7999999999999998e74 < x < 1.9999999999999998e131

   1. Initial program 68.0%

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

   3. Taylor expanded in y around inf 65.0%

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

   if 1.9999999999999998e131 < 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 59.8%

      \[\leadsto \color{blue}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+131}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+191}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+125}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.8e+191) z (if (<= x 9.5e+125) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.8e+191) {
		tmp = z;
	} else if (x <= 9.5e+125) {
		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 <= (-4.8d+191)) then
        tmp = z
    else if (x <= 9.5d+125) 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 <= -4.8e+191) {
		tmp = z;
	} else if (x <= 9.5e+125) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.8e+191:
		tmp = z
	elif x <= 9.5e+125:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.8e+191)
		tmp = z;
	elseif (x <= 9.5e+125)
		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 <= -4.8e+191)
		tmp = z;
	elseif (x <= 9.5e+125)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.8e+191], z, If[LessEqual[x, 9.5e+125], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999972e191 or 9.50000000000000041e125 < x

   1. Initial program 45.8%

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

   3. Taylor expanded in x around inf 64.1%

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

   if -4.79999999999999972e191 < x < 9.50000000000000041e125

   1. Initial program 66.1%

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

   3. Taylor expanded in y around inf 64.1%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+191}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+125}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+231}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+142}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.9e+231) z (if (<= x 7e+142) (+ z a) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.9e+231) {
		tmp = z;
	} else if (x <= 7e+142) {
		tmp = z + 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 (x <= (-2.9d+231)) then
        tmp = z
    else if (x <= 7d+142) then
        tmp = z + 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 (x <= -2.9e+231) {
		tmp = z;
	} else if (x <= 7e+142) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.9e+231:
		tmp = z
	elif x <= 7e+142:
		tmp = z + a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.9e+231)
		tmp = z;
	elseif (x <= 7e+142)
		tmp = Float64(z + a);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.9e+231)
		tmp = z;
	elseif (x <= 7e+142)
		tmp = z + a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.9e+231], z, If[LessEqual[x, 7e+142], N[(z + a), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9000000000000001e231 or 6.99999999999999995e142 < x

   1. Initial program 45.1%

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

   3. Taylor expanded in x around inf 69.3%

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

   if -2.9000000000000001e231 < x < 6.99999999999999995e142

   1. Initial program 65.5%

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

   3. Taylor expanded in b around 0 48.9%

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

   4. Taylor expanded in y around inf 54.5%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+231}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+142}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+69}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+51}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.02e+69) z (if (<= x 2.3e+51) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.02e+69) {
		tmp = z;
	} else if (x <= 2.3e+51) {
		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 (x <= (-1.02d+69)) then
        tmp = z
    else if (x <= 2.3d+51) 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 (x <= -1.02e+69) {
		tmp = z;
	} else if (x <= 2.3e+51) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.02e+69:
		tmp = z
	elif x <= 2.3e+51:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.02e+69)
		tmp = z;
	elseif (x <= 2.3e+51)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.02e+69)
		tmp = z;
	elseif (x <= 2.3e+51)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.02e+69], z, If[LessEqual[x, 2.3e+51], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e69 or 2.30000000000000005e51 < x

   1. Initial program 48.8%

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

   3. Taylor expanded in x around inf 57.9%

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

   if -1.02e69 < x < 2.30000000000000005e51

   1. Initial program 68.2%

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

   3. Taylor expanded in t around inf 49.5%

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

Alternative 12: 32.7% 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 61.0%

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

3. Taylor expanded in t around inf 35.4%

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

Developer Target 1: 81.9% 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 2024135 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ 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)))