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

Percentage Accurate: 60.8% → 87.4%

Time: 16.8s

Alternatives: 8

Speedup: 0.3×

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: 60.8% 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: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{t_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 4 \cdot 10^{+215}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot t_3\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 4e+215)))
     t_3
     (/ (+ (* t a) (+ (* x z) (* y t_3))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 4e+215)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / 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 + (x + t);
	double t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 4e+215)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1
	t_3 = (z + a) - b
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 4e+215):
		tmp = t_3
	else:
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 4e+215))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * t_3))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 4e+215)))
		tmp = t_3;
	else
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	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[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 4e+215]], $MachinePrecision]], t$95$3, N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $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 3.99999999999999963e215 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 12.7%

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

   2. 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)) < 3.99999999999999963e215

   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. Taylor expanded in y around 0 99.7%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+215}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 2: 59.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{x \cdot z + y \cdot t_1}{x + y}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-62}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (/ (+ (* x z) (* y t_1)) (+ x y))))
   (if (<= y -2.4e+49)
     t_1
     (if (<= y -2.6e-161)
       t_2
       (if (<= y 5.6e-62)
         (/ z (/ (+ x (+ y t)) (+ x y)))
         (if (<= y 9.5e+32) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = ((x * z) + (y * t_1)) / (x + y);
	double tmp;
	if (y <= -2.4e+49) {
		tmp = t_1;
	} else if (y <= -2.6e-161) {
		tmp = t_2;
	} else if (y <= 5.6e-62) {
		tmp = z / ((x + (y + t)) / (x + y));
	} else if (y <= 9.5e+32) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = ((x * z) + (y * t_1)) / (x + y)
    if (y <= (-2.4d+49)) then
        tmp = t_1
    else if (y <= (-2.6d-161)) then
        tmp = t_2
    else if (y <= 5.6d-62) then
        tmp = z / ((x + (y + t)) / (x + y))
    else if (y <= 9.5d+32) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = ((x * z) + (y * t_1)) / (x + y);
	double tmp;
	if (y <= -2.4e+49) {
		tmp = t_1;
	} else if (y <= -2.6e-161) {
		tmp = t_2;
	} else if (y <= 5.6e-62) {
		tmp = z / ((x + (y + t)) / (x + y));
	} else if (y <= 9.5e+32) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = ((x * z) + (y * t_1)) / (x + y)
	tmp = 0
	if y <= -2.4e+49:
		tmp = t_1
	elif y <= -2.6e-161:
		tmp = t_2
	elif y <= 5.6e-62:
		tmp = z / ((x + (y + t)) / (x + y))
	elif y <= 9.5e+32:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(Float64(Float64(x * z) + Float64(y * t_1)) / Float64(x + y))
	tmp = 0.0
	if (y <= -2.4e+49)
		tmp = t_1;
	elseif (y <= -2.6e-161)
		tmp = t_2;
	elseif (y <= 5.6e-62)
		tmp = Float64(z / Float64(Float64(x + Float64(y + t)) / Float64(x + y)));
	elseif (y <= 9.5e+32)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = ((x * z) + (y * t_1)) / (x + y);
	tmp = 0.0;
	if (y <= -2.4e+49)
		tmp = t_1;
	elseif (y <= -2.6e-161)
		tmp = t_2;
	elseif (y <= 5.6e-62)
		tmp = z / ((x + (y + t)) / (x + y));
	elseif (y <= 9.5e+32)
		tmp = t_2;
	else
		tmp = t_1;
	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[(N[(N[(x * z), $MachinePrecision] + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+49], t$95$1, If[LessEqual[y, -2.6e-161], t$95$2, If[LessEqual[y, 5.6e-62], N[(z / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+32], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e49 or 9.50000000000000006e32 < y

   1. Initial program 38.1%

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

   2. Taylor expanded in y around inf 76.0%

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

   if -2.4e49 < y < -2.59999999999999995e-161 or 5.60000000000000005e-62 < y < 9.50000000000000006e32

   1. Initial program 89.2%

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

   2. Taylor expanded in y around 0 89.2%

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

   3. Taylor expanded in t around 0 80.9%

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

   if -2.59999999999999995e-161 < y < 5.60000000000000005e-62

   1. Initial program 72.2%

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

   2. Taylor expanded in z around inf 43.6%

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

      1. associate-/l* 58.0%

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

      2. +-commutative 58.0%

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

      3. associate-+r+ 58.0%

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

      4. +-commutative 58.0%

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

   4. Simplified 58.0%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+49}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-161}:\\ \;\;\;\;\frac{x \cdot z + y \cdot \left(\left(z + a\right) - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-62}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{x \cdot z + y \cdot \left(\left(z + a\right) - b\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 3: 58.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-158}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (- (+ z a) b)))
   (if (<= y -1.6e-74)
     t_2
     (if (<= y -2.7e-158)
       (/ a (/ t_1 (+ y t)))
       (if (<= y 2.6e-61) (/ z (/ t_1 (+ x y))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.6e-74) {
		tmp = t_2;
	} else if (y <= -2.7e-158) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 2.6e-61) {
		tmp = z / (t_1 / (x + y));
	} 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 = x + (y + t)
    t_2 = (z + a) - b
    if (y <= (-1.6d-74)) then
        tmp = t_2
    else if (y <= (-2.7d-158)) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 2.6d-61) then
        tmp = z / (t_1 / (x + y))
    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 = x + (y + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.6e-74) {
		tmp = t_2;
	} else if (y <= -2.7e-158) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 2.6e-61) {
		tmp = z / (t_1 / (x + y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -1.6e-74:
		tmp = t_2
	elif y <= -2.7e-158:
		tmp = a / (t_1 / (y + t))
	elif y <= 2.6e-61:
		tmp = z / (t_1 / (x + y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.6e-74)
		tmp = t_2;
	elseif (y <= -2.7e-158)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 2.6e-61)
		tmp = Float64(z / Float64(t_1 / Float64(x + y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.6e-74)
		tmp = t_2;
	elseif (y <= -2.7e-158)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 2.6e-61)
		tmp = z / (t_1 / (x + y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.6e-74], t$95$2, If[LessEqual[y, -2.7e-158], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-61], N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5999999999999999e-74 or 2.6000000000000001e-61 < y

   1. Initial program 52.3%

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

   2. Taylor expanded in y around inf 73.4%

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

   if -1.5999999999999999e-74 < y < -2.6999999999999998e-158

   1. Initial program 86.9%

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

   2. Taylor expanded in a around inf 73.2%

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

      1. associate-/l* 86.2%

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

      2. +-commutative 86.2%

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

      3. associate-+r+ 86.2%

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

   4. Simplified 86.2%

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

   if -2.6999999999999998e-158 < y < 2.6000000000000001e-61

   1. Initial program 72.9%

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

   2. Taylor expanded in z around inf 43.8%

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

      1. associate-/l* 57.8%

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

      2. +-commutative 57.8%

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

      3. associate-+r+ 57.8%

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

      4. +-commutative 57.8%

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

   4. Simplified 57.8%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-74}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-158}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 4: 58.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+193} \lor \neg \left(x \leq 1.5 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -7.5e+193) (not (<= x 1.5e+174)))
   (/ z (/ (+ x t) x))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -7.5e+193) || !(x <= 1.5e+174)) {
		tmp = z / ((x + t) / 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 <= (-7.5d+193)) .or. (.not. (x <= 1.5d+174))) then
        tmp = z / ((x + t) / 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 <= -7.5e+193) || !(x <= 1.5e+174)) {
		tmp = z / ((x + t) / x);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -7.5e+193) or not (x <= 1.5e+174):
		tmp = z / ((x + t) / x)
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -7.5e+193) || !(x <= 1.5e+174))
		tmp = Float64(z / Float64(Float64(x + t) / 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 <= -7.5e+193) || ~((x <= 1.5e+174)))
		tmp = z / ((x + t) / x);
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -7.5e+193], N[Not[LessEqual[x, 1.5e+174]], $MachinePrecision]], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000008e193 or 1.5e174 < x

   1. Initial program 45.5%

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

   2. Taylor expanded in z around inf 27.7%

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

      1. associate-/l* 63.6%

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

      2. +-commutative 63.6%

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

      3. associate-+r+ 63.6%

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

      4. +-commutative 63.6%

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

   4. Simplified 63.6%

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

   5. Taylor expanded in y around 0 63.6%

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

      1. +-commutative 63.6%

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

   7. Simplified 63.6%

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

   if -7.5000000000000008e193 < x < 1.5e174

   1. Initial program 65.6%

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

   2. Taylor expanded in y around inf 68.7%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+193} \lor \neg \left(x \leq 1.5 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 5: 46.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+94}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+160}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.8e+94) a (if (<= a 8.5e+160) (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.8e+94) {
		tmp = a;
	} else if (a <= 8.5e+160) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	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 (a <= (-2.8d+94)) then
        tmp = a
    else if (a <= 8.5d+160) then
        tmp = z - b
    else
        tmp = a
    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 (a <= -2.8e+94) {
		tmp = a;
	} else if (a <= 8.5e+160) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.8e+94:
		tmp = a
	elif a <= 8.5e+160:
		tmp = z - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.8e+94)
		tmp = a;
	elseif (a <= 8.5e+160)
		tmp = Float64(z - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.8e+94)
		tmp = a;
	elseif (a <= 8.5e+160)
		tmp = z - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.8e+94], a, If[LessEqual[a, 8.5e+160], N[(z - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.79999999999999998e94 or 8.49999999999999982e160 < a

   1. Initial program 45.9%

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

   2. Taylor expanded in t around inf 57.5%

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

   if -2.79999999999999998e94 < a < 8.49999999999999982e160

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. associate--l+ 67.9%

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

      3. fma-def 67.9%

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

      4. +-commutative 67.9%

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

      5. +-commutative 67.9%

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

   3. Simplified 67.9%

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

      1. div-inv 67.7%

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

      2. fma-udef 67.7%

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

      3. *-commutative 67.7%

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

      4. fma-def 67.7%

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

      5. +-commutative 67.7%

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

      6. associate-+l+ 67.7%

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

      7. +-commutative 67.7%

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

   5. Applied egg-rr 67.7%

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

   6. Taylor expanded in a around 0 53.9%

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

   7. Taylor expanded in y around inf 56.4%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+94}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+160}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 6: 56.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 9.8 \cdot 10^{+178}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x 9.8e+178) (- (+ z a) b) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 9.8e+178) {
		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 <= 9.8d+178) 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 <= 9.8e+178) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 9.8e+178:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 9.8e+178)
		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 <= 9.8e+178)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 9.8e+178], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < 9.8000000000000003e178

   1. Initial program 63.2%

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

   2. Taylor expanded in y around inf 63.9%

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

   if 9.8000000000000003e178 < 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. Taylor expanded in x around inf 73.8%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 9.8 \cdot 10^{+178}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 42.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+72}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-72}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2e+72) z (if (<= z 3.3e-72) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2e+72) {
		tmp = z;
	} else if (z <= 3.3e-72) {
		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 <= (-2d+72)) then
        tmp = z
    else if (z <= 3.3d-72) 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 <= -2e+72) {
		tmp = z;
	} else if (z <= 3.3e-72) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2e+72:
		tmp = z
	elif z <= 3.3e-72:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2e+72)
		tmp = z;
	elseif (z <= 3.3e-72)
		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 <= -2e+72)
		tmp = z;
	elseif (z <= 3.3e-72)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2e+72], z, If[LessEqual[z, 3.3e-72], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999989e72 or 3.3e-72 < z

   1. Initial program 49.5%

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

   2. Taylor expanded in x around inf 58.5%

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

   if -1.99999999999999989e72 < z < 3.3e-72

   1. Initial program 71.5%

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

   2. Taylor expanded in t around inf 43.0%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+72}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-72}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 8: 32.4% 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 60.7%

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

2. Taylor expanded in t around inf 28.7%

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

3. Final simplification 28.7%

   \[\leadsto a \]

Developer target: 82.2% 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 2023287 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (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)))