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

Percentage Accurate: 61.8% → 88.6%

Time: 11.4s

Alternatives: 11

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.8% 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: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+302} \lor \neg \left(t\_1 \leq 10^{+268}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* (+ x y) z)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 -2e+302) (not (<= t_1 1e+268))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -2e+302) || !(t_1 <= 1e+268)) {
		tmp = (z + a) - b;
	} 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 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t))
    if ((t_1 <= (-2d+302)) .or. (.not. (t_1 <= 1d+268))) then
        tmp = (z + a) - b
    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 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -2e+302) || !(t_1 <= 1e+268)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -2e+302) or not (t_1 <= 1e+268):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(Float64(x + y) * z)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= -2e+302) || !(t_1 <= 1e+268))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -2e+302) || ~((t_1 <= 1e+268)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+302], N[Not[LessEqual[t$95$1, 1e+268]], $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)) < -2.0000000000000002e302 or 9.9999999999999997e267 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.5%

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

   3. Taylor expanded in y around inf 77.4%

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

   if -2.0000000000000002e302 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999997e267

   1. Initial program 99.7%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq -2 \cdot 10^{+302} \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+268}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a - y \cdot \frac{b}{x + \left(y + t\right)}\\ t_2 := \left(x + y\right) + t\\ t_3 := z \cdot \frac{x + y}{t\_2}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+141}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.86 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+73}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-131}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_2}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- a (* y (/ b (+ x (+ y t))))))
        (t_2 (+ (+ x y) t))
        (t_3 (* z (/ (+ x y) t_2))))
   (if (<= z -7.2e+141)
     t_3
     (if (<= z -1.86e+87)
       t_1
       (if (<= z -1.5e+73)
         t_3
         (if (<= z -1.4e-131)
           (* a (/ (+ y t) t_2))
           (if (<= z 1.9e+106) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - (y * (b / (x + (y + t))));
	double t_2 = (x + y) + t;
	double t_3 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -7.2e+141) {
		tmp = t_3;
	} else if (z <= -1.86e+87) {
		tmp = t_1;
	} else if (z <= -1.5e+73) {
		tmp = t_3;
	} else if (z <= -1.4e-131) {
		tmp = a * ((y + t) / t_2);
	} else if (z <= 1.9e+106) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a - (y * (b / (x + (y + t))))
    t_2 = (x + y) + t
    t_3 = z * ((x + y) / t_2)
    if (z <= (-7.2d+141)) then
        tmp = t_3
    else if (z <= (-1.86d+87)) then
        tmp = t_1
    else if (z <= (-1.5d+73)) then
        tmp = t_3
    else if (z <= (-1.4d-131)) then
        tmp = a * ((y + t) / t_2)
    else if (z <= 1.9d+106) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - (y * (b / (x + (y + t))));
	double t_2 = (x + y) + t;
	double t_3 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -7.2e+141) {
		tmp = t_3;
	} else if (z <= -1.86e+87) {
		tmp = t_1;
	} else if (z <= -1.5e+73) {
		tmp = t_3;
	} else if (z <= -1.4e-131) {
		tmp = a * ((y + t) / t_2);
	} else if (z <= 1.9e+106) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a - (y * (b / (x + (y + t))))
	t_2 = (x + y) + t
	t_3 = z * ((x + y) / t_2)
	tmp = 0
	if z <= -7.2e+141:
		tmp = t_3
	elif z <= -1.86e+87:
		tmp = t_1
	elif z <= -1.5e+73:
		tmp = t_3
	elif z <= -1.4e-131:
		tmp = a * ((y + t) / t_2)
	elif z <= 1.9e+106:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a - Float64(y * Float64(b / Float64(x + Float64(y + t)))))
	t_2 = Float64(Float64(x + y) + t)
	t_3 = Float64(z * Float64(Float64(x + y) / t_2))
	tmp = 0.0
	if (z <= -7.2e+141)
		tmp = t_3;
	elseif (z <= -1.86e+87)
		tmp = t_1;
	elseif (z <= -1.5e+73)
		tmp = t_3;
	elseif (z <= -1.4e-131)
		tmp = Float64(a * Float64(Float64(y + t) / t_2));
	elseif (z <= 1.9e+106)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a - (y * (b / (x + (y + t))));
	t_2 = (x + y) + t;
	t_3 = z * ((x + y) / t_2);
	tmp = 0.0;
	if (z <= -7.2e+141)
		tmp = t_3;
	elseif (z <= -1.86e+87)
		tmp = t_1;
	elseif (z <= -1.5e+73)
		tmp = t_3;
	elseif (z <= -1.4e-131)
		tmp = a * ((y + t) / t_2);
	elseif (z <= 1.9e+106)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a - N[(y * N[(b / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+141], t$95$3, If[LessEqual[z, -1.86e+87], t$95$1, If[LessEqual[z, -1.5e+73], t$95$3, If[LessEqual[z, -1.4e-131], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+106], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000003e141 or -1.86000000000000011e87 < z < -1.50000000000000005e73 or 1.8999999999999999e106 < z

   1. Initial program 38.6%

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

   3. Taylor expanded in z around inf 34.6%

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

      1. associate-/l* 83.7%

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

      2. +-commutative 83.7%

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

      3. +-commutative 83.7%

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

   5. Simplified 83.7%

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

   if -7.2000000000000003e141 < z < -1.86000000000000011e87 or -1.4e-131 < z < 1.8999999999999999e106

   1. Initial program 73.9%

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

      1. div-sub 73.9%

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

      2. +-commutative 73.9%

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

      3. *-commutative 73.9%

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

      4. associate-+l+ 73.9%

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

      5. +-commutative 73.9%

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

      6. associate-+l+ 73.9%

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

      7. +-commutative 73.9%

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

      8. associate-/l* 77.5%

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

   4. Applied egg-rr 77.5%

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

   5. Taylor expanded in t around inf 66.1%

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

   if -1.50000000000000005e73 < z < -1.4e-131

   1. Initial program 77.3%

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

   3. Taylor expanded in a around inf 52.0%

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

      1. associate-+l+ 52.0%

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

      2. +-commutative 52.0%

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

      3. associate-+r+ 52.0%

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

      4. associate-*r/ 68.1%

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

      5. *-commutative 68.1%

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

   5. Applied egg-rr 68.1%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{elif}\;z \leq -1.86 \cdot 10^{+87}:\\ \;\;\;\;a - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-131}:\\ \;\;\;\;a \cdot \frac{y + t}{\left(x + y\right) + t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+106}:\\ \;\;\;\;a - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a - y \cdot \frac{b}{x + \left(y + t\right)}\\ t_2 := z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-67}:\\ \;\;\;\;\frac{\left(y \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- a (* y (/ b (+ x (+ y t))))))
        (t_2 (* z (/ (+ x y) (+ (+ x y) t)))))
   (if (<= z -2.4e+142)
     t_2
     (if (<= z -1.16e+40)
       t_1
       (if (<= z -4.8e-67)
         (/ (- (+ (* y a) (* (+ x y) z)) (* y b)) (+ x y))
         (if (<= z 1.7e+106) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - (y * (b / (x + (y + t))));
	double t_2 = z * ((x + y) / ((x + y) + t));
	double tmp;
	if (z <= -2.4e+142) {
		tmp = t_2;
	} else if (z <= -1.16e+40) {
		tmp = t_1;
	} else if (z <= -4.8e-67) {
		tmp = (((y * a) + ((x + y) * z)) - (y * b)) / (x + y);
	} else if (z <= 1.7e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a - (y * (b / (x + (y + t))))
    t_2 = z * ((x + y) / ((x + y) + t))
    if (z <= (-2.4d+142)) then
        tmp = t_2
    else if (z <= (-1.16d+40)) then
        tmp = t_1
    else if (z <= (-4.8d-67)) then
        tmp = (((y * a) + ((x + y) * z)) - (y * b)) / (x + y)
    else if (z <= 1.7d+106) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - (y * (b / (x + (y + t))));
	double t_2 = z * ((x + y) / ((x + y) + t));
	double tmp;
	if (z <= -2.4e+142) {
		tmp = t_2;
	} else if (z <= -1.16e+40) {
		tmp = t_1;
	} else if (z <= -4.8e-67) {
		tmp = (((y * a) + ((x + y) * z)) - (y * b)) / (x + y);
	} else if (z <= 1.7e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a - (y * (b / (x + (y + t))))
	t_2 = z * ((x + y) / ((x + y) + t))
	tmp = 0
	if z <= -2.4e+142:
		tmp = t_2
	elif z <= -1.16e+40:
		tmp = t_1
	elif z <= -4.8e-67:
		tmp = (((y * a) + ((x + y) * z)) - (y * b)) / (x + y)
	elif z <= 1.7e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a - Float64(y * Float64(b / Float64(x + Float64(y + t)))))
	t_2 = Float64(z * Float64(Float64(x + y) / Float64(Float64(x + y) + t)))
	tmp = 0.0
	if (z <= -2.4e+142)
		tmp = t_2;
	elseif (z <= -1.16e+40)
		tmp = t_1;
	elseif (z <= -4.8e-67)
		tmp = Float64(Float64(Float64(Float64(y * a) + Float64(Float64(x + y) * z)) - Float64(y * b)) / Float64(x + y));
	elseif (z <= 1.7e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a - (y * (b / (x + (y + t))));
	t_2 = z * ((x + y) / ((x + y) + t));
	tmp = 0.0;
	if (z <= -2.4e+142)
		tmp = t_2;
	elseif (z <= -1.16e+40)
		tmp = t_1;
	elseif (z <= -4.8e-67)
		tmp = (((y * a) + ((x + y) * z)) - (y * b)) / (x + y);
	elseif (z <= 1.7e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a - N[(y * N[(b / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+142], t$95$2, If[LessEqual[z, -1.16e+40], t$95$1, If[LessEqual[z, -4.8e-67], N[(N[(N[(N[(y * a), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+106], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999999e142 or 1.69999999999999997e106 < z

   1. Initial program 37.5%

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

   3. Taylor expanded in z around inf 33.3%

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

      1. associate-/l* 83.1%

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

      2. +-commutative 83.1%

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

      3. +-commutative 83.1%

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

   5. Simplified 83.1%

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

   if -2.3999999999999999e142 < z < -1.16000000000000012e40 or -4.8e-67 < z < 1.69999999999999997e106

   1. Initial program 72.8%

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

      1. div-sub 72.8%

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

      2. +-commutative 72.8%

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

      3. *-commutative 72.8%

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

      4. associate-+l+ 72.8%

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

      5. +-commutative 72.8%

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

      6. associate-+l+ 72.8%

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

      7. +-commutative 72.8%

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

      8. associate-/l* 75.9%

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

   4. Applied egg-rr 75.9%

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

   5. Taylor expanded in t around inf 66.2%

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

   if -1.16000000000000012e40 < z < -4.8e-67

   1. Initial program 89.3%

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

   3. Taylor expanded in t around 0 71.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+142}:\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{+40}:\\ \;\;\;\;a - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-67}:\\ \;\;\;\;\frac{\left(y \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+106}:\\ \;\;\;\;a - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+142} \lor \neg \left(z \leq 1.2 \cdot 10^{+106}\right):\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1} - y \cdot \frac{b}{x + \left(y + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t)))
   (if (or (<= z -1.2e+142) (not (<= z 1.2e+106)))
     (* z (/ (+ x y) t_1))
     (- (* a (/ (+ y t) 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 = (x + y) + t;
	double tmp;
	if ((z <= -1.2e+142) || !(z <= 1.2e+106)) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = (a * ((y + t) / t_1)) - (y * (b / (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 = (x + y) + t
    if ((z <= (-1.2d+142)) .or. (.not. (z <= 1.2d+106))) then
        tmp = z * ((x + y) / t_1)
    else
        tmp = (a * ((y + t) / t_1)) - (y * (b / (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 = (x + y) + t;
	double tmp;
	if ((z <= -1.2e+142) || !(z <= 1.2e+106)) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = (a * ((y + t) / t_1)) - (y * (b / (x + (y + t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + t
	tmp = 0
	if (z <= -1.2e+142) or not (z <= 1.2e+106):
		tmp = z * ((x + y) / t_1)
	else:
		tmp = (a * ((y + t) / t_1)) - (y * (b / (x + (y + t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	tmp = 0.0
	if ((z <= -1.2e+142) || !(z <= 1.2e+106))
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	else
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_1)) - Float64(y * Float64(b / Float64(x + Float64(y + t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + t;
	tmp = 0.0;
	if ((z <= -1.2e+142) || ~((z <= 1.2e+106)))
		tmp = z * ((x + y) / t_1);
	else
		tmp = (a * ((y + t) / t_1)) - (y * (b / (x + (y + t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, If[Or[LessEqual[z, -1.2e+142], N[Not[LessEqual[z, 1.2e+106]], $MachinePrecision]], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e142 or 1.2e106 < z

   1. Initial program 37.5%

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

   3. Taylor expanded in z around inf 33.3%

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

      1. associate-/l* 83.1%

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

      2. +-commutative 83.1%

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

      3. +-commutative 83.1%

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

   5. Simplified 83.1%

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

   if -1.2e142 < z < 1.2e106

   1. Initial program 74.5%

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

      1. div-sub 74.5%

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

      2. +-commutative 74.5%

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

      3. *-commutative 74.5%

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

      4. associate-+l+ 74.5%

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

      5. +-commutative 74.5%

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

      6. associate-+l+ 74.5%

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

      7. +-commutative 74.5%

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

      8. associate-/l* 77.3%

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

   4. Applied egg-rr 77.3%

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

   5. Taylor expanded in z around 0 61.3%

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

      1. associate-/l* 76.3%

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

      2. +-commutative 76.3%

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

   7. Simplified 76.3%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+142} \lor \neg \left(z \leq 1.2 \cdot 10^{+106}\right):\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{\left(x + y\right) + t} - y \cdot \frac{b}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.1e-66)
     t_1
     (if (<= y -6.2e-108)
       (* z (/ (+ x y) (+ (+ x y) t)))
       (if (<= y 4.5e-88) (* a (/ t (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.1e-66) {
		tmp = t_1;
	} else if (y <= -6.2e-108) {
		tmp = z * ((x + y) / ((x + y) + t));
	} else if (y <= 4.5e-88) {
		tmp = a * (t / (x + 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 = (z + a) - b
    if (y <= (-2.1d-66)) then
        tmp = t_1
    else if (y <= (-6.2d-108)) then
        tmp = z * ((x + y) / ((x + y) + t))
    else if (y <= 4.5d-88) then
        tmp = a * (t / (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.1e-66) {
		tmp = t_1;
	} else if (y <= -6.2e-108) {
		tmp = z * ((x + y) / ((x + y) + t));
	} else if (y <= 4.5e-88) {
		tmp = a * (t / (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.1e-66:
		tmp = t_1
	elif y <= -6.2e-108:
		tmp = z * ((x + y) / ((x + y) + t))
	elif y <= 4.5e-88:
		tmp = a * (t / (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.1e-66)
		tmp = t_1;
	elseif (y <= -6.2e-108)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(Float64(x + y) + t)));
	elseif (y <= 4.5e-88)
		tmp = Float64(a * Float64(t / Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.1e-66)
		tmp = t_1;
	elseif (y <= -6.2e-108)
		tmp = z * ((x + y) / ((x + y) + t));
	elseif (y <= 4.5e-88)
		tmp = a * (t / (x + t));
	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]}, If[LessEqual[y, -2.1e-66], t$95$1, If[LessEqual[y, -6.2e-108], N[(z * N[(N[(x + y), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-88], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1e-66 or 4.49999999999999991e-88 < y

   1. Initial program 50.8%

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

   3. Taylor expanded in y around inf 70.5%

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

   if -2.1e-66 < y < -6.20000000000000028e-108

   1. Initial program 67.2%

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

   3. Taylor expanded in z around inf 57.1%

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

      1. associate-/l* 89.1%

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

      2. +-commutative 89.1%

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

      3. +-commutative 89.1%

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

   5. Simplified 89.1%

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

   if -6.20000000000000028e-108 < y < 4.49999999999999991e-88

   1. Initial program 86.6%

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

   3. Taylor expanded in t around inf 58.6%

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

   4. Taylor expanded in a around inf 50.7%

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

      1. associate-/l* 56.4%

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

   6. Simplified 56.4%

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

   7. Taylor expanded in y around 0 56.4%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-66}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+73} \lor \neg \left(z \leq 1.8 \cdot 10^{+56}\right):\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t)))
   (if (or (<= z -2.7e+73) (not (<= z 1.8e+56)))
     (* z (/ (+ x y) t_1))
     (* a (/ (+ y t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double tmp;
	if ((z <= -2.7e+73) || !(z <= 1.8e+56)) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = a * ((y + t) / 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 = (x + y) + t
    if ((z <= (-2.7d+73)) .or. (.not. (z <= 1.8d+56))) then
        tmp = z * ((x + y) / t_1)
    else
        tmp = a * ((y + t) / 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 = (x + y) + t;
	double tmp;
	if ((z <= -2.7e+73) || !(z <= 1.8e+56)) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = a * ((y + t) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + t
	tmp = 0
	if (z <= -2.7e+73) or not (z <= 1.8e+56):
		tmp = z * ((x + y) / t_1)
	else:
		tmp = a * ((y + t) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	tmp = 0.0
	if ((z <= -2.7e+73) || !(z <= 1.8e+56))
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	else
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + t;
	tmp = 0.0;
	if ((z <= -2.7e+73) || ~((z <= 1.8e+56)))
		tmp = z * ((x + y) / t_1);
	else
		tmp = a * ((y + t) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, If[Or[LessEqual[z, -2.7e+73], N[Not[LessEqual[z, 1.8e+56]], $MachinePrecision]], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e73 or 1.79999999999999999e56 < z

   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 z around inf 34.1%

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

      1. associate-/l* 73.8%

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

      2. +-commutative 73.8%

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

      3. +-commutative 73.8%

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

   5. Simplified 73.8%

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

   if -2.6999999999999999e73 < z < 1.79999999999999999e56

   1. Initial program 75.8%

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

   3. Taylor expanded in a around inf 47.7%

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

      1. associate-+l+ 47.7%

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

      2. +-commutative 47.7%

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

      3. associate-+r+ 47.7%

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

      4. associate-*r/ 61.0%

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

      5. *-commutative 61.0%

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

   5. Applied egg-rr 61.0%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+73} \lor \neg \left(z \leq 1.8 \cdot 10^{+56}\right):\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{\left(x + y\right) + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+168} \lor \neg \left(t \leq 1.5 \cdot 10^{+81}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.15e+168) (not (<= t 1.5e+81)))
   (* a (/ t (+ x t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.15e+168) || !(t <= 1.5e+81)) {
		tmp = a * (t / (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.15d+168)) .or. (.not. (t <= 1.5d+81))) then
        tmp = a * (t / (x + t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.15e+168) || !(t <= 1.5e+81)) {
		tmp = a * (t / (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.15e+168) or not (t <= 1.5e+81):
		tmp = a * (t / (x + t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.15e+168) || !(t <= 1.5e+81))
		tmp = Float64(a * Float64(t / Float64(x + t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.15e+168) || ~((t <= 1.5e+81)))
		tmp = a * (t / (x + t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.15e+168], N[Not[LessEqual[t, 1.5e+81]], $MachinePrecision]], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e168 or 1.49999999999999999e81 < t

   1. Initial program 52.1%

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

   3. Taylor expanded in t around inf 45.4%

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

   4. Taylor expanded in a around inf 37.1%

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

      1. associate-/l* 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in y around 0 62.6%

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

   if -1.15e168 < t < 1.49999999999999999e81

   1. Initial program 67.4%

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

   3. Taylor expanded in y around inf 61.8%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+168} \lor \neg \left(t \leq 1.5 \cdot 10^{+81}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+112}:\\ \;\;\;\;a - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+81}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.4e+112)
   (- a (/ (* y b) (+ y t)))
   (if (<= t 8.6e+81) (- (+ z a) b) (* a (/ t (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.4e+112) {
		tmp = a - ((y * b) / (y + t));
	} else if (t <= 8.6e+81) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.4d+112)) then
        tmp = a - ((y * b) / (y + t))
    else if (t <= 8.6d+81) then
        tmp = (z + a) - b
    else
        tmp = a * (t / (x + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.4e+112) {
		tmp = a - ((y * b) / (y + t));
	} else if (t <= 8.6e+81) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.4e+112:
		tmp = a - ((y * b) / (y + t))
	elif t <= 8.6e+81:
		tmp = (z + a) - b
	else:
		tmp = a * (t / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.4e+112)
		tmp = Float64(a - Float64(Float64(y * b) / Float64(y + t)));
	elseif (t <= 8.6e+81)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(t / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.4e+112)
		tmp = a - ((y * b) / (y + t));
	elseif (t <= 8.6e+81)
		tmp = (z + a) - b;
	else
		tmp = a * (t / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.4e+112], N[(a - N[(N[(y * b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e+81], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4000000000000001e112

   1. Initial program 56.9%

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

      1. div-sub 56.9%

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

      2. +-commutative 56.9%

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

      3. *-commutative 56.9%

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

      4. associate-+l+ 56.9%

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

      5. +-commutative 56.9%

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

      6. associate-+l+ 56.9%

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

      7. +-commutative 56.9%

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

      8. associate-/l* 67.2%

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

   4. Applied egg-rr 67.2%

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

   5. Taylor expanded in z around 0 61.6%

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

      1. associate-/l* 76.6%

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

      2. +-commutative 76.6%

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

   7. Simplified 76.6%

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

   8. Taylor expanded in x around 0 56.6%

      \[\leadsto \color{blue}{a - \frac{b \cdot y}{t + y}} \]
   9. Step-by-step derivation

      1. *-commutative 56.6%

         \[\leadsto a - \frac{\color{blue}{y \cdot b}}{t + y} \]

   10. Simplified 56.6%

       \[\leadsto \color{blue}{a - \frac{y \cdot b}{t + y}} \]

   if -1.4000000000000001e112 < t < 8.6000000000000003e81

   1. Initial program 67.5%

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

   3. Taylor expanded in y around inf 62.2%

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

   if 8.6000000000000003e81 < t

   1. Initial program 51.2%

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

   3. Taylor expanded in t around inf 40.6%

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

   4. Taylor expanded in a around inf 34.0%

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

      1. associate-/l* 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in y around 0 66.3%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+112}:\\ \;\;\;\;a - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+81}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+167}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+147}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.2e+167) a (if (<= t 1.02e+147) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e+167) {
		tmp = a;
	} else if (t <= 1.02e+147) {
		tmp = (z + a) - 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 (t <= (-3.2d+167)) then
        tmp = a
    else if (t <= 1.02d+147) then
        tmp = (z + a) - 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 (t <= -3.2e+167) {
		tmp = a;
	} else if (t <= 1.02e+147) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.2e+167:
		tmp = a
	elif t <= 1.02e+147:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.2e+167)
		tmp = a;
	elseif (t <= 1.02e+147)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.2e+167)
		tmp = a;
	elseif (t <= 1.02e+147)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.2e+167], a, If[LessEqual[t, 1.02e+147], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -3.19999999999999981e167 or 1.0199999999999999e147 < t

   1. Initial program 51.3%

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

   3. Taylor expanded in t around inf 60.5%

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

   if -3.19999999999999981e167 < t < 1.0199999999999999e147

   1. Initial program 66.6%

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

   3. Taylor expanded in y around inf 60.8%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+167}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+147}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+68}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+56}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.95e+68) z (if (<= z 7e+56) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.95e+68) {
		tmp = z;
	} else if (z <= 7e+56) {
		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 <= (-1.95d+68)) then
        tmp = z
    else if (z <= 7d+56) 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 <= -1.95e+68) {
		tmp = z;
	} else if (z <= 7e+56) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.95e+68:
		tmp = z
	elif z <= 7e+56:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.95e+68)
		tmp = z;
	elseif (z <= 7e+56)
		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 <= -1.95e+68)
		tmp = z;
	elseif (z <= 7e+56)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.95e+68], z, If[LessEqual[z, 7e+56], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95000000000000009e68 or 6.99999999999999999e56 < z

   1. Initial program 44.3%

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

   3. Taylor expanded in x around inf 56.2%

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

   if -1.95000000000000009e68 < z < 6.99999999999999999e56

   1. Initial program 76.8%

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

   3. Taylor expanded in t around inf 47.2%

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

Alternative 11: 32.2% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.1%

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

3. Taylor expanded in t around inf 33.7%

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

Developer target: 82.4% 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 2024097 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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