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

Percentage Accurate: 60.4% → 86.2%

Time: 12.7s

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: 60.4% 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: 86.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{y}{t\_1}\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+102} \lor \neg \left(z \leq 2 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\left(t\_2 + \frac{a \cdot \frac{t + y}{z}}{t\_1}\right) - \frac{b \cdot \frac{y}{z}}{t\_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_1} + \left(\left(t\_2 + \frac{z}{a} \cdot \frac{x + y}{t\_1}\right) - \frac{y \cdot b}{t\_1 \cdot a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (/ y t_1)))
   (if (or (<= z -8.8e+102) (not (<= z 2e+29)))
     (*
      z
      (+
       (/ x t_1)
       (- (+ t_2 (/ (* a (/ (+ t y) z)) t_1)) (/ (* b (/ y z)) t_1))))
     (*
      a
      (+
       (/ t t_1)
       (- (+ t_2 (* (/ z a) (/ (+ x y) t_1))) (/ (* y b) (* t_1 a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = y / t_1;
	double tmp;
	if ((z <= -8.8e+102) || !(z <= 2e+29)) {
		tmp = z * ((x / t_1) + ((t_2 + ((a * ((t + y) / z)) / t_1)) - ((b * (y / z)) / t_1)));
	} else {
		tmp = a * ((t / t_1) + ((t_2 + ((z / a) * ((x + y) / t_1))) - ((y * b) / (t_1 * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (x + y)
    t_2 = y / t_1
    if ((z <= (-8.8d+102)) .or. (.not. (z <= 2d+29))) then
        tmp = z * ((x / t_1) + ((t_2 + ((a * ((t + y) / z)) / t_1)) - ((b * (y / z)) / t_1)))
    else
        tmp = a * ((t / t_1) + ((t_2 + ((z / a) * ((x + y) / t_1))) - ((y * b) / (t_1 * 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 t_1 = t + (x + y);
	double t_2 = y / t_1;
	double tmp;
	if ((z <= -8.8e+102) || !(z <= 2e+29)) {
		tmp = z * ((x / t_1) + ((t_2 + ((a * ((t + y) / z)) / t_1)) - ((b * (y / z)) / t_1)));
	} else {
		tmp = a * ((t / t_1) + ((t_2 + ((z / a) * ((x + y) / t_1))) - ((y * b) / (t_1 * a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = y / t_1
	tmp = 0
	if (z <= -8.8e+102) or not (z <= 2e+29):
		tmp = z * ((x / t_1) + ((t_2 + ((a * ((t + y) / z)) / t_1)) - ((b * (y / z)) / t_1)))
	else:
		tmp = a * ((t / t_1) + ((t_2 + ((z / a) * ((x + y) / t_1))) - ((y * b) / (t_1 * a))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(y / t_1)
	tmp = 0.0
	if ((z <= -8.8e+102) || !(z <= 2e+29))
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(Float64(t_2 + Float64(Float64(a * Float64(Float64(t + y) / z)) / t_1)) - Float64(Float64(b * Float64(y / z)) / t_1))));
	else
		tmp = Float64(a * Float64(Float64(t / t_1) + Float64(Float64(t_2 + Float64(Float64(z / a) * Float64(Float64(x + y) / t_1))) - Float64(Float64(y * b) / Float64(t_1 * a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = y / t_1;
	tmp = 0.0;
	if ((z <= -8.8e+102) || ~((z <= 2e+29)))
		tmp = z * ((x / t_1) + ((t_2 + ((a * ((t + y) / z)) / t_1)) - ((b * (y / z)) / t_1)));
	else
		tmp = a * ((t / t_1) + ((t_2 + ((z / a) * ((x + y) / t_1))) - ((y * b) / (t_1 * a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, If[Or[LessEqual[z, -8.8e+102], N[Not[LessEqual[z, 2e+29]], $MachinePrecision]], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(t$95$2 + N[(N[(a * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(y / z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(t$95$2 + N[(N[(z / a), $MachinePrecision] * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(t$95$1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000003e102 or 1.99999999999999983e29 < z

   1. Initial program 44.8%

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

   3. Taylor expanded in z around inf 72.2%

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

      1. associate--l+ 72.2%

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

      2. +-commutative 72.2%

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

      3. +-commutative 72.2%

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

      4. associate-/r* 73.8%

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

      5. associate-/l* 85.1%

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

      6. +-commutative 85.1%

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

      7. associate-/r* 85.5%

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

      8. associate-/l* 94.1%

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

      9. +-commutative 94.1%

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

   5. Simplified 94.1%

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

   if -8.8000000000000003e102 < z < 1.99999999999999983e29

   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 a around inf 82.3%

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

      1. associate--l+ 82.3%

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

      2. +-commutative 82.3%

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

      3. +-commutative 82.3%

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

      4. times-frac 85.5%

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

      5. +-commutative 85.5%

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

      6. +-commutative 85.5%

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

      7. *-commutative 85.5%

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

      8. +-commutative 85.5%

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

   5. Simplified 85.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+102} \lor \neg \left(z \leq 2 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t + \left(x + y\right)} + \left(\left(\frac{y}{t + \left(x + y\right)} + \frac{a \cdot \frac{t + y}{z}}{t + \left(x + y\right)}\right) - \frac{b \cdot \frac{y}{z}}{t + \left(x + y\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t + \left(x + y\right)} + \left(\left(\frac{y}{t + \left(x + y\right)} + \frac{z}{a} \cdot \frac{x + y}{t + \left(x + y\right)}\right) - \frac{y \cdot b}{\left(t + \left(x + y\right)\right) \cdot a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+236}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* a (+ t y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+236))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+236)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+236)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+236):
		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(z * Float64(x + y)) + Float64(a * Float64(t + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+236))
		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 = (((z * (x + y)) + (a * (t + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+236)))
		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[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+236]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.9999999999999997e236 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 12.4%

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

   3. Taylor expanded in y around inf 70.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999997e236

   1. Initial program 99.0%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+236}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-181}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{z \cdot x}{a \cdot \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -7.4e+33)
     t_1
     (if (<= y -6e-181)
       (* z (/ (+ x y) (+ y (+ x t))))
       (if (<= y 4.2e+17)
         (* a (+ (/ t (+ x t)) (/ (* z x) (* a (+ 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 <= -7.4e+33) {
		tmp = t_1;
	} else if (y <= -6e-181) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else if (y <= 4.2e+17) {
		tmp = a * ((t / (x + t)) + ((z * x) / (a * (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 <= (-7.4d+33)) then
        tmp = t_1
    else if (y <= (-6d-181)) then
        tmp = z * ((x + y) / (y + (x + t)))
    else if (y <= 4.2d+17) then
        tmp = a * ((t / (x + t)) + ((z * x) / (a * (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 <= -7.4e+33) {
		tmp = t_1;
	} else if (y <= -6e-181) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else if (y <= 4.2e+17) {
		tmp = a * ((t / (x + t)) + ((z * x) / (a * (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 <= -7.4e+33:
		tmp = t_1
	elif y <= -6e-181:
		tmp = z * ((x + y) / (y + (x + t)))
	elif y <= 4.2e+17:
		tmp = a * ((t / (x + t)) + ((z * x) / (a * (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 <= -7.4e+33)
		tmp = t_1;
	elseif (y <= -6e-181)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	elseif (y <= 4.2e+17)
		tmp = Float64(a * Float64(Float64(t / Float64(x + t)) + Float64(Float64(z * x) / Float64(a * 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 <= -7.4e+33)
		tmp = t_1;
	elseif (y <= -6e-181)
		tmp = z * ((x + y) / (y + (x + t)));
	elseif (y <= 4.2e+17)
		tmp = a * ((t / (x + t)) + ((z * x) / (a * (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, -7.4e+33], t$95$1, If[LessEqual[y, -6e-181], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+17], N[(a * N[(N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(z * x), $MachinePrecision] / N[(a * N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.3999999999999997e33 or 4.2e17 < y

   1. Initial program 33.0%

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

   3. Taylor expanded in y around inf 76.8%

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

   if -7.3999999999999997e33 < y < -5.99999999999999948e-181

   1. Initial program 79.0%

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

   3. Taylor expanded in z around inf 41.9%

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

      1. associate-/l* 57.4%

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

      2. +-commutative 57.4%

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

      3. associate-+r+ 57.4%

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

   5. Simplified 57.4%

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

   if -5.99999999999999948e-181 < y < 4.2e17

   1. Initial program 76.2%

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

   3. Taylor expanded in a around inf 84.0%

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

      1. associate--l+ 84.0%

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

      2. +-commutative 84.0%

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

      3. +-commutative 84.0%

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

      4. times-frac 87.1%

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

      5. +-commutative 87.1%

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

      6. +-commutative 87.1%

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

      7. *-commutative 87.1%

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

      8. +-commutative 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in y around 0 65.8%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+33}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-181}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{z \cdot x}{a \cdot \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-181}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_1}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+83}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) - y \cdot b}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -1.08e+60)
     t_2
     (if (<= z 8.4e-181)
       (* a (/ (+ t y) t_1))
       (if (<= z 2.1e+83) (/ (- (* a (+ t y)) (* y b)) t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -1.08e+60) {
		tmp = t_2;
	} else if (z <= 8.4e-181) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= 2.1e+83) {
		tmp = ((a * (t + y)) - (y * b)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * ((x + y) / t_1)
    if (z <= (-1.08d+60)) then
        tmp = t_2
    else if (z <= 8.4d-181) then
        tmp = a * ((t + y) / t_1)
    else if (z <= 2.1d+83) then
        tmp = ((a * (t + y)) - (y * b)) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -1.08e+60) {
		tmp = t_2;
	} else if (z <= 8.4e-181) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= 2.1e+83) {
		tmp = ((a * (t + y)) - (y * b)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -1.08e+60:
		tmp = t_2
	elif z <= 8.4e-181:
		tmp = a * ((t + y) / t_1)
	elif z <= 2.1e+83:
		tmp = ((a * (t + y)) - (y * b)) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -1.08e+60)
		tmp = t_2;
	elseif (z <= 8.4e-181)
		tmp = Float64(a * Float64(Float64(t + y) / t_1));
	elseif (z <= 2.1e+83)
		tmp = Float64(Float64(Float64(a * Float64(t + y)) - Float64(y * b)) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -1.08e+60)
		tmp = t_2;
	elseif (z <= 8.4e-181)
		tmp = a * ((t + y) / t_1);
	elseif (z <= 2.1e+83)
		tmp = ((a * (t + y)) - (y * b)) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e+60], t$95$2, If[LessEqual[z, 8.4e-181], N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+83], N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.08e60 or 2.10000000000000002e83 < z

   1. Initial program 42.8%

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

   3. Taylor expanded in z around inf 32.7%

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

      1. associate-/l* 73.0%

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

      2. +-commutative 73.0%

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

      3. associate-+r+ 73.0%

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

   5. Simplified 73.0%

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

   if -1.08e60 < z < 8.40000000000000013e-181

   1. Initial program 61.1%

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

   3. Taylor expanded in a around inf 34.7%

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

      1. associate-/l* 64.3%

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

      2. associate-+r+ 64.3%

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

   5. Simplified 64.3%

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

   if 8.40000000000000013e-181 < z < 2.10000000000000002e83

   1. Initial program 80.5%

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

   3. Taylor expanded in z around 0 57.1%

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

      1. *-commutative 57.1%

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

   5. Simplified 57.1%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-181}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+83}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \frac{t + y}{t\_1}\\ \mathbf{if}\;a \leq -3000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-102}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+156}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* a (/ (+ t y) t_1))))
   (if (<= a -3000000000.0)
     t_2
     (if (<= a 1.5e-102)
       (* z (/ (+ x y) t_1))
       (if (<= a 2.1e+156) (- (+ z a) b) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((t + y) / t_1);
	double tmp;
	if (a <= -3000000000.0) {
		tmp = t_2;
	} else if (a <= 1.5e-102) {
		tmp = z * ((x + y) / t_1);
	} else if (a <= 2.1e+156) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a * ((t + y) / t_1)
    if (a <= (-3000000000.0d0)) then
        tmp = t_2
    else if (a <= 1.5d-102) then
        tmp = z * ((x + y) / t_1)
    else if (a <= 2.1d+156) then
        tmp = (z + a) - b
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((t + y) / t_1);
	double tmp;
	if (a <= -3000000000.0) {
		tmp = t_2;
	} else if (a <= 1.5e-102) {
		tmp = z * ((x + y) / t_1);
	} else if (a <= 2.1e+156) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a * ((t + y) / t_1)
	tmp = 0
	if a <= -3000000000.0:
		tmp = t_2
	elif a <= 1.5e-102:
		tmp = z * ((x + y) / t_1)
	elif a <= 2.1e+156:
		tmp = (z + a) - b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a * Float64(Float64(t + y) / t_1))
	tmp = 0.0
	if (a <= -3000000000.0)
		tmp = t_2;
	elseif (a <= 1.5e-102)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	elseif (a <= 2.1e+156)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a * ((t + y) / t_1);
	tmp = 0.0;
	if (a <= -3000000000.0)
		tmp = t_2;
	elseif (a <= 1.5e-102)
		tmp = z * ((x + y) / t_1);
	elseif (a <= 2.1e+156)
		tmp = (z + a) - b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3000000000.0], t$95$2, If[LessEqual[a, 1.5e-102], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+156], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3e9 or 2.09999999999999981e156 < a

   1. Initial program 43.0%

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

   3. Taylor expanded in a around inf 37.2%

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

      1. associate-/l* 77.0%

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

      2. associate-+r+ 77.0%

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

   5. Simplified 77.0%

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

   if -3e9 < a < 1.5e-102

   1. Initial program 69.0%

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

   3. Taylor expanded in z around inf 38.5%

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

      1. associate-/l* 57.9%

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

      2. +-commutative 57.9%

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

      3. associate-+r+ 57.9%

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

   5. Simplified 57.9%

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

   if 1.5e-102 < a < 2.09999999999999981e156

   1. Initial program 60.8%

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

   3. Taylor expanded in y around inf 62.7%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3000000000:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-102}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+156}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+157} \lor \neg \left(b \leq 1.2 \cdot 10^{+181}\right):\\ \;\;\;\;b \cdot \frac{-y}{x + \left(t + y\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.85e+157) (not (<= b 1.2e+181)))
   (* b (/ (- y) (+ x (+ t y))))
   (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.85e+157) || !(b <= 1.2e+181)) {
		tmp = b * (-y / (x + (t + y)));
	} else {
		tmp = z + 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 ((b <= (-1.85d+157)) .or. (.not. (b <= 1.2d+181))) then
        tmp = b * (-y / (x + (t + y)))
    else
        tmp = z + 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 ((b <= -1.85e+157) || !(b <= 1.2e+181)) {
		tmp = b * (-y / (x + (t + y)));
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.85e+157) or not (b <= 1.2e+181):
		tmp = b * (-y / (x + (t + y)))
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.85e+157) || !(b <= 1.2e+181))
		tmp = Float64(b * Float64(Float64(-y) / Float64(x + Float64(t + y))));
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.85e+157) || ~((b <= 1.2e+181)))
		tmp = b * (-y / (x + (t + y)));
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.85e+157], N[Not[LessEqual[b, 1.2e+181]], $MachinePrecision]], N[(b * N[((-y) / N[(x + N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8499999999999999e157 or 1.20000000000000001e181 < b

   1. Initial program 53.1%

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

   3. Taylor expanded in b around inf 33.1%

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

      1. mul-1-neg 33.1%

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

      2. associate-/l* 61.1%

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

      3. distribute-rgt-neg-in 61.1%

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

      4. distribute-neg-frac2 61.1%

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

      5. +-commutative 61.1%

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

      6. associate-+r+ 61.1%

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

      7. distribute-neg-in 61.1%

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

      8. +-commutative 61.1%

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

      9. unsub-neg 61.1%

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

   5. Simplified 61.1%

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

   if -1.8499999999999999e157 < b < 1.20000000000000001e181

   1. Initial program 59.7%

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

   3. Taylor expanded in y around inf 25.2%

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

      1. associate--l+ 28.7%

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

      2. associate-/l* 27.8%

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

      3. associate-/l* 28.0%

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

      4. associate-/l* 37.6%

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

   5. Simplified 37.6%

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

   6. Taylor expanded in z around inf 46.4%

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

   7. Taylor expanded in t around 0 64.5%

      \[\leadsto \color{blue}{a + z} \]
   8. Step-by-step derivation

      1. +-commutative 64.5%

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

   9. Simplified 64.5%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+157} \lor \neg \left(b \leq 1.2 \cdot 10^{+181}\right):\\ \;\;\;\;b \cdot \frac{-y}{x + \left(t + y\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \frac{z - b}{t + \left(x + y\right)}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+180}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{-y}{x + \left(t + y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.4e+157)
   (* y (/ (- z b) (+ t (+ x y))))
   (if (<= b 5.5e+180) (+ z a) (* b (/ (- y) (+ x (+ t y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.4e+157) {
		tmp = y * ((z - b) / (t + (x + y)));
	} else if (b <= 5.5e+180) {
		tmp = z + a;
	} else {
		tmp = b * (-y / (x + (t + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.4d+157)) then
        tmp = y * ((z - b) / (t + (x + y)))
    else if (b <= 5.5d+180) then
        tmp = z + a
    else
        tmp = b * (-y / (x + (t + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.4e+157) {
		tmp = y * ((z - b) / (t + (x + y)));
	} else if (b <= 5.5e+180) {
		tmp = z + a;
	} else {
		tmp = b * (-y / (x + (t + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.4e+157:
		tmp = y * ((z - b) / (t + (x + y)))
	elif b <= 5.5e+180:
		tmp = z + a
	else:
		tmp = b * (-y / (x + (t + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.4e+157)
		tmp = Float64(y * Float64(Float64(z - b) / Float64(t + Float64(x + y))));
	elseif (b <= 5.5e+180)
		tmp = Float64(z + a);
	else
		tmp = Float64(b * Float64(Float64(-y) / Float64(x + Float64(t + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.4e+157)
		tmp = y * ((z - b) / (t + (x + y)));
	elseif (b <= 5.5e+180)
		tmp = z + a;
	else
		tmp = b * (-y / (x + (t + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.4e+157], N[(y * N[(N[(z - b), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+180], N[(z + a), $MachinePrecision], N[(b * N[((-y) / N[(x + N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4000000000000001e157

   1. Initial program 57.8%

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

   3. Taylor expanded in y around inf 36.0%

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

   4. Taylor expanded in a around 0 33.9%

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

      1. associate-/l* 57.6%

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

      2. +-commutative 57.6%

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

   6. Simplified 57.6%

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

   if -1.4000000000000001e157 < b < 5.5000000000000003e180

   1. Initial program 59.7%

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

   3. Taylor expanded in y around inf 25.2%

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

      1. associate--l+ 28.7%

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

      2. associate-/l* 27.8%

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

      3. associate-/l* 28.0%

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

      4. associate-/l* 37.6%

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

   5. Simplified 37.6%

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

   6. Taylor expanded in z around inf 46.4%

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

   7. Taylor expanded in t around 0 64.5%

      \[\leadsto \color{blue}{a + z} \]
   8. Step-by-step derivation

      1. +-commutative 64.5%

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

   9. Simplified 64.5%

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

   if 5.5000000000000003e180 < b

   1. Initial program 46.7%

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

   3. Taylor expanded in b around inf 32.7%

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

      1. mul-1-neg 32.7%

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

      2. associate-/l* 66.8%

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

      3. distribute-rgt-neg-in 66.8%

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

      4. distribute-neg-frac2 66.8%

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

      5. +-commutative 66.8%

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

      6. associate-+r+ 66.8%

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

      7. distribute-neg-in 66.8%

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

      8. +-commutative 66.8%

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

      9. unsub-neg 66.8%

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

   5. Simplified 66.8%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \frac{z - b}{t + \left(x + y\right)}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+180}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{-y}{x + \left(t + y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+31} \lor \neg \left(y \leq 14500000000000\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.6e+31) (not (<= y 14500000000000.0))) (- (+ z a) b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.6e+31) || !(y <= 14500000000000.0)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + 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 ((y <= (-4.6d+31)) .or. (.not. (y <= 14500000000000.0d0))) then
        tmp = (z + a) - b
    else
        tmp = z + 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 ((y <= -4.6e+31) || !(y <= 14500000000000.0)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.6e+31) or not (y <= 14500000000000.0):
		tmp = (z + a) - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.6e+31) || !(y <= 14500000000000.0))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.6e+31) || ~((y <= 14500000000000.0)))
		tmp = (z + a) - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.6e+31], N[Not[LessEqual[y, 14500000000000.0]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999999e31 or 1.45e13 < y

   1. Initial program 33.4%

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

   3. Taylor expanded in y around inf 75.5%

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

   if -4.5999999999999999e31 < y < 1.45e13

   1. Initial program 77.6%

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

   3. Taylor expanded in y around inf 8.7%

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

      1. associate--l+ 12.8%

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

      2. associate-/l* 11.3%

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

      3. associate-/l* 11.4%

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

      4. associate-/l* 8.7%

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

   5. Simplified 8.7%

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

   6. Taylor expanded in z around inf 24.9%

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

   7. Taylor expanded in t around 0 50.5%

      \[\leadsto \color{blue}{a + z} \]
   8. Step-by-step derivation

      1. +-commutative 50.5%

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

   9. Simplified 50.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+31} \lor \neg \left(y \leq 14500000000000\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 45.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+84}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.3e+84) z (if (<= z 2.6e+39) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.3e+84) {
		tmp = z;
	} else if (z <= 2.6e+39) {
		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 <= (-3.3d+84)) then
        tmp = z
    else if (z <= 2.6d+39) 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 <= -3.3e+84) {
		tmp = z;
	} else if (z <= 2.6e+39) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.3e+84:
		tmp = z
	elif z <= 2.6e+39:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.3e+84)
		tmp = z;
	elseif (z <= 2.6e+39)
		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 <= -3.3e+84)
		tmp = z;
	elseif (z <= 2.6e+39)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.3e+84], z, If[LessEqual[z, 2.6e+39], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -3.30000000000000017e84 or 2.6e39 < z

   1. Initial program 44.1%

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

   3. Taylor expanded in x around inf 51.5%

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

   if -3.30000000000000017e84 < z < 2.6e39

   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 t around inf 48.9%

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

Alternative 10: 51.9% accurate, 7.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return z + 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 = z + a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(z + a), $MachinePrecision]

Derivation

1. Initial program 58.1%

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

3. Taylor expanded in y around inf 24.0%

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

   1. associate--l+ 26.7%

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

   2. associate-/l* 25.9%

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

   3. associate-/l* 26.2%

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

   4. associate-/l* 34.2%

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

5. Simplified 34.2%

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

6. Taylor expanded in z around inf 38.4%

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

7. Taylor expanded in t around 0 55.0%

   \[\leadsto \color{blue}{a + z} \]
8. Step-by-step derivation

   1. +-commutative 55.0%

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

9. Simplified 55.0%

   \[\leadsto \color{blue}{z + a} \]
10. Add Preprocessing

Alternative 11: 33.4% 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 58.1%

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

3. Taylor expanded in t around inf 35.9%

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

Developer Target 1: 82.5% 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 2024137 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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