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

Percentage Accurate: 60.4% → 90.6%

Time: 12.5s

Alternatives: 16

Speedup: 0.5×

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: 90.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -720000 \lor \neg \left(z \leq 2.7 \cdot 10^{+66}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\left(\frac{y}{t\_1} + \frac{a}{z} \cdot \frac{t + y}{t\_1}\right) - \frac{b \cdot \frac{y}{z}}{t\_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_2} + \frac{y \cdot \left(z - b\right) + z \cdot x}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (+ y (+ x t))))
   (if (or (<= z -720000.0) (not (<= z 2.7e+66)))
     (*
      z
      (+
       (/ x t_1)
       (- (+ (/ y t_1) (* (/ a z) (/ (+ t y) t_1))) (/ (* b (/ y z)) t_1))))
     (+ (* a (/ (+ t y) t_2)) (/ (+ (* y (- z b)) (* z x)) t_2)))))

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 + (x + t);
	double tmp;
	if ((z <= -720000.0) || !(z <= 2.7e+66)) {
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)));
	} else {
		tmp = (a * ((t + y) / t_2)) + (((y * (z - b)) + (z * x)) / 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 = t + (x + y)
    t_2 = y + (x + t)
    if ((z <= (-720000.0d0)) .or. (.not. (z <= 2.7d+66))) then
        tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)))
    else
        tmp = (a * ((t + y) / t_2)) + (((y * (z - b)) + (z * x)) / 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 = t + (x + y);
	double t_2 = y + (x + t);
	double tmp;
	if ((z <= -720000.0) || !(z <= 2.7e+66)) {
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)));
	} else {
		tmp = (a * ((t + y) / t_2)) + (((y * (z - b)) + (z * x)) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = y + (x + t)
	tmp = 0
	if (z <= -720000.0) or not (z <= 2.7e+66):
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)))
	else:
		tmp = (a * ((t + y) / t_2)) + (((y * (z - b)) + (z * x)) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	tmp = 0.0
	if ((z <= -720000.0) || !(z <= 2.7e+66))
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(Float64(Float64(y / t_1) + Float64(Float64(a / z) * Float64(Float64(t + y) / t_1))) - Float64(Float64(b * Float64(y / z)) / t_1))));
	else
		tmp = Float64(Float64(a * Float64(Float64(t + y) / t_2)) + Float64(Float64(Float64(y * Float64(z - b)) + Float64(z * x)) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = y + (x + t);
	tmp = 0.0;
	if ((z <= -720000.0) || ~((z <= 2.7e+66)))
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)));
	else
		tmp = (a * ((t + y) / t_2)) + (((y * (z - b)) + (z * x)) / t_2);
	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 + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -720000.0], N[Not[LessEqual[z, 2.7e+66]], $MachinePrecision]], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(a / z), $MachinePrecision] * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(y / z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e5 or 2.7e66 < z

   1. Initial program 45.5%

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

   3. Taylor expanded in z around inf 71.0%

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

      1. associate--l+ 71.0%

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

      2. +-commutative 71.0%

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

      3. +-commutative 71.0%

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

      4. times-frac 89.0%

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

      5. +-commutative 89.0%

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

      6. associate-/r* 89.6%

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

      7. associate-/l* 96.4%

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

      8. +-commutative 96.4%

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

   5. Simplified 96.4%

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

   if -7.2e5 < z < 2.7e66

   1. Initial program 70.6%

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

   3. Taylor expanded in b around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. +-commutative 70.6%

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

      3. associate-+l+ 70.6%

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

      4. associate-/l* 89.3%

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

      5. +-commutative 89.3%

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

      6. associate-+r+ 89.3%

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

      7. +-commutative 89.3%

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

      8. associate-+l+ 89.3%

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

      9. sub-neg 89.3%

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

      10. div-sub 89.3%

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

   5. Simplified 89.3%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -720000 \lor \neg \left(z \leq 2.7 \cdot 10^{+66}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t + \left(x + y\right)} + \left(\left(\frac{y}{t + \left(x + y\right)} + \frac{a}{z} \cdot \frac{t + y}{t + \left(x + y\right)}\right) - \frac{b \cdot \frac{y}{z}}{t + \left(x + y\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + \frac{y \cdot \left(z - b\right) + z \cdot x}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ t y)) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+236))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+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 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+236)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+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(a * Float64(t + y)) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+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 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+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[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+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 1.00000000000000005e236 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.4%

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

   3. Taylor expanded in y around inf 74.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000005e236

   1. Initial program 99.8%

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

4. Final simplification 88.7%

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

Alternative 3: 63.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := a \cdot \frac{t + y}{t\_2}\\ t_4 := z \cdot \left(x + y\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+89}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-58}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) + t\_4}{t\_2}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{t\_4 - y \cdot b}{t\_2}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-103}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_2}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \left(\left(\frac{z}{a} - b \cdot \frac{y}{\left(x + y\right) \cdot a}\right) + \frac{y}{x + y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ x t)))
        (t_3 (* a (/ (+ t y) t_2)))
        (t_4 (* z (+ x y))))
   (if (<= a -1.05e+89)
     t_3
     (if (<= a -2.5e+18)
       t_1
       (if (<= a -2.65e-58)
         (/ (+ (* a (+ t y)) t_4) t_2)
         (if (<= a -6.5e-195)
           t_1
           (if (<= a 5.6e-255)
             (/ (- t_4 (* y b)) t_2)
             (if (<= a 1.85e-103)
               (* z (/ (+ x y) t_2))
               (if (<= a 4.5e+139)
                 (* a (+ (- (/ z a) (* b (/ y (* (+ x y) a)))) (/ y (+ x y))))
                 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = a * ((t + y) / t_2);
	double t_4 = z * (x + y);
	double tmp;
	if (a <= -1.05e+89) {
		tmp = t_3;
	} else if (a <= -2.5e+18) {
		tmp = t_1;
	} else if (a <= -2.65e-58) {
		tmp = ((a * (t + y)) + t_4) / t_2;
	} else if (a <= -6.5e-195) {
		tmp = t_1;
	} else if (a <= 5.6e-255) {
		tmp = (t_4 - (y * b)) / t_2;
	} else if (a <= 1.85e-103) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 4.5e+139) {
		tmp = a * (((z / a) - (b * (y / ((x + y) * a)))) + (y / (x + y)));
	} 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) :: t_4
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = a * ((t + y) / t_2)
    t_4 = z * (x + y)
    if (a <= (-1.05d+89)) then
        tmp = t_3
    else if (a <= (-2.5d+18)) then
        tmp = t_1
    else if (a <= (-2.65d-58)) then
        tmp = ((a * (t + y)) + t_4) / t_2
    else if (a <= (-6.5d-195)) then
        tmp = t_1
    else if (a <= 5.6d-255) then
        tmp = (t_4 - (y * b)) / t_2
    else if (a <= 1.85d-103) then
        tmp = z * ((x + y) / t_2)
    else if (a <= 4.5d+139) then
        tmp = a * (((z / a) - (b * (y / ((x + y) * a)))) + (y / (x + y)))
    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 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = a * ((t + y) / t_2);
	double t_4 = z * (x + y);
	double tmp;
	if (a <= -1.05e+89) {
		tmp = t_3;
	} else if (a <= -2.5e+18) {
		tmp = t_1;
	} else if (a <= -2.65e-58) {
		tmp = ((a * (t + y)) + t_4) / t_2;
	} else if (a <= -6.5e-195) {
		tmp = t_1;
	} else if (a <= 5.6e-255) {
		tmp = (t_4 - (y * b)) / t_2;
	} else if (a <= 1.85e-103) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 4.5e+139) {
		tmp = a * (((z / a) - (b * (y / ((x + y) * a)))) + (y / (x + y)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = a * ((t + y) / t_2)
	t_4 = z * (x + y)
	tmp = 0
	if a <= -1.05e+89:
		tmp = t_3
	elif a <= -2.5e+18:
		tmp = t_1
	elif a <= -2.65e-58:
		tmp = ((a * (t + y)) + t_4) / t_2
	elif a <= -6.5e-195:
		tmp = t_1
	elif a <= 5.6e-255:
		tmp = (t_4 - (y * b)) / t_2
	elif a <= 1.85e-103:
		tmp = z * ((x + y) / t_2)
	elif a <= 4.5e+139:
		tmp = a * (((z / a) - (b * (y / ((x + y) * a)))) + (y / (x + y)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(a * Float64(Float64(t + y) / t_2))
	t_4 = Float64(z * Float64(x + y))
	tmp = 0.0
	if (a <= -1.05e+89)
		tmp = t_3;
	elseif (a <= -2.5e+18)
		tmp = t_1;
	elseif (a <= -2.65e-58)
		tmp = Float64(Float64(Float64(a * Float64(t + y)) + t_4) / t_2);
	elseif (a <= -6.5e-195)
		tmp = t_1;
	elseif (a <= 5.6e-255)
		tmp = Float64(Float64(t_4 - Float64(y * b)) / t_2);
	elseif (a <= 1.85e-103)
		tmp = Float64(z * Float64(Float64(x + y) / t_2));
	elseif (a <= 4.5e+139)
		tmp = Float64(a * Float64(Float64(Float64(z / a) - Float64(b * Float64(y / Float64(Float64(x + y) * a)))) + Float64(y / Float64(x + y))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = a * ((t + y) / t_2);
	t_4 = z * (x + y);
	tmp = 0.0;
	if (a <= -1.05e+89)
		tmp = t_3;
	elseif (a <= -2.5e+18)
		tmp = t_1;
	elseif (a <= -2.65e-58)
		tmp = ((a * (t + y)) + t_4) / t_2;
	elseif (a <= -6.5e-195)
		tmp = t_1;
	elseif (a <= 5.6e-255)
		tmp = (t_4 - (y * b)) / t_2;
	elseif (a <= 1.85e-103)
		tmp = z * ((x + y) / t_2);
	elseif (a <= 4.5e+139)
		tmp = a * (((z / a) - (b * (y / ((x + y) * a)))) + (y / (x + y)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+89], t$95$3, If[LessEqual[a, -2.5e+18], t$95$1, If[LessEqual[a, -2.65e-58], N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[a, -6.5e-195], t$95$1, If[LessEqual[a, 5.6e-255], N[(N[(t$95$4 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[a, 1.85e-103], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+139], N[(a * N[(N[(N[(z / a), $MachinePrecision] - N[(b * N[(y / N[(N[(x + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.04999999999999993e89 or 4.4999999999999999e139 < a

   1. Initial program 41.8%

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

   3. Taylor expanded in a around inf 36.7%

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

      1. associate-/l* 81.4%

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

      2. +-commutative 81.4%

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

      3. associate-+r+ 81.4%

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

      4. +-commutative 81.4%

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

      5. associate-+l+ 81.4%

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

   5. Simplified 81.4%

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

   if -1.04999999999999993e89 < a < -2.5e18 or -2.6500000000000002e-58 < a < -6.50000000000000004e-195

   1. Initial program 57.5%

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

   3. Taylor expanded in y around inf 73.9%

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

   if -2.5e18 < a < -2.6500000000000002e-58

   1. Initial program 82.2%

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

   3. Taylor expanded in b around 0 72.8%

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

   if -6.50000000000000004e-195 < a < 5.60000000000000023e-255

   1. Initial program 81.4%

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

   3. Taylor expanded in a around 0 72.5%

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

      1. +-commutative 72.5%

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

      2. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   if 5.60000000000000023e-255 < a < 1.85e-103

   1. Initial program 57.7%

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

   3. Taylor expanded in z around inf 30.5%

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

      1. associate-/l* 72.2%

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

      2. +-commutative 72.2%

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

      3. +-commutative 72.2%

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

      4. associate-+r+ 72.2%

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

      5. +-commutative 72.2%

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

      6. associate-+l+ 72.2%

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

   5. Simplified 72.2%

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

   if 1.85e-103 < a < 4.4999999999999999e139

   1. Initial program 66.9%

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

   3. Taylor expanded in a around inf 76.0%

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

      1. associate--l+ 76.0%

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

      2. +-commutative 76.0%

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

      3. +-commutative 76.0%

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

      4. associate-/l* 85.4%

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

      5. +-commutative 85.4%

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

      6. +-commutative 85.4%

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

      7. *-commutative 85.4%

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

      8. +-commutative 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in t around 0 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-/l* 76.2%

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

   8. Simplified 76.2%

      \[\leadsto \color{blue}{a \cdot \left(\frac{y}{x + y} + \left(\frac{z}{a} - b \cdot \frac{y}{a \cdot \left(x + y\right)}\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-58}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) + z \cdot \left(x + y\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-195}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-103}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \left(\left(\frac{z}{a} - b \cdot \frac{y}{\left(x + y\right) \cdot a}\right) + \frac{y}{x + y}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{a \cdot \left(t + y\right) + t\_1}{t\_2}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+126}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-51}:\\ \;\;\;\;\frac{t\_1 - y \cdot b}{t\_2}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-53}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-294}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \frac{z + a \cdot \frac{t}{x}}{x + t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+24}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ x y)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (+ (* a (+ t y)) t_1) t_2))
        (t_4 (- (+ z a) b)))
   (if (<= y -1.1e+126)
     t_4
     (if (<= y -1.7e-51)
       (/ (- t_1 (* y b)) t_2)
       (if (<= y -2.1e-53)
         a
         (if (<= y 1.1e-294)
           t_3
           (if (<= y 1.35e-160)
             (* x (/ (+ z (* a (/ t x))) (+ x t)))
             (if (<= y 6.5e+24) t_3 t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x + y);
	double t_2 = y + (x + t);
	double t_3 = ((a * (t + y)) + t_1) / t_2;
	double t_4 = (z + a) - b;
	double tmp;
	if (y <= -1.1e+126) {
		tmp = t_4;
	} else if (y <= -1.7e-51) {
		tmp = (t_1 - (y * b)) / t_2;
	} else if (y <= -2.1e-53) {
		tmp = a;
	} else if (y <= 1.1e-294) {
		tmp = t_3;
	} else if (y <= 1.35e-160) {
		tmp = x * ((z + (a * (t / x))) / (x + t));
	} else if (y <= 6.5e+24) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (x + y)
    t_2 = y + (x + t)
    t_3 = ((a * (t + y)) + t_1) / t_2
    t_4 = (z + a) - b
    if (y <= (-1.1d+126)) then
        tmp = t_4
    else if (y <= (-1.7d-51)) then
        tmp = (t_1 - (y * b)) / t_2
    else if (y <= (-2.1d-53)) then
        tmp = a
    else if (y <= 1.1d-294) then
        tmp = t_3
    else if (y <= 1.35d-160) then
        tmp = x * ((z + (a * (t / x))) / (x + t))
    else if (y <= 6.5d+24) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x + y);
	double t_2 = y + (x + t);
	double t_3 = ((a * (t + y)) + t_1) / t_2;
	double t_4 = (z + a) - b;
	double tmp;
	if (y <= -1.1e+126) {
		tmp = t_4;
	} else if (y <= -1.7e-51) {
		tmp = (t_1 - (y * b)) / t_2;
	} else if (y <= -2.1e-53) {
		tmp = a;
	} else if (y <= 1.1e-294) {
		tmp = t_3;
	} else if (y <= 1.35e-160) {
		tmp = x * ((z + (a * (t / x))) / (x + t));
	} else if (y <= 6.5e+24) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (x + y)
	t_2 = y + (x + t)
	t_3 = ((a * (t + y)) + t_1) / t_2
	t_4 = (z + a) - b
	tmp = 0
	if y <= -1.1e+126:
		tmp = t_4
	elif y <= -1.7e-51:
		tmp = (t_1 - (y * b)) / t_2
	elif y <= -2.1e-53:
		tmp = a
	elif y <= 1.1e-294:
		tmp = t_3
	elif y <= 1.35e-160:
		tmp = x * ((z + (a * (t / x))) / (x + t))
	elif y <= 6.5e+24:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(a * Float64(t + y)) + t_1) / t_2)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.1e+126)
		tmp = t_4;
	elseif (y <= -1.7e-51)
		tmp = Float64(Float64(t_1 - Float64(y * b)) / t_2);
	elseif (y <= -2.1e-53)
		tmp = a;
	elseif (y <= 1.1e-294)
		tmp = t_3;
	elseif (y <= 1.35e-160)
		tmp = Float64(x * Float64(Float64(z + Float64(a * Float64(t / x))) / Float64(x + t)));
	elseif (y <= 6.5e+24)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (x + y);
	t_2 = y + (x + t);
	t_3 = ((a * (t + y)) + t_1) / t_2;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.1e+126)
		tmp = t_4;
	elseif (y <= -1.7e-51)
		tmp = (t_1 - (y * b)) / t_2;
	elseif (y <= -2.1e-53)
		tmp = a;
	elseif (y <= 1.1e-294)
		tmp = t_3;
	elseif (y <= 1.35e-160)
		tmp = x * ((z + (a * (t / x))) / (x + t));
	elseif (y <= 6.5e+24)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.1e+126], t$95$4, If[LessEqual[y, -1.7e-51], N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, -2.1e-53], a, If[LessEqual[y, 1.1e-294], t$95$3, If[LessEqual[y, 1.35e-160], N[(x * N[(N[(z + N[(a * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+24], t$95$3, t$95$4]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.09999999999999999e126 or 6.4999999999999996e24 < y

   1. Initial program 36.6%

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

   3. Taylor expanded in y around inf 79.1%

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

   if -1.09999999999999999e126 < y < -1.70000000000000001e-51

   1. Initial program 78.7%

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

   3. Taylor expanded in a around 0 70.4%

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

      1. +-commutative 70.4%

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

      2. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   if -1.70000000000000001e-51 < y < -2.09999999999999977e-53

   1. Initial program 4.8%

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

   3. Taylor expanded in t around inf 100.0%

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

   if -2.09999999999999977e-53 < y < 1.1e-294 or 1.35000000000000005e-160 < y < 6.4999999999999996e24

   1. Initial program 80.6%

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

   3. Taylor expanded in b around 0 73.7%

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

   if 1.1e-294 < y < 1.35000000000000005e-160

   1. Initial program 52.7%

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

   3. Taylor expanded in x around inf 52.7%

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

      1. associate-/l* 48.2%

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

      2. associate-/l* 43.1%

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

   5. Simplified 43.1%

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

   6. Taylor expanded in y around 0 45.4%

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

      1. associate-/l* 56.8%

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

      2. associate-/l* 64.3%

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

      3. +-commutative 64.3%

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

   8. Simplified 64.3%

      \[\leadsto \color{blue}{x \cdot \frac{z + a \cdot \frac{t}{x}}{x + t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+126}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-51}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-53}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-294}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) + z \cdot \left(x + y\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \frac{z + a \cdot \frac{t}{x}}{x + t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) + z \cdot \left(x + y\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := a \cdot \frac{t + y}{t\_2}\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-54}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-255}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t\_2}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_2}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ y (+ x t))) (t_3 (* a (/ (+ t y) t_2))))
   (if (<= a -5.4e+88)
     t_3
     (if (<= a -1.05e+18)
       t_1
       (if (<= a -3.6e-54)
         (/ (+ (* t a) (* z x)) (+ x t))
         (if (<= a -2.2e-196)
           t_1
           (if (<= a 3.4e-255)
             (/ (- (* z (+ x y)) (* y b)) t_2)
             (if (<= a 9.2e-88)
               (* z (/ (+ x y) t_2))
               (if (<= a 2.4e+138) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = a * ((t + y) / t_2);
	double tmp;
	if (a <= -5.4e+88) {
		tmp = t_3;
	} else if (a <= -1.05e+18) {
		tmp = t_1;
	} else if (a <= -3.6e-54) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (a <= -2.2e-196) {
		tmp = t_1;
	} else if (a <= 3.4e-255) {
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	} else if (a <= 9.2e-88) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 2.4e+138) {
		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 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = a * ((t + y) / t_2)
    if (a <= (-5.4d+88)) then
        tmp = t_3
    else if (a <= (-1.05d+18)) then
        tmp = t_1
    else if (a <= (-3.6d-54)) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else if (a <= (-2.2d-196)) then
        tmp = t_1
    else if (a <= 3.4d-255) then
        tmp = ((z * (x + y)) - (y * b)) / t_2
    else if (a <= 9.2d-88) then
        tmp = z * ((x + y) / t_2)
    else if (a <= 2.4d+138) 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 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = a * ((t + y) / t_2);
	double tmp;
	if (a <= -5.4e+88) {
		tmp = t_3;
	} else if (a <= -1.05e+18) {
		tmp = t_1;
	} else if (a <= -3.6e-54) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (a <= -2.2e-196) {
		tmp = t_1;
	} else if (a <= 3.4e-255) {
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	} else if (a <= 9.2e-88) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 2.4e+138) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = a * ((t + y) / t_2)
	tmp = 0
	if a <= -5.4e+88:
		tmp = t_3
	elif a <= -1.05e+18:
		tmp = t_1
	elif a <= -3.6e-54:
		tmp = ((t * a) + (z * x)) / (x + t)
	elif a <= -2.2e-196:
		tmp = t_1
	elif a <= 3.4e-255:
		tmp = ((z * (x + y)) - (y * b)) / t_2
	elif a <= 9.2e-88:
		tmp = z * ((x + y) / t_2)
	elif a <= 2.4e+138:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(a * Float64(Float64(t + y) / t_2))
	tmp = 0.0
	if (a <= -5.4e+88)
		tmp = t_3;
	elseif (a <= -1.05e+18)
		tmp = t_1;
	elseif (a <= -3.6e-54)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	elseif (a <= -2.2e-196)
		tmp = t_1;
	elseif (a <= 3.4e-255)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / t_2);
	elseif (a <= 9.2e-88)
		tmp = Float64(z * Float64(Float64(x + y) / t_2));
	elseif (a <= 2.4e+138)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = a * ((t + y) / t_2);
	tmp = 0.0;
	if (a <= -5.4e+88)
		tmp = t_3;
	elseif (a <= -1.05e+18)
		tmp = t_1;
	elseif (a <= -3.6e-54)
		tmp = ((t * a) + (z * x)) / (x + t);
	elseif (a <= -2.2e-196)
		tmp = t_1;
	elseif (a <= 3.4e-255)
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	elseif (a <= 9.2e-88)
		tmp = z * ((x + y) / t_2);
	elseif (a <= 2.4e+138)
		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[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.4e+88], t$95$3, If[LessEqual[a, -1.05e+18], t$95$1, If[LessEqual[a, -3.6e-54], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.2e-196], t$95$1, If[LessEqual[a, 3.4e-255], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[a, 9.2e-88], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+138], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.40000000000000031e88 or 2.4000000000000001e138 < a

   1. Initial program 41.8%

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

   3. Taylor expanded in a around inf 36.7%

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

      1. associate-/l* 81.4%

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

      2. +-commutative 81.4%

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

      3. associate-+r+ 81.4%

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

      4. +-commutative 81.4%

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

      5. associate-+l+ 81.4%

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

   5. Simplified 81.4%

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

   if -5.40000000000000031e88 < a < -1.05e18 or -3.59999999999999976e-54 < a < -2.20000000000000015e-196 or 9.19999999999999945e-88 < a < 2.4000000000000001e138

   1. Initial program 60.6%

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

   3. Taylor expanded in y around inf 72.0%

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

   if -1.05e18 < a < -3.59999999999999976e-54

   1. Initial program 82.2%

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

   3. Taylor expanded in y around 0 66.4%

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

   if -2.20000000000000015e-196 < a < 3.39999999999999983e-255

   1. Initial program 81.4%

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

   3. Taylor expanded in a around 0 72.5%

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

      1. +-commutative 72.5%

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

      2. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   if 3.39999999999999983e-255 < a < 9.19999999999999945e-88

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf 35.2%

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

      1. associate-/l* 72.7%

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

      2. +-commutative 72.7%

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

      3. +-commutative 72.7%

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

      4. associate-+r+ 72.7%

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

      5. +-commutative 72.7%

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

      6. associate-+l+ 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-54}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-196}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-255}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+138}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := a \cdot \frac{t + y}{t\_2}\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-54}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-254}:\\ \;\;\;\;\frac{z \cdot x - y \cdot b}{t\_2}\\ \mathbf{elif}\;a \leq 1.96 \cdot 10^{-87}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_2}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ y (+ x t))) (t_3 (* a (/ (+ t y) t_2))))
   (if (<= a -5.8e+88)
     t_3
     (if (<= a -3e+17)
       t_1
       (if (<= a -3.8e-54)
         (/ (+ (* t a) (* z x)) (+ x t))
         (if (<= a -8e-196)
           t_1
           (if (<= a 1.06e-254)
             (/ (- (* z x) (* y b)) t_2)
             (if (<= a 1.96e-87)
               (* z (/ (+ x y) t_2))
               (if (<= a 6.6e+138) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = a * ((t + y) / t_2);
	double tmp;
	if (a <= -5.8e+88) {
		tmp = t_3;
	} else if (a <= -3e+17) {
		tmp = t_1;
	} else if (a <= -3.8e-54) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (a <= -8e-196) {
		tmp = t_1;
	} else if (a <= 1.06e-254) {
		tmp = ((z * x) - (y * b)) / t_2;
	} else if (a <= 1.96e-87) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 6.6e+138) {
		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 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = a * ((t + y) / t_2)
    if (a <= (-5.8d+88)) then
        tmp = t_3
    else if (a <= (-3d+17)) then
        tmp = t_1
    else if (a <= (-3.8d-54)) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else if (a <= (-8d-196)) then
        tmp = t_1
    else if (a <= 1.06d-254) then
        tmp = ((z * x) - (y * b)) / t_2
    else if (a <= 1.96d-87) then
        tmp = z * ((x + y) / t_2)
    else if (a <= 6.6d+138) 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 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = a * ((t + y) / t_2);
	double tmp;
	if (a <= -5.8e+88) {
		tmp = t_3;
	} else if (a <= -3e+17) {
		tmp = t_1;
	} else if (a <= -3.8e-54) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (a <= -8e-196) {
		tmp = t_1;
	} else if (a <= 1.06e-254) {
		tmp = ((z * x) - (y * b)) / t_2;
	} else if (a <= 1.96e-87) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 6.6e+138) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = a * ((t + y) / t_2)
	tmp = 0
	if a <= -5.8e+88:
		tmp = t_3
	elif a <= -3e+17:
		tmp = t_1
	elif a <= -3.8e-54:
		tmp = ((t * a) + (z * x)) / (x + t)
	elif a <= -8e-196:
		tmp = t_1
	elif a <= 1.06e-254:
		tmp = ((z * x) - (y * b)) / t_2
	elif a <= 1.96e-87:
		tmp = z * ((x + y) / t_2)
	elif a <= 6.6e+138:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(a * Float64(Float64(t + y) / t_2))
	tmp = 0.0
	if (a <= -5.8e+88)
		tmp = t_3;
	elseif (a <= -3e+17)
		tmp = t_1;
	elseif (a <= -3.8e-54)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	elseif (a <= -8e-196)
		tmp = t_1;
	elseif (a <= 1.06e-254)
		tmp = Float64(Float64(Float64(z * x) - Float64(y * b)) / t_2);
	elseif (a <= 1.96e-87)
		tmp = Float64(z * Float64(Float64(x + y) / t_2));
	elseif (a <= 6.6e+138)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = a * ((t + y) / t_2);
	tmp = 0.0;
	if (a <= -5.8e+88)
		tmp = t_3;
	elseif (a <= -3e+17)
		tmp = t_1;
	elseif (a <= -3.8e-54)
		tmp = ((t * a) + (z * x)) / (x + t);
	elseif (a <= -8e-196)
		tmp = t_1;
	elseif (a <= 1.06e-254)
		tmp = ((z * x) - (y * b)) / t_2;
	elseif (a <= 1.96e-87)
		tmp = z * ((x + y) / t_2);
	elseif (a <= 6.6e+138)
		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[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e+88], t$95$3, If[LessEqual[a, -3e+17], t$95$1, If[LessEqual[a, -3.8e-54], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8e-196], t$95$1, If[LessEqual[a, 1.06e-254], N[(N[(N[(z * x), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[a, 1.96e-87], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e+138], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.7999999999999999e88 or 6.59999999999999956e138 < a

   1. Initial program 41.8%

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

   3. Taylor expanded in a around inf 36.7%

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

      1. associate-/l* 81.4%

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

      2. +-commutative 81.4%

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

      3. associate-+r+ 81.4%

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

      4. +-commutative 81.4%

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

      5. associate-+l+ 81.4%

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

   5. Simplified 81.4%

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

   if -5.7999999999999999e88 < a < -3e17 or -3.8000000000000002e-54 < a < -8.0000000000000004e-196 or 1.96000000000000011e-87 < a < 6.59999999999999956e138

   1. Initial program 60.6%

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

   3. Taylor expanded in y around inf 72.0%

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

   if -3e17 < a < -3.8000000000000002e-54

   1. Initial program 82.2%

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

   3. Taylor expanded in y around 0 66.4%

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

   if -8.0000000000000004e-196 < a < 1.0600000000000001e-254

   1. Initial program 81.4%

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

   3. Taylor expanded in x around inf 76.8%

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

      1. associate-/l* 65.1%

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

      2. associate-/l* 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in x around inf 66.7%

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

   if 1.0600000000000001e-254 < a < 1.96000000000000011e-87

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf 35.2%

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

      1. associate-/l* 72.7%

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

      2. +-commutative 72.7%

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

      3. +-commutative 72.7%

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

      4. associate-+r+ 72.7%

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

      5. +-commutative 72.7%

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

      6. associate-+l+ 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+17}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-54}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-196}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-254}:\\ \;\;\;\;\frac{z \cdot x - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 1.96 \cdot 10^{-87}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+138}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := a \cdot \frac{t + y}{t\_2}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-57}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_2}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ y (+ x t))) (t_3 (* a (/ (+ t y) t_2))))
   (if (<= a -8.2e+88)
     t_3
     (if (<= a -7.5e+18)
       t_1
       (if (<= a -4e-57)
         (/ (+ (* t a) (* z x)) (+ x t))
         (if (<= a -3.15e-199)
           t_1
           (if (<= a 7.2e-88)
             (* z (/ (+ x y) t_2))
             (if (<= a 2.1e+136) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = a * ((t + y) / t_2);
	double tmp;
	if (a <= -8.2e+88) {
		tmp = t_3;
	} else if (a <= -7.5e+18) {
		tmp = t_1;
	} else if (a <= -4e-57) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (a <= -3.15e-199) {
		tmp = t_1;
	} else if (a <= 7.2e-88) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 2.1e+136) {
		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 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = a * ((t + y) / t_2)
    if (a <= (-8.2d+88)) then
        tmp = t_3
    else if (a <= (-7.5d+18)) then
        tmp = t_1
    else if (a <= (-4d-57)) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else if (a <= (-3.15d-199)) then
        tmp = t_1
    else if (a <= 7.2d-88) then
        tmp = z * ((x + y) / t_2)
    else if (a <= 2.1d+136) 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 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = a * ((t + y) / t_2);
	double tmp;
	if (a <= -8.2e+88) {
		tmp = t_3;
	} else if (a <= -7.5e+18) {
		tmp = t_1;
	} else if (a <= -4e-57) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (a <= -3.15e-199) {
		tmp = t_1;
	} else if (a <= 7.2e-88) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 2.1e+136) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = a * ((t + y) / t_2)
	tmp = 0
	if a <= -8.2e+88:
		tmp = t_3
	elif a <= -7.5e+18:
		tmp = t_1
	elif a <= -4e-57:
		tmp = ((t * a) + (z * x)) / (x + t)
	elif a <= -3.15e-199:
		tmp = t_1
	elif a <= 7.2e-88:
		tmp = z * ((x + y) / t_2)
	elif a <= 2.1e+136:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(a * Float64(Float64(t + y) / t_2))
	tmp = 0.0
	if (a <= -8.2e+88)
		tmp = t_3;
	elseif (a <= -7.5e+18)
		tmp = t_1;
	elseif (a <= -4e-57)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	elseif (a <= -3.15e-199)
		tmp = t_1;
	elseif (a <= 7.2e-88)
		tmp = Float64(z * Float64(Float64(x + y) / t_2));
	elseif (a <= 2.1e+136)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = a * ((t + y) / t_2);
	tmp = 0.0;
	if (a <= -8.2e+88)
		tmp = t_3;
	elseif (a <= -7.5e+18)
		tmp = t_1;
	elseif (a <= -4e-57)
		tmp = ((t * a) + (z * x)) / (x + t);
	elseif (a <= -3.15e-199)
		tmp = t_1;
	elseif (a <= 7.2e-88)
		tmp = z * ((x + y) / t_2);
	elseif (a <= 2.1e+136)
		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[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+88], t$95$3, If[LessEqual[a, -7.5e+18], t$95$1, If[LessEqual[a, -4e-57], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.15e-199], t$95$1, If[LessEqual[a, 7.2e-88], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+136], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.20000000000000055e88 or 2.0999999999999999e136 < a

   1. Initial program 41.8%

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

   3. Taylor expanded in a around inf 36.7%

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

      1. associate-/l* 81.4%

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

      2. +-commutative 81.4%

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

      3. associate-+r+ 81.4%

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

      4. +-commutative 81.4%

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

      5. associate-+l+ 81.4%

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

   5. Simplified 81.4%

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

   if -8.20000000000000055e88 < a < -7.5e18 or -3.99999999999999982e-57 < a < -3.1499999999999998e-199 or 7.1999999999999999e-88 < a < 2.0999999999999999e136

   1. Initial program 61.5%

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

   3. Taylor expanded in y around inf 71.5%

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

   if -7.5e18 < a < -3.99999999999999982e-57

   1. Initial program 82.2%

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

   3. Taylor expanded in y around 0 66.4%

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

   if -3.1499999999999998e-199 < a < 7.1999999999999999e-88

   1. Initial program 72.5%

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

   3. Taylor expanded in z around inf 37.6%

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

      1. associate-/l* 61.8%

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

      2. +-commutative 61.8%

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

      3. +-commutative 61.8%

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

      4. associate-+r+ 61.8%

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

      5. +-commutative 61.8%

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

      6. associate-+l+ 61.8%

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

   5. Simplified 61.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+18}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-57}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-199}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+136}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := a \cdot \frac{t + y}{t\_2}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+89}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_2}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ y (+ x t))) (t_3 (* a (/ (+ t y) t_2))))
   (if (<= a -1.1e+89)
     t_3
     (if (<= a -1.8e+17)
       t_1
       (if (<= a 2.2e-89)
         (* z (/ (+ x y) t_2))
         (if (<= a 2.3e+138) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = a * ((t + y) / t_2);
	double tmp;
	if (a <= -1.1e+89) {
		tmp = t_3;
	} else if (a <= -1.8e+17) {
		tmp = t_1;
	} else if (a <= 2.2e-89) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 2.3e+138) {
		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 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = a * ((t + y) / t_2)
    if (a <= (-1.1d+89)) then
        tmp = t_3
    else if (a <= (-1.8d+17)) then
        tmp = t_1
    else if (a <= 2.2d-89) then
        tmp = z * ((x + y) / t_2)
    else if (a <= 2.3d+138) 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 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = a * ((t + y) / t_2);
	double tmp;
	if (a <= -1.1e+89) {
		tmp = t_3;
	} else if (a <= -1.8e+17) {
		tmp = t_1;
	} else if (a <= 2.2e-89) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 2.3e+138) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = a * ((t + y) / t_2)
	tmp = 0
	if a <= -1.1e+89:
		tmp = t_3
	elif a <= -1.8e+17:
		tmp = t_1
	elif a <= 2.2e-89:
		tmp = z * ((x + y) / t_2)
	elif a <= 2.3e+138:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(a * Float64(Float64(t + y) / t_2))
	tmp = 0.0
	if (a <= -1.1e+89)
		tmp = t_3;
	elseif (a <= -1.8e+17)
		tmp = t_1;
	elseif (a <= 2.2e-89)
		tmp = Float64(z * Float64(Float64(x + y) / t_2));
	elseif (a <= 2.3e+138)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = a * ((t + y) / t_2);
	tmp = 0.0;
	if (a <= -1.1e+89)
		tmp = t_3;
	elseif (a <= -1.8e+17)
		tmp = t_1;
	elseif (a <= 2.2e-89)
		tmp = z * ((x + y) / t_2);
	elseif (a <= 2.3e+138)
		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[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e+89], t$95$3, If[LessEqual[a, -1.8e+17], t$95$1, If[LessEqual[a, 2.2e-89], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+138], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1e89 or 2.30000000000000008e138 < a

   1. Initial program 41.8%

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

   3. Taylor expanded in a around inf 36.7%

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

      1. associate-/l* 81.4%

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

      2. +-commutative 81.4%

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

      3. associate-+r+ 81.4%

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

      4. +-commutative 81.4%

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

      5. associate-+l+ 81.4%

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

   5. Simplified 81.4%

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

   if -1.1e89 < a < -1.8e17 or 2.20000000000000012e-89 < a < 2.30000000000000008e138

   1. Initial program 60.4%

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

   3. Taylor expanded in y around inf 73.6%

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

   if -1.8e17 < a < 2.20000000000000012e-89

   1. Initial program 71.4%

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

   3. Taylor expanded in z around inf 36.8%

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

      1. associate-/l* 59.8%

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

      2. +-commutative 59.8%

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

      3. +-commutative 59.8%

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

      4. associate-+r+ 59.8%

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

      5. +-commutative 59.8%

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

      6. associate-+l+ 59.8%

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

   5. Simplified 59.8%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+17}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+138}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-137}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-248}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t + y}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+32}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ (+ t y) (+ y (+ x t))))))
   (if (<= a -1.2e+89)
     t_1
     (if (<= a -6.2e-137)
       (- (+ z a) b)
       (if (<= a 7.8e-248)
         (* b (- (/ a b) (/ y (+ t y))))
         (if (<= a 2.8e+32) (- z (/ (* y b) (+ x y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * ((t + y) / (y + (x + t)));
	double tmp;
	if (a <= -1.2e+89) {
		tmp = t_1;
	} else if (a <= -6.2e-137) {
		tmp = (z + a) - b;
	} else if (a <= 7.8e-248) {
		tmp = b * ((a / b) - (y / (t + y)));
	} else if (a <= 2.8e+32) {
		tmp = z - ((y * b) / (x + y));
	} 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 = a * ((t + y) / (y + (x + t)))
    if (a <= (-1.2d+89)) then
        tmp = t_1
    else if (a <= (-6.2d-137)) then
        tmp = (z + a) - b
    else if (a <= 7.8d-248) then
        tmp = b * ((a / b) - (y / (t + y)))
    else if (a <= 2.8d+32) then
        tmp = z - ((y * b) / (x + y))
    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 = a * ((t + y) / (y + (x + t)));
	double tmp;
	if (a <= -1.2e+89) {
		tmp = t_1;
	} else if (a <= -6.2e-137) {
		tmp = (z + a) - b;
	} else if (a <= 7.8e-248) {
		tmp = b * ((a / b) - (y / (t + y)));
	} else if (a <= 2.8e+32) {
		tmp = z - ((y * b) / (x + y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * ((t + y) / (y + (x + t)))
	tmp = 0
	if a <= -1.2e+89:
		tmp = t_1
	elif a <= -6.2e-137:
		tmp = (z + a) - b
	elif a <= 7.8e-248:
		tmp = b * ((a / b) - (y / (t + y)))
	elif a <= 2.8e+32:
		tmp = z - ((y * b) / (x + y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(Float64(t + y) / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (a <= -1.2e+89)
		tmp = t_1;
	elseif (a <= -6.2e-137)
		tmp = Float64(Float64(z + a) - b);
	elseif (a <= 7.8e-248)
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / Float64(t + y))));
	elseif (a <= 2.8e+32)
		tmp = Float64(z - Float64(Float64(y * b) / Float64(x + y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * ((t + y) / (y + (x + t)));
	tmp = 0.0;
	if (a <= -1.2e+89)
		tmp = t_1;
	elseif (a <= -6.2e-137)
		tmp = (z + a) - b;
	elseif (a <= 7.8e-248)
		tmp = b * ((a / b) - (y / (t + y)));
	elseif (a <= 2.8e+32)
		tmp = z - ((y * b) / (x + y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(N[(t + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e+89], t$95$1, If[LessEqual[a, -6.2e-137], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[a, 7.8e-248], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+32], N[(z - N[(N[(y * b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.20000000000000002e89 or 2.8e32 < a

   1. Initial program 44.2%

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

   3. Taylor expanded in a around inf 36.5%

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

      1. associate-/l* 77.3%

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

      2. +-commutative 77.3%

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

      3. associate-+r+ 77.3%

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

      4. +-commutative 77.3%

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

      5. associate-+l+ 77.3%

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

   5. Simplified 77.3%

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

   if -1.20000000000000002e89 < a < -6.19999999999999955e-137

   1. Initial program 67.1%

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

   3. Taylor expanded in y around inf 66.9%

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

   if -6.19999999999999955e-137 < a < 7.800000000000001e-248

   1. Initial program 72.9%

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

   3. Taylor expanded in z around 0 43.4%

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

      1. *-commutative 43.4%

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

   5. Simplified 43.4%

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

   6. Taylor expanded in x around 0 39.8%

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

   7. Taylor expanded in b around inf 46.2%

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

      1. +-commutative 46.2%

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

      2. mul-1-neg 46.2%

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

      3. unsub-neg 46.2%

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

      4. +-commutative 46.2%

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

   9. Simplified 46.2%

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

   if 7.800000000000001e-248 < a < 2.8e32

   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 a around inf 68.8%

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

      1. associate--l+ 68.8%

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

      2. +-commutative 68.8%

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

      3. +-commutative 68.8%

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

      4. associate-/l* 77.7%

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

      5. +-commutative 77.7%

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

      6. +-commutative 77.7%

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

      7. *-commutative 77.7%

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

      8. +-commutative 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in t around 0 61.4%

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

      1. associate--l+ 61.4%

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

      2. associate-/l* 63.7%

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

   8. Simplified 63.7%

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

   9. Taylor expanded in a around 0 71.3%

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

       1. +-commutative 71.3%

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

   11. Simplified 71.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-137}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-248}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t + y}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+32}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.3 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.5e-178)
     t_1
     (if (<= y 7.3e-180)
       (* a (/ t (+ x t)))
       (if (<= y 8e+51) (* a (+ (/ z a) (/ y (+ x y)))) 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 <= -2.5e-178) {
		tmp = t_1;
	} else if (y <= 7.3e-180) {
		tmp = a * (t / (x + t));
	} else if (y <= 8e+51) {
		tmp = a * ((z / a) + (y / (x + y)));
	} 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 <= (-2.5d-178)) then
        tmp = t_1
    else if (y <= 7.3d-180) then
        tmp = a * (t / (x + t))
    else if (y <= 8d+51) then
        tmp = a * ((z / a) + (y / (x + y)))
    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 <= -2.5e-178) {
		tmp = t_1;
	} else if (y <= 7.3e-180) {
		tmp = a * (t / (x + t));
	} else if (y <= 8e+51) {
		tmp = a * ((z / a) + (y / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.5e-178:
		tmp = t_1
	elif y <= 7.3e-180:
		tmp = a * (t / (x + t))
	elif y <= 8e+51:
		tmp = a * ((z / a) + (y / (x + y)))
	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 <= -2.5e-178)
		tmp = t_1;
	elseif (y <= 7.3e-180)
		tmp = Float64(a * Float64(t / Float64(x + t)));
	elseif (y <= 8e+51)
		tmp = Float64(a * Float64(Float64(z / a) + Float64(y / Float64(x + y))));
	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 <= -2.5e-178)
		tmp = t_1;
	elseif (y <= 7.3e-180)
		tmp = a * (t / (x + t));
	elseif (y <= 8e+51)
		tmp = a * ((z / a) + (y / (x + y)));
	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, -2.5e-178], t$95$1, If[LessEqual[y, 7.3e-180], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+51], N[(a * N[(N[(z / a), $MachinePrecision] + N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999988e-178 or 8e51 < y

   1. Initial program 49.2%

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

   3. Taylor expanded in y around inf 69.9%

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

   if -2.49999999999999988e-178 < y < 7.2999999999999996e-180

   1. Initial program 67.1%

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

   3. Taylor expanded in z around 0 42.4%

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

      1. *-commutative 42.4%

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

   5. Simplified 42.4%

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

   6. Taylor expanded in y around 0 38.1%

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

      1. associate-/l* 55.0%

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

      2. +-commutative 55.0%

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

   8. Simplified 55.0%

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

   if 7.2999999999999996e-180 < y < 8e51

   1. Initial program 79.9%

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

   3. Taylor expanded in a around inf 89.3%

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

      1. associate--l+ 89.3%

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

      2. +-commutative 89.3%

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

      3. +-commutative 89.3%

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

      4. associate-/l* 93.6%

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

      5. +-commutative 93.6%

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

      6. +-commutative 93.6%

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

      7. *-commutative 93.6%

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

      8. +-commutative 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in t around 0 58.6%

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

      1. associate--l+ 58.6%

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

      2. associate-/l* 58.6%

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

   8. Simplified 58.6%

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

   9. Taylor expanded in b around 0 58.0%

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

       1. +-commutative 58.0%

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

   11. Simplified 58.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-178}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 7.3 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-180} \lor \neg \left(y \leq 3.45 \cdot 10^{+55}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.75e-180) (not (<= y 3.45e+55)))
   (- (+ z a) b)
   (* a (/ (+ t y) (+ y (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.75e-180) || !(y <= 3.45e+55)) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((t + y) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.75d-180)) .or. (.not. (y <= 3.45d+55))) then
        tmp = (z + a) - b
    else
        tmp = a * ((t + y) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.75e-180) || !(y <= 3.45e+55)) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((t + y) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.75e-180) or not (y <= 3.45e+55):
		tmp = (z + a) - b
	else:
		tmp = a * ((t + y) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.75e-180) || !(y <= 3.45e+55))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(Float64(t + y) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.75e-180) || ~((y <= 3.45e+55)))
		tmp = (z + a) - b;
	else
		tmp = a * ((t + y) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.75e-180], N[Not[LessEqual[y, 3.45e+55]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(N[(t + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75e-180 or 3.4500000000000002e55 < y

   1. Initial program 49.1%

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

   3. Taylor expanded in y around inf 70.1%

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

   if -1.75e-180 < y < 3.4500000000000002e55

   1. Initial program 72.1%

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

   3. Taylor expanded in a around inf 39.8%

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

      1. associate-/l* 56.0%

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

      2. +-commutative 56.0%

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

      3. associate-+r+ 56.0%

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

      4. +-commutative 56.0%

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

      5. associate-+l+ 56.0%

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

   5. Simplified 56.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-180} \lor \neg \left(y \leq 3.45 \cdot 10^{+55}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-178} \lor \neg \left(y \leq 1.2 \cdot 10^{+20}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.8e-178) (not (<= y 1.2e+20)))
   (- (+ 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 ((y <= -4.8e-178) || !(y <= 1.2e+20)) {
		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 ((y <= (-4.8d-178)) .or. (.not. (y <= 1.2d+20))) 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 ((y <= -4.8e-178) || !(y <= 1.2e+20)) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.8e-178) or not (y <= 1.2e+20):
		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 ((y <= -4.8e-178) || !(y <= 1.2e+20))
		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 ((y <= -4.8e-178) || ~((y <= 1.2e+20)))
		tmp = (z + a) - b;
	else
		tmp = a * (t / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.8e-178], N[Not[LessEqual[y, 1.2e+20]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8000000000000001e-178 or 1.2e20 < y

   1. Initial program 50.6%

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

   3. Taylor expanded in y around inf 69.0%

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

   if -4.8000000000000001e-178 < y < 1.2e20

   1. Initial program 72.1%

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

   3. Taylor expanded in z around 0 46.8%

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

      1. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in y around 0 35.7%

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

      1. associate-/l* 50.8%

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

      2. +-commutative 50.8%

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

   8. Simplified 50.8%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-178} \lor \neg \left(y \leq 1.2 \cdot 10^{+20}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+61}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.5) z (if (<= z 5.2e+61) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.5) {
		tmp = z;
	} else if (z <= 5.2e+61) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-7.5d0)) then
        tmp = z
    else if (z <= 5.2d+61) then
        tmp = a - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.5) {
		tmp = z;
	} else if (z <= 5.2e+61) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.5:
		tmp = z
	elif z <= 5.2e+61:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.5)
		tmp = z;
	elseif (z <= 5.2e+61)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7.5)
		tmp = z;
	elseif (z <= 5.2e+61)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.5], z, If[LessEqual[z, 5.2e+61], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5 or 5.19999999999999945e61 < z

   1. Initial program 46.9%

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

   3. Taylor expanded in x around inf 56.3%

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

   if -7.5 < z < 5.19999999999999945e61

   1. Initial program 70.0%

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

   3. Taylor expanded in z around 0 54.1%

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

      1. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in y around inf 50.5%

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

Alternative 14: 44.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-32}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+61}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.55e-32) z (if (<= z 4.6e+61) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.55e-32) {
		tmp = z;
	} else if (z <= 4.6e+61) {
		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 <= (-1.55d-32)) then
        tmp = z
    else if (z <= 4.6d+61) 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 <= -1.55e-32) {
		tmp = z;
	} else if (z <= 4.6e+61) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.55e-32:
		tmp = z
	elif z <= 4.6e+61:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.55e-32)
		tmp = z;
	elseif (z <= 4.6e+61)
		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 <= -1.55e-32)
		tmp = z;
	elseif (z <= 4.6e+61)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.55e-32], z, If[LessEqual[z, 4.6e+61], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55000000000000005e-32 or 4.5999999999999999e61 < z

   1. Initial program 47.0%

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

   3. Taylor expanded in x around inf 55.5%

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

   if -1.55000000000000005e-32 < z < 4.5999999999999999e61

   1. Initial program 70.2%

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

   3. Taylor expanded in t around inf 46.3%

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

Alternative 15: 57.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.6 \cdot 10^{+167}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= t 6.6e+167) (- (+ z a) b) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 6.6e+167) {
		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 <= 6.6d+167) 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 <= 6.6e+167) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 6.6e+167:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 6.6e+167)
		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 <= 6.6e+167)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 6.6e+167], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if t < 6.60000000000000036e167

   1. Initial program 62.3%

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

   3. Taylor expanded in y around inf 57.8%

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

   if 6.60000000000000036e167 < t

   1. Initial program 40.9%

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

   3. Taylor expanded in t around inf 67.7%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.6 \cdot 10^{+167}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.3% 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 59.4%

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

3. Taylor expanded in t around inf 34.6%

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

Developer target: 82.2% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024086 
(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)))