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

Percentage Accurate: 60.8% → 93.0%

Time: 16.0s

Alternatives: 12

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{1}{\frac{y + \left(x + t\right)}{y + x}}\\ t_2 := t + \left(y + x\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+185} \lor \neg \left(y \leq 10^{+149}\right):\\ \;\;\;\;\left(a + t_1\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 + a \cdot \left(\frac{t}{t_2} + \frac{y}{t_2}\right)\right) - \frac{y \cdot b}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ 1.0 (/ (+ y (+ x t)) (+ y x))))) (t_2 (+ t (+ y x))))
   (if (or (<= y -1.02e+185) (not (<= y 1e+149)))
     (- (+ a t_1) b)
     (- (+ t_1 (* a (+ (/ t t_2) (/ y t_2)))) (/ (* y b) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 / ((y + (x + t)) / (y + x)));
	double t_2 = t + (y + x);
	double tmp;
	if ((y <= -1.02e+185) || !(y <= 1e+149)) {
		tmp = (a + t_1) - b;
	} else {
		tmp = (t_1 + (a * ((t / t_2) + (y / t_2)))) - ((y * b) / 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 = z * (1.0d0 / ((y + (x + t)) / (y + x)))
    t_2 = t + (y + x)
    if ((y <= (-1.02d+185)) .or. (.not. (y <= 1d+149))) then
        tmp = (a + t_1) - b
    else
        tmp = (t_1 + (a * ((t / t_2) + (y / t_2)))) - ((y * b) / 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 = z * (1.0 / ((y + (x + t)) / (y + x)));
	double t_2 = t + (y + x);
	double tmp;
	if ((y <= -1.02e+185) || !(y <= 1e+149)) {
		tmp = (a + t_1) - b;
	} else {
		tmp = (t_1 + (a * ((t / t_2) + (y / t_2)))) - ((y * b) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 / ((y + (x + t)) / (y + x)))
	t_2 = t + (y + x)
	tmp = 0
	if (y <= -1.02e+185) or not (y <= 1e+149):
		tmp = (a + t_1) - b
	else:
		tmp = (t_1 + (a * ((t / t_2) + (y / t_2)))) - ((y * b) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 / Float64(Float64(y + Float64(x + t)) / Float64(y + x))))
	t_2 = Float64(t + Float64(y + x))
	tmp = 0.0
	if ((y <= -1.02e+185) || !(y <= 1e+149))
		tmp = Float64(Float64(a + t_1) - b);
	else
		tmp = Float64(Float64(t_1 + Float64(a * Float64(Float64(t / t_2) + Float64(y / t_2)))) - Float64(Float64(y * b) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 / ((y + (x + t)) / (y + x)));
	t_2 = t + (y + x);
	tmp = 0.0;
	if ((y <= -1.02e+185) || ~((y <= 1e+149)))
		tmp = (a + t_1) - b;
	else
		tmp = (t_1 + (a * ((t / t_2) + (y / t_2)))) - ((y * b) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -1.02e+185], N[Not[LessEqual[y, 1e+149]], $MachinePrecision]], N[(N[(a + t$95$1), $MachinePrecision] - b), $MachinePrecision], N[(N[(t$95$1 + N[(a * N[(N[(t / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0200000000000001e185 or 1.00000000000000005e149 < y

   1. Initial program 23.9%

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

   3. Taylor expanded in a around 0 40.6%

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

      1. associate-/l* 60.7%

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

      2. associate-+r+ 60.7%

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

      3. +-commutative 60.7%

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

      4. div-inv 60.7%

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

      5. +-commutative 60.7%

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

      6. +-commutative 60.7%

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

      7. +-commutative 60.7%

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

   5. Applied egg-rr 60.7%

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

   6. Taylor expanded in t around inf 59.2%

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

   7. Taylor expanded in y around inf 86.3%

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

   if -1.0200000000000001e185 < y < 1.00000000000000005e149

   1. Initial program 68.5%

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

   3. Taylor expanded in a around 0 83.6%

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

      1. associate-/l* 96.4%

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

      2. associate-+r+ 96.4%

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

      3. +-commutative 96.4%

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

      4. div-inv 96.3%

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

      5. +-commutative 96.3%

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

      6. +-commutative 96.3%

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

      7. +-commutative 96.3%

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

   5. Applied egg-rr 96.3%

      \[\leadsto \left(a \cdot \left(\frac{t}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \color{blue}{z \cdot \frac{1}{\frac{y + \left(x + t\right)}{x + y}}}\right) - \frac{b \cdot y}{t + \left(x + y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+185} \lor \neg \left(y \leq 10^{+149}\right):\\ \;\;\;\;\left(a + z \cdot \frac{1}{\frac{y + \left(x + t\right)}{y + x}}\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \frac{1}{\frac{y + \left(x + t\right)}{y + x}} + a \cdot \left(\frac{t}{t + \left(y + x\right)} + \frac{y}{t + \left(y + x\right)}\right)\right) - \frac{y \cdot b}{t + \left(y + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(z \cdot \left(y + x\right) + t_1\right) - y \cdot b}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 2 \cdot 10^{+264}\right):\\ \;\;\;\;\left(a + z \cdot \frac{1}{\frac{t_2}{y + x}}\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_2} + \frac{y}{t_2}\right) + \frac{t_1 - y \cdot b}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* z (+ y x)) t_1) (* y b)) t_2)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 2e+264)))
     (- (+ a (* z (/ 1.0 (/ t_2 (+ y x))))) b)
     (+ (* z (+ (/ x t_2) (/ y t_2))) (/ (- t_1 (* y b)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 2e+264)) {
		tmp = (a + (z * (1.0 / (t_2 / (y + x))))) - b;
	} else {
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (y * b)) / t_2);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 2e+264)) {
		tmp = (a + (z * (1.0 / (t_2 / (y + x))))) - b;
	} else {
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (y * b)) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = y + (x + t)
	t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 2e+264):
		tmp = (a + (z * (1.0 / (t_2 / (y + x))))) - b
	else:
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (y * b)) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + t_1) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 2e+264))
		tmp = Float64(Float64(a + Float64(z * Float64(1.0 / Float64(t_2 / Float64(y + x))))) - b);
	else
		tmp = Float64(Float64(z * Float64(Float64(x / t_2) + Float64(y / t_2))) + Float64(Float64(t_1 - Float64(y * b)) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = y + (x + t);
	t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2;
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 2e+264)))
		tmp = (a + (z * (1.0 / (t_2 / (y + x))))) - b;
	else
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (y * b)) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 2e+264]], $MachinePrecision]], N[(N[(a + N[(z * N[(1.0 / N[(t$95$2 / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], N[(N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.00000000000000009e264 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in a around 0 40.5%

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

      1. associate-/l* 72.5%

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

      2. associate-+r+ 72.5%

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

      3. +-commutative 72.5%

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

      4. div-inv 72.4%

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

      5. +-commutative 72.4%

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

      6. +-commutative 72.4%

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

      7. +-commutative 72.4%

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

   5. Applied egg-rr 72.4%

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

   6. Taylor expanded in t around inf 68.2%

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

   7. Taylor expanded in y around inf 80.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000009e264

   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. Taylor expanded in z around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-+r+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. div-sub 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-+r+ 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+264}\right):\\ \;\;\;\;\left(a + z \cdot \frac{1}{\frac{y + \left(x + t\right)}{y + x}}\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{y + \left(x + t\right)} + \frac{y}{y + \left(x + t\right)}\right) + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+264}\right):\\ \;\;\;\;\left(a + z \cdot \frac{1}{\frac{t_1}{y + x}}\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}} + \frac{y \cdot \left(z - b\right) + z \cdot x}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+264)))
     (- (+ a (* z (/ 1.0 (/ t_1 (+ y x))))) b)
     (+ (/ a (/ t_1 (+ y t))) (/ (+ (* y (- z b)) (* z x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+264)) {
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b;
	} else {
		tmp = (a / (t_1 / (y + t))) + (((y * (z - b)) + (z * x)) / t_1);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+264)) {
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b;
	} else {
		tmp = (a / (t_1 / (y + t))) + (((y * (z - b)) + (z * x)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+264):
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b
	else:
		tmp = (a / (t_1 / (y + t))) + (((y * (z - b)) + (z * x)) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+264))
		tmp = Float64(Float64(a + Float64(z * Float64(1.0 / Float64(t_1 / Float64(y + x))))) - b);
	else
		tmp = Float64(Float64(a / Float64(t_1 / Float64(y + t))) + Float64(Float64(Float64(y * Float64(z - b)) + Float64(z * x)) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+264)))
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b;
	else
		tmp = (a / (t_1 / (y + t))) + (((y * (z - b)) + (z * x)) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+264]], $MachinePrecision]], N[(N[(a + N[(z * N[(1.0 / N[(t$95$1 / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], N[(N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.00000000000000009e264 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in a around 0 40.5%

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

      1. associate-/l* 72.5%

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

      2. associate-+r+ 72.5%

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

      3. +-commutative 72.5%

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

      4. div-inv 72.4%

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

      5. +-commutative 72.4%

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

      6. +-commutative 72.4%

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

      7. +-commutative 72.4%

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

   5. Applied egg-rr 72.4%

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

   6. Taylor expanded in t around inf 68.2%

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

   7. Taylor expanded in y around inf 80.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000009e264

   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. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-/l* 99.8%

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

      3. associate-+r+ 99.8%

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

      4. div-sub 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+264}\right):\\ \;\;\;\;\left(a + z \cdot \frac{1}{\frac{y + \left(x + t\right)}{y + x}}\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \frac{y \cdot \left(z - b\right) + z \cdot x}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+264}\right):\\ \;\;\;\;\left(a + z \cdot \frac{1}{\frac{t_1}{y + x}}\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+264)))
     (- (+ a (* z (/ 1.0 (/ t_1 (+ y x))))) b)
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+264)) {
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+264)) {
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+264):
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+264))
		tmp = Float64(Float64(a + Float64(z * Float64(1.0 / Float64(t_1 / Float64(y + x))))) - b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+264)))
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+264]], $MachinePrecision]], N[(N[(a + N[(z * N[(1.0 / N[(t$95$1 / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], t$95$2]]]

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 2.00000000000000009e264 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in a around 0 40.5%

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

      1. associate-/l* 72.5%

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

      2. associate-+r+ 72.5%

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

      3. +-commutative 72.5%

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

      4. div-inv 72.4%

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

      5. +-commutative 72.4%

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

      6. +-commutative 72.4%

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

      7. +-commutative 72.4%

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

   5. Applied egg-rr 72.4%

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

   6. Taylor expanded in t around inf 68.2%

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

   7. Taylor expanded in y around inf 80.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000009e264

   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 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+264}\right):\\ \;\;\;\;\left(a + z \cdot \frac{1}{\frac{y + \left(x + t\right)}{y + x}}\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+163}:\\ \;\;\;\;y \cdot \frac{-b}{t_1}\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+244}:\\ \;\;\;\;\left(a + z \cdot \frac{1}{\frac{t_1}{y + x}}\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{\frac{t_1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= b -2.15e+163)
     (* y (/ (- b) t_1))
     (if (<= b 5.3e+244)
       (- (+ a (* z (/ 1.0 (/ t_1 (+ y x))))) b)
       (/ (- b) (/ t_1 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (b <= -2.15e+163) {
		tmp = y * (-b / t_1);
	} else if (b <= 5.3e+244) {
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b;
	} else {
		tmp = -b / (t_1 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (b <= (-2.15d+163)) then
        tmp = y * (-b / t_1)
    else if (b <= 5.3d+244) then
        tmp = (a + (z * (1.0d0 / (t_1 / (y + x))))) - b
    else
        tmp = -b / (t_1 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (b <= -2.15e+163) {
		tmp = y * (-b / t_1);
	} else if (b <= 5.3e+244) {
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b;
	} else {
		tmp = -b / (t_1 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if b <= -2.15e+163:
		tmp = y * (-b / t_1)
	elif b <= 5.3e+244:
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b
	else:
		tmp = -b / (t_1 / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (b <= -2.15e+163)
		tmp = Float64(y * Float64(Float64(-b) / t_1));
	elseif (b <= 5.3e+244)
		tmp = Float64(Float64(a + Float64(z * Float64(1.0 / Float64(t_1 / Float64(y + x))))) - b);
	else
		tmp = Float64(Float64(-b) / Float64(t_1 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (b <= -2.15e+163)
		tmp = y * (-b / t_1);
	elseif (b <= 5.3e+244)
		tmp = (a + (z * (1.0 / (t_1 / (y + x))))) - b;
	else
		tmp = -b / (t_1 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.15e+163], N[(y * N[((-b) / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.3e+244], N[(N[(a + N[(z * N[(1.0 / N[(t$95$1 / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], N[((-b) / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1500000000000001e163

   1. Initial program 51.4%

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

   3. Taylor expanded in x around inf 45.4%

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

      1. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in z around 0 29.5%

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

      1. mul-1-neg 29.5%

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

      2. associate-/l* 46.9%

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

      3. +-commutative 46.9%

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

      4. +-commutative 46.9%

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

      5. associate-+r+ 46.9%

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

      6. associate-/r/ 50.2%

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

      7. distribute-rgt-neg-in 50.2%

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

      8. +-commutative 50.2%

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

   8. Simplified 50.2%

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

   if -2.1500000000000001e163 < b < 5.2999999999999997e244

   1. Initial program 59.2%

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

   3. Taylor expanded in a around 0 75.9%

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

      1. associate-/l* 92.9%

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

      2. associate-+r+ 92.9%

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

      3. +-commutative 92.9%

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

      4. div-inv 92.9%

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

      5. +-commutative 92.9%

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

      6. +-commutative 92.9%

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

      7. +-commutative 92.9%

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

   5. Applied egg-rr 92.9%

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

   6. Taylor expanded in t around inf 83.0%

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

   7. Taylor expanded in y around inf 74.6%

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

   if 5.2999999999999997e244 < b

   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 b around inf 38.9%

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

      1. mul-1-neg 38.9%

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

      2. associate-/l* 71.3%

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

      3. distribute-neg-frac 71.3%

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

      4. associate-+r+ 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+163}:\\ \;\;\;\;y \cdot \frac{-b}{y + \left(x + t\right)}\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+244}:\\ \;\;\;\;\left(a + z \cdot \frac{1}{\frac{y + \left(x + t\right)}{y + x}}\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{\frac{y + \left(x + t\right)}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+53}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{z}{t_1}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-295} \lor \neg \left(z \leq 2.6 \cdot 10^{-153}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= z -2.4e+53)
     (* (+ y x) (/ z t_1))
     (if (or (<= z 1.45e-295) (not (<= z 2.6e-153)))
       (- (+ a z) b)
       (/ a (/ t_1 (+ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (z <= -2.4e+53) {
		tmp = (y + x) * (z / t_1);
	} else if ((z <= 1.45e-295) || !(z <= 2.6e-153)) {
		tmp = (a + z) - b;
	} else {
		tmp = a / (t_1 / (y + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (z <= (-2.4d+53)) then
        tmp = (y + x) * (z / t_1)
    else if ((z <= 1.45d-295) .or. (.not. (z <= 2.6d-153))) then
        tmp = (a + z) - b
    else
        tmp = a / (t_1 / (y + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (z <= -2.4e+53) {
		tmp = (y + x) * (z / t_1);
	} else if ((z <= 1.45e-295) || !(z <= 2.6e-153)) {
		tmp = (a + z) - b;
	} else {
		tmp = a / (t_1 / (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if z <= -2.4e+53:
		tmp = (y + x) * (z / t_1)
	elif (z <= 1.45e-295) or not (z <= 2.6e-153):
		tmp = (a + z) - b
	else:
		tmp = a / (t_1 / (y + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (z <= -2.4e+53)
		tmp = Float64(Float64(y + x) * Float64(z / t_1));
	elseif ((z <= 1.45e-295) || !(z <= 2.6e-153))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (z <= -2.4e+53)
		tmp = (y + x) * (z / t_1);
	elseif ((z <= 1.45e-295) || ~((z <= 2.6e-153)))
		tmp = (a + z) - b;
	else
		tmp = a / (t_1 / (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+53], N[(N[(y + x), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.45e-295], N[Not[LessEqual[z, 2.6e-153]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4e53

   1. Initial program 48.7%

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

   3. Taylor expanded in z around inf 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* 75.6%

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

      2. associate-+r+ 75.6%

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

      3. +-commutative 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in z around 0 36.8%

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

      1. +-commutative 36.8%

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

      2. +-commutative 36.8%

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

      3. associate-+r+ 36.8%

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

      4. associate-*l/ 75.6%

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

      5. *-commutative 75.6%

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

      6. +-commutative 75.6%

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

      7. +-commutative 75.6%

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

   8. Simplified 75.6%

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

   if -2.4e53 < z < 1.45000000000000008e-295 or 2.6000000000000001e-153 < z

   1. Initial program 57.4%

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

   3. Taylor expanded in y around inf 65.0%

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

   if 1.45000000000000008e-295 < z < 2.6000000000000001e-153

   1. Initial program 68.5%

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

   3. Taylor expanded in a around inf 45.7%

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

      1. associate-/l* 70.6%

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

      2. associate-+r+ 70.6%

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

   5. Simplified 70.6%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+53}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-295} \lor \neg \left(z \leq 2.6 \cdot 10^{-153}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+50}:\\ \;\;\;\;\frac{z}{\frac{t_1}{y + x}}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-297} \lor \neg \left(z \leq 4.5 \cdot 10^{-154}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= z -4e+50)
     (/ z (/ t_1 (+ y x)))
     (if (or (<= z 7.6e-297) (not (<= z 4.5e-154)))
       (- (+ a z) b)
       (/ a (/ t_1 (+ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (z <= -4e+50) {
		tmp = z / (t_1 / (y + x));
	} else if ((z <= 7.6e-297) || !(z <= 4.5e-154)) {
		tmp = (a + z) - b;
	} else {
		tmp = a / (t_1 / (y + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (z <= (-4d+50)) then
        tmp = z / (t_1 / (y + x))
    else if ((z <= 7.6d-297) .or. (.not. (z <= 4.5d-154))) then
        tmp = (a + z) - b
    else
        tmp = a / (t_1 / (y + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (z <= -4e+50) {
		tmp = z / (t_1 / (y + x));
	} else if ((z <= 7.6e-297) || !(z <= 4.5e-154)) {
		tmp = (a + z) - b;
	} else {
		tmp = a / (t_1 / (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if z <= -4e+50:
		tmp = z / (t_1 / (y + x))
	elif (z <= 7.6e-297) or not (z <= 4.5e-154):
		tmp = (a + z) - b
	else:
		tmp = a / (t_1 / (y + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (z <= -4e+50)
		tmp = Float64(z / Float64(t_1 / Float64(y + x)));
	elseif ((z <= 7.6e-297) || !(z <= 4.5e-154))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (z <= -4e+50)
		tmp = z / (t_1 / (y + x));
	elseif ((z <= 7.6e-297) || ~((z <= 4.5e-154)))
		tmp = (a + z) - b;
	else
		tmp = a / (t_1 / (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+50], N[(z / N[(t$95$1 / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 7.6e-297], N[Not[LessEqual[z, 4.5e-154]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000003e50

   1. Initial program 48.7%

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

   3. Taylor expanded in z around inf 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* 75.6%

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

      2. associate-+r+ 75.6%

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

      3. +-commutative 75.6%

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

   5. Simplified 75.6%

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

   if -4.0000000000000003e50 < z < 7.6000000000000001e-297 or 4.4999999999999997e-154 < z

   1. Initial program 57.4%

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

   3. Taylor expanded in y around inf 65.0%

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

   if 7.6000000000000001e-297 < z < 4.4999999999999997e-154

   1. Initial program 68.5%

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

   3. Taylor expanded in a around inf 45.7%

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

      1. associate-/l* 70.6%

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

      2. associate-+r+ 70.6%

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

   5. Simplified 70.6%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+50}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{y + x}}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-297} \lor \neg \left(z \leq 4.5 \cdot 10^{-154}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+172} \lor \neg \left(t \leq 5 \cdot 10^{+97}\right):\\ \;\;\;\;a + \left(\frac{y}{\frac{t}{z}} - y \cdot \frac{b}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.06e+172) (not (<= t 5e+97)))
   (+ a (- (/ y (/ t z)) (* y (/ b t))))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.06e+172) || !(t <= 5e+97)) {
		tmp = a + ((y / (t / z)) - (y * (b / t)));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.06d+172)) .or. (.not. (t <= 5d+97))) then
        tmp = a + ((y / (t / z)) - (y * (b / t)))
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.06e+172) || !(t <= 5e+97)) {
		tmp = a + ((y / (t / z)) - (y * (b / t)));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.06e+172) or not (t <= 5e+97):
		tmp = a + ((y / (t / z)) - (y * (b / t)))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.06e+172) || !(t <= 5e+97))
		tmp = Float64(a + Float64(Float64(y / Float64(t / z)) - Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.06e+172) || ~((t <= 5e+97)))
		tmp = a + ((y / (t / z)) - (y * (b / t)));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.06e+172], N[Not[LessEqual[t, 5e+97]], $MachinePrecision]], N[(a + N[(N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05999999999999996e172 or 4.99999999999999999e97 < t

   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. Step-by-step derivation

      1. associate--l+ 50.6%

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

      2. fma-def 50.7%

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

      3. fma-neg 50.7%

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

      4. +-commutative 50.7%

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

      5. distribute-rgt-neg-out 50.7%

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

      6. associate-+l+ 50.7%

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

      7. +-commutative 50.7%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in t around inf 55.5%

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

      1. associate-+r+ 55.5%

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

      2. mul-1-neg 55.5%

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

      3. unsub-neg 55.5%

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

      4. associate-/l* 57.4%

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

      5. associate-/l* 57.5%

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

      6. associate-/l* 66.3%

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

      7. +-commutative 66.3%

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

      8. associate-/l* 76.0%

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

      9. +-commutative 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in x around 0 59.1%

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

      1. associate--l+ 59.1%

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

      2. associate-/l* 62.2%

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

      3. associate-*l/ 67.2%

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

      4. *-commutative 67.2%

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

   10. Simplified 67.2%

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

   if -1.05999999999999996e172 < t < 4.99999999999999999e97

   1. Initial program 60.9%

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

   3. Taylor expanded in y around inf 70.5%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+172} \lor \neg \left(t \leq 5 \cdot 10^{+97}\right):\\ \;\;\;\;a + \left(\frac{y}{\frac{t}{z}} - y \cdot \frac{b}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+53}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.75e+53) (* (+ y x) (/ z (+ y (+ x t)))) (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.75e+53) {
		tmp = (y + x) * (z / (y + (x + t)));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.75d+53)) then
        tmp = (y + x) * (z / (y + (x + t)))
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.75e+53) {
		tmp = (y + x) * (z / (y + (x + t)));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.75e+53:
		tmp = (y + x) * (z / (y + (x + t)))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.75e+53)
		tmp = Float64(Float64(y + x) * Float64(z / Float64(y + Float64(x + t))));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.75e+53)
		tmp = (y + x) * (z / (y + (x + t)));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.75e+53], N[(N[(y + x), $MachinePrecision] * N[(z / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75000000000000009e53

   1. Initial program 48.7%

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

   3. Taylor expanded in z around inf 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* 75.6%

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

      2. associate-+r+ 75.6%

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

      3. +-commutative 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in z around 0 36.8%

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

      1. +-commutative 36.8%

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

      2. +-commutative 36.8%

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

      3. associate-+r+ 36.8%

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

      4. associate-*l/ 75.6%

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

      5. *-commutative 75.6%

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

      6. +-commutative 75.6%

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

      7. +-commutative 75.6%

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

   8. Simplified 75.6%

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

   if -1.75000000000000009e53 < z

   1. Initial program 59.1%

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

   3. Taylor expanded in y around inf 60.9%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+53}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{z}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+172}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+136}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.25e+172) a (if (<= t 2.25e+136) (- (+ a z) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.25e+172) {
		tmp = a;
	} else if (t <= 2.25e+136) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.25d+172)) then
        tmp = a
    else if (t <= 2.25d+136) then
        tmp = (a + z) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.25e+172) {
		tmp = a;
	} else if (t <= 2.25e+136) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.25e+172:
		tmp = a
	elif t <= 2.25e+136:
		tmp = (a + z) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.25e+172)
		tmp = a;
	elseif (t <= 2.25e+136)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.25e+172)
		tmp = a;
	elseif (t <= 2.25e+136)
		tmp = (a + z) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.25e+172], a, If[LessEqual[t, 2.25e+136], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25e172 or 2.25e136 < t

   1. Initial program 50.4%

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

   3. Taylor expanded in t around inf 48.8%

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

   if -1.25e172 < t < 2.25e136

   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 69.8%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+172}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+136}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-61}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.2e+33) a (if (<= t 5.6e-61) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+33) {
		tmp = a;
	} else if (t <= 5.6e-61) {
		tmp = z;
	} 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 <= (-7.2d+33)) then
        tmp = a
    else if (t <= 5.6d-61) then
        tmp = z
    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 <= -7.2e+33) {
		tmp = a;
	} else if (t <= 5.6e-61) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.2e+33:
		tmp = a
	elif t <= 5.6e-61:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.2e+33)
		tmp = a;
	elseif (t <= 5.6e-61)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.2e+33)
		tmp = a;
	elseif (t <= 5.6e-61)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.2e+33], a, If[LessEqual[t, 5.6e-61], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -7.2000000000000005e33 or 5.6000000000000002e-61 < t

   1. Initial program 52.8%

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

   3. Taylor expanded in t around inf 47.9%

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

   if -7.2000000000000005e33 < t < 5.6000000000000002e-61

   1. Initial program 61.8%

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

   3. Taylor expanded in x around inf 48.1%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-61}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 33.1% 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 57.2%

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

3. Taylor expanded in t around inf 34.1%

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

4. Final simplification 34.1%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.1% 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 2024021 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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