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

Percentage Accurate: 61.3% → 89.2%

Time: 18.0s

Alternatives: 15

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.3% 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: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{y \cdot b}{t_1}\\ t_3 := a \cdot \left(\frac{t}{t_1} + \frac{y}{t_1}\right)\\ t_4 := z \cdot \left(x + y\right)\\ t_5 := \frac{\left(t_4 + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_6 := z + t_3\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_6 - t_2\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+277}:\\ \;\;\;\;\left(t_3 + \frac{t_4}{t_1}\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_6 - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (/ (* y b) t_1))
        (t_3 (* a (+ (/ t t_1) (/ y t_1))))
        (t_4 (* z (+ x y)))
        (t_5 (/ (- (+ t_4 (* a (+ y t))) (* y b)) (+ y (+ x t))))
        (t_6 (+ z t_3)))
   (if (<= t_5 (- INFINITY))
     (- t_6 t_2)
     (if (<= t_5 2e+277) (- (+ t_3 (/ t_4 t_1)) t_2) (- t_6 b)))))

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 * b) / t_1;
	double t_3 = a * ((t / t_1) + (y / t_1));
	double t_4 = z * (x + y);
	double t_5 = ((t_4 + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_6 = z + t_3;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_6 - t_2;
	} else if (t_5 <= 2e+277) {
		tmp = (t_3 + (t_4 / t_1)) - t_2;
	} else {
		tmp = t_6 - b;
	}
	return tmp;
}

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 * b) / t_1;
	double t_3 = a * ((t / t_1) + (y / t_1));
	double t_4 = z * (x + y);
	double t_5 = ((t_4 + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_6 = z + t_3;
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = t_6 - t_2;
	} else if (t_5 <= 2e+277) {
		tmp = (t_3 + (t_4 / t_1)) - t_2;
	} else {
		tmp = t_6 - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = (y * b) / t_1
	t_3 = a * ((t / t_1) + (y / t_1))
	t_4 = z * (x + y)
	t_5 = ((t_4 + (a * (y + t))) - (y * b)) / (y + (x + t))
	t_6 = z + t_3
	tmp = 0
	if t_5 <= -math.inf:
		tmp = t_6 - t_2
	elif t_5 <= 2e+277:
		tmp = (t_3 + (t_4 / t_1)) - t_2
	else:
		tmp = t_6 - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(Float64(y * b) / t_1)
	t_3 = Float64(a * Float64(Float64(t / t_1) + Float64(y / t_1)))
	t_4 = Float64(z * Float64(x + y))
	t_5 = Float64(Float64(Float64(t_4 + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_6 = Float64(z + t_3)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = Float64(t_6 - t_2);
	elseif (t_5 <= 2e+277)
		tmp = Float64(Float64(t_3 + Float64(t_4 / t_1)) - t_2);
	else
		tmp = Float64(t_6 - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = (y * b) / t_1;
	t_3 = a * ((t / t_1) + (y / t_1));
	t_4 = z * (x + y);
	t_5 = ((t_4 + (a * (y + t))) - (y * b)) / (y + (x + t));
	t_6 = z + t_3;
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = t_6 - t_2;
	elseif (t_5 <= 2e+277)
		tmp = (t_3 + (t_4 / t_1)) - t_2;
	else
		tmp = t_6 - b;
	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[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(z + t$95$3), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], N[(t$95$6 - t$95$2), $MachinePrecision], If[LessEqual[t$95$5, 2e+277], N[(N[(t$95$3 + N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$6 - b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 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

   1. Initial program 6.7%

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

   2. Taylor expanded in a around 0 40.5%

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

   3. Taylor expanded in x around inf 78.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000001e277

   1. Initial program 99.7%

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

   2. Taylor expanded in a around 0 99.7%

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

   if 2.00000000000000001e277 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.1%

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

   2. Taylor expanded in a around 0 31.9%

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

   3. Taylor expanded in x around inf 59.3%

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

   4. Taylor expanded in y around inf 74.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right)\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+277}:\\ \;\;\;\;\left(a \cdot \left(\frac{t}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)}\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right)\right) - b\\ \end{array} \]

Alternative 2: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+277}\right):\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{t_1} + \frac{y}{t_1}\right)\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+277)))
     (- (+ z (* a (+ (/ t t_1) (/ y t_1)))) b)
     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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+277)) {
		tmp = (z + (a * ((t / t_1) + (y / t_1)))) - 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 = t + (x + y);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+277)) {
		tmp = (z + (a * ((t / t_1) + (y / t_1)))) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+277):
		tmp = (z + (a * ((t / t_1) + (y / t_1)))) - b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+277))
		tmp = Float64(Float64(z + Float64(a * Float64(Float64(t / t_1) + Float64(y / t_1)))) - b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+277)))
		tmp = (z + (a * ((t / t_1) + (y / t_1)))) - b;
	else
		tmp = 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[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+277]], $MachinePrecision]], N[(N[(z + N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(y / t$95$1), $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 2.00000000000000001e277 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.9%

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

   2. Taylor expanded in a around 0 36.0%

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

   3. Taylor expanded in x around inf 68.3%

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

   4. Taylor expanded in y around inf 74.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000001e277

   1. Initial program 99.7%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+277}\right):\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right)\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 3: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := t + \left(x + y\right)\\ t_3 := z + a \cdot \left(\frac{t}{t_2} + \frac{y}{t_2}\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_3 - \frac{y \cdot b}{t_2}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+277}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3 - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t))))
        (t_2 (+ t (+ x y)))
        (t_3 (+ z (* a (+ (/ t t_2) (/ y t_2))))))
   (if (<= t_1 (- INFINITY))
     (- t_3 (/ (* y b) t_2))
     (if (<= t_1 2e+277) t_1 (- t_3 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = t + (x + y);
	double t_3 = z + (a * ((t / t_2) + (y / t_2)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_3 - ((y * b) / t_2);
	} else if (t_1 <= 2e+277) {
		tmp = t_1;
	} else {
		tmp = t_3 - b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = t + (x + y);
	double t_3 = z + (a * ((t / t_2) + (y / t_2)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3 - ((y * b) / t_2);
	} else if (t_1 <= 2e+277) {
		tmp = t_1;
	} else {
		tmp = t_3 - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	t_2 = t + (x + y)
	t_3 = z + (a * ((t / t_2) + (y / t_2)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_3 - ((y * b) / t_2)
	elif t_1 <= 2e+277:
		tmp = t_1
	else:
		tmp = t_3 - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(t + Float64(x + y))
	t_3 = Float64(z + Float64(a * Float64(Float64(t / t_2) + Float64(y / t_2))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t_3 - Float64(Float64(y * b) / t_2));
	elseif (t_1 <= 2e+277)
		tmp = t_1;
	else
		tmp = Float64(t_3 - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	t_2 = t + (x + y);
	t_3 = z + (a * ((t / t_2) + (y / t_2)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_3 - ((y * b) / t_2);
	elseif (t_1 <= 2e+277)
		tmp = t_1;
	else
		tmp = t_3 - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z + N[(a * N[(N[(t / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t$95$3 - N[(N[(y * b), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+277], t$95$1, N[(t$95$3 - b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 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

   1. Initial program 6.7%

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

   2. Taylor expanded in a around 0 40.5%

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

   3. Taylor expanded in x around inf 78.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000001e277

   1. Initial program 99.7%

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

   if 2.00000000000000001e277 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.1%

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

   2. Taylor expanded in a around 0 31.9%

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

   3. Taylor expanded in x around inf 59.3%

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

   4. Taylor expanded in y around inf 74.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right)\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+277}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right)\right) - b\\ \end{array} \]

Alternative 4: 70.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ t_2 := t + \left(x + y\right)\\ \mathbf{if}\;t \leq -2.45 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-126}:\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{t_2} + \frac{y}{t_2}\right)\right) - b\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+61}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - \frac{y \cdot b}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (* y (- (/ z t) (/ b t))))) (t_2 (+ t (+ x y))))
   (if (<= t -2.45e+79)
     t_1
     (if (<= t -7e-126)
       (- (+ z (* a (+ (/ t t_2) (/ y t_2)))) b)
       (if (<= t 1.45e+61)
         (- (+ z (/ a (/ (+ x y) y))) (/ (* y b) t_2))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (y * ((z / t) - (b / t)));
	double t_2 = t + (x + y);
	double tmp;
	if (t <= -2.45e+79) {
		tmp = t_1;
	} else if (t <= -7e-126) {
		tmp = (z + (a * ((t / t_2) + (y / t_2)))) - b;
	} else if (t <= 1.45e+61) {
		tmp = (z + (a / ((x + y) / y))) - ((y * b) / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (y * ((z / t) - (b / t)))
    t_2 = t + (x + y)
    if (t <= (-2.45d+79)) then
        tmp = t_1
    else if (t <= (-7d-126)) then
        tmp = (z + (a * ((t / t_2) + (y / t_2)))) - b
    else if (t <= 1.45d+61) then
        tmp = (z + (a / ((x + y) / y))) - ((y * b) / t_2)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (y * ((z / t) - (b / t)));
	double t_2 = t + (x + y);
	double tmp;
	if (t <= -2.45e+79) {
		tmp = t_1;
	} else if (t <= -7e-126) {
		tmp = (z + (a * ((t / t_2) + (y / t_2)))) - b;
	} else if (t <= 1.45e+61) {
		tmp = (z + (a / ((x + y) / y))) - ((y * b) / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (y * ((z / t) - (b / t)))
	t_2 = t + (x + y)
	tmp = 0
	if t <= -2.45e+79:
		tmp = t_1
	elif t <= -7e-126:
		tmp = (z + (a * ((t / t_2) + (y / t_2)))) - b
	elif t <= 1.45e+61:
		tmp = (z + (a / ((x + y) / y))) - ((y * b) / t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(y * Float64(Float64(z / t) - Float64(b / t))))
	t_2 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (t <= -2.45e+79)
		tmp = t_1;
	elseif (t <= -7e-126)
		tmp = Float64(Float64(z + Float64(a * Float64(Float64(t / t_2) + Float64(y / t_2)))) - b);
	elseif (t <= 1.45e+61)
		tmp = Float64(Float64(z + Float64(a / Float64(Float64(x + y) / y))) - Float64(Float64(y * b) / t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (y * ((z / t) - (b / t)));
	t_2 = t + (x + y);
	tmp = 0.0;
	if (t <= -2.45e+79)
		tmp = t_1;
	elseif (t <= -7e-126)
		tmp = (z + (a * ((t / t_2) + (y / t_2)))) - b;
	elseif (t <= 1.45e+61)
		tmp = (z + (a / ((x + y) / y))) - ((y * b) / t_2);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(y * N[(N[(z / t), $MachinePrecision] - N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.45e+79], t$95$1, If[LessEqual[t, -7e-126], N[(N[(z + N[(a * N[(N[(t / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 1.45e+61], N[(N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4499999999999999e79 or 1.45e61 < t

   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. Taylor expanded in t around inf 58.6%

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

      1. associate--l+ 58.6%

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

      2. associate-/l* 58.9%

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

      3. +-commutative 58.9%

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

      4. associate-/l* 63.6%

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

      5. +-commutative 63.6%

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

      6. associate-/l* 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in y around inf 67.9%

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

   if -2.4499999999999999e79 < t < -7e-126

   1. Initial program 69.6%

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

   2. Taylor expanded in a around 0 71.9%

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

   3. Taylor expanded in x around inf 65.1%

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

   4. Taylor expanded in y around inf 66.4%

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

   if -7e-126 < t < 1.45e61

   1. Initial program 63.5%

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

   2. Taylor expanded in a around 0 70.2%

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

   3. Taylor expanded in x around inf 88.8%

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

   4. Taylor expanded in t around 0 78.3%

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

      1. associate-/l* 86.7%

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

      2. +-commutative 86.7%

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

   6. Simplified 86.7%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+79}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-126}:\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right)\right) - b\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+61}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \end{array} \]

Alternative 5: 70.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+91} \lor \neg \left(t \leq 1.5 \cdot 10^{+61}\right):\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.65e+91) (not (<= t 1.5e+61)))
   (+ a (* y (- (/ z t) (/ b t))))
   (- (+ z (/ a (/ (+ x y) y))) (/ (* y b) (+ t (+ x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.65e+91) || !(t <= 1.5e+61)) {
		tmp = a + (y * ((z / t) - (b / t)));
	} else {
		tmp = (z + (a / ((x + y) / y))) - ((y * b) / (t + (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.65d+91)) .or. (.not. (t <= 1.5d+61))) then
        tmp = a + (y * ((z / t) - (b / t)))
    else
        tmp = (z + (a / ((x + y) / y))) - ((y * b) / (t + (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.65e+91) || !(t <= 1.5e+61)) {
		tmp = a + (y * ((z / t) - (b / t)));
	} else {
		tmp = (z + (a / ((x + y) / y))) - ((y * b) / (t + (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.65e+91) or not (t <= 1.5e+61):
		tmp = a + (y * ((z / t) - (b / t)))
	else:
		tmp = (z + (a / ((x + y) / y))) - ((y * b) / (t + (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.65e+91) || !(t <= 1.5e+61))
		tmp = Float64(a + Float64(y * Float64(Float64(z / t) - Float64(b / t))));
	else
		tmp = Float64(Float64(z + Float64(a / Float64(Float64(x + y) / y))) - Float64(Float64(y * b) / Float64(t + Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.65e+91) || ~((t <= 1.5e+61)))
		tmp = a + (y * ((z / t) - (b / t)));
	else
		tmp = (z + (a / ((x + y) / y))) - ((y * b) / (t + (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.65e+91], N[Not[LessEqual[t, 1.5e+61]], $MachinePrecision]], N[(a + N[(y * N[(N[(z / t), $MachinePrecision] - N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65000000000000009e91 or 1.5e61 < t

   1. Initial program 50.9%

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

   2. Taylor expanded in t around inf 59.1%

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

      1. associate--l+ 59.1%

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

      2. associate-/l* 59.4%

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

      3. +-commutative 59.4%

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

      4. associate-/l* 64.1%

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

      5. +-commutative 64.1%

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

      6. associate-/l* 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in y around inf 68.6%

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

   if -1.65000000000000009e91 < t < 1.5e61

   1. Initial program 65.4%

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

   2. Taylor expanded in a around 0 70.8%

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

   3. Taylor expanded in x around inf 82.2%

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

   4. Taylor expanded in t around 0 70.8%

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

      1. associate-/l* 77.6%

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

      2. +-commutative 77.6%

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

   6. Simplified 77.6%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+91} \lor \neg \left(t \leq 1.5 \cdot 10^{+61}\right):\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \end{array} \]

Alternative 6: 60.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+42}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ a (* y (- (/ z t) (/ b t))))))
   (if (<= t -9.5e+26)
     t_2
     (if (<= t 2.95e+21)
       t_1
       (if (<= t 2e+42)
         (/ z (+ 1.0 (/ t (+ x y))))
         (if (<= t 1.3e+61) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (y * ((z / t) - (b / t)));
	double tmp;
	if (t <= -9.5e+26) {
		tmp = t_2;
	} else if (t <= 2.95e+21) {
		tmp = t_1;
	} else if (t <= 2e+42) {
		tmp = z / (1.0 + (t / (x + y)));
	} else if (t <= 1.3e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a + (y * ((z / t) - (b / t)))
    if (t <= (-9.5d+26)) then
        tmp = t_2
    else if (t <= 2.95d+21) then
        tmp = t_1
    else if (t <= 2d+42) then
        tmp = z / (1.0d0 + (t / (x + y)))
    else if (t <= 1.3d+61) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (y * ((z / t) - (b / t)));
	double tmp;
	if (t <= -9.5e+26) {
		tmp = t_2;
	} else if (t <= 2.95e+21) {
		tmp = t_1;
	} else if (t <= 2e+42) {
		tmp = z / (1.0 + (t / (x + y)));
	} else if (t <= 1.3e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a + (y * ((z / t) - (b / t)))
	tmp = 0
	if t <= -9.5e+26:
		tmp = t_2
	elif t <= 2.95e+21:
		tmp = t_1
	elif t <= 2e+42:
		tmp = z / (1.0 + (t / (x + y)))
	elif t <= 1.3e+61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a + Float64(y * Float64(Float64(z / t) - Float64(b / t))))
	tmp = 0.0
	if (t <= -9.5e+26)
		tmp = t_2;
	elseif (t <= 2.95e+21)
		tmp = t_1;
	elseif (t <= 2e+42)
		tmp = Float64(z / Float64(1.0 + Float64(t / Float64(x + y))));
	elseif (t <= 1.3e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a + (y * ((z / t) - (b / t)));
	tmp = 0.0;
	if (t <= -9.5e+26)
		tmp = t_2;
	elseif (t <= 2.95e+21)
		tmp = t_1;
	elseif (t <= 2e+42)
		tmp = z / (1.0 + (t / (x + y)));
	elseif (t <= 1.3e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(y * N[(N[(z / t), $MachinePrecision] - N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+26], t$95$2, If[LessEqual[t, 2.95e+21], t$95$1, If[LessEqual[t, 2e+42], N[(z / N[(1.0 + N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+61], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.50000000000000054e26 or 1.29999999999999986e61 < t

   1. Initial program 54.4%

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

   2. Taylor expanded in t around inf 56.5%

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

      1. associate--l+ 56.5%

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

      2. associate-/l* 56.8%

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

      3. +-commutative 56.8%

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

      4. associate-/l* 61.8%

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

      5. +-commutative 61.8%

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

      6. associate-/l* 63.7%

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

   4. Simplified 63.7%

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

   5. Taylor expanded in y around inf 64.8%

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

   if -9.50000000000000054e26 < t < 2.95e21 or 2.00000000000000009e42 < t < 1.29999999999999986e61

   1. Initial program 63.4%

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

   2. Taylor expanded in y around inf 66.1%

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

   if 2.95e21 < t < 2.00000000000000009e42

   1. Initial program 80.8%

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

      1. +-commutative 80.8%

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

      2. associate--l+ 80.8%

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

      3. fma-def 80.8%

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

      4. +-commutative 80.8%

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

      5. +-commutative 80.8%

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

   3. Simplified 80.8%

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

      1. div-inv 80.2%

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

      2. fma-udef 80.2%

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

      3. *-commutative 80.2%

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

      4. fma-def 80.2%

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

      5. +-commutative 80.2%

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

      6. associate-+l+ 80.2%

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

      7. +-commutative 80.2%

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

   5. Applied egg-rr 80.2%

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

   6. Taylor expanded in z around inf 80.8%

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

      1. associate-/l* 99.7%

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

      2. associate-+r+ 99.7%

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

      3. +-commutative 99.7%

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

      4. +-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in t around 0 99.7%

      \[\leadsto \frac{z}{\color{blue}{1 + \frac{t}{x + y}}} \]
   10. Step-by-step derivation

       1. +-commutative 99.7%

          \[\leadsto \frac{z}{1 + \frac{t}{\color{blue}{y + x}}} \]

   11. Simplified 99.7%

       \[\leadsto \frac{z}{\color{blue}{1 + \frac{t}{y + x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+26}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+21}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+42}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+61}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \end{array} \]

Alternative 7: 62.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+26}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{elif}\;t \leq -1.36 \cdot 10^{-219}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+162}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;a + z \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.5e+26)
   (+ a (* y (- (/ z t) (/ b t))))
   (if (<= t -1.36e-219)
     (- (+ z a) b)
     (if (<= t 3.1e+162)
       (- (+ z a) (/ (* y b) (+ t (+ x y))))
       (+ a (* z (+ (/ y t) (/ x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e+26) {
		tmp = a + (y * ((z / t) - (b / t)));
	} else if (t <= -1.36e-219) {
		tmp = (z + a) - b;
	} else if (t <= 3.1e+162) {
		tmp = (z + a) - ((y * b) / (t + (x + y)));
	} else {
		tmp = a + (z * ((y / t) + (x / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9.5d+26)) then
        tmp = a + (y * ((z / t) - (b / t)))
    else if (t <= (-1.36d-219)) then
        tmp = (z + a) - b
    else if (t <= 3.1d+162) then
        tmp = (z + a) - ((y * b) / (t + (x + y)))
    else
        tmp = a + (z * ((y / t) + (x / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e+26) {
		tmp = a + (y * ((z / t) - (b / t)));
	} else if (t <= -1.36e-219) {
		tmp = (z + a) - b;
	} else if (t <= 3.1e+162) {
		tmp = (z + a) - ((y * b) / (t + (x + y)));
	} else {
		tmp = a + (z * ((y / t) + (x / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.5e+26:
		tmp = a + (y * ((z / t) - (b / t)))
	elif t <= -1.36e-219:
		tmp = (z + a) - b
	elif t <= 3.1e+162:
		tmp = (z + a) - ((y * b) / (t + (x + y)))
	else:
		tmp = a + (z * ((y / t) + (x / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.5e+26)
		tmp = Float64(a + Float64(y * Float64(Float64(z / t) - Float64(b / t))));
	elseif (t <= -1.36e-219)
		tmp = Float64(Float64(z + a) - b);
	elseif (t <= 3.1e+162)
		tmp = Float64(Float64(z + a) - Float64(Float64(y * b) / Float64(t + Float64(x + y))));
	else
		tmp = Float64(a + Float64(z * Float64(Float64(y / t) + Float64(x / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.5e+26)
		tmp = a + (y * ((z / t) - (b / t)));
	elseif (t <= -1.36e-219)
		tmp = (z + a) - b;
	elseif (t <= 3.1e+162)
		tmp = (z + a) - ((y * b) / (t + (x + y)));
	else
		tmp = a + (z * ((y / t) + (x / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.5e+26], N[(a + N[(y * N[(N[(z / t), $MachinePrecision] - N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.36e-219], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 3.1e+162], N[(N[(z + a), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z * N[(N[(y / t), $MachinePrecision] + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.50000000000000054e26

   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. Taylor expanded in t around inf 57.5%

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

      1. associate--l+ 57.5%

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

      2. associate-/l* 57.9%

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

      3. +-commutative 57.9%

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

      4. associate-/l* 64.6%

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

      5. +-commutative 64.6%

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

      6. associate-/l* 65.6%

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

   4. Simplified 65.6%

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

   5. Taylor expanded in y around inf 65.9%

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

   if -9.50000000000000054e26 < t < -1.35999999999999997e-219

   1. Initial program 67.5%

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

   2. Taylor expanded in y around inf 71.1%

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

   if -1.35999999999999997e-219 < t < 3.1e162

   1. Initial program 63.0%

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

   2. Taylor expanded in a around 0 72.6%

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

   3. Taylor expanded in x around inf 87.2%

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

   4. Taylor expanded in t around inf 69.5%

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

   if 3.1e162 < t

   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. Taylor expanded in t around inf 53.0%

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

      1. associate--l+ 53.0%

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

      2. associate-/l* 53.2%

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

      3. +-commutative 53.2%

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

      4. associate-/l* 56.3%

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

      5. +-commutative 56.3%

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

      6. associate-/l* 61.2%

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

   4. Simplified 61.2%

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

   5. Taylor expanded in z around inf 66.3%

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

      1. +-commutative 66.3%

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

   7. Simplified 66.3%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+26}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{elif}\;t \leq -1.36 \cdot 10^{-219}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+162}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;a + z \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \end{array} \]

Alternative 8: 58.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a - y \cdot \frac{b}{t}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+21}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- a (* y (/ b t)))))
   (if (<= t -5.6e+128)
     t_1
     (if (<= t 2.95e+21)
       (- (+ z a) b)
       (if (<= t 8.5e+80) (* (+ x y) (/ z (+ x (+ y t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - (y * (b / t));
	double tmp;
	if (t <= -5.6e+128) {
		tmp = t_1;
	} else if (t <= 2.95e+21) {
		tmp = (z + a) - b;
	} else if (t <= 8.5e+80) {
		tmp = (x + y) * (z / (x + (y + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a - (y * (b / t))
    if (t <= (-5.6d+128)) then
        tmp = t_1
    else if (t <= 2.95d+21) then
        tmp = (z + a) - b
    else if (t <= 8.5d+80) then
        tmp = (x + y) * (z / (x + (y + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - (y * (b / t));
	double tmp;
	if (t <= -5.6e+128) {
		tmp = t_1;
	} else if (t <= 2.95e+21) {
		tmp = (z + a) - b;
	} else if (t <= 8.5e+80) {
		tmp = (x + y) * (z / (x + (y + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a - (y * (b / t))
	tmp = 0
	if t <= -5.6e+128:
		tmp = t_1
	elif t <= 2.95e+21:
		tmp = (z + a) - b
	elif t <= 8.5e+80:
		tmp = (x + y) * (z / (x + (y + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a - Float64(y * Float64(b / t)))
	tmp = 0.0
	if (t <= -5.6e+128)
		tmp = t_1;
	elseif (t <= 2.95e+21)
		tmp = Float64(Float64(z + a) - b);
	elseif (t <= 8.5e+80)
		tmp = Float64(Float64(x + y) * Float64(z / Float64(x + Float64(y + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a - (y * (b / t));
	tmp = 0.0;
	if (t <= -5.6e+128)
		tmp = t_1;
	elseif (t <= 2.95e+21)
		tmp = (z + a) - b;
	elseif (t <= 8.5e+80)
		tmp = (x + y) * (z / (x + (y + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+128], t$95$1, If[LessEqual[t, 2.95e+21], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 8.5e+80], N[(N[(x + y), $MachinePrecision] * N[(z / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.59999999999999965e128 or 8.50000000000000007e80 < t

   1. Initial program 47.9%

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

   2. Taylor expanded in t around inf 58.5%

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

      1. associate--l+ 58.5%

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

      2. associate-/l* 58.8%

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

      3. +-commutative 58.8%

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

      4. associate-/l* 63.0%

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

      5. +-commutative 63.0%

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

      6. associate-/l* 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in b around inf 55.9%

      \[\leadsto a + \color{blue}{-1 \cdot \frac{b \cdot y}{t}} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.9%

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

      2. associate-*l/ 61.9%

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

      3. *-commutative 61.9%

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

      4. distribute-rgt-neg-in 61.9%

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

      5. distribute-frac-neg 61.9%

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

   7. Simplified 61.9%

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

   if -5.59999999999999965e128 < t < 2.95e21

   1. Initial program 66.4%

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

   2. Taylor expanded in y around inf 62.3%

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

   if 2.95e21 < t < 8.50000000000000007e80

   1. Initial program 61.2%

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

      1. +-commutative 61.2%

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

      2. associate--l+ 61.2%

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

      3. fma-def 61.2%

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

      4. +-commutative 61.2%

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

      5. +-commutative 61.2%

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

   3. Simplified 61.2%

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

      1. div-inv 60.8%

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

      2. fma-udef 60.8%

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

      3. *-commutative 60.8%

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

      4. fma-def 60.8%

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

      5. +-commutative 60.8%

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

      6. associate-+l+ 60.8%

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

      7. +-commutative 60.8%

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

   5. Applied egg-rr 60.8%

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

   6. Taylor expanded in z around inf 52.6%

      \[\leadsto \color{blue}{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)}} \]
   7. 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%

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

      4. +-commutative 75.6%

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

   8. Simplified 75.6%

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

   9. Taylor expanded in z around 0 52.6%

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

       1. +-commutative 52.6%

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

       2. associate-+r+ 52.6%

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

       3. associate-*l/ 75.9%

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

       4. *-commutative 75.9%

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

       5. +-commutative 75.9%

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

       6. +-commutative 75.9%

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

       7. +-commutative 75.9%

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

       8. +-commutative 75.9%

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

   11. Simplified 75.9%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+128}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+21}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \end{array} \]

Alternative 9: 58.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a - y \cdot \frac{b}{t}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+21}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- a (* y (/ b t)))))
   (if (<= t -5.5e+129)
     t_1
     (if (<= t 2.7e+21)
       (- (+ z a) b)
       (if (<= t 3.5e+80) (/ z (+ 1.0 (/ t (+ x y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - (y * (b / t));
	double tmp;
	if (t <= -5.5e+129) {
		tmp = t_1;
	} else if (t <= 2.7e+21) {
		tmp = (z + a) - b;
	} else if (t <= 3.5e+80) {
		tmp = z / (1.0 + (t / (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 - (y * (b / t))
    if (t <= (-5.5d+129)) then
        tmp = t_1
    else if (t <= 2.7d+21) then
        tmp = (z + a) - b
    else if (t <= 3.5d+80) then
        tmp = z / (1.0d0 + (t / (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 - (y * (b / t));
	double tmp;
	if (t <= -5.5e+129) {
		tmp = t_1;
	} else if (t <= 2.7e+21) {
		tmp = (z + a) - b;
	} else if (t <= 3.5e+80) {
		tmp = z / (1.0 + (t / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a - (y * (b / t))
	tmp = 0
	if t <= -5.5e+129:
		tmp = t_1
	elif t <= 2.7e+21:
		tmp = (z + a) - b
	elif t <= 3.5e+80:
		tmp = z / (1.0 + (t / (x + y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a - Float64(y * Float64(b / t)))
	tmp = 0.0
	if (t <= -5.5e+129)
		tmp = t_1;
	elseif (t <= 2.7e+21)
		tmp = Float64(Float64(z + a) - b);
	elseif (t <= 3.5e+80)
		tmp = Float64(z / Float64(1.0 + Float64(t / 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 - (y * (b / t));
	tmp = 0.0;
	if (t <= -5.5e+129)
		tmp = t_1;
	elseif (t <= 2.7e+21)
		tmp = (z + a) - b;
	elseif (t <= 3.5e+80)
		tmp = z / (1.0 + (t / (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[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+129], t$95$1, If[LessEqual[t, 2.7e+21], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 3.5e+80], N[(z / N[(1.0 + N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.49999999999999984e129 or 3.49999999999999994e80 < t

   1. Initial program 47.9%

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

   2. Taylor expanded in t around inf 58.5%

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

      1. associate--l+ 58.5%

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

      2. associate-/l* 58.8%

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

      3. +-commutative 58.8%

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

      4. associate-/l* 63.0%

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

      5. +-commutative 63.0%

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

      6. associate-/l* 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in b around inf 55.9%

      \[\leadsto a + \color{blue}{-1 \cdot \frac{b \cdot y}{t}} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.9%

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

      2. associate-*l/ 61.9%

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

      3. *-commutative 61.9%

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

      4. distribute-rgt-neg-in 61.9%

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

      5. distribute-frac-neg 61.9%

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

   7. Simplified 61.9%

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

   if -5.49999999999999984e129 < t < 2.7e21

   1. Initial program 66.4%

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

   2. Taylor expanded in y around inf 62.3%

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

   if 2.7e21 < t < 3.49999999999999994e80

   1. Initial program 61.2%

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

      1. +-commutative 61.2%

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

      2. associate--l+ 61.2%

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

      3. fma-def 61.2%

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

      4. +-commutative 61.2%

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

      5. +-commutative 61.2%

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

   3. Simplified 61.2%

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

      1. div-inv 60.8%

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

      2. fma-udef 60.8%

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

      3. *-commutative 60.8%

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

      4. fma-def 60.8%

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

      5. +-commutative 60.8%

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

      6. associate-+l+ 60.8%

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

      7. +-commutative 60.8%

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

   5. Applied egg-rr 60.8%

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

   6. Taylor expanded in z around inf 52.6%

      \[\leadsto \color{blue}{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)}} \]
   7. 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%

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

      4. +-commutative 75.6%

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

   8. Simplified 75.6%

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

   9. Taylor expanded in t around 0 75.6%

      \[\leadsto \frac{z}{\color{blue}{1 + \frac{t}{x + y}}} \]
   10. Step-by-step derivation

       1. +-commutative 75.6%

          \[\leadsto \frac{z}{1 + \frac{t}{\color{blue}{y + x}}} \]

   11. Simplified 75.6%

       \[\leadsto \frac{z}{\color{blue}{1 + \frac{t}{y + x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+129}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+21}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \end{array} \]

Alternative 10: 58.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+99} \lor \neg \left(x \leq 5.5 \cdot 10^{+216}\right):\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -5e+99) (not (<= x 5.5e+216)))
   (/ z (/ (+ x t) x))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5e+99) || !(x <= 5.5e+216)) {
		tmp = z / ((x + t) / x);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-5d+99)) .or. (.not. (x <= 5.5d+216))) then
        tmp = z / ((x + t) / x)
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5e+99) || !(x <= 5.5e+216)) {
		tmp = z / ((x + t) / x);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -5e+99) or not (x <= 5.5e+216):
		tmp = z / ((x + t) / x)
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -5e+99) || !(x <= 5.5e+216))
		tmp = Float64(z / Float64(Float64(x + t) / x));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -5e+99) || ~((x <= 5.5e+216)))
		tmp = z / ((x + t) / x);
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -5e+99], N[Not[LessEqual[x, 5.5e+216]], $MachinePrecision]], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000008e99 or 5.5e216 < x

   1. Initial program 50.7%

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

      1. +-commutative 50.7%

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

      2. associate--l+ 50.7%

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

      3. fma-def 50.8%

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

      4. +-commutative 50.8%

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

      5. +-commutative 50.8%

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

   3. Simplified 50.8%

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

      1. div-inv 50.7%

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

      2. fma-udef 50.5%

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

      3. *-commutative 50.5%

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

      4. fma-def 50.7%

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

      5. +-commutative 50.7%

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

      6. associate-+l+ 50.7%

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

      7. +-commutative 50.7%

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

   5. Applied egg-rr 50.7%

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

   6. Taylor expanded in z around inf 27.4%

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

      1. associate-/l* 62.3%

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

      2. associate-+r+ 62.3%

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

      3. +-commutative 62.3%

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

      4. +-commutative 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in y around 0 60.8%

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

   if -5.00000000000000008e99 < x < 5.5e216

   1. Initial program 63.0%

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

   2. Taylor expanded in y around inf 58.9%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+99} \lor \neg \left(x \leq 5.5 \cdot 10^{+216}\right):\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 60.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+129} \lor \neg \left(t \leq 2.45 \cdot 10^{+162}\right):\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9e+129) (not (<= t 2.45e+162)))
   (- a (* y (/ b t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9e+129) || !(t <= 2.45e+162)) {
		tmp = a - (y * (b / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-9d+129)) .or. (.not. (t <= 2.45d+162))) then
        tmp = a - (y * (b / t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9e+129) || !(t <= 2.45e+162)) {
		tmp = a - (y * (b / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9e+129) or not (t <= 2.45e+162):
		tmp = a - (y * (b / t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9e+129) || !(t <= 2.45e+162))
		tmp = Float64(a - Float64(y * Float64(b / t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9e+129) || ~((t <= 2.45e+162)))
		tmp = a - (y * (b / t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9e+129], N[Not[LessEqual[t, 2.45e+162]], $MachinePrecision]], N[(a - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.0000000000000003e129 or 2.45000000000000017e162 < t

   1. Initial program 46.1%

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

   2. Taylor expanded in t around inf 59.5%

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

      1. associate--l+ 59.5%

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

      2. associate-/l* 59.8%

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

      3. +-commutative 59.8%

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

      4. associate-/l* 64.5%

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

      5. +-commutative 64.5%

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

      6. associate-/l* 67.3%

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

   4. Simplified 67.3%

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

   5. Taylor expanded in b around inf 56.7%

      \[\leadsto a + \color{blue}{-1 \cdot \frac{b \cdot y}{t}} \]
   6. Step-by-step derivation

      1. mul-1-neg 56.7%

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

      2. associate-*l/ 63.5%

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

      3. *-commutative 63.5%

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

      4. distribute-rgt-neg-in 63.5%

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

      5. distribute-frac-neg 63.5%

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

   7. Simplified 63.5%

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

   if -9.0000000000000003e129 < t < 2.45000000000000017e162

   1. Initial program 65.8%

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

   2. Taylor expanded in y around inf 60.1%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+129} \lor \neg \left(t \leq 2.45 \cdot 10^{+162}\right):\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 12: 57.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+153}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+219}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.4e+153) z (if (<= x 8.8e+219) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.4e+153) {
		tmp = z;
	} else if (x <= 8.8e+219) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.4d+153)) then
        tmp = z
    else if (x <= 8.8d+219) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.4e+153) {
		tmp = z;
	} else if (x <= 8.8e+219) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.4e+153:
		tmp = z
	elif x <= 8.8e+219:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.4e+153)
		tmp = z;
	elseif (x <= 8.8e+219)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.4e+153)
		tmp = z;
	elseif (x <= 8.8e+219)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.4e+153], z, If[LessEqual[x, 8.8e+219], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999993e153 or 8.8000000000000006e219 < x

   1. Initial program 45.7%

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

   2. Taylor expanded in x around inf 58.6%

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

   if -1.39999999999999993e153 < x < 8.8000000000000006e219

   1. Initial program 63.5%

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

   2. Taylor expanded in y around inf 57.6%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+153}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+219}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 13: 47.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+119}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+138}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.4e+119) z (if (<= x 5.8e+138) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.4e+119) {
		tmp = z;
	} else if (x <= 5.8e+138) {
		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 (x <= (-5.4d+119)) then
        tmp = z
    else if (x <= 5.8d+138) 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 (x <= -5.4e+119) {
		tmp = z;
	} else if (x <= 5.8e+138) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.4e+119:
		tmp = z
	elif x <= 5.8e+138:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.4e+119)
		tmp = z;
	elseif (x <= 5.8e+138)
		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 (x <= -5.4e+119)
		tmp = z;
	elseif (x <= 5.8e+138)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.4e+119], z, If[LessEqual[x, 5.8e+138], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -5.3999999999999997e119 or 5.80000000000000019e138 < x

   1. Initial program 48.8%

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

   2. Taylor expanded in x around inf 53.2%

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

   if -5.3999999999999997e119 < x < 5.80000000000000019e138

   1. Initial program 64.8%

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

      1. +-commutative 64.8%

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

      2. associate--l+ 64.8%

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

      3. fma-def 64.9%

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

      4. +-commutative 64.9%

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

      5. +-commutative 64.9%

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

   3. Simplified 64.9%

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

      1. div-inv 64.7%

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

      2. fma-udef 64.6%

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

      3. *-commutative 64.6%

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

      4. fma-def 64.7%

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

      5. +-commutative 64.7%

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

      6. associate-+l+ 64.7%

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

      7. +-commutative 64.7%

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

   5. Applied egg-rr 64.7%

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

   6. Taylor expanded in z around 0 42.3%

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

   7. Taylor expanded in y around inf 46.6%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+119}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+138}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 14: 44.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+28}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-6}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6e+28) a (if (<= a 1.52e-6) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6e+28) {
		tmp = a;
	} else if (a <= 1.52e-6) {
		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 (a <= (-6d+28)) then
        tmp = a
    else if (a <= 1.52d-6) 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 (a <= -6e+28) {
		tmp = a;
	} else if (a <= 1.52e-6) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6e+28:
		tmp = a
	elif a <= 1.52e-6:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6e+28)
		tmp = a;
	elseif (a <= 1.52e-6)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6e+28)
		tmp = a;
	elseif (a <= 1.52e-6)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6e+28], a, If[LessEqual[a, 1.52e-6], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -6.0000000000000002e28 or 1.52000000000000006e-6 < a

   1. Initial program 49.9%

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

   2. Taylor expanded in t around inf 53.1%

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

   if -6.0000000000000002e28 < a < 1.52000000000000006e-6

   1. Initial program 69.5%

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

   2. Taylor expanded in x around inf 40.2%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+28}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-6}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 15: 32.2% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.7%

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

2. Taylor expanded in t around inf 32.9%

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

3. Final simplification 32.9%

   \[\leadsto a \]

Developer target: 82.3% 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 2023285 
(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)))