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

Percentage Accurate: 60.6% → 87.4%

Time: 12.2s

Alternatives: 15

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.6% 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: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \left(y + t\right) \cdot a\\ t_3 := \frac{\left(t_2 + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 10^{+247}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right) + \frac{t_2}{t_1}\right) - \frac{y \cdot b}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (* (+ y t) a))
        (t_3 (/ (- (+ t_2 (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 1e+247)))
     (- (+ z a) b)
     (- (+ (* z (+ (/ x t_1) (/ y t_1))) (/ t_2 t_1)) (/ (* y b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = (y + t) * a;
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 1e+247)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1);
	}
	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 + t) * a;
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 1e+247)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = (y + t) * a
	t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 1e+247):
		tmp = (z + a) - b
	else:
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(Float64(y + t) * a)
	t_3 = Float64(Float64(Float64(t_2 + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 1e+247))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))) + Float64(t_2 / t_1)) - Float64(Float64(y * b) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = (y + t) * a;
	t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 1e+247)))
		tmp = (z + a) - b;
	else
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1);
	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 + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 1e+247]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 9.99999999999999952e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.5%

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

   2. Taylor expanded in y around inf 77.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999952e246

   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 z around 0 99.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+247}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \frac{\left(y + t\right) \cdot a}{t + \left(x + y\right)}\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \end{array} \]

Alternative 2: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+264} \lor \neg \left(t_1 \leq 10^{+247}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 -1e+264) (not (<= t_1 1e+247))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -1e+264) || !(t_1 <= 1e+247)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t))
    if ((t_1 <= (-1d+264)) .or. (.not. (t_1 <= 1d+247))) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -1e+264) || !(t_1 <= 1e+247)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -1e+264) or not (t_1 <= 1e+247):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= -1e+264) || !(t_1 <= 1e+247))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -1e+264) || ~((t_1 <= 1e+247)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+264], N[Not[LessEqual[t$95$1, 1e+247]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.00000000000000004e264 or 9.99999999999999952e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 10.6%

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

   2. Taylor expanded in y around inf 77.9%

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

   if -1.00000000000000004e264 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999952e246

   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 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+264} \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+247}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 3: 60.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-296}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-182}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-63}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+24}:\\ \;\;\;\;\frac{\left(y \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ z (/ (+ x (+ y t)) (+ x y)))))
   (if (<= z -2.2e+19)
     t_1
     (if (<= z -3.7e-296)
       (- (+ z a) (/ (* y b) (+ t (+ x y))))
       (if (<= z 1.05e-260)
         (* y (/ (- a b) (+ x y)))
         (if (<= z 1.1e-182)
           (/ (- (* (+ y t) a) (* y b)) (+ y (+ x t)))
           (if (<= z 7.4e-63)
             (- (+ z a) b)
             (if (<= z 1.05e+24)
               (/ (- (+ (* y a) (* z (+ x y))) (* y b)) (+ x y))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / ((x + (y + t)) / (x + y));
	double tmp;
	if (z <= -2.2e+19) {
		tmp = t_1;
	} else if (z <= -3.7e-296) {
		tmp = (z + a) - ((y * b) / (t + (x + y)));
	} else if (z <= 1.05e-260) {
		tmp = y * ((a - b) / (x + y));
	} else if (z <= 1.1e-182) {
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	} else if (z <= 7.4e-63) {
		tmp = (z + a) - b;
	} else if (z <= 1.05e+24) {
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / ((x + (y + t)) / (x + y))
    if (z <= (-2.2d+19)) then
        tmp = t_1
    else if (z <= (-3.7d-296)) then
        tmp = (z + a) - ((y * b) / (t + (x + y)))
    else if (z <= 1.05d-260) then
        tmp = y * ((a - b) / (x + y))
    else if (z <= 1.1d-182) then
        tmp = (((y + t) * a) - (y * b)) / (y + (x + t))
    else if (z <= 7.4d-63) then
        tmp = (z + a) - b
    else if (z <= 1.05d+24) then
        tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / ((x + (y + t)) / (x + y));
	double tmp;
	if (z <= -2.2e+19) {
		tmp = t_1;
	} else if (z <= -3.7e-296) {
		tmp = (z + a) - ((y * b) / (t + (x + y)));
	} else if (z <= 1.05e-260) {
		tmp = y * ((a - b) / (x + y));
	} else if (z <= 1.1e-182) {
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	} else if (z <= 7.4e-63) {
		tmp = (z + a) - b;
	} else if (z <= 1.05e+24) {
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z / ((x + (y + t)) / (x + y))
	tmp = 0
	if z <= -2.2e+19:
		tmp = t_1
	elif z <= -3.7e-296:
		tmp = (z + a) - ((y * b) / (t + (x + y)))
	elif z <= 1.05e-260:
		tmp = y * ((a - b) / (x + y))
	elif z <= 1.1e-182:
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t))
	elif z <= 7.4e-63:
		tmp = (z + a) - b
	elif z <= 1.05e+24:
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z / Float64(Float64(x + Float64(y + t)) / Float64(x + y)))
	tmp = 0.0
	if (z <= -2.2e+19)
		tmp = t_1;
	elseif (z <= -3.7e-296)
		tmp = Float64(Float64(z + a) - Float64(Float64(y * b) / Float64(t + Float64(x + y))));
	elseif (z <= 1.05e-260)
		tmp = Float64(y * Float64(Float64(a - b) / Float64(x + y)));
	elseif (z <= 1.1e-182)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (z <= 7.4e-63)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= 1.05e+24)
		tmp = Float64(Float64(Float64(Float64(y * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(x + y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z / ((x + (y + t)) / (x + y));
	tmp = 0.0;
	if (z <= -2.2e+19)
		tmp = t_1;
	elseif (z <= -3.7e-296)
		tmp = (z + a) - ((y * b) / (t + (x + y)));
	elseif (z <= 1.05e-260)
		tmp = y * ((a - b) / (x + y));
	elseif (z <= 1.1e-182)
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	elseif (z <= 7.4e-63)
		tmp = (z + a) - b;
	elseif (z <= 1.05e+24)
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+19], t$95$1, If[LessEqual[z, -3.7e-296], N[(N[(z + a), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-260], N[(y * N[(N[(a - b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-182], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e-63], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, 1.05e+24], N[(N[(N[(N[(y * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.2e19 or 1.0500000000000001e24 < z

   1. Initial program 53.1%

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

   2. Taylor expanded in z around inf 43.3%

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

      1. associate-/l* 75.6%

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

      2. +-commutative 75.6%

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

      3. associate-+r+ 75.6%

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

      4. +-commutative 75.6%

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

   4. Simplified 75.6%

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

   if -2.2e19 < z < -3.70000000000000027e-296

   1. Initial program 64.4%

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

   2. Taylor expanded in z around 0 64.5%

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

   3. Taylor expanded in t around inf 70.7%

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

   4. Taylor expanded in x around inf 66.4%

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

   if -3.70000000000000027e-296 < z < 1.05000000000000002e-260

   1. Initial program 39.4%

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

   2. Taylor expanded in z around 0 39.4%

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

   3. Taylor expanded in t around 0 39.0%

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

      1. distribute-rgt-out-- 41.8%

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

      2. +-commutative 41.8%

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

   5. Simplified 41.8%

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

      1. expm1-log1p-u 24.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{y + x}\right)\right)} \]

      2. expm1-udef 2.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{y + x}\right)} - 1} \]

      3. +-commutative 2.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{\color{blue}{x + y}}\right)} - 1 \]

   7. Applied egg-rr 2.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{x + y}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 24.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{x + y}\right)\right)} \]

      2. expm1-log1p 41.8%

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

      3. associate-*r/ 77.6%

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

      4. +-commutative 77.6%

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

   9. Simplified 77.6%

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

   if 1.05000000000000002e-260 < z < 1.1e-182

   1. Initial program 70.5%

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

   2. Taylor expanded in z around 0 64.6%

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

   if 1.1e-182 < z < 7.40000000000000025e-63

   1. Initial program 53.9%

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

   2. Taylor expanded in y around inf 68.5%

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

   if 7.40000000000000025e-63 < z < 1.0500000000000001e24

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0 80.5%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-296}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-182}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-63}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+24}:\\ \;\;\;\;\frac{\left(y \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \end{array} \]

Alternative 4: 60.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-296}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-262}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-63}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* (+ y t) a) (* y b)) (+ y (+ x t))))
        (t_2 (/ z (/ (+ x (+ y t)) (+ x y)))))
   (if (<= z -3.6e+20)
     t_2
     (if (<= z -2.45e-296)
       (- (+ z a) (/ (* y b) (+ t (+ x y))))
       (if (<= z 5.8e-262)
         (* y (/ (- a b) (+ x y)))
         (if (<= z 2.8e-180)
           t_1
           (if (<= z 7.8e-63) (- (+ z a) b) (if (<= z 8.5e+22) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((y + t) * a) - (y * b)) / (y + (x + t));
	double t_2 = z / ((x + (y + t)) / (x + y));
	double tmp;
	if (z <= -3.6e+20) {
		tmp = t_2;
	} else if (z <= -2.45e-296) {
		tmp = (z + a) - ((y * b) / (t + (x + y)));
	} else if (z <= 5.8e-262) {
		tmp = y * ((a - b) / (x + y));
	} else if (z <= 2.8e-180) {
		tmp = t_1;
	} else if (z <= 7.8e-63) {
		tmp = (z + a) - b;
	} else if (z <= 8.5e+22) {
		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 = (((y + t) * a) - (y * b)) / (y + (x + t))
    t_2 = z / ((x + (y + t)) / (x + y))
    if (z <= (-3.6d+20)) then
        tmp = t_2
    else if (z <= (-2.45d-296)) then
        tmp = (z + a) - ((y * b) / (t + (x + y)))
    else if (z <= 5.8d-262) then
        tmp = y * ((a - b) / (x + y))
    else if (z <= 2.8d-180) then
        tmp = t_1
    else if (z <= 7.8d-63) then
        tmp = (z + a) - b
    else if (z <= 8.5d+22) 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 = (((y + t) * a) - (y * b)) / (y + (x + t));
	double t_2 = z / ((x + (y + t)) / (x + y));
	double tmp;
	if (z <= -3.6e+20) {
		tmp = t_2;
	} else if (z <= -2.45e-296) {
		tmp = (z + a) - ((y * b) / (t + (x + y)));
	} else if (z <= 5.8e-262) {
		tmp = y * ((a - b) / (x + y));
	} else if (z <= 2.8e-180) {
		tmp = t_1;
	} else if (z <= 7.8e-63) {
		tmp = (z + a) - b;
	} else if (z <= 8.5e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((y + t) * a) - (y * b)) / (y + (x + t))
	t_2 = z / ((x + (y + t)) / (x + y))
	tmp = 0
	if z <= -3.6e+20:
		tmp = t_2
	elif z <= -2.45e-296:
		tmp = (z + a) - ((y * b) / (t + (x + y)))
	elif z <= 5.8e-262:
		tmp = y * ((a - b) / (x + y))
	elif z <= 2.8e-180:
		tmp = t_1
	elif z <= 7.8e-63:
		tmp = (z + a) - b
	elif z <= 8.5e+22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(z / Float64(Float64(x + Float64(y + t)) / Float64(x + y)))
	tmp = 0.0
	if (z <= -3.6e+20)
		tmp = t_2;
	elseif (z <= -2.45e-296)
		tmp = Float64(Float64(z + a) - Float64(Float64(y * b) / Float64(t + Float64(x + y))));
	elseif (z <= 5.8e-262)
		tmp = Float64(y * Float64(Float64(a - b) / Float64(x + y)));
	elseif (z <= 2.8e-180)
		tmp = t_1;
	elseif (z <= 7.8e-63)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= 8.5e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((y + t) * a) - (y * b)) / (y + (x + t));
	t_2 = z / ((x + (y + t)) / (x + y));
	tmp = 0.0;
	if (z <= -3.6e+20)
		tmp = t_2;
	elseif (z <= -2.45e-296)
		tmp = (z + a) - ((y * b) / (t + (x + y)));
	elseif (z <= 5.8e-262)
		tmp = y * ((a - b) / (x + y));
	elseif (z <= 2.8e-180)
		tmp = t_1;
	elseif (z <= 7.8e-63)
		tmp = (z + a) - b;
	elseif (z <= 8.5e+22)
		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[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+20], t$95$2, If[LessEqual[z, -2.45e-296], N[(N[(z + a), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-262], N[(y * N[(N[(a - b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-180], t$95$1, If[LessEqual[z, 7.8e-63], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, 8.5e+22], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.6e20 or 8.49999999999999979e22 < z

   1. Initial program 53.1%

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

   2. Taylor expanded in z around inf 43.3%

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

      1. associate-/l* 75.6%

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

      2. +-commutative 75.6%

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

      3. associate-+r+ 75.6%

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

      4. +-commutative 75.6%

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

   4. Simplified 75.6%

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

   if -3.6e20 < z < -2.4499999999999999e-296

   1. Initial program 64.4%

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

   2. Taylor expanded in z around 0 64.5%

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

   3. Taylor expanded in t around inf 70.7%

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

   4. Taylor expanded in x around inf 66.4%

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

   if -2.4499999999999999e-296 < z < 5.79999999999999993e-262

   1. Initial program 39.4%

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

   2. Taylor expanded in z around 0 39.4%

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

   3. Taylor expanded in t around 0 39.0%

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

      1. distribute-rgt-out-- 41.8%

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

      2. +-commutative 41.8%

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

   5. Simplified 41.8%

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

      1. expm1-log1p-u 24.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{y + x}\right)\right)} \]

      2. expm1-udef 2.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{y + x}\right)} - 1} \]

      3. +-commutative 2.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{\color{blue}{x + y}}\right)} - 1 \]

   7. Applied egg-rr 2.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{x + y}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 24.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{x + y}\right)\right)} \]

      2. expm1-log1p 41.8%

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

      3. associate-*r/ 77.6%

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

      4. +-commutative 77.6%

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

   9. Simplified 77.6%

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

   if 5.79999999999999993e-262 < z < 2.79999999999999997e-180 or 7.80000000000000044e-63 < z < 8.49999999999999979e22

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0 67.7%

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

   if 2.79999999999999997e-180 < z < 7.80000000000000044e-63

   1. Initial program 56.0%

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

   2. Taylor expanded in y around inf 69.9%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-296}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-262}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-180}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-63}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \end{array} \]

Alternative 5: 69.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_1} - \frac{b}{\frac{t_1}{y}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{\left(y \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (/ z (/ (+ x (+ y t)) (+ x y)))))
   (if (<= z -2.2e+19)
     t_2
     (if (<= z 3.6e-63)
       (- (* (+ y t) (/ a t_1)) (/ b (/ t_1 y)))
       (if (<= z 9.2e+24)
         (/ (- (+ (* y a) (* z (+ x y))) (* y b)) (+ x y))
         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 + t)) / (x + y));
	double tmp;
	if (z <= -2.2e+19) {
		tmp = t_2;
	} else if (z <= 3.6e-63) {
		tmp = ((y + t) * (a / t_1)) - (b / (t_1 / y));
	} else if (z <= 9.2e+24) {
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	} 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 = t + (x + y)
    t_2 = z / ((x + (y + t)) / (x + y))
    if (z <= (-2.2d+19)) then
        tmp = t_2
    else if (z <= 3.6d-63) then
        tmp = ((y + t) * (a / t_1)) - (b / (t_1 / y))
    else if (z <= 9.2d+24) then
        tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y)
    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 = t + (x + y);
	double t_2 = z / ((x + (y + t)) / (x + y));
	double tmp;
	if (z <= -2.2e+19) {
		tmp = t_2;
	} else if (z <= 3.6e-63) {
		tmp = ((y + t) * (a / t_1)) - (b / (t_1 / y));
	} else if (z <= 9.2e+24) {
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	} 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 + t)) / (x + y))
	tmp = 0
	if z <= -2.2e+19:
		tmp = t_2
	elif z <= 3.6e-63:
		tmp = ((y + t) * (a / t_1)) - (b / (t_1 / y))
	elif z <= 9.2e+24:
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y)
	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(z / Float64(Float64(x + Float64(y + t)) / Float64(x + y)))
	tmp = 0.0
	if (z <= -2.2e+19)
		tmp = t_2;
	elseif (z <= 3.6e-63)
		tmp = Float64(Float64(Float64(y + t) * Float64(a / t_1)) - Float64(b / Float64(t_1 / y)));
	elseif (z <= 9.2e+24)
		tmp = Float64(Float64(Float64(Float64(y * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(x + y));
	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 + t)) / (x + y));
	tmp = 0.0;
	if (z <= -2.2e+19)
		tmp = t_2;
	elseif (z <= 3.6e-63)
		tmp = ((y + t) * (a / t_1)) - (b / (t_1 / y));
	elseif (z <= 9.2e+24)
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	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[(z / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+19], t$95$2, If[LessEqual[z, 3.6e-63], N[(N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(b / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+24], N[(N[(N[(N[(y * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e19 or 9.1999999999999996e24 < z

   1. Initial program 53.1%

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

   2. Taylor expanded in z around inf 43.3%

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

      1. associate-/l* 75.6%

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

      2. +-commutative 75.6%

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

      3. associate-+r+ 75.6%

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

      4. +-commutative 75.6%

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

   4. Simplified 75.6%

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

   if -2.2e19 < z < 3.60000000000000008e-63

   1. Initial program 60.7%

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

   2. Taylor expanded in z around 0 50.6%

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

      1. div-sub 50.6%

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

      2. +-commutative 50.6%

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

      3. associate-+r+ 50.6%

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

      4. associate-/l* 68.3%

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

      5. +-commutative 68.3%

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

      6. associate-+l+ 68.3%

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

      7. associate-/r/ 63.8%

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

      8. associate-+l+ 63.8%

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

      9. +-commutative 63.8%

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

      10. associate-+r+ 63.8%

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

      11. associate-/l* 83.4%

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

      12. +-commutative 83.4%

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

   4. Applied egg-rr 83.4%

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

   if 3.60000000000000008e-63 < z < 9.1999999999999996e24

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0 80.5%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t + \left(x + y\right)} - \frac{b}{\frac{t + \left(x + y\right)}{y}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{\left(y \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \end{array} \]

Alternative 6: 59.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z \cdot \frac{x + y}{y + \left(x + t\right)}\\ t_3 := \frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-301}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-184}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (* z (/ (+ x y) (+ y (+ x t)))))
        (t_3 (/ a (/ (+ x (+ y t)) (+ y t)))))
   (if (<= z -2e+20)
     t_2
     (if (<= z -2.7e-161)
       t_1
       (if (<= z -3.8e-301)
         t_3
         (if (<= z 1.9e-260)
           (* y (/ (- a b) (+ x y)))
           (if (<= z 2.9e-184) t_3 (if (<= z 3.1e+45) 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 = z * ((x + y) / (y + (x + t)));
	double t_3 = a / ((x + (y + t)) / (y + t));
	double tmp;
	if (z <= -2e+20) {
		tmp = t_2;
	} else if (z <= -2.7e-161) {
		tmp = t_1;
	} else if (z <= -3.8e-301) {
		tmp = t_3;
	} else if (z <= 1.9e-260) {
		tmp = y * ((a - b) / (x + y));
	} else if (z <= 2.9e-184) {
		tmp = t_3;
	} else if (z <= 3.1e+45) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z * ((x + y) / (y + (x + t)))
    t_3 = a / ((x + (y + t)) / (y + t))
    if (z <= (-2d+20)) then
        tmp = t_2
    else if (z <= (-2.7d-161)) then
        tmp = t_1
    else if (z <= (-3.8d-301)) then
        tmp = t_3
    else if (z <= 1.9d-260) then
        tmp = y * ((a - b) / (x + y))
    else if (z <= 2.9d-184) then
        tmp = t_3
    else if (z <= 3.1d+45) 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 = z * ((x + y) / (y + (x + t)));
	double t_3 = a / ((x + (y + t)) / (y + t));
	double tmp;
	if (z <= -2e+20) {
		tmp = t_2;
	} else if (z <= -2.7e-161) {
		tmp = t_1;
	} else if (z <= -3.8e-301) {
		tmp = t_3;
	} else if (z <= 1.9e-260) {
		tmp = y * ((a - b) / (x + y));
	} else if (z <= 2.9e-184) {
		tmp = t_3;
	} else if (z <= 3.1e+45) {
		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 = z * ((x + y) / (y + (x + t)))
	t_3 = a / ((x + (y + t)) / (y + t))
	tmp = 0
	if z <= -2e+20:
		tmp = t_2
	elif z <= -2.7e-161:
		tmp = t_1
	elif z <= -3.8e-301:
		tmp = t_3
	elif z <= 1.9e-260:
		tmp = y * ((a - b) / (x + y))
	elif z <= 2.9e-184:
		tmp = t_3
	elif z <= 3.1e+45:
		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(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))))
	t_3 = Float64(a / Float64(Float64(x + Float64(y + t)) / Float64(y + t)))
	tmp = 0.0
	if (z <= -2e+20)
		tmp = t_2;
	elseif (z <= -2.7e-161)
		tmp = t_1;
	elseif (z <= -3.8e-301)
		tmp = t_3;
	elseif (z <= 1.9e-260)
		tmp = Float64(y * Float64(Float64(a - b) / Float64(x + y)));
	elseif (z <= 2.9e-184)
		tmp = t_3;
	elseif (z <= 3.1e+45)
		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 = z * ((x + y) / (y + (x + t)));
	t_3 = a / ((x + (y + t)) / (y + t));
	tmp = 0.0;
	if (z <= -2e+20)
		tmp = t_2;
	elseif (z <= -2.7e-161)
		tmp = t_1;
	elseif (z <= -3.8e-301)
		tmp = t_3;
	elseif (z <= 1.9e-260)
		tmp = y * ((a - b) / (x + y));
	elseif (z <= 2.9e-184)
		tmp = t_3;
	elseif (z <= 3.1e+45)
		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[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+20], t$95$2, If[LessEqual[z, -2.7e-161], t$95$1, If[LessEqual[z, -3.8e-301], t$95$3, If[LessEqual[z, 1.9e-260], N[(y * N[(N[(a - b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-184], t$95$3, If[LessEqual[z, 3.1e+45], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2e20 or 3.09999999999999988e45 < z

   1. Initial program 53.6%

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

   2. Taylor expanded in z around inf 43.4%

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

      1. associate-/l* 76.2%

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

      2. +-commutative 76.2%

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

      3. associate-+r+ 76.2%

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

      4. +-commutative 76.2%

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

   4. Simplified 76.2%

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

   5. Taylor expanded in z around 0 43.4%

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

      1. associate-+r+ 43.4%

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

      2. +-commutative 43.4%

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

      3. associate-+r+ 43.4%

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

      4. *-lft-identity 43.4%

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

      5. times-frac 76.2%

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

      6. /-rgt-identity 76.2%

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

      7. +-commutative 76.2%

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

      8. +-commutative 76.2%

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

      9. +-commutative 76.2%

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

      10. associate-+l+ 76.2%

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

   7. Simplified 76.2%

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

   if -2e20 < z < -2.6999999999999999e-161 or 2.90000000000000014e-184 < z < 3.09999999999999988e45

   1. Initial program 68.0%

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

   2. Taylor expanded in y around inf 63.7%

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

   if -2.6999999999999999e-161 < z < -3.79999999999999996e-301 or 1.9000000000000002e-260 < z < 2.90000000000000014e-184

   1. Initial program 64.3%

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

   2. Taylor expanded in a around inf 39.4%

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

      1. associate-/l* 65.5%

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

      2. +-commutative 65.5%

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

      3. associate-+r+ 65.5%

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

   4. Simplified 65.5%

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

   if -3.79999999999999996e-301 < z < 1.9000000000000002e-260

   1. Initial program 42.4%

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

   2. Taylor expanded in z around 0 42.4%

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

   3. Taylor expanded in t around 0 42.0%

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

      1. distribute-rgt-out-- 45.1%

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

      2. +-commutative 45.1%

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

   5. Simplified 45.1%

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

      1. expm1-log1p-u 25.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{y + x}\right)\right)} \]

      2. expm1-udef 2.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{y + x}\right)} - 1} \]

      3. +-commutative 2.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{\color{blue}{x + y}}\right)} - 1 \]

   7. Applied egg-rr 2.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{x + y}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 25.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{x + y}\right)\right)} \]

      2. expm1-log1p 45.1%

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

      3. associate-*r/ 83.8%

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

      4. +-commutative 83.8%

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

   9. Simplified 83.8%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-161}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-184}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+45}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 7: 59.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := x + \left(y + t\right)\\ t_3 := \frac{z}{\frac{t_2}{x + y}}\\ t_4 := \frac{a}{\frac{t_2}{y + t}}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-300}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-183}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ x (+ y t)))
        (t_3 (/ z (/ t_2 (+ x y))))
        (t_4 (/ a (/ t_2 (+ y t)))))
   (if (<= z -1.35e+20)
     t_3
     (if (<= z -2e-161)
       t_1
       (if (<= z -1.1e-300)
         t_4
         (if (<= z 9.5e-261)
           (* y (/ (- a b) (+ x y)))
           (if (<= z 2.2e-183) t_4 (if (<= z 4.2e+52) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = x + (y + t);
	double t_3 = z / (t_2 / (x + y));
	double t_4 = a / (t_2 / (y + t));
	double tmp;
	if (z <= -1.35e+20) {
		tmp = t_3;
	} else if (z <= -2e-161) {
		tmp = t_1;
	} else if (z <= -1.1e-300) {
		tmp = t_4;
	} else if (z <= 9.5e-261) {
		tmp = y * ((a - b) / (x + y));
	} else if (z <= 2.2e-183) {
		tmp = t_4;
	} else if (z <= 4.2e+52) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = x + (y + t)
    t_3 = z / (t_2 / (x + y))
    t_4 = a / (t_2 / (y + t))
    if (z <= (-1.35d+20)) then
        tmp = t_3
    else if (z <= (-2d-161)) then
        tmp = t_1
    else if (z <= (-1.1d-300)) then
        tmp = t_4
    else if (z <= 9.5d-261) then
        tmp = y * ((a - b) / (x + y))
    else if (z <= 2.2d-183) then
        tmp = t_4
    else if (z <= 4.2d+52) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = x + (y + t);
	double t_3 = z / (t_2 / (x + y));
	double t_4 = a / (t_2 / (y + t));
	double tmp;
	if (z <= -1.35e+20) {
		tmp = t_3;
	} else if (z <= -2e-161) {
		tmp = t_1;
	} else if (z <= -1.1e-300) {
		tmp = t_4;
	} else if (z <= 9.5e-261) {
		tmp = y * ((a - b) / (x + y));
	} else if (z <= 2.2e-183) {
		tmp = t_4;
	} else if (z <= 4.2e+52) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = x + (y + t)
	t_3 = z / (t_2 / (x + y))
	t_4 = a / (t_2 / (y + t))
	tmp = 0
	if z <= -1.35e+20:
		tmp = t_3
	elif z <= -2e-161:
		tmp = t_1
	elif z <= -1.1e-300:
		tmp = t_4
	elif z <= 9.5e-261:
		tmp = y * ((a - b) / (x + y))
	elif z <= 2.2e-183:
		tmp = t_4
	elif z <= 4.2e+52:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(z / Float64(t_2 / Float64(x + y)))
	t_4 = Float64(a / Float64(t_2 / Float64(y + t)))
	tmp = 0.0
	if (z <= -1.35e+20)
		tmp = t_3;
	elseif (z <= -2e-161)
		tmp = t_1;
	elseif (z <= -1.1e-300)
		tmp = t_4;
	elseif (z <= 9.5e-261)
		tmp = Float64(y * Float64(Float64(a - b) / Float64(x + y)));
	elseif (z <= 2.2e-183)
		tmp = t_4;
	elseif (z <= 4.2e+52)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = x + (y + t);
	t_3 = z / (t_2 / (x + y));
	t_4 = a / (t_2 / (y + t));
	tmp = 0.0;
	if (z <= -1.35e+20)
		tmp = t_3;
	elseif (z <= -2e-161)
		tmp = t_1;
	elseif (z <= -1.1e-300)
		tmp = t_4;
	elseif (z <= 9.5e-261)
		tmp = y * ((a - b) / (x + y));
	elseif (z <= 2.2e-183)
		tmp = t_4;
	elseif (z <= 4.2e+52)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / N[(t$95$2 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+20], t$95$3, If[LessEqual[z, -2e-161], t$95$1, If[LessEqual[z, -1.1e-300], t$95$4, If[LessEqual[z, 9.5e-261], N[(y * N[(N[(a - b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-183], t$95$4, If[LessEqual[z, 4.2e+52], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35e20 or 4.2e52 < z

   1. Initial program 53.6%

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

   2. Taylor expanded in z around inf 43.4%

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

      1. associate-/l* 76.2%

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

      2. +-commutative 76.2%

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

      3. associate-+r+ 76.2%

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

      4. +-commutative 76.2%

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

   4. Simplified 76.2%

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

   if -1.35e20 < z < -2.00000000000000006e-161 or 2.2e-183 < z < 4.2e52

   1. Initial program 68.0%

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

   2. Taylor expanded in y around inf 63.7%

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

   if -2.00000000000000006e-161 < z < -1.10000000000000001e-300 or 9.5000000000000008e-261 < z < 2.2e-183

   1. Initial program 64.3%

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

   2. Taylor expanded in a around inf 39.4%

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

      1. associate-/l* 65.5%

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

      2. +-commutative 65.5%

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

      3. associate-+r+ 65.5%

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

   4. Simplified 65.5%

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

   if -1.10000000000000001e-300 < z < 9.5000000000000008e-261

   1. Initial program 42.4%

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

   2. Taylor expanded in z around 0 42.4%

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

   3. Taylor expanded in t around 0 42.0%

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

      1. distribute-rgt-out-- 45.1%

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

      2. +-commutative 45.1%

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

   5. Simplified 45.1%

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

      1. expm1-log1p-u 25.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{y + x}\right)\right)} \]

      2. expm1-udef 2.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{y + x}\right)} - 1} \]

      3. +-commutative 2.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{\color{blue}{x + y}}\right)} - 1 \]

   7. Applied egg-rr 2.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{x + y}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 25.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{x + y}\right)\right)} \]

      2. expm1-log1p 45.1%

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

      3. associate-*r/ 83.8%

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

      4. +-commutative 83.8%

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

   9. Simplified 83.8%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-300}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+52}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \end{array} \]

Alternative 8: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ t_2 := x + \left(y + t\right)\\ t_3 := \frac{z}{\frac{t_2}{x + y}}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-63}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{a}{\frac{t_2}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) (/ (* y b) (+ t (+ x y)))))
        (t_2 (+ x (+ y t)))
        (t_3 (/ z (/ t_2 (+ x y)))))
   (if (<= z -2e+20)
     t_3
     (if (<= z -2.55e-297)
       t_1
       (if (<= z 2e-270)
         (* y (/ (- a b) (+ x y)))
         (if (<= z 1.1e-181)
           t_1
           (if (<= z 7.8e-63)
             (- (+ z a) b)
             (if (<= z 1.7e+18) (/ a (/ t_2 (+ y t))) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - ((y * b) / (t + (x + y)));
	double t_2 = x + (y + t);
	double t_3 = z / (t_2 / (x + y));
	double tmp;
	if (z <= -2e+20) {
		tmp = t_3;
	} else if (z <= -2.55e-297) {
		tmp = t_1;
	} else if (z <= 2e-270) {
		tmp = y * ((a - b) / (x + y));
	} else if (z <= 1.1e-181) {
		tmp = t_1;
	} else if (z <= 7.8e-63) {
		tmp = (z + a) - b;
	} else if (z <= 1.7e+18) {
		tmp = a / (t_2 / (y + t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z + a) - ((y * b) / (t + (x + y)))
    t_2 = x + (y + t)
    t_3 = z / (t_2 / (x + y))
    if (z <= (-2d+20)) then
        tmp = t_3
    else if (z <= (-2.55d-297)) then
        tmp = t_1
    else if (z <= 2d-270) then
        tmp = y * ((a - b) / (x + y))
    else if (z <= 1.1d-181) then
        tmp = t_1
    else if (z <= 7.8d-63) then
        tmp = (z + a) - b
    else if (z <= 1.7d+18) then
        tmp = a / (t_2 / (y + t))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - ((y * b) / (t + (x + y)));
	double t_2 = x + (y + t);
	double t_3 = z / (t_2 / (x + y));
	double tmp;
	if (z <= -2e+20) {
		tmp = t_3;
	} else if (z <= -2.55e-297) {
		tmp = t_1;
	} else if (z <= 2e-270) {
		tmp = y * ((a - b) / (x + y));
	} else if (z <= 1.1e-181) {
		tmp = t_1;
	} else if (z <= 7.8e-63) {
		tmp = (z + a) - b;
	} else if (z <= 1.7e+18) {
		tmp = a / (t_2 / (y + t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - ((y * b) / (t + (x + y)))
	t_2 = x + (y + t)
	t_3 = z / (t_2 / (x + y))
	tmp = 0
	if z <= -2e+20:
		tmp = t_3
	elif z <= -2.55e-297:
		tmp = t_1
	elif z <= 2e-270:
		tmp = y * ((a - b) / (x + y))
	elif z <= 1.1e-181:
		tmp = t_1
	elif z <= 7.8e-63:
		tmp = (z + a) - b
	elif z <= 1.7e+18:
		tmp = a / (t_2 / (y + t))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - Float64(Float64(y * b) / Float64(t + Float64(x + y))))
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(z / Float64(t_2 / Float64(x + y)))
	tmp = 0.0
	if (z <= -2e+20)
		tmp = t_3;
	elseif (z <= -2.55e-297)
		tmp = t_1;
	elseif (z <= 2e-270)
		tmp = Float64(y * Float64(Float64(a - b) / Float64(x + y)));
	elseif (z <= 1.1e-181)
		tmp = t_1;
	elseif (z <= 7.8e-63)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= 1.7e+18)
		tmp = Float64(a / Float64(t_2 / Float64(y + t)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - ((y * b) / (t + (x + y)));
	t_2 = x + (y + t);
	t_3 = z / (t_2 / (x + y));
	tmp = 0.0;
	if (z <= -2e+20)
		tmp = t_3;
	elseif (z <= -2.55e-297)
		tmp = t_1;
	elseif (z <= 2e-270)
		tmp = y * ((a - b) / (x + y));
	elseif (z <= 1.1e-181)
		tmp = t_1;
	elseif (z <= 7.8e-63)
		tmp = (z + a) - b;
	elseif (z <= 1.7e+18)
		tmp = a / (t_2 / (y + t));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / N[(t$95$2 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+20], t$95$3, If[LessEqual[z, -2.55e-297], t$95$1, If[LessEqual[z, 2e-270], N[(y * N[(N[(a - b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-181], t$95$1, If[LessEqual[z, 7.8e-63], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, 1.7e+18], N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2e20 or 1.7e18 < z

   1. Initial program 53.9%

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

   2. Taylor expanded in z around inf 43.4%

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

      1. associate-/l* 75.2%

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

      2. +-commutative 75.2%

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

      3. associate-+r+ 75.2%

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

      4. +-commutative 75.2%

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

   4. Simplified 75.2%

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

   if -2e20 < z < -2.55000000000000004e-297 or 2.0000000000000001e-270 < z < 1.09999999999999999e-181

   1. Initial program 66.0%

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

   2. Taylor expanded in z around 0 66.0%

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

   3. Taylor expanded in t around inf 70.8%

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

   4. Taylor expanded in x around inf 66.2%

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

   if -2.55000000000000004e-297 < z < 2.0000000000000001e-270

   1. Initial program 23.6%

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

   2. Taylor expanded in z around 0 23.6%

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

   3. Taylor expanded in t around 0 23.0%

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

      1. distribute-rgt-out-- 26.3%

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

      2. +-commutative 26.3%

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

   5. Simplified 26.3%

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

      1. expm1-log1p-u 12.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{y + x}\right)\right)} \]

      2. expm1-udef 2.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{y + x}\right)} - 1} \]

      3. +-commutative 2.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{\color{blue}{x + y}}\right)} - 1 \]

   7. Applied egg-rr 2.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{x + y}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 12.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - b\right)}{x + y}\right)\right)} \]

      2. expm1-log1p 26.3%

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

      3. associate-*r/ 78.1%

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

      4. +-commutative 78.1%

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

   9. Simplified 78.1%

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

   if 1.09999999999999999e-181 < z < 7.80000000000000044e-63

   1. Initial program 56.0%

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

   2. Taylor expanded in y around inf 69.9%

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

   if 7.80000000000000044e-63 < z < 1.7e18

   1. Initial program 99.5%

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

   2. Taylor expanded in a around inf 66.2%

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

      1. associate-/l* 66.4%

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

      2. +-commutative 66.4%

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

      3. associate-+r+ 66.4%

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

   4. Simplified 66.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-297}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-181}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-63}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \end{array} \]

Alternative 9: 56.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x + y}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-117}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ (+ x y) (+ y (+ x t))))) (t_2 (- (+ z a) b)))
   (if (<= y -2.7e+18)
     t_2
     (if (<= y -6.7e-116)
       t_1
       (if (<= y 1.1e-117)
         (/ a (+ 1.0 (/ x t)))
         (if (<= y 3.1e+28) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((x + y) / (y + (x + t)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2.7e+18) {
		tmp = t_2;
	} else if (y <= -6.7e-116) {
		tmp = t_1;
	} else if (y <= 1.1e-117) {
		tmp = a / (1.0 + (x / t));
	} else if (y <= 3.1e+28) {
		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 * ((x + y) / (y + (x + t)))
    t_2 = (z + a) - b
    if (y <= (-2.7d+18)) then
        tmp = t_2
    else if (y <= (-6.7d-116)) then
        tmp = t_1
    else if (y <= 1.1d-117) then
        tmp = a / (1.0d0 + (x / t))
    else if (y <= 3.1d+28) 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 * ((x + y) / (y + (x + t)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2.7e+18) {
		tmp = t_2;
	} else if (y <= -6.7e-116) {
		tmp = t_1;
	} else if (y <= 1.1e-117) {
		tmp = a / (1.0 + (x / t));
	} else if (y <= 3.1e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * ((x + y) / (y + (x + t)))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -2.7e+18:
		tmp = t_2
	elif y <= -6.7e-116:
		tmp = t_1
	elif y <= 1.1e-117:
		tmp = a / (1.0 + (x / t))
	elif y <= 3.1e+28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.7e+18)
		tmp = t_2;
	elseif (y <= -6.7e-116)
		tmp = t_1;
	elseif (y <= 1.1e-117)
		tmp = Float64(a / Float64(1.0 + Float64(x / t)));
	elseif (y <= 3.1e+28)
		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 * ((x + y) / (y + (x + t)));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.7e+18)
		tmp = t_2;
	elseif (y <= -6.7e-116)
		tmp = t_1;
	elseif (y <= 1.1e-117)
		tmp = a / (1.0 + (x / t));
	elseif (y <= 3.1e+28)
		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[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.7e+18], t$95$2, If[LessEqual[y, -6.7e-116], t$95$1, If[LessEqual[y, 1.1e-117], N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e18 or 3.1000000000000001e28 < y

   1. Initial program 33.7%

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

   2. Taylor expanded in y around inf 76.1%

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

   if -2.7e18 < y < -6.69999999999999993e-116 or 1.1000000000000001e-117 < y < 3.1000000000000001e28

   1. Initial program 81.6%

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

   2. Taylor expanded in z around inf 55.4%

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

      1. associate-/l* 70.3%

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

      2. +-commutative 70.3%

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

      3. associate-+r+ 70.3%

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

      4. +-commutative 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in z around 0 55.4%

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

      1. associate-+r+ 55.4%

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

      2. +-commutative 55.4%

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

      3. associate-+r+ 55.4%

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

      4. *-lft-identity 55.4%

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

      5. times-frac 70.3%

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

      6. /-rgt-identity 70.3%

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

      7. +-commutative 70.3%

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

      8. +-commutative 70.3%

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

      9. +-commutative 70.3%

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

      10. associate-+l+ 70.3%

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

   7. Simplified 70.3%

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

   if -6.69999999999999993e-116 < y < 1.1000000000000001e-117

   1. Initial program 84.7%

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

   2. Taylor expanded in a around inf 44.7%

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

      1. associate-/l* 56.0%

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

      2. +-commutative 56.0%

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

      3. associate-+r+ 56.0%

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

   4. Simplified 56.0%

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

   5. Taylor expanded in t around inf 53.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+18}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-117}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 60.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+160} \lor \neg \left(x \leq 6.2 \cdot 10^{+157}\right):\\ \;\;\;\;z - \frac{y}{\frac{x}{b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -2.15e+160) (not (<= x 6.2e+157)))
   (- z (/ y (/ x b)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.15e+160) || !(x <= 6.2e+157)) {
		tmp = z - (y / (x / b));
	} 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 <= (-2.15d+160)) .or. (.not. (x <= 6.2d+157))) then
        tmp = z - (y / (x / b))
    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 <= -2.15e+160) || !(x <= 6.2e+157)) {
		tmp = z - (y / (x / b));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -2.15e+160) or not (x <= 6.2e+157):
		tmp = z - (y / (x / b))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -2.15e+160) || !(x <= 6.2e+157))
		tmp = Float64(z - Float64(y / Float64(x / b)));
	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 <= -2.15e+160) || ~((x <= 6.2e+157)))
		tmp = z - (y / (x / b));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -2.15e+160], N[Not[LessEqual[x, 6.2e+157]], $MachinePrecision]], N[(z - N[(y / N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.14999999999999994e160 or 6.1999999999999994e157 < x

   1. Initial program 47.1%

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

   2. Taylor expanded in x around inf 54.7%

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

      1. associate--l+ 54.7%

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

      2. associate-/l* 59.3%

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

      3. associate-/l* 61.9%

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

      4. associate-/l* 62.4%

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

   4. Simplified 62.4%

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

   5. Taylor expanded in b around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. *-commutative 57.4%

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

   7. Simplified 57.4%

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

      1. unsub-neg 57.4%

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

      2. associate-/l* 66.0%

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

   9. Applied egg-rr 66.0%

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

   if -2.14999999999999994e160 < x < 6.1999999999999994e157

   1. Initial program 63.3%

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

   2. Taylor expanded in y around inf 61.4%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+160} \lor \neg \left(x \leq 6.2 \cdot 10^{+157}\right):\\ \;\;\;\;z - \frac{y}{\frac{x}{b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 56.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+163}:\\ \;\;\;\;z + z \cdot \frac{t}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.5e+163) (+ z (* z (/ t x))) (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+163) {
		tmp = z + (z * (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 <= (-2.5d+163)) then
        tmp = z + (z * (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 <= -2.5e+163) {
		tmp = z + (z * (t / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.5e+163:
		tmp = z + (z * (t / x))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.5e+163)
		tmp = Float64(z + Float64(z * Float64(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 <= -2.5e+163)
		tmp = z + (z * (t / x));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.5e+163], N[(z + N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5e163

   1. Initial program 48.1%

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

   2. Taylor expanded in x around inf 60.6%

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

      1. associate--l+ 60.6%

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

      2. associate-/l* 66.5%

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

      3. associate-/l* 65.2%

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

      4. associate-/l* 65.9%

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

   4. Simplified 65.9%

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

   5. Taylor expanded in z around inf 53.2%

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

      1. expm1-log1p-u 38.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(z + -1 \cdot \frac{t \cdot z}{x}\right)\right)} \]

      2. expm1-udef 27.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(z + -1 \cdot \frac{t \cdot z}{x}\right)} - 1} \]

   7. Applied egg-rr 29.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(z + \frac{z}{\frac{x}{t}}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 41.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(z + \frac{z}{\frac{x}{t}}\right)\right)} \]

      2. expm1-log1p 56.3%

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

      3. associate-/l* 53.3%

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

      4. associate-*r/ 56.3%

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

      5. *-commutative 56.3%

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

      6. *-commutative 56.3%

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

   9. Simplified 56.3%

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

   if -2.5e163 < x

   1. Initial program 61.0%

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

   2. Taylor expanded in y around inf 59.3%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+163}:\\ \;\;\;\;z + z \cdot \frac{t}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 12: 48.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 760000000000:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.35e+20) z (if (<= z 760000000000.0) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.35e+20) {
		tmp = z;
	} else if (z <= 760000000000.0) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.35d+20)) then
        tmp = z
    else if (z <= 760000000000.0d0) then
        tmp = a - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.35e+20) {
		tmp = z;
	} else if (z <= 760000000000.0) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.35e+20:
		tmp = z
	elif z <= 760000000000.0:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.35e+20)
		tmp = z;
	elseif (z <= 760000000000.0)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.35e+20)
		tmp = z;
	elseif (z <= 760000000000.0)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.35e+20], z, If[LessEqual[z, 760000000000.0], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e20 or 7.6e11 < z

   1. Initial program 53.9%

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

   2. Taylor expanded in x around inf 56.1%

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

   if -1.35e20 < z < 7.6e11

   1. Initial program 64.5%

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

   2. Taylor expanded in z around 0 52.4%

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

   3. Taylor expanded in y around inf 50.7%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 760000000000:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 13: 56.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+164}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.55e+164) z (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.55e+164) {
		tmp = z;
	} 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 <= (-1.55d+164)) then
        tmp = z
    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 <= -1.55e+164) {
		tmp = z;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.55e+164:
		tmp = z
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.55e+164)
		tmp = z;
	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 <= -1.55e+164)
		tmp = z;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.55e+164], z, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5500000000000001e164

   1. Initial program 48.1%

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

   2. Taylor expanded in x around inf 56.1%

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

   if -1.5500000000000001e164 < x

   1. Initial program 61.0%

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

   2. Taylor expanded in y around inf 59.3%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+164}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 14: 45.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+18}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.35e+20) z (if (<= z 2.9e+18) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.35e+20) {
		tmp = z;
	} else if (z <= 2.9e+18) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.35d+20)) then
        tmp = z
    else if (z <= 2.9d+18) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.35e+20) {
		tmp = z;
	} else if (z <= 2.9e+18) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.35e+20:
		tmp = z
	elif z <= 2.9e+18:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.35e+20)
		tmp = z;
	elseif (z <= 2.9e+18)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.35e+20)
		tmp = z;
	elseif (z <= 2.9e+18)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.35e+20], z, If[LessEqual[z, 2.9e+18], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e20 or 2.9e18 < z

   1. Initial program 53.9%

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

   2. Taylor expanded in x around inf 56.1%

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

   if -1.35e20 < z < 2.9e18

   1. Initial program 64.5%

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

   2. Taylor expanded in t around inf 44.0%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+18}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 15: 32.5% 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 59.3%

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

2. Taylor expanded in t around inf 32.2%

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

3. Final simplification 32.2%

   \[\leadsto a \]

Developer target: 82.0% 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 2023290 
(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)))