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

Percentage Accurate: 60.4% → 94.4%

Time: 12.5s

Alternatives: 13

Speedup: 1.9×

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: 60.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) \cdot a\\ t_2 := \left(x + y\right) + t\\ t_3 := \frac{y}{t_2}\\ t_4 := \frac{\left(\left(x + y\right) \cdot z + t_1\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_4 \leq -1 \cdot 10^{+304} \lor \neg \left(t_4 \leq 5 \cdot 10^{+268}\right):\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{t_2} + t_3\right)\right) - \frac{b}{\frac{x + y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(t_3 + \frac{x}{t_2}\right) + \frac{t_1}{t_2}\right) - \frac{y \cdot b}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y t) a))
        (t_2 (+ (+ x y) t))
        (t_3 (/ y t_2))
        (t_4 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_4 -1e+304) (not (<= t_4 5e+268)))
     (- (+ z (* a (+ (/ t t_2) t_3))) (/ b (/ (+ x y) y)))
     (- (+ (* z (+ t_3 (/ x t_2))) (/ t_1 t_2)) (/ (* y b) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * a;
	double t_2 = (x + y) + t;
	double t_3 = y / t_2;
	double t_4 = ((((x + y) * z) + t_1) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_4 <= -1e+304) || !(t_4 <= 5e+268)) {
		tmp = (z + (a * ((t / t_2) + t_3))) - (b / ((x + y) / y));
	} else {
		tmp = ((z * (t_3 + (x / t_2))) + (t_1 / t_2)) - ((y * b) / t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (y + t) * a
    t_2 = (x + y) + t
    t_3 = y / t_2
    t_4 = ((((x + y) * z) + t_1) - (y * b)) / (y + (x + t))
    if ((t_4 <= (-1d+304)) .or. (.not. (t_4 <= 5d+268))) then
        tmp = (z + (a * ((t / t_2) + t_3))) - (b / ((x + y) / y))
    else
        tmp = ((z * (t_3 + (x / t_2))) + (t_1 / t_2)) - ((y * b) / t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * a;
	double t_2 = (x + y) + t;
	double t_3 = y / t_2;
	double t_4 = ((((x + y) * z) + t_1) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_4 <= -1e+304) || !(t_4 <= 5e+268)) {
		tmp = (z + (a * ((t / t_2) + t_3))) - (b / ((x + y) / y));
	} else {
		tmp = ((z * (t_3 + (x / t_2))) + (t_1 / t_2)) - ((y * b) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + t) * a
	t_2 = (x + y) + t
	t_3 = y / t_2
	t_4 = ((((x + y) * z) + t_1) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_4 <= -1e+304) or not (t_4 <= 5e+268):
		tmp = (z + (a * ((t / t_2) + t_3))) - (b / ((x + y) / y))
	else:
		tmp = ((z * (t_3 + (x / t_2))) + (t_1 / t_2)) - ((y * b) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) * a)
	t_2 = Float64(Float64(x + y) + t)
	t_3 = Float64(y / t_2)
	t_4 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_4 <= -1e+304) || !(t_4 <= 5e+268))
		tmp = Float64(Float64(z + Float64(a * Float64(Float64(t / t_2) + t_3))) - Float64(b / Float64(Float64(x + y) / y)));
	else
		tmp = Float64(Float64(Float64(z * Float64(t_3 + Float64(x / t_2))) + Float64(t_1 / t_2)) - Float64(Float64(y * b) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + t) * a;
	t_2 = (x + y) + t;
	t_3 = y / t_2;
	t_4 = ((((x + y) * z) + t_1) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_4 <= -1e+304) || ~((t_4 <= 5e+268)))
		tmp = (z + (a * ((t / t_2) + t_3))) - (b / ((x + y) / y));
	else
		tmp = ((z * (t_3 + (x / t_2))) + (t_1 / t_2)) - ((y * b) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$4, -1e+304], N[Not[LessEqual[t$95$4, 5e+268]], $MachinePrecision]], N[(N[(z + N[(a * N[(N[(t / t$95$2), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t$95$3 + N[(x / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.9999999999999994e303 or 5.0000000000000002e268 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.7%

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

   2. Taylor expanded in a around 0 39.8%

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

   3. Taylor expanded in x around inf 65.8%

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

   4. Taylor expanded in t around 0 64.9%

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

      1. associate-/l* 87.3%

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

      2. +-commutative 87.3%

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

   6. Simplified 87.3%

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

   if -9.9999999999999994e303 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000002e268

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 99.1%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+304} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+268}\right):\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{\left(x + y\right) + t} + \frac{y}{\left(x + y\right) + t}\right)\right) - \frac{b}{\frac{x + y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\frac{y}{\left(x + y\right) + t} + \frac{x}{\left(x + y\right) + t}\right) + \frac{\left(y + t\right) \cdot a}{\left(x + y\right) + t}\right) - \frac{y \cdot b}{\left(x + y\right) + t}\\ \end{array} \]

Alternative 2: 94.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+304} \lor \neg \left(t_2 \leq 5 \cdot 10^{+268}\right):\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{t_1} + \frac{y}{t_1}\right)\right) - \frac{b}{\frac{x + y}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_2 -1e+304) (not (<= t_2 5e+268)))
     (- (+ z (* a (+ (/ t t_1) (/ y t_1)))) (/ b (/ (+ x y) y)))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -1e+304) || !(t_2 <= 5e+268)) {
		tmp = (z + (a * ((t / t_1) + (y / t_1)))) - (b / ((x + y) / 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 = (x + y) + t
    t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t))
    if ((t_2 <= (-1d+304)) .or. (.not. (t_2 <= 5d+268))) then
        tmp = (z + (a * ((t / t_1) + (y / t_1)))) - (b / ((x + y) / 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 = (x + y) + t;
	double t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -1e+304) || !(t_2 <= 5e+268)) {
		tmp = (z + (a * ((t / t_1) + (y / t_1)))) - (b / ((x + y) / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + t
	t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_2 <= -1e+304) or not (t_2 <= 5e+268):
		tmp = (z + (a * ((t / t_1) + (y / t_1)))) - (b / ((x + y) / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_2 <= -1e+304) || !(t_2 <= 5e+268))
		tmp = Float64(Float64(z + Float64(a * Float64(Float64(t / t_1) + Float64(y / t_1)))) - Float64(b / Float64(Float64(x + y) / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + t;
	t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_2 <= -1e+304) || ~((t_2 <= 5e+268)))
		tmp = (z + (a * ((t / t_1) + (y / t_1)))) - (b / ((x + y) / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -1e+304], N[Not[LessEqual[t$95$2, 5e+268]], $MachinePrecision]], N[(N[(z + N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.9999999999999994e303 or 5.0000000000000002e268 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.7%

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

   2. Taylor expanded in a around 0 39.8%

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

   3. Taylor expanded in x around inf 65.8%

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

   4. Taylor expanded in t around 0 64.9%

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

      1. associate-/l* 87.3%

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

      2. +-commutative 87.3%

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

   6. Simplified 87.3%

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

   if -9.9999999999999994e303 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000002e268

   1. Initial program 99.0%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+304} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+268}\right):\\ \;\;\;\;\left(z + a \cdot \left(\frac{t}{\left(x + y\right) + t} + \frac{y}{\left(x + y\right) + t}\right)\right) - \frac{b}{\frac{x + y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 3: 89.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+304}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+268}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - \frac{b}{\frac{x + y}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) (+ y (+ x t)))))
   (if (<= t_1 -1e+304)
     (- (+ z a) b)
     (if (<= t_1 5e+268) t_1 (- (+ z a) (/ b (/ (+ x y) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_1 <= -1e+304) {
		tmp = (z + a) - b;
	} else if (t_1 <= 5e+268) {
		tmp = t_1;
	} else {
		tmp = (z + a) - (b / ((x + y) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t))
    if (t_1 <= (-1d+304)) then
        tmp = (z + a) - b
    else if (t_1 <= 5d+268) then
        tmp = t_1
    else
        tmp = (z + a) - (b / ((x + y) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_1 <= -1e+304) {
		tmp = (z + a) - b;
	} else if (t_1 <= 5e+268) {
		tmp = t_1;
	} else {
		tmp = (z + a) - (b / ((x + y) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t))
	tmp = 0
	if t_1 <= -1e+304:
		tmp = (z + a) - b
	elif t_1 <= 5e+268:
		tmp = t_1
	else:
		tmp = (z + a) - (b / ((x + y) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if (t_1 <= -1e+304)
		tmp = Float64(Float64(z + a) - b);
	elseif (t_1 <= 5e+268)
		tmp = t_1;
	else
		tmp = Float64(Float64(z + a) - Float64(b / Float64(Float64(x + y) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if (t_1 <= -1e+304)
		tmp = (z + a) - b;
	elseif (t_1 <= 5e+268)
		tmp = t_1;
	else
		tmp = (z + a) - (b / ((x + y) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+304], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$1, 5e+268], t$95$1, N[(N[(z + a), $MachinePrecision] - N[(b / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.9999999999999994e303

   1. Initial program 8.5%

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

   2. Taylor expanded in y around inf 85.4%

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

   if -9.9999999999999994e303 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000002e268

   1. Initial program 99.0%

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

   if 5.0000000000000002e268 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.9%

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

   2. Taylor expanded in a around 0 33.1%

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

   3. Taylor expanded in x around inf 61.2%

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

   4. Taylor expanded in t around 0 60.0%

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

      1. associate-/l* 88.2%

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

      2. +-commutative 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in t around inf 79.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+304}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - \frac{b}{\frac{x + y}{y}}\\ \end{array} \]

Alternative 4: 56.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-89}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+118}:\\ \;\;\;\;\frac{z}{\frac{t}{x + y} + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ (+ y t) (+ y (+ x t))))))
   (if (<= t -2.5e+106)
     t_1
     (if (<= t 4.8e-89)
       (- (+ z a) b)
       (if (<= t 2.1e+118) (/ z (+ (/ t (+ x y)) 1.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * ((y + t) / (y + (x + t)));
	double tmp;
	if (t <= -2.5e+106) {
		tmp = t_1;
	} else if (t <= 4.8e-89) {
		tmp = (z + a) - b;
	} else if (t <= 2.1e+118) {
		tmp = z / ((t / (x + y)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((y + t) / (y + (x + t)))
    if (t <= (-2.5d+106)) then
        tmp = t_1
    else if (t <= 4.8d-89) then
        tmp = (z + a) - b
    else if (t <= 2.1d+118) then
        tmp = z / ((t / (x + y)) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * ((y + t) / (y + (x + t)));
	double tmp;
	if (t <= -2.5e+106) {
		tmp = t_1;
	} else if (t <= 4.8e-89) {
		tmp = (z + a) - b;
	} else if (t <= 2.1e+118) {
		tmp = z / ((t / (x + y)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * ((y + t) / (y + (x + t)))
	tmp = 0
	if t <= -2.5e+106:
		tmp = t_1
	elif t <= 4.8e-89:
		tmp = (z + a) - b
	elif t <= 2.1e+118:
		tmp = z / ((t / (x + y)) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (t <= -2.5e+106)
		tmp = t_1;
	elseif (t <= 4.8e-89)
		tmp = Float64(Float64(z + a) - b);
	elseif (t <= 2.1e+118)
		tmp = Float64(z / Float64(Float64(t / Float64(x + y)) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * ((y + t) / (y + (x + t)));
	tmp = 0.0;
	if (t <= -2.5e+106)
		tmp = t_1;
	elseif (t <= 4.8e-89)
		tmp = (z + a) - b;
	elseif (t <= 2.1e+118)
		tmp = z / ((t / (x + y)) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+106], t$95$1, If[LessEqual[t, 4.8e-89], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 2.1e+118], N[(z / N[(N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4999999999999999e106 or 2.1e118 < t

   1. Initial program 46.3%

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

   2. Taylor expanded in a around inf 31.7%

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

      1. div-inv 31.6%

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

      2. +-commutative 31.6%

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

      3. associate-+l+ 31.6%

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

      4. +-commutative 31.6%

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

   4. Applied egg-rr 31.6%

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

   5. Taylor expanded in a around 0 31.7%

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

      1. associate-+r+ 31.7%

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

      2. +-commutative 31.7%

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

      3. +-commutative 31.7%

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

      4. associate-*r/ 67.6%

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

      5. +-commutative 67.6%

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

   7. Simplified 67.6%

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

   if -2.4999999999999999e106 < t < 4.80000000000000032e-89

   1. Initial program 67.4%

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

   2. Taylor expanded in y around inf 65.7%

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

   if 4.80000000000000032e-89 < t < 2.1e118

   1. Initial program 63.4%

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

      1. +-commutative 63.4%

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

      2. associate--l+ 63.4%

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

      3. fma-def 63.7%

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

      4. +-commutative 63.7%

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

      5. +-commutative 63.7%

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

   3. Simplified 63.7%

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

      1. div-inv 63.7%

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

      2. fma-udef 63.4%

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

      3. *-commutative 63.4%

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

      4. fma-def 63.7%

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

      5. +-commutative 63.7%

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

      6. associate-+l+ 63.7%

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

      7. +-commutative 63.7%

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

   5. Applied egg-rr 63.7%

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

   6. Taylor expanded in z around inf 38.0%

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

      1. associate-/l* 60.2%

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

      2. +-commutative 60.2%

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

      3. associate-+r+ 60.2%

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

      4. +-commutative 60.2%

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

      5. +-commutative 60.2%

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

      6. +-commutative 60.2%

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

      7. +-commutative 60.2%

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

   8. Simplified 60.2%

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

   9. Taylor expanded in t around 0 60.2%

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

       1. +-commutative 60.2%

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

   11. Simplified 60.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-89}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+118}:\\ \;\;\;\;\frac{z}{\frac{t}{x + y} + 1}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 5: 57.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+148}:\\ \;\;\;\;a + x \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{-81}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+118}:\\ \;\;\;\;\frac{z}{\frac{t}{x + y} + 1}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7e+148)
   (+ a (* x (- (/ z t) (/ a t))))
   (if (<= t 3.55e-81)
     (- (+ z a) b)
     (if (<= t 8.2e+118)
       (/ z (+ (/ t (+ x y)) 1.0))
       (* a (/ (+ y t) (+ y (+ x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7e+148) {
		tmp = a + (x * ((z / t) - (a / t)));
	} else if (t <= 3.55e-81) {
		tmp = (z + a) - b;
	} else if (t <= 8.2e+118) {
		tmp = z / ((t / (x + y)) + 1.0);
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7d+148)) then
        tmp = a + (x * ((z / t) - (a / t)))
    else if (t <= 3.55d-81) then
        tmp = (z + a) - b
    else if (t <= 8.2d+118) then
        tmp = z / ((t / (x + y)) + 1.0d0)
    else
        tmp = a * ((y + t) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7e+148) {
		tmp = a + (x * ((z / t) - (a / t)));
	} else if (t <= 3.55e-81) {
		tmp = (z + a) - b;
	} else if (t <= 8.2e+118) {
		tmp = z / ((t / (x + y)) + 1.0);
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7e+148:
		tmp = a + (x * ((z / t) - (a / t)))
	elif t <= 3.55e-81:
		tmp = (z + a) - b
	elif t <= 8.2e+118:
		tmp = z / ((t / (x + y)) + 1.0)
	else:
		tmp = a * ((y + t) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7e+148)
		tmp = Float64(a + Float64(x * Float64(Float64(z / t) - Float64(a / t))));
	elseif (t <= 3.55e-81)
		tmp = Float64(Float64(z + a) - b);
	elseif (t <= 8.2e+118)
		tmp = Float64(z / Float64(Float64(t / Float64(x + y)) + 1.0));
	else
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7e+148)
		tmp = a + (x * ((z / t) - (a / t)));
	elseif (t <= 3.55e-81)
		tmp = (z + a) - b;
	elseif (t <= 8.2e+118)
		tmp = z / ((t / (x + y)) + 1.0);
	else
		tmp = a * ((y + t) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7e+148], N[(a + N[(x * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.55e-81], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 8.2e+118], N[(z / N[(N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.9999999999999998e148

   1. Initial program 45.6%

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

   2. Taylor expanded in t around inf 66.0%

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

      1. associate--l+ 66.0%

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

      2. associate-/l* 66.8%

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

      3. +-commutative 66.8%

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

      4. associate-/l* 72.8%

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

      5. +-commutative 72.8%

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

      6. associate-/l* 73.7%

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

   4. Simplified 73.7%

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

   5. Taylor expanded in x around inf 69.2%

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

   if -6.9999999999999998e148 < t < 3.5500000000000001e-81

   1. Initial program 68.3%

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

   2. Taylor expanded in y around inf 64.0%

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

   if 3.5500000000000001e-81 < t < 8.1999999999999994e118

   1. Initial program 63.4%

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

      1. +-commutative 63.4%

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

      2. associate--l+ 63.4%

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

      3. fma-def 63.7%

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

      4. +-commutative 63.7%

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

      5. +-commutative 63.7%

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

   3. Simplified 63.7%

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

      1. div-inv 63.7%

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

      2. fma-udef 63.4%

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

      3. *-commutative 63.4%

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

      4. fma-def 63.7%

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

      5. +-commutative 63.7%

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

      6. associate-+l+ 63.7%

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

      7. +-commutative 63.7%

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

   5. Applied egg-rr 63.7%

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

   6. Taylor expanded in z around inf 38.0%

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

      1. associate-/l* 60.2%

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

      2. +-commutative 60.2%

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

      3. associate-+r+ 60.2%

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

      4. +-commutative 60.2%

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

      5. +-commutative 60.2%

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

      6. +-commutative 60.2%

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

      7. +-commutative 60.2%

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

   8. Simplified 60.2%

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

   9. Taylor expanded in t around 0 60.2%

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

       1. +-commutative 60.2%

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

   11. Simplified 60.2%

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

   if 8.1999999999999994e118 < t

   1. Initial program 39.7%

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

   2. Taylor expanded in a around inf 29.9%

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

      1. div-inv 29.9%

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

      2. +-commutative 29.9%

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

      3. associate-+l+ 29.9%

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

      4. +-commutative 29.9%

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

   4. Applied egg-rr 29.9%

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

   5. Taylor expanded in a around 0 29.9%

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

      1. associate-+r+ 29.9%

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

      2. +-commutative 29.9%

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

      3. +-commutative 29.9%

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

      4. associate-*r/ 74.0%

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

      5. +-commutative 74.0%

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

   7. Simplified 74.0%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+148}:\\ \;\;\;\;a + x \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{-81}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+118}:\\ \;\;\;\;\frac{z}{\frac{t}{x + y} + 1}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 6: 58.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+141}:\\ \;\;\;\;a + z \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-84}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{z}{\frac{t}{x + y} + 1}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.5e+141)
   (+ a (* z (+ (/ y t) (/ x t))))
   (if (<= t 8e-84)
     (- (+ z a) b)
     (if (<= t 8.8e+117)
       (/ z (+ (/ t (+ x y)) 1.0))
       (* a (/ (+ y t) (+ y (+ x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.5e+141) {
		tmp = a + (z * ((y / t) + (x / t)));
	} else if (t <= 8e-84) {
		tmp = (z + a) - b;
	} else if (t <= 8.8e+117) {
		tmp = z / ((t / (x + y)) + 1.0);
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.5d+141)) then
        tmp = a + (z * ((y / t) + (x / t)))
    else if (t <= 8d-84) then
        tmp = (z + a) - b
    else if (t <= 8.8d+117) then
        tmp = z / ((t / (x + y)) + 1.0d0)
    else
        tmp = a * ((y + t) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.5e+141) {
		tmp = a + (z * ((y / t) + (x / t)));
	} else if (t <= 8e-84) {
		tmp = (z + a) - b;
	} else if (t <= 8.8e+117) {
		tmp = z / ((t / (x + y)) + 1.0);
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.5e+141:
		tmp = a + (z * ((y / t) + (x / t)))
	elif t <= 8e-84:
		tmp = (z + a) - b
	elif t <= 8.8e+117:
		tmp = z / ((t / (x + y)) + 1.0)
	else:
		tmp = a * ((y + t) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.5e+141)
		tmp = Float64(a + Float64(z * Float64(Float64(y / t) + Float64(x / t))));
	elseif (t <= 8e-84)
		tmp = Float64(Float64(z + a) - b);
	elseif (t <= 8.8e+117)
		tmp = Float64(z / Float64(Float64(t / Float64(x + y)) + 1.0));
	else
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.5e+141)
		tmp = a + (z * ((y / t) + (x / t)));
	elseif (t <= 8e-84)
		tmp = (z + a) - b;
	elseif (t <= 8.8e+117)
		tmp = z / ((t / (x + y)) + 1.0);
	else
		tmp = a * ((y + t) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.5e+141], N[(a + N[(z * N[(N[(y / t), $MachinePrecision] + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-84], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 8.8e+117], N[(z / N[(N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.4999999999999999e141

   1. Initial program 46.2%

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

   2. Taylor expanded in t around inf 65.1%

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

      1. associate--l+ 65.1%

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

      2. associate-/l* 65.9%

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

      3. +-commutative 65.9%

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

      4. associate-/l* 71.6%

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

      5. +-commutative 71.6%

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

      6. associate-/l* 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in z around inf 74.4%

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

      1. +-commutative 74.4%

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

   7. Simplified 74.4%

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

   if -1.4999999999999999e141 < t < 8.0000000000000003e-84

   1. Initial program 68.5%

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

   2. Taylor expanded in y around inf 64.2%

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

   if 8.0000000000000003e-84 < t < 8.80000000000000056e117

   1. Initial program 63.4%

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

      1. +-commutative 63.4%

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

      2. associate--l+ 63.4%

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

      3. fma-def 63.7%

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

      4. +-commutative 63.7%

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

      5. +-commutative 63.7%

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

   3. Simplified 63.7%

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

      1. div-inv 63.7%

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

      2. fma-udef 63.4%

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

      3. *-commutative 63.4%

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

      4. fma-def 63.7%

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

      5. +-commutative 63.7%

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

      6. associate-+l+ 63.7%

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

      7. +-commutative 63.7%

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

   5. Applied egg-rr 63.7%

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

   6. Taylor expanded in z around inf 38.0%

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

      1. associate-/l* 60.2%

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

      2. +-commutative 60.2%

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

      3. associate-+r+ 60.2%

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

      4. +-commutative 60.2%

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

      5. +-commutative 60.2%

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

      6. +-commutative 60.2%

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

      7. +-commutative 60.2%

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

   8. Simplified 60.2%

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

   9. Taylor expanded in t around 0 60.2%

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

       1. +-commutative 60.2%

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

   11. Simplified 60.2%

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

   if 8.80000000000000056e117 < t

   1. Initial program 39.7%

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

   2. Taylor expanded in a around inf 29.9%

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

      1. div-inv 29.9%

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

      2. +-commutative 29.9%

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

      3. associate-+l+ 29.9%

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

      4. +-commutative 29.9%

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

   4. Applied egg-rr 29.9%

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

   5. Taylor expanded in a around 0 29.9%

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

      1. associate-+r+ 29.9%

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

      2. +-commutative 29.9%

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

      3. +-commutative 29.9%

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

      4. associate-*r/ 74.0%

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

      5. +-commutative 74.0%

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

   7. Simplified 74.0%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+141}:\\ \;\;\;\;a + z \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-84}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{z}{\frac{t}{x + y} + 1}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 7: 57.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+113}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-81}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+119}:\\ \;\;\;\;\frac{z}{\frac{t}{x + y} + 1}\\ \mathbf{else}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.45e+113)
   (/ a (/ (+ x t) t))
   (if (<= t 2.5e-81)
     (- (+ z a) b)
     (if (<= t 1.55e+119) (/ z (+ (/ t (+ x y)) 1.0)) (- a (* y (/ b t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.45e+113) {
		tmp = a / ((x + t) / t);
	} else if (t <= 2.5e-81) {
		tmp = (z + a) - b;
	} else if (t <= 1.55e+119) {
		tmp = z / ((t / (x + y)) + 1.0);
	} else {
		tmp = a - (y * (b / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.45d+113)) then
        tmp = a / ((x + t) / t)
    else if (t <= 2.5d-81) then
        tmp = (z + a) - b
    else if (t <= 1.55d+119) then
        tmp = z / ((t / (x + y)) + 1.0d0)
    else
        tmp = a - (y * (b / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.45e+113) {
		tmp = a / ((x + t) / t);
	} else if (t <= 2.5e-81) {
		tmp = (z + a) - b;
	} else if (t <= 1.55e+119) {
		tmp = z / ((t / (x + y)) + 1.0);
	} else {
		tmp = a - (y * (b / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.45e+113:
		tmp = a / ((x + t) / t)
	elif t <= 2.5e-81:
		tmp = (z + a) - b
	elif t <= 1.55e+119:
		tmp = z / ((t / (x + y)) + 1.0)
	else:
		tmp = a - (y * (b / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.45e+113)
		tmp = Float64(a / Float64(Float64(x + t) / t));
	elseif (t <= 2.5e-81)
		tmp = Float64(Float64(z + a) - b);
	elseif (t <= 1.55e+119)
		tmp = Float64(z / Float64(Float64(t / Float64(x + y)) + 1.0));
	else
		tmp = Float64(a - Float64(y * Float64(b / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.45e+113)
		tmp = a / ((x + t) / t);
	elseif (t <= 2.5e-81)
		tmp = (z + a) - b;
	elseif (t <= 1.55e+119)
		tmp = z / ((t / (x + y)) + 1.0);
	else
		tmp = a - (y * (b / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.45e+113], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-81], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 1.55e+119], N[(z / N[(N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(a - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.45000000000000011e113

   1. Initial program 54.0%

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

   2. Taylor expanded in a around inf 33.7%

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

      1. div-inv 33.6%

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

      2. +-commutative 33.6%

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

      3. associate-+l+ 33.6%

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

      4. +-commutative 33.6%

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

   4. Applied egg-rr 33.6%

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

   5. Taylor expanded in y around 0 33.7%

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

      1. associate-/l* 60.2%

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

      2. +-commutative 60.2%

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

   7. Simplified 60.2%

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

   if -2.45000000000000011e113 < t < 2.4999999999999999e-81

   1. Initial program 67.4%

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

   2. Taylor expanded in y around inf 65.7%

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

   if 2.4999999999999999e-81 < t < 1.54999999999999998e119

   1. Initial program 63.4%

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

      1. +-commutative 63.4%

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

      2. associate--l+ 63.4%

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

      3. fma-def 63.7%

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

      4. +-commutative 63.7%

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

      5. +-commutative 63.7%

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

   3. Simplified 63.7%

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

      1. div-inv 63.7%

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

      2. fma-udef 63.4%

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

      3. *-commutative 63.4%

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

      4. fma-def 63.7%

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

      5. +-commutative 63.7%

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

      6. associate-+l+ 63.7%

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

      7. +-commutative 63.7%

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

   5. Applied egg-rr 63.7%

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

   6. Taylor expanded in z around inf 38.0%

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

      1. associate-/l* 60.2%

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

      2. +-commutative 60.2%

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

      3. associate-+r+ 60.2%

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

      4. +-commutative 60.2%

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

      5. +-commutative 60.2%

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

      6. +-commutative 60.2%

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

      7. +-commutative 60.2%

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

   8. Simplified 60.2%

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

   9. Taylor expanded in t around 0 60.2%

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

       1. +-commutative 60.2%

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

   11. Simplified 60.2%

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

   if 1.54999999999999998e119 < t

   1. Initial program 39.7%

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

   2. Taylor expanded in t around inf 54.9%

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

      1. associate--l+ 55.5%

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

      2. associate-/l* 55.7%

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

      3. +-commutative 55.7%

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

      4. associate-/l* 63.7%

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

      5. +-commutative 63.7%

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

      6. associate-/l* 65.7%

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

   4. Simplified 65.7%

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

   5. Taylor expanded in b around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. associate-*l/ 72.2%

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

      3. *-commutative 72.2%

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

      4. distribute-lft-neg-in 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in a around 0 70.0%

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

      1. associate-*r/ 70.0%

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

      2. mul-1-neg 70.0%

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

      3. *-commutative 70.0%

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

      4. distribute-lft-neg-out 70.0%

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

      5. associate-*r/ 72.2%

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

      6. *-commutative 72.2%

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

      7. distribute-rgt-neg-in 72.2%

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

      8. associate-/r/ 72.1%

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

      9. unsub-neg 72.1%

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

      10. associate-/r/ 72.2%

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

      11. *-commutative 72.2%

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

   10. Simplified 72.2%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+113}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-81}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+119}:\\ \;\;\;\;\frac{z}{\frac{t}{x + y} + 1}\\ \mathbf{else}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \end{array} \]

Alternative 8: 68.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+141}:\\ \;\;\;\;a + z \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+120}:\\ \;\;\;\;\left(z + a\right) - \frac{b}{\frac{x + y}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.2e+141)
   (+ a (* z (+ (/ y t) (/ x t))))
   (if (<= t 1.35e+120)
     (- (+ z a) (/ b (/ (+ x y) y)))
     (* a (/ (+ y t) (+ y (+ x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e+141) {
		tmp = a + (z * ((y / t) + (x / t)));
	} else if (t <= 1.35e+120) {
		tmp = (z + a) - (b / ((x + y) / y));
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.2d+141)) then
        tmp = a + (z * ((y / t) + (x / t)))
    else if (t <= 1.35d+120) then
        tmp = (z + a) - (b / ((x + y) / y))
    else
        tmp = a * ((y + t) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e+141) {
		tmp = a + (z * ((y / t) + (x / t)));
	} else if (t <= 1.35e+120) {
		tmp = (z + a) - (b / ((x + y) / y));
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.2e+141:
		tmp = a + (z * ((y / t) + (x / t)))
	elif t <= 1.35e+120:
		tmp = (z + a) - (b / ((x + y) / y))
	else:
		tmp = a * ((y + t) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.2e+141)
		tmp = Float64(a + Float64(z * Float64(Float64(y / t) + Float64(x / t))));
	elseif (t <= 1.35e+120)
		tmp = Float64(Float64(z + a) - Float64(b / Float64(Float64(x + y) / y)));
	else
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.2e+141)
		tmp = a + (z * ((y / t) + (x / t)));
	elseif (t <= 1.35e+120)
		tmp = (z + a) - (b / ((x + y) / y));
	else
		tmp = a * ((y + t) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.2e+141], N[(a + N[(z * N[(N[(y / t), $MachinePrecision] + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+120], N[(N[(z + a), $MachinePrecision] - N[(b / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.19999999999999999e141

   1. Initial program 46.2%

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

   2. Taylor expanded in t around inf 65.1%

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

      1. associate--l+ 65.1%

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

      2. associate-/l* 65.9%

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

      3. +-commutative 65.9%

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

      4. associate-/l* 71.6%

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

      5. +-commutative 71.6%

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

      6. associate-/l* 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in z around inf 74.4%

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

      1. +-commutative 74.4%

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

   7. Simplified 74.4%

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

   if -1.19999999999999999e141 < t < 1.35e120

   1. Initial program 67.5%

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

   2. Taylor expanded in a around 0 71.6%

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

   3. Taylor expanded in x around inf 80.5%

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

   4. Taylor expanded in t around 0 76.1%

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

      1. associate-/l* 87.4%

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

      2. +-commutative 87.4%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in t around inf 73.5%

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

   if 1.35e120 < t

   1. Initial program 39.7%

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

   2. Taylor expanded in a around inf 29.9%

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

      1. div-inv 29.9%

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

      2. +-commutative 29.9%

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

      3. associate-+l+ 29.9%

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

      4. +-commutative 29.9%

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

   4. Applied egg-rr 29.9%

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

   5. Taylor expanded in a around 0 29.9%

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

      1. associate-+r+ 29.9%

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

      2. +-commutative 29.9%

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

      3. +-commutative 29.9%

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

      4. associate-*r/ 74.0%

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

      5. +-commutative 74.0%

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

   7. Simplified 74.0%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+141}:\\ \;\;\;\;a + z \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+120}:\\ \;\;\;\;\left(z + a\right) - \frac{b}{\frac{x + y}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 9: 60.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+141} \lor \neg \left(t \leq 5.4 \cdot 10^{+119}\right):\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.32e+141) (not (<= t 5.4e+119)))
   (- a (* y (/ b t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.32e+141) || !(t <= 5.4e+119)) {
		tmp = a - (y * (b / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.32d+141)) .or. (.not. (t <= 5.4d+119))) then
        tmp = a - (y * (b / t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.32e+141) || !(t <= 5.4e+119)) {
		tmp = a - (y * (b / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.32e+141) or not (t <= 5.4e+119):
		tmp = a - (y * (b / t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.32e+141) || !(t <= 5.4e+119))
		tmp = Float64(a - Float64(y * Float64(b / t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.32e+141) || ~((t <= 5.4e+119)))
		tmp = a - (y * (b / t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.32e+141], N[Not[LessEqual[t, 5.4e+119]], $MachinePrecision]], N[(a - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3200000000000001e141 or 5.3999999999999997e119 < t

   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 t around inf 59.1%

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

      1. associate--l+ 59.4%

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

      2. associate-/l* 59.9%

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

      3. +-commutative 59.9%

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

      4. associate-/l* 66.9%

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

      5. +-commutative 66.9%

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

      6. associate-/l* 68.4%

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

   4. Simplified 68.4%

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

   5. Taylor expanded in b around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. associate-*l/ 67.4%

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

      3. *-commutative 67.4%

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

      4. distribute-lft-neg-in 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in a around 0 65.8%

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

      1. associate-*r/ 65.8%

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

      2. mul-1-neg 65.8%

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

      3. *-commutative 65.8%

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

      4. distribute-lft-neg-out 65.8%

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

      5. associate-*r/ 67.4%

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

      6. *-commutative 67.4%

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

      7. distribute-rgt-neg-in 67.4%

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

      8. associate-/r/ 67.4%

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

      9. unsub-neg 67.4%

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

      10. associate-/r/ 67.4%

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

      11. *-commutative 67.4%

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

   10. Simplified 67.4%

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

   if -1.3200000000000001e141 < t < 5.3999999999999997e119

   1. Initial program 67.5%

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

   2. Taylor expanded in y around inf 60.7%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+141} \lor \neg \left(t \leq 5.4 \cdot 10^{+119}\right):\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 59.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+107}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+119}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.6e+107)
   (/ a (/ (+ x t) t))
   (if (<= t 2e+119) (- (+ z a) b) (- a (* y (/ b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.6e+107) {
		tmp = a / ((x + t) / t);
	} else if (t <= 2e+119) {
		tmp = (z + a) - b;
	} else {
		tmp = a - (y * (b / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.6d+107)) then
        tmp = a / ((x + t) / t)
    else if (t <= 2d+119) then
        tmp = (z + a) - b
    else
        tmp = a - (y * (b / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.6e+107) {
		tmp = a / ((x + t) / t);
	} else if (t <= 2e+119) {
		tmp = (z + a) - b;
	} else {
		tmp = a - (y * (b / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.6e+107:
		tmp = a / ((x + t) / t)
	elif t <= 2e+119:
		tmp = (z + a) - b
	else:
		tmp = a - (y * (b / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.6e+107)
		tmp = Float64(a / Float64(Float64(x + t) / t));
	elseif (t <= 2e+119)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a - Float64(y * Float64(b / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.6e+107)
		tmp = a / ((x + t) / t);
	elseif (t <= 2e+119)
		tmp = (z + a) - b;
	else
		tmp = a - (y * (b / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.6e+107], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+119], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.60000000000000015e107

   1. Initial program 54.0%

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

   2. Taylor expanded in a around inf 33.7%

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

      1. div-inv 33.6%

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

      2. +-commutative 33.6%

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

      3. associate-+l+ 33.6%

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

      4. +-commutative 33.6%

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

   4. Applied egg-rr 33.6%

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

   5. Taylor expanded in y around 0 33.7%

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

      1. associate-/l* 60.2%

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

      2. +-commutative 60.2%

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

   7. Simplified 60.2%

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

   if -1.60000000000000015e107 < t < 1.99999999999999989e119

   1. Initial program 66.5%

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

   2. Taylor expanded in y around inf 61.7%

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

   if 1.99999999999999989e119 < t

   1. Initial program 39.7%

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

   2. Taylor expanded in t around inf 54.9%

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

      1. associate--l+ 55.5%

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

      2. associate-/l* 55.7%

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

      3. +-commutative 55.7%

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

      4. associate-/l* 63.7%

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

      5. +-commutative 63.7%

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

      6. associate-/l* 65.7%

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

   4. Simplified 65.7%

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

   5. Taylor expanded in b around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. associate-*l/ 72.2%

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

      3. *-commutative 72.2%

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

      4. distribute-lft-neg-in 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in a around 0 70.0%

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

      1. associate-*r/ 70.0%

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

      2. mul-1-neg 70.0%

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

      3. *-commutative 70.0%

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

      4. distribute-lft-neg-out 70.0%

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

      5. associate-*r/ 72.2%

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

      6. *-commutative 72.2%

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

      7. distribute-rgt-neg-in 72.2%

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

      8. associate-/r/ 72.1%

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

      9. unsub-neg 72.1%

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

      10. associate-/r/ 72.2%

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

      11. *-commutative 72.2%

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

   10. Simplified 72.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+107}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+119}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \end{array} \]

Alternative 11: 58.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+141}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+119}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7e+141) a (if (<= t 5.8e+119) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7e+141) {
		tmp = a;
	} else if (t <= 5.8e+119) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7d+141)) then
        tmp = a
    else if (t <= 5.8d+119) then
        tmp = (z + a) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7e+141) {
		tmp = a;
	} else if (t <= 5.8e+119) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7e+141:
		tmp = a
	elif t <= 5.8e+119:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7e+141)
		tmp = a;
	elseif (t <= 5.8e+119)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7e+141)
		tmp = a;
	elseif (t <= 5.8e+119)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7e+141], a, If[LessEqual[t, 5.8e+119], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -6.9999999999999999e141 or 5.80000000000000014e119 < t

   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 t around inf 63.4%

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

   if -6.9999999999999999e141 < t < 5.80000000000000014e119

   1. Initial program 67.5%

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

   2. Taylor expanded in y around inf 60.7%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+141}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+119}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 12: 44.1% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+46}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-34}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.5e+46) a (if (<= a 1.2e-34) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.5e+46) {
		tmp = a;
	} else if (a <= 1.2e-34) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.5d+46)) then
        tmp = a
    else if (a <= 1.2d-34) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.5e+46) {
		tmp = a;
	} else if (a <= 1.2e-34) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.5e+46:
		tmp = a
	elif a <= 1.2e-34:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.5e+46)
		tmp = a;
	elseif (a <= 1.2e-34)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.5e+46)
		tmp = a;
	elseif (a <= 1.2e-34)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.5e+46], a, If[LessEqual[a, 1.2e-34], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.5000000000000001e46 or 1.19999999999999996e-34 < a

   1. Initial program 48.0%

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

   2. Taylor expanded in t around inf 57.2%

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

   if -2.5000000000000001e46 < a < 1.19999999999999996e-34

   1. Initial program 71.4%

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

   2. Taylor expanded in x around inf 46.6%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+46}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-34}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 13: 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 59.4%

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

2. Taylor expanded in t around inf 36.5%

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

3. Final simplification 36.5%

   \[\leadsto a \]

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 2023271 
(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)))