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

Percentage Accurate: 61.0% → 88.7%

Time: 32.2s

Alternatives: 13

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.0% 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: 88.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 5 \cdot 10^{+283}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot t\_3\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+283)))
     t_3
     (/ (+ (* t a) (+ (* x z) (* y t_3))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+283)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+283)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
	t_3 = (z + a) - b
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+283):
		tmp = t_3
	else:
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+283))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * t_3))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+283)))
		tmp = t_3;
	else
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+283]], $MachinePrecision]], t$95$3, N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.0000000000000004e283 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.2%

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

   3. Taylor expanded in y around inf 74.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000004e283

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 99.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+283}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{t\_1}\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-125}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-238}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{t \cdot a}{z \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (* y (* (+ a (- z b)) (/ 1.0 t_1)))))
   (if (<= y -6e+93)
     t_2
     (if (<= y -2.4e-125)
       (/ (- (* a (+ y t)) (* y b)) (+ y (+ x t)))
       (if (<= y 8.2e-238)
         (* z (+ (/ x (+ x t)) (/ (* t a) (* z (+ x t)))))
         (if (<= y 6.5e-29) (* z (+ (/ x t_1) (/ a z))) 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 = y * ((a + (z - b)) * (1.0 / t_1));
	double tmp;
	if (y <= -6e+93) {
		tmp = t_2;
	} else if (y <= -2.4e-125) {
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	} else if (y <= 8.2e-238) {
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	} else if (y <= 6.5e-29) {
		tmp = z * ((x / t_1) + (a / z));
	} 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 = y * ((a + (z - b)) * (1.0d0 / t_1))
    if (y <= (-6d+93)) then
        tmp = t_2
    else if (y <= (-2.4d-125)) then
        tmp = ((a * (y + t)) - (y * b)) / (y + (x + t))
    else if (y <= 8.2d-238) then
        tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))))
    else if (y <= 6.5d-29) then
        tmp = z * ((x / t_1) + (a / z))
    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 = y * ((a + (z - b)) * (1.0 / t_1));
	double tmp;
	if (y <= -6e+93) {
		tmp = t_2;
	} else if (y <= -2.4e-125) {
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	} else if (y <= 8.2e-238) {
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	} else if (y <= 6.5e-29) {
		tmp = z * ((x / t_1) + (a / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = y * ((a + (z - b)) * (1.0 / t_1))
	tmp = 0
	if y <= -6e+93:
		tmp = t_2
	elif y <= -2.4e-125:
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t))
	elif y <= 8.2e-238:
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))))
	elif y <= 6.5e-29:
		tmp = z * ((x / t_1) + (a / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(y * Float64(Float64(a + Float64(z - b)) * Float64(1.0 / t_1)))
	tmp = 0.0
	if (y <= -6e+93)
		tmp = t_2;
	elseif (y <= -2.4e-125)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (y <= 8.2e-238)
		tmp = Float64(z * Float64(Float64(x / Float64(x + t)) + Float64(Float64(t * a) / Float64(z * Float64(x + t)))));
	elseif (y <= 6.5e-29)
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(a / z)));
	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 = y * ((a + (z - b)) * (1.0 / t_1));
	tmp = 0.0;
	if (y <= -6e+93)
		tmp = t_2;
	elseif (y <= -2.4e-125)
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	elseif (y <= 8.2e-238)
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	elseif (y <= 6.5e-29)
		tmp = z * ((x / t_1) + (a / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+93], t$95$2, If[LessEqual[y, -2.4e-125], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-238], N[(z * N[(N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] / N[(z * N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-29], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.99999999999999957e93 or 6.5e-29 < y

   1. Initial program 35.3%

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

   3. Taylor expanded in y around inf 30.4%

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

      1. div-inv 30.3%

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

      2. +-commutative 30.3%

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

      3. associate-+r+ 30.3%

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

      4. associate--l+ 30.3%

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

      5. associate-+r+ 30.3%

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

      6. +-commutative 30.3%

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

      7. associate-+l+ 30.3%

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

      8. +-commutative 30.3%

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

   5. Applied egg-rr 30.3%

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

      1. associate-*l* 82.4%

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

   7. Simplified 82.4%

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

   if -5.99999999999999957e93 < y < -2.4000000000000001e-125

   1. Initial program 77.0%

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

   3. Taylor expanded in z around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if -2.4000000000000001e-125 < y < 8.2000000000000002e-238

   1. Initial program 79.7%

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

   3. Taylor expanded in z around inf 90.1%

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

      1. associate--l+ 90.1%

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

      2. +-commutative 90.1%

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

      3. associate-+r+ 90.1%

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

      4. +-commutative 90.1%

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

      5. associate-+r+ 90.1%

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

      6. times-frac 92.9%

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

      7. +-commutative 92.9%

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

      8. +-commutative 92.9%

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

      9. associate-+r+ 92.9%

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

      10. associate-/r* 94.8%

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

   5. Simplified 94.8%

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

   6. Taylor expanded in y around 0 79.3%

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

   if 8.2000000000000002e-238 < y < 6.5e-29

   1. Initial program 70.2%

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

   3. Taylor expanded in z around inf 61.1%

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

      1. associate--l+ 61.1%

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

      2. +-commutative 61.1%

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

      3. associate-+r+ 61.1%

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

      4. +-commutative 61.1%

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

      5. associate-+r+ 61.1%

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

      6. times-frac 87.9%

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

      7. +-commutative 87.9%

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

      8. +-commutative 87.9%

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

      9. associate-+r+ 87.9%

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

      10. associate-/r* 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in t around inf 68.0%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{x + \left(y + t\right)}\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-125}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-238}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{t \cdot a}{z \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{x + \left(y + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{t\_1}\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7.9 \cdot 10^{-112}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (* y (* (+ a (- z b)) (/ 1.0 t_1)))))
   (if (<= y -6e+93)
     t_2
     (if (<= y -7.9e-112)
       (/ (- (* a (+ y t)) (* y b)) (+ y (+ x t)))
       (if (<= y 1.8e-29) (* z (+ (/ x t_1) (/ a z))) 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 = y * ((a + (z - b)) * (1.0 / t_1));
	double tmp;
	if (y <= -6e+93) {
		tmp = t_2;
	} else if (y <= -7.9e-112) {
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	} else if (y <= 1.8e-29) {
		tmp = z * ((x / t_1) + (a / z));
	} 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 = y * ((a + (z - b)) * (1.0d0 / t_1))
    if (y <= (-6d+93)) then
        tmp = t_2
    else if (y <= (-7.9d-112)) then
        tmp = ((a * (y + t)) - (y * b)) / (y + (x + t))
    else if (y <= 1.8d-29) then
        tmp = z * ((x / t_1) + (a / z))
    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 = y * ((a + (z - b)) * (1.0 / t_1));
	double tmp;
	if (y <= -6e+93) {
		tmp = t_2;
	} else if (y <= -7.9e-112) {
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	} else if (y <= 1.8e-29) {
		tmp = z * ((x / t_1) + (a / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = y * ((a + (z - b)) * (1.0 / t_1))
	tmp = 0
	if y <= -6e+93:
		tmp = t_2
	elif y <= -7.9e-112:
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t))
	elif y <= 1.8e-29:
		tmp = z * ((x / t_1) + (a / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(y * Float64(Float64(a + Float64(z - b)) * Float64(1.0 / t_1)))
	tmp = 0.0
	if (y <= -6e+93)
		tmp = t_2;
	elseif (y <= -7.9e-112)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (y <= 1.8e-29)
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(a / z)));
	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 = y * ((a + (z - b)) * (1.0 / t_1));
	tmp = 0.0;
	if (y <= -6e+93)
		tmp = t_2;
	elseif (y <= -7.9e-112)
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	elseif (y <= 1.8e-29)
		tmp = z * ((x / t_1) + (a / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+93], t$95$2, If[LessEqual[y, -7.9e-112], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-29], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999957e93 or 1.79999999999999987e-29 < y

   1. Initial program 35.3%

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

   3. Taylor expanded in y around inf 30.4%

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

      1. div-inv 30.3%

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

      2. +-commutative 30.3%

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

      3. associate-+r+ 30.3%

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

      4. associate--l+ 30.3%

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

      5. associate-+r+ 30.3%

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

      6. +-commutative 30.3%

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

      7. associate-+l+ 30.3%

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

      8. +-commutative 30.3%

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

   5. Applied egg-rr 30.3%

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

      1. associate-*l* 82.4%

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

   7. Simplified 82.4%

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

   if -5.99999999999999957e93 < y < -7.8999999999999999e-112

   1. Initial program 77.0%

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

   3. Taylor expanded in z around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if -7.8999999999999999e-112 < y < 1.79999999999999987e-29

   1. Initial program 75.1%

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

   3. Taylor expanded in z around inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. +-commutative 76.1%

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

      3. associate-+r+ 76.1%

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

      4. +-commutative 76.1%

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

      5. associate-+r+ 76.1%

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

      6. times-frac 90.5%

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

      7. +-commutative 90.5%

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

      8. +-commutative 90.5%

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

      9. associate-+r+ 90.5%

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

      10. associate-/r* 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in t around inf 66.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{x + \left(y + t\right)}\right)\\ \mathbf{elif}\;y \leq -7.9 \cdot 10^{-112}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{x + \left(y + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{a}{z}\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+22}:\\ \;\;\;\;\frac{y \cdot t\_1}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4.2e-37)
     t_1
     (if (<= y 5e-29)
       (* z (+ (/ x (+ x (+ y t))) (/ a z)))
       (if (<= y 6e+22) (/ (* y t_1) (+ y (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.2e-37) {
		tmp = t_1;
	} else if (y <= 5e-29) {
		tmp = z * ((x / (x + (y + t))) + (a / z));
	} else if (y <= 6e+22) {
		tmp = (y * t_1) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-4.2d-37)) then
        tmp = t_1
    else if (y <= 5d-29) then
        tmp = z * ((x / (x + (y + t))) + (a / z))
    else if (y <= 6d+22) then
        tmp = (y * t_1) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.2e-37) {
		tmp = t_1;
	} else if (y <= 5e-29) {
		tmp = z * ((x / (x + (y + t))) + (a / z));
	} else if (y <= 6e+22) {
		tmp = (y * t_1) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -4.2e-37:
		tmp = t_1
	elif y <= 5e-29:
		tmp = z * ((x / (x + (y + t))) + (a / z))
	elif y <= 6e+22:
		tmp = (y * t_1) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4.2e-37)
		tmp = t_1;
	elseif (y <= 5e-29)
		tmp = Float64(z * Float64(Float64(x / Float64(x + Float64(y + t))) + Float64(a / z)));
	elseif (y <= 6e+22)
		tmp = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -4.2e-37)
		tmp = t_1;
	elseif (y <= 5e-29)
		tmp = z * ((x / (x + (y + t))) + (a / z));
	elseif (y <= 6e+22)
		tmp = (y * t_1) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4.2e-37], t$95$1, If[LessEqual[y, 5e-29], N[(z * N[(N[(x / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+22], N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2000000000000002e-37 or 6e22 < y

   1. Initial program 38.6%

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

   3. Taylor expanded in y around inf 73.1%

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

   if -4.2000000000000002e-37 < y < 4.99999999999999986e-29

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 75.6%

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

      1. associate--l+ 75.6%

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

      2. +-commutative 75.6%

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

      3. associate-+r+ 75.6%

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

      4. +-commutative 75.6%

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

      5. associate-+r+ 75.6%

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

      6. times-frac 87.8%

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

      7. +-commutative 87.8%

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

      8. +-commutative 87.8%

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

      9. associate-+r+ 87.8%

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

      10. associate-/r* 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in t around inf 63.8%

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

   if 4.99999999999999986e-29 < y < 6e22

   1. Initial program 83.5%

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

   3. Taylor expanded in y around inf 75.4%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-37}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{a}{z}\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+22}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ \mathbf{if}\;y \leq -4200000000000 \lor \neg \left(y \leq 2.9 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \frac{a}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))))
   (if (or (<= y -4200000000000.0) (not (<= y 2.9e-29)))
     (* y (* (+ a (- z b)) (/ 1.0 t_1)))
     (* z (+ (/ x t_1) (/ a z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if ((y <= -4200000000000.0) || !(y <= 2.9e-29)) {
		tmp = y * ((a + (z - b)) * (1.0 / t_1));
	} else {
		tmp = z * ((x / t_1) + (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y + t)
    if ((y <= (-4200000000000.0d0)) .or. (.not. (y <= 2.9d-29))) then
        tmp = y * ((a + (z - b)) * (1.0d0 / t_1))
    else
        tmp = z * ((x / t_1) + (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if ((y <= -4200000000000.0) || !(y <= 2.9e-29)) {
		tmp = y * ((a + (z - b)) * (1.0 / t_1));
	} else {
		tmp = z * ((x / t_1) + (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	tmp = 0
	if (y <= -4200000000000.0) or not (y <= 2.9e-29):
		tmp = y * ((a + (z - b)) * (1.0 / t_1))
	else:
		tmp = z * ((x / t_1) + (a / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	tmp = 0.0
	if ((y <= -4200000000000.0) || !(y <= 2.9e-29))
		tmp = Float64(y * Float64(Float64(a + Float64(z - b)) * Float64(1.0 / t_1)));
	else
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	tmp = 0.0;
	if ((y <= -4200000000000.0) || ~((y <= 2.9e-29)))
		tmp = y * ((a + (z - b)) * (1.0 / t_1));
	else
		tmp = z * ((x / t_1) + (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -4200000000000.0], N[Not[LessEqual[y, 2.9e-29]], $MachinePrecision]], N[(y * N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e12 or 2.90000000000000024e-29 < y

   1. Initial program 40.7%

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

   3. Taylor expanded in y around inf 32.1%

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

      1. div-inv 32.0%

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

      2. +-commutative 32.0%

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

      3. associate-+r+ 32.0%

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

      4. associate--l+ 32.0%

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

      5. associate-+r+ 32.0%

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

      6. +-commutative 32.0%

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

      7. associate-+l+ 32.0%

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

      8. +-commutative 32.0%

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

   5. Applied egg-rr 32.0%

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

      1. associate-*l* 78.3%

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

   7. Simplified 78.3%

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

   if -4.2e12 < y < 2.90000000000000024e-29

   1. Initial program 75.9%

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

   3. Taylor expanded in z around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. +-commutative 75.1%

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

      3. associate-+r+ 75.1%

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

      4. +-commutative 75.1%

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

      5. associate-+r+ 75.1%

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

      6. times-frac 87.2%

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

      7. +-commutative 87.2%

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

      8. +-commutative 87.2%

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

      9. associate-+r+ 87.2%

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

      10. associate-/r* 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in t around inf 63.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4200000000000 \lor \neg \left(y \leq 2.9 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{a}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + z \cdot \frac{x + y}{t}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-87}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+127}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (* z (/ (+ x y) t)))))
   (if (<= t -2.1e+94)
     t_1
     (if (<= t -2.35e-87)
       (* a (+ (/ z a) (/ y (+ x y))))
       (if (<= t 3.8e+127) (- (+ z a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z * ((x + y) / t));
	double tmp;
	if (t <= -2.1e+94) {
		tmp = t_1;
	} else if (t <= -2.35e-87) {
		tmp = a * ((z / a) + (y / (x + y)));
	} else if (t <= 3.8e+127) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (z * ((x + y) / t))
    if (t <= (-2.1d+94)) then
        tmp = t_1
    else if (t <= (-2.35d-87)) then
        tmp = a * ((z / a) + (y / (x + y)))
    else if (t <= 3.8d+127) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z * ((x + y) / t));
	double tmp;
	if (t <= -2.1e+94) {
		tmp = t_1;
	} else if (t <= -2.35e-87) {
		tmp = a * ((z / a) + (y / (x + y)));
	} else if (t <= 3.8e+127) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z * ((x + y) / t))
	tmp = 0
	if t <= -2.1e+94:
		tmp = t_1
	elif t <= -2.35e-87:
		tmp = a * ((z / a) + (y / (x + y)))
	elif t <= 3.8e+127:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z * Float64(Float64(x + y) / t)))
	tmp = 0.0
	if (t <= -2.1e+94)
		tmp = t_1;
	elseif (t <= -2.35e-87)
		tmp = Float64(a * Float64(Float64(z / a) + Float64(y / Float64(x + y))));
	elseif (t <= 3.8e+127)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z * ((x + y) / t));
	tmp = 0.0;
	if (t <= -2.1e+94)
		tmp = t_1;
	elseif (t <= -2.35e-87)
		tmp = a * ((z / a) + (y / (x + y)));
	elseif (t <= 3.8e+127)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+94], t$95$1, If[LessEqual[t, -2.35e-87], N[(a * N[(N[(z / a), $MachinePrecision] + N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+127], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.09999999999999989e94 or 3.7999999999999998e127 < t

   1. Initial program 55.1%

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

   3. Taylor expanded in a around -inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. distribute-rgt-neg-in 80.1%

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

      3. mul-1-neg 80.1%

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

      4. unsub-neg 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around inf 60.6%

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

   7. Taylor expanded in z around -inf 64.2%

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

      1. associate-/l* 73.0%

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

   9. Simplified 73.0%

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

   if -2.09999999999999989e94 < t < -2.35e-87

   1. Initial program 63.3%

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

   3. Taylor expanded in a around -inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. distribute-rgt-neg-in 70.5%

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

      3. mul-1-neg 70.5%

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

      4. unsub-neg 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in b around 0 55.3%

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

      1. times-frac 68.0%

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

      2. mul-1-neg 68.0%

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

   8. Simplified 68.0%

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

   9. Taylor expanded in t around 0 59.5%

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

       1. +-commutative 59.5%

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

   11. Simplified 59.5%

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

   if -2.35e-87 < t < 3.7999999999999998e127

   1. Initial program 58.4%

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

   3. Taylor expanded in y around inf 68.3%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+94}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-87}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{y}{x + y}\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+127}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+94} \lor \neg \left(t \leq 7.5 \cdot 10^{+127}\right):\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8.6e+94) (not (<= t 7.5e+127)))
   (+ a (* z (/ (+ x y) t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.6e+94) || !(t <= 7.5e+127)) {
		tmp = a + (z * ((x + y) / 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 <= (-8.6d+94)) .or. (.not. (t <= 7.5d+127))) then
        tmp = a + (z * ((x + y) / 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 <= -8.6e+94) || !(t <= 7.5e+127)) {
		tmp = a + (z * ((x + y) / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8.6e+94) or not (t <= 7.5e+127):
		tmp = a + (z * ((x + y) / t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -8.6e+94) || !(t <= 7.5e+127))
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / 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 <= -8.6e+94) || ~((t <= 7.5e+127)))
		tmp = a + (z * ((x + y) / t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -8.6e+94], N[Not[LessEqual[t, 7.5e+127]], $MachinePrecision]], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.6e94 or 7.4999999999999996e127 < t

   1. Initial program 55.1%

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

   3. Taylor expanded in a around -inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. distribute-rgt-neg-in 80.1%

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

      3. mul-1-neg 80.1%

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

      4. unsub-neg 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around inf 60.6%

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

   7. Taylor expanded in z around -inf 64.2%

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

      1. associate-/l* 73.0%

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

   9. Simplified 73.0%

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

   if -8.6e94 < t < 7.4999999999999996e127

   1. Initial program 59.5%

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

   3. Taylor expanded in y around inf 63.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+94} \lor \neg \left(t \leq 7.5 \cdot 10^{+127}\right):\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+94} \lor \neg \left(t \leq 1.15 \cdot 10^{+128}\right):\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8.5e+94) (not (<= t 1.15e+128)))
   (- 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 <= -8.5e+94) || !(t <= 1.15e+128)) {
		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 <= (-8.5d+94)) .or. (.not. (t <= 1.15d+128))) 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 <= -8.5e+94) || !(t <= 1.15e+128)) {
		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 <= -8.5e+94) or not (t <= 1.15e+128):
		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 <= -8.5e+94) || !(t <= 1.15e+128))
		tmp = Float64(a - Float64(Float64(y * 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 <= -8.5e+94) || ~((t <= 1.15e+128)))
		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, -8.5e+94], N[Not[LessEqual[t, 1.15e+128]], $MachinePrecision]], N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000054e94 or 1.14999999999999999e128 < t

   1. Initial program 55.1%

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

   3. Taylor expanded in a around -inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. distribute-rgt-neg-in 80.1%

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

      3. mul-1-neg 80.1%

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

      4. unsub-neg 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around inf 60.6%

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

   7. Taylor expanded in b around inf 62.8%

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

      1. associate-*r/ 62.8%

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

      2. associate-*r* 62.8%

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

      3. neg-mul-1 62.8%

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

   9. Simplified 62.8%

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

   if -8.50000000000000054e94 < t < 1.14999999999999999e128

   1. Initial program 59.5%

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

   3. Taylor expanded in y around inf 63.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+94} \lor \neg \left(t \leq 1.15 \cdot 10^{+128}\right):\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+95}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+171}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.1e+95) a (if (<= t 1.1e+171) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.1e+95) {
		tmp = a;
	} else if (t <= 1.1e+171) {
		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 <= (-3.1d+95)) then
        tmp = a
    else if (t <= 1.1d+171) 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 <= -3.1e+95) {
		tmp = a;
	} else if (t <= 1.1e+171) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.1e+95:
		tmp = a
	elif t <= 1.1e+171:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.1e+95)
		tmp = a;
	elseif (t <= 1.1e+171)
		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 <= -3.1e+95)
		tmp = a;
	elseif (t <= 1.1e+171)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.1e+95], a, If[LessEqual[t, 1.1e+171], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1000000000000003e95 or 1.1e171 < t

   1. Initial program 57.8%

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

   3. Taylor expanded in t around inf 55.7%

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

   if -3.1000000000000003e95 < t < 1.1e171

   1. Initial program 58.1%

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

   3. Taylor expanded in y around inf 63.2%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+95}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+171}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+115}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+183}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.05e+115) z (if (<= x 4.5e+183) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.05e+115) {
		tmp = z;
	} else if (x <= 4.5e+183) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.05d+115)) then
        tmp = z
    else if (x <= 4.5d+183) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.05e+115) {
		tmp = z;
	} else if (x <= 4.5e+183) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.05e+115:
		tmp = z
	elif x <= 4.5e+183:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.05e+115)
		tmp = z;
	elseif (x <= 4.5e+183)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.05e+115)
		tmp = z;
	elseif (x <= 4.5e+183)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.05e+115], z, If[LessEqual[x, 4.5e+183], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05000000000000002e115 or 4.50000000000000017e183 < x

   1. Initial program 47.1%

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

   3. Taylor expanded in x around inf 58.8%

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

   if -1.05000000000000002e115 < x < 4.50000000000000017e183

   1. Initial program 61.4%

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

   3. Taylor expanded in t around inf 45.6%

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

Alternative 11: 51.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5 \cdot 10^{+153}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 5e+153) (+ z a) (- a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5e+153) {
		tmp = z + a;
	} else {
		tmp = 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 (b <= 5d+153) then
        tmp = z + a
    else
        tmp = 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 (b <= 5e+153) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5e+153:
		tmp = z + a
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5e+153)
		tmp = Float64(z + a);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5e+153)
		tmp = z + a;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5e+153], N[(z + a), $MachinePrecision], N[(a - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.00000000000000018e153

   1. Initial program 59.5%

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

   3. Taylor expanded in b around 0 49.9%

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

   4. Taylor expanded in y around inf 54.8%

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

   if 5.00000000000000018e153 < b

   1. Initial program 48.7%

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

   3. Taylor expanded in y around inf 59.9%

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

   4. Taylor expanded in z around 0 54.6%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5 \cdot 10^{+153}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.15 \cdot 10^{+162}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 1.15e+162) (+ z a) (- b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.15e+162) {
		tmp = z + a;
	} else {
		tmp = -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 (b <= 1.15d+162) then
        tmp = z + a
    else
        tmp = -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 (b <= 1.15e+162) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.15e+162:
		tmp = z + a
	else:
		tmp = -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.15e+162)
		tmp = Float64(z + a);
	else
		tmp = Float64(-b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.15e+162)
		tmp = z + a;
	else
		tmp = -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.15e+162], N[(z + a), $MachinePrecision], (-b)]

Derivation

1. Split input into 2 regimes

2. if b < 1.14999999999999997e162

   1. Initial program 59.0%

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

   3. Taylor expanded in b around 0 49.5%

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

   4. Taylor expanded in y around inf 54.8%

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

   if 1.14999999999999997e162 < b

   1. Initial program 51.1%

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

   3. Taylor expanded in y around inf 56.5%

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

   4. Taylor expanded in b around inf 48.1%

      \[\leadsto \color{blue}{-1 \cdot b} \]
   5. Step-by-step derivation

      1. neg-mul-1 48.1%

         \[\leadsto \color{blue}{-b} \]

   6. Simplified 48.1%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.15 \cdot 10^{+162}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.8% 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 58.0%

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

3. Taylor expanded in t around inf 36.4%

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

Developer Target 1: 83.1% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024143 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ 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)))