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

Percentage Accurate: 60.1% → 87.3%

Time: 19.7s

Alternatives: 16

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(x + y\right) + t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(a + z \cdot \left(\frac{x}{t_2} + \frac{y}{t_2}\right)\right) - \frac{y \cdot b}{t_2}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+265}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* (+ x y) z)) (* y b)) (+ y (+ x t))))
        (t_2 (+ (+ x y) t)))
   (if (<= t_1 (- INFINITY))
     (- (+ a (* z (+ (/ x t_2) (/ y t_2)))) (/ (* y b) t_2))
     (if (<= t_1 2e+265) t_1 (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double t_2 = (x + y) + t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (a + (z * ((x / t_2) + (y / t_2)))) - ((y * b) / t_2);
	} else if (t_1 <= 2e+265) {
		tmp = t_1;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double t_2 = (x + y) + t;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (a + (z * ((x / t_2) + (y / t_2)))) - ((y * b) / t_2);
	} else if (t_1 <= 2e+265) {
		tmp = t_1;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t))
	t_2 = (x + y) + t
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (a + (z * ((x / t_2) + (y / t_2)))) - ((y * b) / t_2)
	elif t_1 <= 2e+265:
		tmp = t_1
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(Float64(x + y) * z)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(Float64(x + y) + t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(a + Float64(z * Float64(Float64(x / t_2) + Float64(y / t_2)))) - Float64(Float64(y * b) / t_2));
	elseif (t_1 <= 2e+265)
		tmp = t_1;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	t_2 = (x + y) + t;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (a + (z * ((x / t_2) + (y / t_2)))) - ((y * b) / t_2);
	elseif (t_1 <= 2e+265)
		tmp = t_1;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(a + N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+265], t$95$1, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.1%

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

   2. Taylor expanded in z around 0 42.5%

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

   3. Taylor expanded in t around inf 74.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000013e265

   1. Initial program 99.7%

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

   if 2.00000000000000013e265 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.4%

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

   2. Taylor expanded in y around inf 74.4%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(a + z \cdot \left(\frac{x}{\left(x + y\right) + t} + \frac{y}{\left(x + y\right) + t}\right)\right) - \frac{y \cdot b}{\left(x + y\right) + t}\\ \mathbf{elif}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+265}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 2: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+265}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* (+ x y) z)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+265))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+265)) {
		tmp = (z + a) - b;
	} else {
		tmp = 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 + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+265)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+265):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(Float64(x + y) * z)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+265))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+265)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+265]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.00000000000000013e265 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.1%

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

   2. Taylor expanded in y around inf 73.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000013e265

   1. Initial program 99.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+265}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 3: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-302}:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-155}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-11}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (- (+ z a) b)))
   (if (<= y -7.8e-75)
     t_2
     (if (<= y -1.3e-302)
       (/ z (/ t_1 (+ x y)))
       (if (<= y 5.5e-155)
         (/ a (/ t_1 (+ y t)))
         (if (<= y 1.45e-11)
           (/ (- (* (+ x y) z) (* y b)) (+ y (+ x t)))
           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 = (z + a) - b;
	double tmp;
	if (y <= -7.8e-75) {
		tmp = t_2;
	} else if (y <= -1.3e-302) {
		tmp = z / (t_1 / (x + y));
	} else if (y <= 5.5e-155) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 1.45e-11) {
		tmp = (((x + y) * z) - (y * b)) / (y + (x + t));
	} 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 = (z + a) - b
    if (y <= (-7.8d-75)) then
        tmp = t_2
    else if (y <= (-1.3d-302)) then
        tmp = z / (t_1 / (x + y))
    else if (y <= 5.5d-155) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 1.45d-11) then
        tmp = (((x + y) * z) - (y * b)) / (y + (x + t))
    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 = (z + a) - b;
	double tmp;
	if (y <= -7.8e-75) {
		tmp = t_2;
	} else if (y <= -1.3e-302) {
		tmp = z / (t_1 / (x + y));
	} else if (y <= 5.5e-155) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 1.45e-11) {
		tmp = (((x + y) * z) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -7.8e-75:
		tmp = t_2
	elif y <= -1.3e-302:
		tmp = z / (t_1 / (x + y))
	elif y <= 5.5e-155:
		tmp = a / (t_1 / (y + t))
	elif y <= 1.45e-11:
		tmp = (((x + y) * z) - (y * b)) / (y + (x + t))
	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(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -7.8e-75)
		tmp = t_2;
	elseif (y <= -1.3e-302)
		tmp = Float64(z / Float64(t_1 / Float64(x + y)));
	elseif (y <= 5.5e-155)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 1.45e-11)
		tmp = Float64(Float64(Float64(Float64(x + y) * z) - Float64(y * b)) / Float64(y + Float64(x + t)));
	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 = (z + a) - b;
	tmp = 0.0;
	if (y <= -7.8e-75)
		tmp = t_2;
	elseif (y <= -1.3e-302)
		tmp = z / (t_1 / (x + y));
	elseif (y <= 5.5e-155)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 1.45e-11)
		tmp = (((x + y) * z) - (y * b)) / (y + (x + t));
	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[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -7.8e-75], t$95$2, If[LessEqual[y, -1.3e-302], N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-155], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-11], N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.8000000000000003e-75 or 1.45e-11 < y

   1. Initial program 47.5%

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

   2. Taylor expanded in y around inf 72.0%

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

   if -7.8000000000000003e-75 < y < -1.30000000000000006e-302

   1. Initial program 71.7%

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

   2. Taylor expanded in z around inf 43.0%

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

      1. associate-/l* 66.1%

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

      2. +-commutative 66.1%

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

      3. associate-+r+ 66.1%

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

      4. +-commutative 66.1%

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

   4. Simplified 66.1%

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

   if -1.30000000000000006e-302 < y < 5.50000000000000018e-155

   1. Initial program 81.7%

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

   2. Taylor expanded in a around inf 62.5%

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

      1. associate-/l* 73.0%

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

      2. +-commutative 73.0%

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

      3. associate-+r+ 73.0%

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

   4. Simplified 73.0%

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

   if 5.50000000000000018e-155 < y < 1.45e-11

   1. Initial program 88.2%

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

   2. Taylor expanded in a around 0 77.5%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-75}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-302}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-155}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-11}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 4: 59.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{z}{\frac{t_1}{x + y}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-73}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-305}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-155}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (/ z (/ t_1 (+ x y)))) (t_3 (- (+ z a) b)))
   (if (<= y -1.45e-73)
     t_3
     (if (<= y -9.5e-305)
       t_2
       (if (<= y 6.2e-155)
         (/ a (/ t_1 (+ y t)))
         (if (<= y 6.5e-38) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = z / (t_1 / (x + y));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -1.45e-73) {
		tmp = t_3;
	} else if (y <= -9.5e-305) {
		tmp = t_2;
	} else if (y <= 6.2e-155) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 6.5e-38) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (y + t)
    t_2 = z / (t_1 / (x + y))
    t_3 = (z + a) - b
    if (y <= (-1.45d-73)) then
        tmp = t_3
    else if (y <= (-9.5d-305)) then
        tmp = t_2
    else if (y <= 6.2d-155) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 6.5d-38) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = z / (t_1 / (x + y));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -1.45e-73) {
		tmp = t_3;
	} else if (y <= -9.5e-305) {
		tmp = t_2;
	} else if (y <= 6.2e-155) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 6.5e-38) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = z / (t_1 / (x + y))
	t_3 = (z + a) - b
	tmp = 0
	if y <= -1.45e-73:
		tmp = t_3
	elif y <= -9.5e-305:
		tmp = t_2
	elif y <= 6.2e-155:
		tmp = a / (t_1 / (y + t))
	elif y <= 6.5e-38:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(z / Float64(t_1 / Float64(x + y)))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.45e-73)
		tmp = t_3;
	elseif (y <= -9.5e-305)
		tmp = t_2;
	elseif (y <= 6.2e-155)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 6.5e-38)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = z / (t_1 / (x + y));
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.45e-73)
		tmp = t_3;
	elseif (y <= -9.5e-305)
		tmp = t_2;
	elseif (y <= 6.2e-155)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 6.5e-38)
		tmp = t_2;
	else
		tmp = t_3;
	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[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.45e-73], t$95$3, If[LessEqual[y, -9.5e-305], t$95$2, If[LessEqual[y, 6.2e-155], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-38], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e-73 or 6.49999999999999949e-38 < y

   1. Initial program 48.6%

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

   2. Taylor expanded in y around inf 71.3%

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

   if -1.45e-73 < y < -9.49999999999999902e-305 or 6.2e-155 < y < 6.49999999999999949e-38

   1. Initial program 80.2%

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

   2. Taylor expanded in z around inf 48.4%

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

      1. associate-/l* 63.5%

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

      2. +-commutative 63.5%

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

      3. associate-+r+ 63.5%

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

      4. +-commutative 63.5%

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

   4. Simplified 63.5%

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

   if -9.49999999999999902e-305 < y < 6.2e-155

   1. Initial program 81.7%

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

   2. Taylor expanded in a around inf 62.5%

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

      1. associate-/l* 73.0%

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

      2. +-commutative 73.0%

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

      3. associate-+r+ 73.0%

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

   4. Simplified 73.0%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-73}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-305}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-155}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 5: 56.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \frac{b}{\frac{x}{y}}\\ \mathbf{if}\;x \leq -1 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{a}{x + t}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+31}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-131}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (/ b (/ x y)))))
   (if (<= x -1e+117)
     t_1
     (if (<= x -1.45e+65)
       (* t (/ a (+ x t)))
       (if (<= x -2.4e+31)
         (- z b)
         (if (<= x -2.6e-131)
           (+ z a)
           (if (<= x 4.2e+91) (- (+ z a) b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (b / (x / y));
	double tmp;
	if (x <= -1e+117) {
		tmp = t_1;
	} else if (x <= -1.45e+65) {
		tmp = t * (a / (x + t));
	} else if (x <= -2.4e+31) {
		tmp = z - b;
	} else if (x <= -2.6e-131) {
		tmp = z + a;
	} else if (x <= 4.2e+91) {
		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 = z - (b / (x / y))
    if (x <= (-1d+117)) then
        tmp = t_1
    else if (x <= (-1.45d+65)) then
        tmp = t * (a / (x + t))
    else if (x <= (-2.4d+31)) then
        tmp = z - b
    else if (x <= (-2.6d-131)) then
        tmp = z + a
    else if (x <= 4.2d+91) 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 = z - (b / (x / y));
	double tmp;
	if (x <= -1e+117) {
		tmp = t_1;
	} else if (x <= -1.45e+65) {
		tmp = t * (a / (x + t));
	} else if (x <= -2.4e+31) {
		tmp = z - b;
	} else if (x <= -2.6e-131) {
		tmp = z + a;
	} else if (x <= 4.2e+91) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - (b / (x / y))
	tmp = 0
	if x <= -1e+117:
		tmp = t_1
	elif x <= -1.45e+65:
		tmp = t * (a / (x + t))
	elif x <= -2.4e+31:
		tmp = z - b
	elif x <= -2.6e-131:
		tmp = z + a
	elif x <= 4.2e+91:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(b / Float64(x / y)))
	tmp = 0.0
	if (x <= -1e+117)
		tmp = t_1;
	elseif (x <= -1.45e+65)
		tmp = Float64(t * Float64(a / Float64(x + t)));
	elseif (x <= -2.4e+31)
		tmp = Float64(z - b);
	elseif (x <= -2.6e-131)
		tmp = Float64(z + a);
	elseif (x <= 4.2e+91)
		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 = z - (b / (x / y));
	tmp = 0.0;
	if (x <= -1e+117)
		tmp = t_1;
	elseif (x <= -1.45e+65)
		tmp = t * (a / (x + t));
	elseif (x <= -2.4e+31)
		tmp = z - b;
	elseif (x <= -2.6e-131)
		tmp = z + a;
	elseif (x <= 4.2e+91)
		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[(z - N[(b / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+117], t$95$1, If[LessEqual[x, -1.45e+65], N[(t * N[(a / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e+31], N[(z - b), $MachinePrecision], If[LessEqual[x, -2.6e-131], N[(z + a), $MachinePrecision], If[LessEqual[x, 4.2e+91], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.00000000000000005e117 or 4.20000000000000015e91 < x

   1. Initial program 51.9%

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

   2. Taylor expanded in x around inf 49.1%

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

      1. associate--l+ 52.0%

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

      2. associate-/l* 56.4%

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

      3. associate-/l* 60.8%

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

      4. associate-/l* 65.9%

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

   4. Simplified 65.9%

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

   5. Taylor expanded in b around inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. associate-*l/ 62.0%

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

      3. *-commutative 62.0%

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

      4. distribute-lft-neg-in 62.0%

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

   7. Simplified 62.0%

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

   8. Taylor expanded in z around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. *-commutative 52.2%

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

      3. associate-/l* 62.2%

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

      4. sub-neg 62.2%

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

      5. associate-/l* 52.2%

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

      6. *-commutative 52.2%

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

      7. associate-/l* 61.0%

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

   10. Simplified 61.0%

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

   if -1.00000000000000005e117 < x < -1.45e65

   1. Initial program 71.5%

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

   2. Taylor expanded in a around inf 48.7%

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

      1. associate-/l* 58.0%

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

      2. +-commutative 58.0%

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

      3. associate-+r+ 58.0%

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

   4. Simplified 58.0%

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

   5. Taylor expanded in y around 0 48.5%

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

      1. +-commutative 48.5%

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

   7. Simplified 48.5%

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

      1. associate-/r/ 48.1%

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

   9. Applied egg-rr 48.1%

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

   if -1.45e65 < x < -2.39999999999999982e31

   1. Initial program 45.3%

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

   2. Taylor expanded in y around inf 73.1%

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

   3. Taylor expanded in a around 0 79.2%

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

   if -2.39999999999999982e31 < x < -2.59999999999999996e-131

   1. Initial program 74.3%

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

   2. Taylor expanded in y around inf 70.3%

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

   3. Taylor expanded in b around 0 75.4%

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

   if -2.59999999999999996e-131 < x < 4.20000000000000015e91

   1. Initial program 63.3%

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

   2. Taylor expanded in y around inf 67.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+117}:\\ \;\;\;\;z - \frac{b}{\frac{x}{y}}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{a}{x + t}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+31}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-131}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b}{\frac{x}{y}}\\ \end{array} \]

Alternative 6: 57.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \frac{y}{\frac{x}{b}}\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{a}{x + t}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+31}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-131}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (/ y (/ x b)))))
   (if (<= x -1.05e+118)
     t_1
     (if (<= x -7.5e+66)
       (* t (/ a (+ x t)))
       (if (<= x -2e+31)
         (- z b)
         (if (<= x -8e-131) (+ z a) (if (<= x 3.5e+91) (- (+ z a) b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (y / (x / b));
	double tmp;
	if (x <= -1.05e+118) {
		tmp = t_1;
	} else if (x <= -7.5e+66) {
		tmp = t * (a / (x + t));
	} else if (x <= -2e+31) {
		tmp = z - b;
	} else if (x <= -8e-131) {
		tmp = z + a;
	} else if (x <= 3.5e+91) {
		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 = z - (y / (x / b))
    if (x <= (-1.05d+118)) then
        tmp = t_1
    else if (x <= (-7.5d+66)) then
        tmp = t * (a / (x + t))
    else if (x <= (-2d+31)) then
        tmp = z - b
    else if (x <= (-8d-131)) then
        tmp = z + a
    else if (x <= 3.5d+91) 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 = z - (y / (x / b));
	double tmp;
	if (x <= -1.05e+118) {
		tmp = t_1;
	} else if (x <= -7.5e+66) {
		tmp = t * (a / (x + t));
	} else if (x <= -2e+31) {
		tmp = z - b;
	} else if (x <= -8e-131) {
		tmp = z + a;
	} else if (x <= 3.5e+91) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - (y / (x / b))
	tmp = 0
	if x <= -1.05e+118:
		tmp = t_1
	elif x <= -7.5e+66:
		tmp = t * (a / (x + t))
	elif x <= -2e+31:
		tmp = z - b
	elif x <= -8e-131:
		tmp = z + a
	elif x <= 3.5e+91:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(y / Float64(x / b)))
	tmp = 0.0
	if (x <= -1.05e+118)
		tmp = t_1;
	elseif (x <= -7.5e+66)
		tmp = Float64(t * Float64(a / Float64(x + t)));
	elseif (x <= -2e+31)
		tmp = Float64(z - b);
	elseif (x <= -8e-131)
		tmp = Float64(z + a);
	elseif (x <= 3.5e+91)
		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 = z - (y / (x / b));
	tmp = 0.0;
	if (x <= -1.05e+118)
		tmp = t_1;
	elseif (x <= -7.5e+66)
		tmp = t * (a / (x + t));
	elseif (x <= -2e+31)
		tmp = z - b;
	elseif (x <= -8e-131)
		tmp = z + a;
	elseif (x <= 3.5e+91)
		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[(z - N[(y / N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e+118], t$95$1, If[LessEqual[x, -7.5e+66], N[(t * N[(a / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2e+31], N[(z - b), $MachinePrecision], If[LessEqual[x, -8e-131], N[(z + a), $MachinePrecision], If[LessEqual[x, 3.5e+91], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.05e118 or 3.50000000000000001e91 < x

   1. Initial program 51.9%

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

   2. Taylor expanded in x around inf 49.1%

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

      1. associate--l+ 52.0%

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

      2. associate-/l* 56.4%

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

      3. associate-/l* 60.8%

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

      4. associate-/l* 65.9%

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

   4. Simplified 65.9%

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

   5. Taylor expanded in b around inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. associate-*l/ 62.0%

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

      3. *-commutative 62.0%

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

      4. distribute-lft-neg-in 62.0%

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

   7. Simplified 62.0%

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

      1. distribute-lft-neg-out 62.0%

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

      2. unsub-neg 62.0%

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

      3. clear-num 62.1%

         \[\leadsto z - y \cdot \color{blue}{\frac{1}{\frac{x}{b}}} \]

      4. un-div-inv 62.2%

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

   9. Applied egg-rr 62.2%

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

   if -1.05e118 < x < -7.50000000000000024e66

   1. Initial program 71.5%

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

   2. Taylor expanded in a around inf 48.7%

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

      1. associate-/l* 58.0%

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

      2. +-commutative 58.0%

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

      3. associate-+r+ 58.0%

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

   4. Simplified 58.0%

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

   5. Taylor expanded in y around 0 48.5%

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

      1. +-commutative 48.5%

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

   7. Simplified 48.5%

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

      1. associate-/r/ 48.1%

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

   9. Applied egg-rr 48.1%

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

   if -7.50000000000000024e66 < x < -1.9999999999999999e31

   1. Initial program 45.3%

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

   2. Taylor expanded in y around inf 73.1%

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

   3. Taylor expanded in a around 0 79.2%

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

   if -1.9999999999999999e31 < x < -7.9999999999999999e-131

   1. Initial program 74.3%

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

   2. Taylor expanded in y around inf 70.3%

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

   3. Taylor expanded in b around 0 75.4%

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

   if -7.9999999999999999e-131 < x < 3.50000000000000001e91

   1. Initial program 63.3%

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

   2. Taylor expanded in y around inf 67.9%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+118}:\\ \;\;\;\;z - \frac{y}{\frac{x}{b}}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{a}{x + t}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+31}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-131}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{y}{\frac{x}{b}}\\ \end{array} \]

Alternative 7: 57.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \frac{y}{\frac{x}{b}}\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{+66}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+31}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-131}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (/ y (/ x b)))))
   (if (<= x -7.5e+118)
     t_1
     (if (<= x -3.3e+66)
       (/ a (+ 1.0 (/ x t)))
       (if (<= x -2.4e+31)
         (- z b)
         (if (<= x -8e-131) (+ z a) (if (<= x 4.8e+91) (- (+ z a) b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (y / (x / b));
	double tmp;
	if (x <= -7.5e+118) {
		tmp = t_1;
	} else if (x <= -3.3e+66) {
		tmp = a / (1.0 + (x / t));
	} else if (x <= -2.4e+31) {
		tmp = z - b;
	} else if (x <= -8e-131) {
		tmp = z + a;
	} else if (x <= 4.8e+91) {
		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 = z - (y / (x / b))
    if (x <= (-7.5d+118)) then
        tmp = t_1
    else if (x <= (-3.3d+66)) then
        tmp = a / (1.0d0 + (x / t))
    else if (x <= (-2.4d+31)) then
        tmp = z - b
    else if (x <= (-8d-131)) then
        tmp = z + a
    else if (x <= 4.8d+91) 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 = z - (y / (x / b));
	double tmp;
	if (x <= -7.5e+118) {
		tmp = t_1;
	} else if (x <= -3.3e+66) {
		tmp = a / (1.0 + (x / t));
	} else if (x <= -2.4e+31) {
		tmp = z - b;
	} else if (x <= -8e-131) {
		tmp = z + a;
	} else if (x <= 4.8e+91) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - (y / (x / b))
	tmp = 0
	if x <= -7.5e+118:
		tmp = t_1
	elif x <= -3.3e+66:
		tmp = a / (1.0 + (x / t))
	elif x <= -2.4e+31:
		tmp = z - b
	elif x <= -8e-131:
		tmp = z + a
	elif x <= 4.8e+91:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(y / Float64(x / b)))
	tmp = 0.0
	if (x <= -7.5e+118)
		tmp = t_1;
	elseif (x <= -3.3e+66)
		tmp = Float64(a / Float64(1.0 + Float64(x / t)));
	elseif (x <= -2.4e+31)
		tmp = Float64(z - b);
	elseif (x <= -8e-131)
		tmp = Float64(z + a);
	elseif (x <= 4.8e+91)
		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 = z - (y / (x / b));
	tmp = 0.0;
	if (x <= -7.5e+118)
		tmp = t_1;
	elseif (x <= -3.3e+66)
		tmp = a / (1.0 + (x / t));
	elseif (x <= -2.4e+31)
		tmp = z - b;
	elseif (x <= -8e-131)
		tmp = z + a;
	elseif (x <= 4.8e+91)
		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[(z - N[(y / N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e+118], t$95$1, If[LessEqual[x, -3.3e+66], N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e+31], N[(z - b), $MachinePrecision], If[LessEqual[x, -8e-131], N[(z + a), $MachinePrecision], If[LessEqual[x, 4.8e+91], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7.50000000000000003e118 or 4.79999999999999966e91 < x

   1. Initial program 51.9%

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

   2. Taylor expanded in x around inf 49.1%

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

      1. associate--l+ 52.0%

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

      2. associate-/l* 56.4%

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

      3. associate-/l* 60.8%

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

      4. associate-/l* 65.9%

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

   4. Simplified 65.9%

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

   5. Taylor expanded in b around inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. associate-*l/ 62.0%

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

      3. *-commutative 62.0%

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

      4. distribute-lft-neg-in 62.0%

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

   7. Simplified 62.0%

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

      1. distribute-lft-neg-out 62.0%

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

      2. unsub-neg 62.0%

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

      3. clear-num 62.1%

         \[\leadsto z - y \cdot \color{blue}{\frac{1}{\frac{x}{b}}} \]

      4. un-div-inv 62.2%

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

   9. Applied egg-rr 62.2%

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

   if -7.50000000000000003e118 < x < -3.3000000000000001e66

   1. Initial program 71.5%

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

   2. Taylor expanded in a around inf 48.7%

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

      1. associate-/l* 58.0%

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

      2. +-commutative 58.0%

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

      3. associate-+r+ 58.0%

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

   4. Simplified 58.0%

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

   5. Taylor expanded in t around inf 48.5%

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

   if -3.3000000000000001e66 < x < -2.39999999999999982e31

   1. Initial program 45.3%

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

   2. Taylor expanded in y around inf 73.1%

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

   3. Taylor expanded in a around 0 79.2%

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

   if -2.39999999999999982e31 < x < -7.9999999999999999e-131

   1. Initial program 74.3%

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

   2. Taylor expanded in y around inf 70.3%

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

   3. Taylor expanded in b around 0 75.4%

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

   if -7.9999999999999999e-131 < x < 4.79999999999999966e91

   1. Initial program 63.3%

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

   2. Taylor expanded in y around inf 67.9%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+118}:\\ \;\;\;\;z - \frac{y}{\frac{x}{b}}\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{+66}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+31}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-131}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - \frac{y}{\frac{x}{b}}\\ \end{array} \]

Alternative 8: 57.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-154}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-40}:\\ \;\;\;\;z - \frac{b}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.5e-75)
     t_1
     (if (<= y -8.5e-301)
       (/ x (/ (+ x t) z))
       (if (<= y 1.9e-154)
         (/ a (+ 1.0 (/ x t)))
         (if (<= y 1.75e-40) (- z (/ b (/ x y))) 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 <= -1.5e-75) {
		tmp = t_1;
	} else if (y <= -8.5e-301) {
		tmp = x / ((x + t) / z);
	} else if (y <= 1.9e-154) {
		tmp = a / (1.0 + (x / t));
	} else if (y <= 1.75e-40) {
		tmp = z - (b / (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.5d-75)) then
        tmp = t_1
    else if (y <= (-8.5d-301)) then
        tmp = x / ((x + t) / z)
    else if (y <= 1.9d-154) then
        tmp = a / (1.0d0 + (x / t))
    else if (y <= 1.75d-40) then
        tmp = z - (b / (x / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.5e-75) {
		tmp = t_1;
	} else if (y <= -8.5e-301) {
		tmp = x / ((x + t) / z);
	} else if (y <= 1.9e-154) {
		tmp = a / (1.0 + (x / t));
	} else if (y <= 1.75e-40) {
		tmp = z - (b / (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.5e-75:
		tmp = t_1
	elif y <= -8.5e-301:
		tmp = x / ((x + t) / z)
	elif y <= 1.9e-154:
		tmp = a / (1.0 + (x / t))
	elif y <= 1.75e-40:
		tmp = z - (b / (x / y))
	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 <= -1.5e-75)
		tmp = t_1;
	elseif (y <= -8.5e-301)
		tmp = Float64(x / Float64(Float64(x + t) / z));
	elseif (y <= 1.9e-154)
		tmp = Float64(a / Float64(1.0 + Float64(x / t)));
	elseif (y <= 1.75e-40)
		tmp = Float64(z - Float64(b / Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.5e-75)
		tmp = t_1;
	elseif (y <= -8.5e-301)
		tmp = x / ((x + t) / z);
	elseif (y <= 1.9e-154)
		tmp = a / (1.0 + (x / t));
	elseif (y <= 1.75e-40)
		tmp = z - (b / (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.5e-75], t$95$1, If[LessEqual[y, -8.5e-301], N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-154], N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-40], N[(z - N[(b / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.4999999999999999e-75 or 1.7500000000000001e-40 < y

   1. Initial program 48.9%

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

   2. Taylor expanded in y around inf 70.9%

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

   if -1.4999999999999999e-75 < y < -8.50000000000000046e-301

   1. Initial program 71.7%

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

   2. Taylor expanded in x around inf 43.0%

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

      1. *-commutative 43.0%

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

   4. Simplified 43.0%

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

   5. Taylor expanded in y around 0 43.0%

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

      1. associate-/l* 60.7%

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

   7. Simplified 60.7%

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

   if -8.50000000000000046e-301 < y < 1.90000000000000005e-154

   1. Initial program 82.2%

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

   2. Taylor expanded in a around inf 60.8%

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

      1. associate-/l* 71.1%

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

      2. +-commutative 71.1%

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

      3. associate-+r+ 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in t around inf 68.5%

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

   if 1.90000000000000005e-154 < y < 1.7500000000000001e-40

   1. Initial program 91.7%

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

   2. Taylor expanded in x around inf 50.8%

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

      1. associate--l+ 50.8%

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

      2. associate-/l* 50.8%

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

      3. associate-/l* 50.9%

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

      4. associate-/l* 58.9%

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

   4. Simplified 58.9%

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

   5. Taylor expanded in b around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-*l/ 59.9%

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

      3. *-commutative 59.9%

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

      4. distribute-lft-neg-in 59.9%

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

   7. Simplified 59.9%

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

   8. Taylor expanded in z around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-/l* 60.0%

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

      4. sub-neg 60.0%

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

      5. associate-/l* 60.0%

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

      6. *-commutative 60.0%

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

      7. associate-/l* 60.0%

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

   10. Simplified 60.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-75}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-154}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-40}:\\ \;\;\;\;z - \frac{b}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 9: 58.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-300}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-154}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-40}:\\ \;\;\;\;z - \frac{b}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.4e-75)
     t_1
     (if (<= y -2.1e-300)
       (/ z (/ (+ y (+ x t)) x))
       (if (<= y 2.3e-154)
         (/ a (+ 1.0 (/ x t)))
         (if (<= y 2.1e-40) (- z (/ b (/ x y))) 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 <= -2.4e-75) {
		tmp = t_1;
	} else if (y <= -2.1e-300) {
		tmp = z / ((y + (x + t)) / x);
	} else if (y <= 2.3e-154) {
		tmp = a / (1.0 + (x / t));
	} else if (y <= 2.1e-40) {
		tmp = z - (b / (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.4d-75)) then
        tmp = t_1
    else if (y <= (-2.1d-300)) then
        tmp = z / ((y + (x + t)) / x)
    else if (y <= 2.3d-154) then
        tmp = a / (1.0d0 + (x / t))
    else if (y <= 2.1d-40) then
        tmp = z - (b / (x / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.4e-75) {
		tmp = t_1;
	} else if (y <= -2.1e-300) {
		tmp = z / ((y + (x + t)) / x);
	} else if (y <= 2.3e-154) {
		tmp = a / (1.0 + (x / t));
	} else if (y <= 2.1e-40) {
		tmp = z - (b / (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.4e-75:
		tmp = t_1
	elif y <= -2.1e-300:
		tmp = z / ((y + (x + t)) / x)
	elif y <= 2.3e-154:
		tmp = a / (1.0 + (x / t))
	elif y <= 2.1e-40:
		tmp = z - (b / (x / y))
	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 <= -2.4e-75)
		tmp = t_1;
	elseif (y <= -2.1e-300)
		tmp = Float64(z / Float64(Float64(y + Float64(x + t)) / x));
	elseif (y <= 2.3e-154)
		tmp = Float64(a / Float64(1.0 + Float64(x / t)));
	elseif (y <= 2.1e-40)
		tmp = Float64(z - Float64(b / Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.4e-75)
		tmp = t_1;
	elseif (y <= -2.1e-300)
		tmp = z / ((y + (x + t)) / x);
	elseif (y <= 2.3e-154)
		tmp = a / (1.0 + (x / t));
	elseif (y <= 2.1e-40)
		tmp = z - (b / (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.4e-75], t$95$1, If[LessEqual[y, -2.1e-300], N[(z / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-154], N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-40], N[(z - N[(b / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.40000000000000019e-75 or 2.10000000000000018e-40 < y

   1. Initial program 48.9%

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

   2. Taylor expanded in y around inf 70.9%

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

   if -2.40000000000000019e-75 < y < -2.10000000000000004e-300

   1. Initial program 71.7%

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

   2. Taylor expanded in x around inf 43.0%

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

      1. *-commutative 43.0%

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

   4. Simplified 43.0%

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

      1. *-un-lft-identity 43.0%

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

      2. times-frac 66.0%

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

      3. +-commutative 66.0%

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

   6. Applied egg-rr 66.0%

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

      1. frac-times 43.0%

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

      2. *-un-lft-identity 43.0%

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

      3. associate-/l* 66.0%

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

   8. Applied egg-rr 66.0%

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

   if -2.10000000000000004e-300 < y < 2.3e-154

   1. Initial program 82.2%

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

   2. Taylor expanded in a around inf 60.8%

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

      1. associate-/l* 71.1%

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

      2. +-commutative 71.1%

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

      3. associate-+r+ 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in t around inf 68.5%

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

   if 2.3e-154 < y < 2.10000000000000018e-40

   1. Initial program 91.7%

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

   2. Taylor expanded in x around inf 50.8%

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

      1. associate--l+ 50.8%

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

      2. associate-/l* 50.8%

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

      3. associate-/l* 50.9%

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

      4. associate-/l* 58.9%

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

   4. Simplified 58.9%

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

   5. Taylor expanded in b around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-*l/ 59.9%

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

      3. *-commutative 59.9%

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

      4. distribute-lft-neg-in 59.9%

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

   7. Simplified 59.9%

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

   8. Taylor expanded in z around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-/l* 60.0%

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

      4. sub-neg 60.0%

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

      5. associate-/l* 60.0%

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

      6. *-commutative 60.0%

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

      7. associate-/l* 60.0%

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

   10. Simplified 60.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-75}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-300}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-154}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-40}:\\ \;\;\;\;z - \frac{b}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 57.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+144} \lor \neg \left(a \leq 650000000000\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.2e+144) (not (<= a 650000000000.0)))
   (* (+ y t) (/ a (+ y (+ x t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.2e+144) || !(a <= 650000000000.0)) {
		tmp = (y + t) * (a / (y + (x + 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 ((a <= (-4.2d+144)) .or. (.not. (a <= 650000000000.0d0))) then
        tmp = (y + t) * (a / (y + (x + 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 ((a <= -4.2e+144) || !(a <= 650000000000.0)) {
		tmp = (y + t) * (a / (y + (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4.2e+144) or not (a <= 650000000000.0):
		tmp = (y + t) * (a / (y + (x + t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4.2e+144) || !(a <= 650000000000.0))
		tmp = Float64(Float64(y + t) * Float64(a / Float64(y + Float64(x + 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 ((a <= -4.2e+144) || ~((a <= 650000000000.0)))
		tmp = (y + t) * (a / (y + (x + t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.2e+144], N[Not[LessEqual[a, 650000000000.0]], $MachinePrecision]], N[(N[(y + t), $MachinePrecision] * N[(a / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.19999999999999993e144 or 6.5e11 < a

   1. Initial program 56.1%

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

   2. Taylor expanded in a around inf 43.9%

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

      1. associate-/l* 72.0%

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

      2. +-commutative 72.0%

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

      3. associate-+r+ 72.0%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in a around 0 43.9%

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

      1. +-commutative 43.9%

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

      2. associate-*l/ 69.1%

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

      3. *-commutative 69.1%

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

      4. +-commutative 69.1%

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

      5. +-commutative 69.1%

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

      6. associate-+r+ 69.1%

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

      7. +-commutative 69.1%

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

   7. Simplified 69.1%

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

   if -4.19999999999999993e144 < a < 6.5e11

   1. Initial program 64.1%

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

   2. Taylor expanded in y around inf 60.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+144} \lor \neg \left(a \leq 650000000000\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 58.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+143} \lor \neg \left(a \leq 720000000000\right):\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4e+143) (not (<= a 720000000000.0)))
   (/ a (/ (+ x (+ y t)) (+ y t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4e+143) || !(a <= 720000000000.0)) {
		tmp = a / ((x + (y + t)) / (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 ((a <= (-4d+143)) .or. (.not. (a <= 720000000000.0d0))) then
        tmp = a / ((x + (y + t)) / (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 ((a <= -4e+143) || !(a <= 720000000000.0)) {
		tmp = a / ((x + (y + t)) / (y + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4e+143) or not (a <= 720000000000.0):
		tmp = a / ((x + (y + t)) / (y + t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4e+143) || !(a <= 720000000000.0))
		tmp = Float64(a / Float64(Float64(x + Float64(y + t)) / Float64(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 ((a <= -4e+143) || ~((a <= 720000000000.0)))
		tmp = a / ((x + (y + t)) / (y + t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4e+143], N[Not[LessEqual[a, 720000000000.0]], $MachinePrecision]], N[(a / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.0000000000000001e143 or 7.2e11 < a

   1. Initial program 56.1%

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

   2. Taylor expanded in a around inf 43.9%

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

      1. associate-/l* 72.0%

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

      2. +-commutative 72.0%

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

      3. associate-+r+ 72.0%

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

   4. Simplified 72.0%

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

   if -4.0000000000000001e143 < a < 7.2e11

   1. Initial program 64.1%

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

   2. Taylor expanded in y around inf 60.8%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+143} \lor \neg \left(a \leq 720000000000\right):\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 12: 50.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+129}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-30}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.8e+129) z (if (<= z 2e-30) (- a b) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.8e+129) {
		tmp = z;
	} else if (z <= 2e-30) {
		tmp = a - b;
	} else {
		tmp = z + 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 (z <= (-3.8d+129)) then
        tmp = z
    else if (z <= 2d-30) then
        tmp = a - b
    else
        tmp = z + 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 (z <= -3.8e+129) {
		tmp = z;
	} else if (z <= 2e-30) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.8e+129:
		tmp = z
	elif z <= 2e-30:
		tmp = a - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.8e+129)
		tmp = z;
	elseif (z <= 2e-30)
		tmp = Float64(a - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.8e+129)
		tmp = z;
	elseif (z <= 2e-30)
		tmp = a - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.8e+129], z, If[LessEqual[z, 2e-30], N[(a - b), $MachinePrecision], N[(z + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000005e129

   1. Initial program 30.4%

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

   2. Taylor expanded in x around inf 68.9%

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

   if -3.80000000000000005e129 < z < 2e-30

   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. Taylor expanded in y around inf 51.1%

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

   3. Taylor expanded in z around 0 50.1%

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

   if 2e-30 < z

   1. Initial program 58.9%

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

   2. Taylor expanded in y around inf 64.0%

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

   3. Taylor expanded in b around 0 63.2%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+129}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-30}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 13: 57.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x 4.8e+91) (- (+ z a) b) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.8e+91) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 4.8d+91) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.8e+91) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 4.8e+91:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 4.8e+91)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 4.8e+91)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 4.8e+91], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < 4.79999999999999966e91

   1. Initial program 62.5%

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

   2. Taylor expanded in y around inf 63.2%

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

   if 4.79999999999999966e91 < x

   1. Initial program 54.4%

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

   2. Taylor expanded in x around inf 45.5%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 14: 44.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+44}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+65}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.25e+44) z (if (<= z 1.3e+65) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.25e+44) {
		tmp = z;
	} else if (z <= 1.3e+65) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.25d+44)) then
        tmp = z
    else if (z <= 1.3d+65) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.25e+44) {
		tmp = z;
	} else if (z <= 1.3e+65) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.25e+44:
		tmp = z
	elif z <= 1.3e+65:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.25e+44)
		tmp = z;
	elseif (z <= 1.3e+65)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.25e+44)
		tmp = z;
	elseif (z <= 1.3e+65)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.25e+44], z, If[LessEqual[z, 1.3e+65], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2499999999999999e44 or 1.30000000000000001e65 < z

   1. Initial program 44.1%

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

   2. Taylor expanded in x around inf 59.2%

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

   if -1.2499999999999999e44 < z < 1.30000000000000001e65

   1. Initial program 73.2%

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

   2. Taylor expanded in t around inf 43.7%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+44}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+65}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 15: 51.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+269}:\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b -8.8e+269) (- b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.8e+269) {
		tmp = -b;
	} else {
		tmp = z + 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 (b <= (-8.8d+269)) then
        tmp = -b
    else
        tmp = z + 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 (b <= -8.8e+269) {
		tmp = -b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.8e+269:
		tmp = -b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.8e+269)
		tmp = Float64(-b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.8e+269)
		tmp = -b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.8e+269], (-b), N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.7999999999999995e269

   1. Initial program 55.0%

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

   2. Taylor expanded in y around inf 82.2%

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

   3. Taylor expanded in b around inf 82.0%

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

      1. neg-mul-1 82.0%

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

   5. Simplified 82.0%

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

   if -8.7999999999999995e269 < b

   1. Initial program 61.2%

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

   2. Taylor expanded in y around inf 56.4%

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

   3. Taylor expanded in b around 0 52.7%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+269}:\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 16: 32.9% 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 61.0%

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

2. Taylor expanded in t around inf 32.6%

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

3. Final simplification 32.6%

   \[\leadsto a \]

Developer target: 82.3% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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