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

Percentage Accurate: 60.6% → 88.0%

Time: 17.4s

Alternatives: 15

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+280}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+280))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+280)) {
		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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+280)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+280):
		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(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+280))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+280)))
		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[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+280]], $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 2.0000000000000001e280 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Taylor expanded in y around inf 76.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e280

   1. Initial program 99.1%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+280}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-140}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-187}:\\ \;\;\;\;\frac{z}{\frac{t_2}{x + y}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-97}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t_2}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+34}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ y (+ x t))))
   (if (<= y -5e+68)
     t_1
     (if (<= y -2e-140)
       (+ a (/ y (/ (+ y t) z)))
       (if (<= y -1.1e-187)
         (/ z (/ t_2 (+ x y)))
         (if (<= y 8.5e-97)
           (/ (+ (* t a) (* x z)) (+ x t))
           (if (<= y 4.9e+17)
             (/ (- (* a (+ y t)) (* y b)) t_2)
             (if (<= y 4.2e+34) (+ z a) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double tmp;
	if (y <= -5e+68) {
		tmp = t_1;
	} else if (y <= -2e-140) {
		tmp = a + (y / ((y + t) / z));
	} else if (y <= -1.1e-187) {
		tmp = z / (t_2 / (x + y));
	} else if (y <= 8.5e-97) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.9e+17) {
		tmp = ((a * (y + t)) - (y * b)) / t_2;
	} else if (y <= 4.2e+34) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    if (y <= (-5d+68)) then
        tmp = t_1
    else if (y <= (-2d-140)) then
        tmp = a + (y / ((y + t) / z))
    else if (y <= (-1.1d-187)) then
        tmp = z / (t_2 / (x + y))
    else if (y <= 8.5d-97) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 4.9d+17) then
        tmp = ((a * (y + t)) - (y * b)) / t_2
    else if (y <= 4.2d+34) then
        tmp = z + a
    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 t_2 = y + (x + t);
	double tmp;
	if (y <= -5e+68) {
		tmp = t_1;
	} else if (y <= -2e-140) {
		tmp = a + (y / ((y + t) / z));
	} else if (y <= -1.1e-187) {
		tmp = z / (t_2 / (x + y));
	} else if (y <= 8.5e-97) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.9e+17) {
		tmp = ((a * (y + t)) - (y * b)) / t_2;
	} else if (y <= 4.2e+34) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	tmp = 0
	if y <= -5e+68:
		tmp = t_1
	elif y <= -2e-140:
		tmp = a + (y / ((y + t) / z))
	elif y <= -1.1e-187:
		tmp = z / (t_2 / (x + y))
	elif y <= 8.5e-97:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 4.9e+17:
		tmp = ((a * (y + t)) - (y * b)) / t_2
	elif y <= 4.2e+34:
		tmp = z + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -5e+68)
		tmp = t_1;
	elseif (y <= -2e-140)
		tmp = Float64(a + Float64(y / Float64(Float64(y + t) / z)));
	elseif (y <= -1.1e-187)
		tmp = Float64(z / Float64(t_2 / Float64(x + y)));
	elseif (y <= 8.5e-97)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 4.9e+17)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_2);
	elseif (y <= 4.2e+34)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	tmp = 0.0;
	if (y <= -5e+68)
		tmp = t_1;
	elseif (y <= -2e-140)
		tmp = a + (y / ((y + t) / z));
	elseif (y <= -1.1e-187)
		tmp = z / (t_2 / (x + y));
	elseif (y <= 8.5e-97)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 4.9e+17)
		tmp = ((a * (y + t)) - (y * b)) / t_2;
	elseif (y <= 4.2e+34)
		tmp = z + a;
	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]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+68], t$95$1, If[LessEqual[y, -2e-140], N[(a + N[(y / N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-187], N[(z / N[(t$95$2 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-97], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+17], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 4.2e+34], N[(z + a), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.0000000000000004e68 or 4.20000000000000035e34 < y

   1. Initial program 38.3%

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

   3. Taylor expanded in y around inf 81.2%

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

   if -5.0000000000000004e68 < y < -2e-140

   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. Add Preprocessing

   3. Taylor expanded in z around 0 81.1%

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

      1. associate--l+ 81.1%

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

      2. associate-+r+ 81.1%

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

      3. associate-+r+ 81.1%

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

      4. div-sub 81.1%

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

      5. *-commutative 81.1%

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

      6. associate-+r+ 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around inf 71.6%

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

   7. Taylor expanded in x around 0 62.7%

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

      1. associate-/l* 59.2%

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

      2. +-commutative 59.2%

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

   9. Simplified 59.2%

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

   if -2e-140 < y < -1.10000000000000004e-187

   1. Initial program 71.8%

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

   3. Taylor expanded in z around inf 33.2%

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

      1. associate-/l* 61.3%

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

      2. associate-+r+ 61.3%

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

      3. +-commutative 61.3%

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

   5. Simplified 61.3%

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

   if -1.10000000000000004e-187 < y < 8.5000000000000002e-97

   1. Initial program 82.8%

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

   3. Taylor expanded in y around 0 73.3%

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

   if 8.5000000000000002e-97 < y < 4.9e17

   1. Initial program 82.1%

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

   3. Taylor expanded in z around 0 70.3%

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

      1. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   if 4.9e17 < y < 4.20000000000000035e34

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-+r+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. div-sub 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-+r+ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 100.0%

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

   7. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{z} + a \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+68}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-140}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-187}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-97}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+34}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-136}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-187}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-95}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+17}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+34}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)))
   (if (<= y -2.3e+70)
     t_2
     (if (<= y -2.3e-136)
       (+ a (/ y (/ (+ y t) z)))
       (if (<= y -5.1e-187)
         (/ (- (* z (+ x y)) (* y b)) t_1)
         (if (<= y 2.8e-95)
           (/ (+ (* t a) (* x z)) (+ x t))
           (if (<= y 5e+17)
             (/ (- (* a (+ y t)) (* y b)) t_1)
             (if (<= y 4e+34) (+ z a) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2.3e+70) {
		tmp = t_2;
	} else if (y <= -2.3e-136) {
		tmp = a + (y / ((y + t) / z));
	} else if (y <= -5.1e-187) {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	} else if (y <= 2.8e-95) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 5e+17) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else if (y <= 4e+34) {
		tmp = z + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (z + a) - b
    if (y <= (-2.3d+70)) then
        tmp = t_2
    else if (y <= (-2.3d-136)) then
        tmp = a + (y / ((y + t) / z))
    else if (y <= (-5.1d-187)) then
        tmp = ((z * (x + y)) - (y * b)) / t_1
    else if (y <= 2.8d-95) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 5d+17) then
        tmp = ((a * (y + t)) - (y * b)) / t_1
    else if (y <= 4d+34) then
        tmp = z + a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2.3e+70) {
		tmp = t_2;
	} else if (y <= -2.3e-136) {
		tmp = a + (y / ((y + t) / z));
	} else if (y <= -5.1e-187) {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	} else if (y <= 2.8e-95) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 5e+17) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else if (y <= 4e+34) {
		tmp = z + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -2.3e+70:
		tmp = t_2
	elif y <= -2.3e-136:
		tmp = a + (y / ((y + t) / z))
	elif y <= -5.1e-187:
		tmp = ((z * (x + y)) - (y * b)) / t_1
	elif y <= 2.8e-95:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 5e+17:
		tmp = ((a * (y + t)) - (y * b)) / t_1
	elif y <= 4e+34:
		tmp = z + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.3e+70)
		tmp = t_2;
	elseif (y <= -2.3e-136)
		tmp = Float64(a + Float64(y / Float64(Float64(y + t) / z)));
	elseif (y <= -5.1e-187)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / t_1);
	elseif (y <= 2.8e-95)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 5e+17)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_1);
	elseif (y <= 4e+34)
		tmp = Float64(z + a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.3e+70)
		tmp = t_2;
	elseif (y <= -2.3e-136)
		tmp = a + (y / ((y + t) / z));
	elseif (y <= -5.1e-187)
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	elseif (y <= 2.8e-95)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 5e+17)
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	elseif (y <= 4e+34)
		tmp = z + a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.3e+70], t$95$2, If[LessEqual[y, -2.3e-136], N[(a + N[(y / N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.1e-187], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.8e-95], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+17], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 4e+34], N[(z + a), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.29999999999999994e70 or 3.99999999999999978e34 < y

   1. Initial program 38.3%

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

   3. Taylor expanded in y around inf 81.2%

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

   if -2.29999999999999994e70 < y < -2.29999999999999998e-136

   1. Initial program 70.9%

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

   3. Taylor expanded in z around 0 80.6%

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

      1. associate--l+ 80.6%

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

      2. associate-+r+ 80.6%

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

      3. associate-+r+ 80.6%

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

      4. div-sub 80.6%

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

      5. *-commutative 80.6%

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

      6. associate-+r+ 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in t around inf 73.4%

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

   7. Taylor expanded in x around 0 64.2%

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

      1. associate-/l* 60.6%

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

      2. +-commutative 60.6%

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

   9. Simplified 60.6%

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

   if -2.29999999999999998e-136 < y < -5.09999999999999971e-187

   1. Initial program 71.8%

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

   3. Taylor expanded in a around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   if -5.09999999999999971e-187 < y < 2.7999999999999999e-95

   1. Initial program 83.0%

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

   3. Taylor expanded in y around 0 73.7%

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

   if 2.7999999999999999e-95 < y < 5e17

   1. Initial program 82.1%

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

   3. Taylor expanded in z around 0 70.3%

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

      1. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   if 5e17 < y < 3.99999999999999978e34

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-+r+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. div-sub 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-+r+ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 100.0%

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

   7. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{z} + a \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+70}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-136}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-187}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-95}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+17}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+34}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \left(y + t\right)\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{\left(t_2 + y \cdot z\right) - y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-187}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-99}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{t_2 - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+34}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* a (+ y t))) (t_3 (- (+ z a) b)))
   (if (<= y -5.5e+105)
     t_3
     (if (<= y -3.8e-125)
       (/ (- (+ t_2 (* y z)) (* y b)) (+ y t))
       (if (<= y -2.15e-187)
         (/ (- (* z (+ x y)) (* y b)) t_1)
         (if (<= y 4e-99)
           (/ (+ (* t a) (* x z)) (+ x t))
           (if (<= y 1.4e+17)
             (/ (- t_2 (* y b)) t_1)
             (if (<= y 4.5e+34) (+ z a) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * (y + t);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -5.5e+105) {
		tmp = t_3;
	} else if (y <= -3.8e-125) {
		tmp = ((t_2 + (y * z)) - (y * b)) / (y + t);
	} else if (y <= -2.15e-187) {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	} else if (y <= 4e-99) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.4e+17) {
		tmp = (t_2 - (y * b)) / t_1;
	} else if (y <= 4.5e+34) {
		tmp = z + a;
	} 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 = y + (x + t)
    t_2 = a * (y + t)
    t_3 = (z + a) - b
    if (y <= (-5.5d+105)) then
        tmp = t_3
    else if (y <= (-3.8d-125)) then
        tmp = ((t_2 + (y * z)) - (y * b)) / (y + t)
    else if (y <= (-2.15d-187)) then
        tmp = ((z * (x + y)) - (y * b)) / t_1
    else if (y <= 4d-99) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 1.4d+17) then
        tmp = (t_2 - (y * b)) / t_1
    else if (y <= 4.5d+34) then
        tmp = z + a
    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 = y + (x + t);
	double t_2 = a * (y + t);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -5.5e+105) {
		tmp = t_3;
	} else if (y <= -3.8e-125) {
		tmp = ((t_2 + (y * z)) - (y * b)) / (y + t);
	} else if (y <= -2.15e-187) {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	} else if (y <= 4e-99) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.4e+17) {
		tmp = (t_2 - (y * b)) / t_1;
	} else if (y <= 4.5e+34) {
		tmp = z + a;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a * (y + t)
	t_3 = (z + a) - b
	tmp = 0
	if y <= -5.5e+105:
		tmp = t_3
	elif y <= -3.8e-125:
		tmp = ((t_2 + (y * z)) - (y * b)) / (y + t)
	elif y <= -2.15e-187:
		tmp = ((z * (x + y)) - (y * b)) / t_1
	elif y <= 4e-99:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 1.4e+17:
		tmp = (t_2 - (y * b)) / t_1
	elif y <= 4.5e+34:
		tmp = z + a
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a * Float64(y + t))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -5.5e+105)
		tmp = t_3;
	elseif (y <= -3.8e-125)
		tmp = Float64(Float64(Float64(t_2 + Float64(y * z)) - Float64(y * b)) / Float64(y + t));
	elseif (y <= -2.15e-187)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / t_1);
	elseif (y <= 4e-99)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 1.4e+17)
		tmp = Float64(Float64(t_2 - Float64(y * b)) / t_1);
	elseif (y <= 4.5e+34)
		tmp = Float64(z + a);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a * (y + t);
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -5.5e+105)
		tmp = t_3;
	elseif (y <= -3.8e-125)
		tmp = ((t_2 + (y * z)) - (y * b)) / (y + t);
	elseif (y <= -2.15e-187)
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	elseif (y <= 4e-99)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 1.4e+17)
		tmp = (t_2 - (y * b)) / t_1;
	elseif (y <= 4.5e+34)
		tmp = z + a;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5.5e+105], t$95$3, If[LessEqual[y, -3.8e-125], N[(N[(N[(t$95$2 + N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-187], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 4e-99], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+17], N[(N[(t$95$2 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 4.5e+34], N[(z + a), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.49999999999999979e105 or 4.5e34 < y

   1. Initial program 36.4%

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

   3. Taylor expanded in y around inf 82.0%

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

   if -5.49999999999999979e105 < y < -3.8000000000000001e-125

   1. Initial program 73.1%

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

   3. Taylor expanded in x around 0 62.4%

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

   if -3.8000000000000001e-125 < y < -2.15e-187

   1. Initial program 68.4%

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

   3. Taylor expanded in a around 0 60.2%

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

      1. +-commutative 60.2%

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

      2. *-commutative 60.2%

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

   5. Simplified 60.2%

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

   if -2.15e-187 < y < 4.0000000000000001e-99

   1. Initial program 83.0%

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

   3. Taylor expanded in y around 0 73.7%

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

   if 4.0000000000000001e-99 < y < 1.4e17

   1. Initial program 82.1%

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

   3. Taylor expanded in z around 0 70.3%

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

      1. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   if 1.4e17 < y < 4.5e34

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-+r+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. div-sub 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-+r+ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 100.0%

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

   7. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{z} + a \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+105}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + y \cdot z\right) - y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-187}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-99}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+34}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -7.7 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-141}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-189}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;y \leq 2500000000:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -7.7e+68)
     t_1
     (if (<= y -6.5e-141)
       (+ a (/ y (/ (+ y t) z)))
       (if (<= y -1.35e-189)
         (/ z (/ (+ y (+ x t)) (+ x y)))
         (if (<= y 2500000000.0) (/ (+ (* t a) (* x z)) (+ x t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -7.7e+68) {
		tmp = t_1;
	} else if (y <= -6.5e-141) {
		tmp = a + (y / ((y + t) / z));
	} else if (y <= -1.35e-189) {
		tmp = z / ((y + (x + t)) / (x + y));
	} else if (y <= 2500000000.0) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-7.7d+68)) then
        tmp = t_1
    else if (y <= (-6.5d-141)) then
        tmp = a + (y / ((y + t) / z))
    else if (y <= (-1.35d-189)) then
        tmp = z / ((y + (x + t)) / (x + y))
    else if (y <= 2500000000.0d0) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -7.7e+68) {
		tmp = t_1;
	} else if (y <= -6.5e-141) {
		tmp = a + (y / ((y + t) / z));
	} else if (y <= -1.35e-189) {
		tmp = z / ((y + (x + t)) / (x + y));
	} else if (y <= 2500000000.0) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -7.7e+68:
		tmp = t_1
	elif y <= -6.5e-141:
		tmp = a + (y / ((y + t) / z))
	elif y <= -1.35e-189:
		tmp = z / ((y + (x + t)) / (x + y))
	elif y <= 2500000000.0:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -7.7e+68)
		tmp = t_1;
	elseif (y <= -6.5e-141)
		tmp = Float64(a + Float64(y / Float64(Float64(y + t) / z)));
	elseif (y <= -1.35e-189)
		tmp = Float64(z / Float64(Float64(y + Float64(x + t)) / Float64(x + y)));
	elseif (y <= 2500000000.0)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -7.7e+68)
		tmp = t_1;
	elseif (y <= -6.5e-141)
		tmp = a + (y / ((y + t) / z));
	elseif (y <= -1.35e-189)
		tmp = z / ((y + (x + t)) / (x + y));
	elseif (y <= 2500000000.0)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -7.7e+68], t$95$1, If[LessEqual[y, -6.5e-141], N[(a + N[(y / N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-189], N[(z / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2500000000.0], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.6999999999999998e68 or 2.5e9 < y

   1. Initial program 39.9%

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

   3. Taylor expanded in y around inf 80.4%

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

   if -7.6999999999999998e68 < y < -6.4999999999999995e-141

   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. Add Preprocessing

   3. Taylor expanded in z around 0 81.1%

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

      1. associate--l+ 81.1%

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

      2. associate-+r+ 81.1%

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

      3. associate-+r+ 81.1%

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

      4. div-sub 81.1%

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

      5. *-commutative 81.1%

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

      6. associate-+r+ 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around inf 71.6%

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

   7. Taylor expanded in x around 0 62.7%

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

      1. associate-/l* 59.2%

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

      2. +-commutative 59.2%

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

   9. Simplified 59.2%

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

   if -6.4999999999999995e-141 < y < -1.35e-189

   1. Initial program 71.8%

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

   3. Taylor expanded in z around inf 33.2%

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

      1. associate-/l* 61.3%

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

      2. associate-+r+ 61.3%

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

      3. +-commutative 61.3%

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

   5. Simplified 61.3%

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

   if -1.35e-189 < y < 2.5e9

   1. Initial program 83.4%

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

   3. Taylor expanded in y around 0 69.2%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{+68}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-141}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-189}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;y \leq 2500000000:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a + z \cdot \frac{x + y}{t}\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-295}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ a (* z (/ (+ x y) t)))))
   (if (<= t -2.25e+108)
     t_2
     (if (<= t -1.04e-286)
       t_1
       (if (<= t 9.5e-295) z (if (<= t 5.5e+190) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (z * ((x + y) / t));
	double tmp;
	if (t <= -2.25e+108) {
		tmp = t_2;
	} else if (t <= -1.04e-286) {
		tmp = t_1;
	} else if (t <= 9.5e-295) {
		tmp = z;
	} else if (t <= 5.5e+190) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a + (z * ((x + y) / t))
    if (t <= (-2.25d+108)) then
        tmp = t_2
    else if (t <= (-1.04d-286)) then
        tmp = t_1
    else if (t <= 9.5d-295) then
        tmp = z
    else if (t <= 5.5d+190) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (z * ((x + y) / t));
	double tmp;
	if (t <= -2.25e+108) {
		tmp = t_2;
	} else if (t <= -1.04e-286) {
		tmp = t_1;
	} else if (t <= 9.5e-295) {
		tmp = z;
	} else if (t <= 5.5e+190) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a + (z * ((x + y) / t))
	tmp = 0
	if t <= -2.25e+108:
		tmp = t_2
	elif t <= -1.04e-286:
		tmp = t_1
	elif t <= 9.5e-295:
		tmp = z
	elif t <= 5.5e+190:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a + Float64(z * Float64(Float64(x + y) / t)))
	tmp = 0.0
	if (t <= -2.25e+108)
		tmp = t_2;
	elseif (t <= -1.04e-286)
		tmp = t_1;
	elseif (t <= 9.5e-295)
		tmp = z;
	elseif (t <= 5.5e+190)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a + (z * ((x + y) / t));
	tmp = 0.0;
	if (t <= -2.25e+108)
		tmp = t_2;
	elseif (t <= -1.04e-286)
		tmp = t_1;
	elseif (t <= 9.5e-295)
		tmp = z;
	elseif (t <= 5.5e+190)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+108], t$95$2, If[LessEqual[t, -1.04e-286], t$95$1, If[LessEqual[t, 9.5e-295], z, If[LessEqual[t, 5.5e+190], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.25e108 or 5.5e190 < t

   1. Initial program 56.4%

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

   3. Taylor expanded in z around 0 63.7%

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

      1. associate--l+ 63.7%

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

      2. associate-+r+ 63.7%

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

      3. associate-+r+ 63.7%

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

      4. div-sub 63.7%

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

      5. *-commutative 63.7%

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

      6. associate-+r+ 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in t around inf 74.2%

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

   7. Taylor expanded in t around inf 68.1%

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

      1. +-commutative 68.1%

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

   9. Simplified 68.1%

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

   if -2.25e108 < t < -1.04e-286 or 9.5e-295 < t < 5.5e190

   1. Initial program 60.3%

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

   3. Taylor expanded in y around inf 66.2%

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

   if -1.04e-286 < t < 9.5e-295

   1. Initial program 68.6%

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

   3. Taylor expanded in x around inf 69.5%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+108}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-286}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-295}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+190}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+189} \lor \neg \left(b \leq 2.8 \cdot 10^{+209}\right):\\ \;\;\;\;\frac{-b}{\frac{t_1}{y}}\\ \mathbf{else}:\\ \;\;\;\;a + z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (or (<= b -4.1e+189) (not (<= b 2.8e+209)))
     (/ (- b) (/ t_1 y))
     (+ a (* z (+ (/ x t_1) (/ y t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((b <= -4.1e+189) || !(b <= 2.8e+209)) {
		tmp = -b / (t_1 / y);
	} else {
		tmp = a + (z * ((x / t_1) + (y / t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if ((b <= (-4.1d+189)) .or. (.not. (b <= 2.8d+209))) then
        tmp = -b / (t_1 / y)
    else
        tmp = a + (z * ((x / t_1) + (y / t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((b <= -4.1e+189) || !(b <= 2.8e+209)) {
		tmp = -b / (t_1 / y);
	} else {
		tmp = a + (z * ((x / t_1) + (y / t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if (b <= -4.1e+189) or not (b <= 2.8e+209):
		tmp = -b / (t_1 / y)
	else:
		tmp = a + (z * ((x / t_1) + (y / t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if ((b <= -4.1e+189) || !(b <= 2.8e+209))
		tmp = Float64(Float64(-b) / Float64(t_1 / y));
	else
		tmp = Float64(a + Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if ((b <= -4.1e+189) || ~((b <= 2.8e+209)))
		tmp = -b / (t_1 / y);
	else
		tmp = a + (z * ((x / t_1) + (y / t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -4.1e+189], N[Not[LessEqual[b, 2.8e+209]], $MachinePrecision]], N[((-b) / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], N[(a + N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.1000000000000002e189 or 2.80000000000000013e209 < b

   1. Initial program 41.9%

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

   3. Taylor expanded in b around inf 34.4%

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

      1. mul-1-neg 34.4%

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

      2. associate-/l* 75.5%

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

      3. distribute-neg-frac 75.5%

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

      4. associate-+r+ 75.5%

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

   5. Simplified 75.5%

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

   if -4.1000000000000002e189 < b < 2.80000000000000013e209

   1. Initial program 63.4%

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

   3. Taylor expanded in z around 0 76.5%

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

      1. associate--l+ 76.5%

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

      2. associate-+r+ 76.5%

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

      3. associate-+r+ 76.5%

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

      4. div-sub 76.5%

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

      5. *-commutative 76.5%

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

      6. associate-+r+ 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in t around inf 73.4%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+189} \lor \neg \left(b \leq 2.8 \cdot 10^{+209}\right):\\ \;\;\;\;\frac{-b}{\frac{y + \left(x + t\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;a + z \cdot \left(\frac{x}{y + \left(x + t\right)} + \frac{y}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-141}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-221}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+34}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -6.2e+66)
     t_1
     (if (<= y -5.1e-141)
       (+ a (/ y (/ (+ y t) z)))
       (if (<= y 7.2e-221)
         (* (+ x y) (/ z (+ x (+ y t))))
         (if (<= y 7e+34) (+ z a) 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 <= -6.2e+66) {
		tmp = t_1;
	} else if (y <= -5.1e-141) {
		tmp = a + (y / ((y + t) / z));
	} else if (y <= 7.2e-221) {
		tmp = (x + y) * (z / (x + (y + t)));
	} else if (y <= 7e+34) {
		tmp = z + a;
	} 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 <= (-6.2d+66)) then
        tmp = t_1
    else if (y <= (-5.1d-141)) then
        tmp = a + (y / ((y + t) / z))
    else if (y <= 7.2d-221) then
        tmp = (x + y) * (z / (x + (y + t)))
    else if (y <= 7d+34) then
        tmp = z + a
    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 <= -6.2e+66) {
		tmp = t_1;
	} else if (y <= -5.1e-141) {
		tmp = a + (y / ((y + t) / z));
	} else if (y <= 7.2e-221) {
		tmp = (x + y) * (z / (x + (y + t)));
	} else if (y <= 7e+34) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -6.2e+66:
		tmp = t_1
	elif y <= -5.1e-141:
		tmp = a + (y / ((y + t) / z))
	elif y <= 7.2e-221:
		tmp = (x + y) * (z / (x + (y + t)))
	elif y <= 7e+34:
		tmp = z + a
	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 <= -6.2e+66)
		tmp = t_1;
	elseif (y <= -5.1e-141)
		tmp = Float64(a + Float64(y / Float64(Float64(y + t) / z)));
	elseif (y <= 7.2e-221)
		tmp = Float64(Float64(x + y) * Float64(z / Float64(x + Float64(y + t))));
	elseif (y <= 7e+34)
		tmp = Float64(z + a);
	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 <= -6.2e+66)
		tmp = t_1;
	elseif (y <= -5.1e-141)
		tmp = a + (y / ((y + t) / z));
	elseif (y <= 7.2e-221)
		tmp = (x + y) * (z / (x + (y + t)));
	elseif (y <= 7e+34)
		tmp = z + a;
	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, -6.2e+66], t$95$1, If[LessEqual[y, -5.1e-141], N[(a + N[(y / N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-221], N[(N[(x + y), $MachinePrecision] * N[(z / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+34], N[(z + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.20000000000000037e66 or 6.99999999999999996e34 < y

   1. Initial program 38.3%

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

   3. Taylor expanded in y around inf 81.2%

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

   if -6.20000000000000037e66 < y < -5.09999999999999977e-141

   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. Add Preprocessing

   3. Taylor expanded in z around 0 81.1%

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

      1. associate--l+ 81.1%

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

      2. associate-+r+ 81.1%

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

      3. associate-+r+ 81.1%

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

      4. div-sub 81.1%

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

      5. *-commutative 81.1%

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

      6. associate-+r+ 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around inf 71.6%

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

   7. Taylor expanded in x around 0 62.7%

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

      1. associate-/l* 59.2%

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

      2. +-commutative 59.2%

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

   9. Simplified 59.2%

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

   if -5.09999999999999977e-141 < y < 7.20000000000000022e-221

   1. Initial program 77.5%

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

   3. Taylor expanded in z around inf 35.2%

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

      1. +-commutative 35.2%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in z around 0 35.2%

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

      1. associate-/l* 48.2%

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

      2. +-commutative 48.2%

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

      3. +-commutative 48.2%

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

      4. associate-/r/ 50.0%

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

      5. associate-+r+ 50.0%

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

      6. +-commutative 50.0%

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

   8. Simplified 50.0%

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

   if 7.20000000000000022e-221 < y < 6.99999999999999996e34

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0 95.6%

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

      1. associate--l+ 95.6%

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

      2. associate-+r+ 95.6%

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

      3. associate-+r+ 95.6%

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

      4. div-sub 95.6%

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

      5. *-commutative 95.6%

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

      6. associate-+r+ 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in t around inf 60.6%

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

   7. Taylor expanded in x around inf 51.6%

      \[\leadsto \color{blue}{z} + a \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+66}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-141}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-221}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+34}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-260}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+219}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (* t (- (/ a x) (/ z x))))))
   (if (<= x -1.9e+116)
     t_1
     (if (<= x 2.1e-260)
       (+ a (/ y (/ (+ y t) z)))
       (if (<= x 9.8e+219) (- (+ z a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (t * ((a / x) - (z / x)));
	double tmp;
	if (x <= -1.9e+116) {
		tmp = t_1;
	} else if (x <= 2.1e-260) {
		tmp = a + (y / ((y + t) / z));
	} else if (x <= 9.8e+219) {
		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 + (t * ((a / x) - (z / x)))
    if (x <= (-1.9d+116)) then
        tmp = t_1
    else if (x <= 2.1d-260) then
        tmp = a + (y / ((y + t) / z))
    else if (x <= 9.8d+219) 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 + (t * ((a / x) - (z / x)));
	double tmp;
	if (x <= -1.9e+116) {
		tmp = t_1;
	} else if (x <= 2.1e-260) {
		tmp = a + (y / ((y + t) / z));
	} else if (x <= 9.8e+219) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (t * ((a / x) - (z / x)))
	tmp = 0
	if x <= -1.9e+116:
		tmp = t_1
	elif x <= 2.1e-260:
		tmp = a + (y / ((y + t) / z))
	elif x <= 9.8e+219:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(t * Float64(Float64(a / x) - Float64(z / x))))
	tmp = 0.0
	if (x <= -1.9e+116)
		tmp = t_1;
	elseif (x <= 2.1e-260)
		tmp = Float64(a + Float64(y / Float64(Float64(y + t) / z)));
	elseif (x <= 9.8e+219)
		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 + (t * ((a / x) - (z / x)));
	tmp = 0.0;
	if (x <= -1.9e+116)
		tmp = t_1;
	elseif (x <= 2.1e-260)
		tmp = a + (y / ((y + t) / z));
	elseif (x <= 9.8e+219)
		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[(t * N[(N[(a / x), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+116], t$95$1, If[LessEqual[x, 2.1e-260], N[(a + N[(y / N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e+219], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8999999999999999e116 or 9.80000000000000007e219 < x

   1. Initial program 52.8%

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

   3. Taylor expanded in y around 0 48.0%

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

   4. Taylor expanded in t around 0 69.7%

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

   if -1.8999999999999999e116 < x < 2.10000000000000005e-260

   1. Initial program 67.9%

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

   3. Taylor expanded in z around 0 72.2%

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

      1. associate--l+ 72.2%

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

      2. associate-+r+ 72.2%

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

      3. associate-+r+ 72.2%

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

      4. div-sub 72.2%

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

      5. *-commutative 72.2%

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

      6. associate-+r+ 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around inf 72.4%

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

   7. Taylor expanded in x around 0 57.4%

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

      1. associate-/l* 65.2%

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

      2. +-commutative 65.2%

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

   9. Simplified 65.2%

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

   if 2.10000000000000005e-260 < x < 9.80000000000000007e219

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf 64.0%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-260}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+219}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+105}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-262}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+220}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.85e+105)
   (/ z (/ (+ y (+ x t)) (+ x y)))
   (if (<= x 4.2e-262)
     (+ a (/ y (/ (+ y t) z)))
     (if (<= x 1.8e+220) (- (+ z a) b) (+ z (* t (- (/ a x) (/ z x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.85e+105) {
		tmp = z / ((y + (x + t)) / (x + y));
	} else if (x <= 4.2e-262) {
		tmp = a + (y / ((y + t) / z));
	} else if (x <= 1.8e+220) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (t * ((a / x) - (z / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.85d+105)) then
        tmp = z / ((y + (x + t)) / (x + y))
    else if (x <= 4.2d-262) then
        tmp = a + (y / ((y + t) / z))
    else if (x <= 1.8d+220) then
        tmp = (z + a) - b
    else
        tmp = z + (t * ((a / x) - (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.85e+105) {
		tmp = z / ((y + (x + t)) / (x + y));
	} else if (x <= 4.2e-262) {
		tmp = a + (y / ((y + t) / z));
	} else if (x <= 1.8e+220) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (t * ((a / x) - (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.85e+105:
		tmp = z / ((y + (x + t)) / (x + y))
	elif x <= 4.2e-262:
		tmp = a + (y / ((y + t) / z))
	elif x <= 1.8e+220:
		tmp = (z + a) - b
	else:
		tmp = z + (t * ((a / x) - (z / x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.85e+105)
		tmp = Float64(z / Float64(Float64(y + Float64(x + t)) / Float64(x + y)));
	elseif (x <= 4.2e-262)
		tmp = Float64(a + Float64(y / Float64(Float64(y + t) / z)));
	elseif (x <= 1.8e+220)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + Float64(t * Float64(Float64(a / x) - Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.85e+105)
		tmp = z / ((y + (x + t)) / (x + y));
	elseif (x <= 4.2e-262)
		tmp = a + (y / ((y + t) / z));
	elseif (x <= 1.8e+220)
		tmp = (z + a) - b;
	else
		tmp = z + (t * ((a / x) - (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.85e+105], N[(z / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-262], N[(a + N[(y / N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+220], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(t * N[(N[(a / x), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.84999999999999992e105

   1. Initial program 55.6%

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

   3. Taylor expanded in z around inf 43.4%

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

      1. associate-/l* 71.8%

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

      2. associate-+r+ 71.8%

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

      3. +-commutative 71.8%

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

   5. Simplified 71.8%

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

   if -1.84999999999999992e105 < x < 4.1999999999999999e-262

   1. Initial program 67.6%

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

   3. Taylor expanded in z around 0 72.0%

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

      1. associate--l+ 72.0%

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

      2. associate-+r+ 72.0%

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

      3. associate-+r+ 72.0%

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

      4. div-sub 71.9%

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

      5. *-commutative 71.9%

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

      6. associate-+r+ 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in t around inf 72.2%

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

   7. Taylor expanded in x around 0 57.9%

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

      1. associate-/l* 65.8%

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

      2. +-commutative 65.8%

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

   9. Simplified 65.8%

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

   if 4.1999999999999999e-262 < x < 1.80000000000000009e220

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf 64.0%

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

   if 1.80000000000000009e220 < x

   1. Initial program 49.4%

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

   3. Taylor expanded in y around 0 42.1%

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

   4. Taylor expanded in t around 0 71.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+105}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-262}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+220}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-219}:\\ \;\;\;\;\frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+34}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.5e+67)
     t_1
     (if (<= y -5.5e-141)
       (+ a (/ y (/ (+ y t) z)))
       (if (<= y 6.2e-219)
         (/ x (/ (+ x t) z))
         (if (<= y 2e+34) (+ z a) 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 <= -2.5e+67) {
		tmp = t_1;
	} else if (y <= -5.5e-141) {
		tmp = a + (y / ((y + t) / z));
	} else if (y <= 6.2e-219) {
		tmp = x / ((x + t) / z);
	} else if (y <= 2e+34) {
		tmp = z + a;
	} 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 <= (-2.5d+67)) then
        tmp = t_1
    else if (y <= (-5.5d-141)) then
        tmp = a + (y / ((y + t) / z))
    else if (y <= 6.2d-219) then
        tmp = x / ((x + t) / z)
    else if (y <= 2d+34) then
        tmp = z + a
    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 <= -2.5e+67) {
		tmp = t_1;
	} else if (y <= -5.5e-141) {
		tmp = a + (y / ((y + t) / z));
	} else if (y <= 6.2e-219) {
		tmp = x / ((x + t) / z);
	} else if (y <= 2e+34) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.5e+67:
		tmp = t_1
	elif y <= -5.5e-141:
		tmp = a + (y / ((y + t) / z))
	elif y <= 6.2e-219:
		tmp = x / ((x + t) / z)
	elif y <= 2e+34:
		tmp = z + a
	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 <= -2.5e+67)
		tmp = t_1;
	elseif (y <= -5.5e-141)
		tmp = Float64(a + Float64(y / Float64(Float64(y + t) / z)));
	elseif (y <= 6.2e-219)
		tmp = Float64(x / Float64(Float64(x + t) / z));
	elseif (y <= 2e+34)
		tmp = Float64(z + a);
	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 <= -2.5e+67)
		tmp = t_1;
	elseif (y <= -5.5e-141)
		tmp = a + (y / ((y + t) / z));
	elseif (y <= 6.2e-219)
		tmp = x / ((x + t) / z);
	elseif (y <= 2e+34)
		tmp = z + a;
	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, -2.5e+67], t$95$1, If[LessEqual[y, -5.5e-141], N[(a + N[(y / N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-219], N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+34], N[(z + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.49999999999999988e67 or 1.99999999999999989e34 < y

   1. Initial program 38.3%

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

   3. Taylor expanded in y around inf 81.2%

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

   if -2.49999999999999988e67 < y < -5.4999999999999998e-141

   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. Add Preprocessing

   3. Taylor expanded in z around 0 81.1%

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

      1. associate--l+ 81.1%

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

      2. associate-+r+ 81.1%

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

      3. associate-+r+ 81.1%

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

      4. div-sub 81.1%

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

      5. *-commutative 81.1%

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

      6. associate-+r+ 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around inf 71.6%

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

   7. Taylor expanded in x around 0 62.7%

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

      1. associate-/l* 59.2%

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

      2. +-commutative 59.2%

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

   9. Simplified 59.2%

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

   if -5.4999999999999998e-141 < y < 6.1999999999999994e-219

   1. Initial program 77.5%

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

   3. Taylor expanded in y around 0 64.4%

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

   4. Taylor expanded in a around 0 34.1%

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

      1. associate-/l* 48.9%

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

   6. Simplified 48.9%

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

   if 6.1999999999999994e-219 < y < 1.99999999999999989e34

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0 95.6%

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

      1. associate--l+ 95.6%

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

      2. associate-+r+ 95.6%

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

      3. associate-+r+ 95.6%

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

      4. div-sub 95.6%

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

      5. *-commutative 95.6%

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

      6. associate-+r+ 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in t around inf 60.6%

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

   7. Taylor expanded in x around inf 51.6%

      \[\leadsto \color{blue}{z} + a \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+67}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-219}:\\ \;\;\;\;\frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+34}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+141}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 10^{+216}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.16e+141) z (if (<= x 1e+216) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.16e+141) {
		tmp = z;
	} else if (x <= 1e+216) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.16d+141)) then
        tmp = z
    else if (x <= 1d+216) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.16e+141) {
		tmp = z;
	} else if (x <= 1e+216) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.16e+141:
		tmp = z
	elif x <= 1e+216:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.16e+141)
		tmp = z;
	elseif (x <= 1e+216)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.16e+141)
		tmp = z;
	elseif (x <= 1e+216)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.16e+141], z, If[LessEqual[x, 1e+216], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.16e141 or 1e216 < x

   1. Initial program 50.4%

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

   3. Taylor expanded in x around inf 65.0%

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

   if -1.16e141 < x < 1e216

   1. Initial program 61.3%

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

   3. Taylor expanded in y around inf 61.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+141}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 10^{+216}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.9 \cdot 10^{+200} \lor \neg \left(b \leq 5.2 \cdot 10^{+235}\right):\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.9e+200) (not (<= b 5.2e+235))) (- b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.9e+200) || !(b <= 5.2e+235)) {
		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 <= (-4.9d+200)) .or. (.not. (b <= 5.2d+235))) 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 <= -4.9e+200) || !(b <= 5.2e+235)) {
		tmp = -b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.9e+200) or not (b <= 5.2e+235):
		tmp = -b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.9e+200) || !(b <= 5.2e+235))
		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 <= -4.9e+200) || ~((b <= 5.2e+235)))
		tmp = -b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.9e+200], N[Not[LessEqual[b, 5.2e+235]], $MachinePrecision]], (-b), N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.89999999999999982e200 or 5.1999999999999996e235 < b

   1. Initial program 47.3%

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

   3. Taylor expanded in b around inf 36.7%

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

      1. associate-*r* 36.7%

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

      2. mul-1-neg 36.7%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in y around inf 46.0%

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

      1. neg-mul-1 46.0%

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

   8. Simplified 46.0%

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

   if -4.89999999999999982e200 < b < 5.1999999999999996e235

   1. Initial program 61.4%

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

   3. Taylor expanded in z around 0 73.8%

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

      1. associate--l+ 73.8%

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

      2. associate-+r+ 73.8%

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

      3. associate-+r+ 73.8%

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

      4. div-sub 73.8%

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

      5. *-commutative 73.8%

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

      6. associate-+r+ 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in t around inf 71.3%

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

   7. Taylor expanded in x around inf 57.0%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.9 \cdot 10^{+200} \lor \neg \left(b \leq 5.2 \cdot 10^{+235}\right):\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-25}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+26}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.5e-25) a (if (<= t 1.2e+26) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e-25) {
		tmp = a;
	} else if (t <= 1.2e+26) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.5d-25)) then
        tmp = a
    else if (t <= 1.2d+26) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e-25) {
		tmp = a;
	} else if (t <= 1.2e+26) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.5e-25:
		tmp = a
	elif t <= 1.2e+26:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.5e-25)
		tmp = a;
	elseif (t <= 1.2e+26)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.5e-25)
		tmp = a;
	elseif (t <= 1.2e+26)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.5e-25], a, If[LessEqual[t, 1.2e+26], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -7.49999999999999989e-25 or 1.20000000000000002e26 < t

   1. Initial program 57.0%

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

   3. Taylor expanded in t around inf 46.4%

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

   if -7.49999999999999989e-25 < t < 1.20000000000000002e26

   1. Initial program 62.1%

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

   3. Taylor expanded in x around inf 46.7%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-25}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+26}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.6%

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

3. Taylor expanded in t around inf 34.3%

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

4. Final simplification 34.3%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.2% 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 2024019 
(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)))