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

Percentage Accurate: 61.1% → 87.3%

Time: 18.2s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+238} \lor \neg \left(t_2 \leq 5 \cdot 10^{+242}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot t_3\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (or (<= t_2 -2e+238) (not (<= t_2 5e+242)))
     t_3
     (/ (+ (* t a) (+ (* x z) (* y t_3))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -2e+238) || !(t_2 <= 5e+242)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / 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) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1
    t_3 = (z + a) - b
    if ((t_2 <= (-2d+238)) .or. (.not. (t_2 <= 5d+242))) then
        tmp = t_3
    else
        tmp = ((t * a) + ((x * z) + (y * t_3))) / 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 t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -2e+238) || !(t_2 <= 5e+242)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1
	t_3 = (z + a) - b
	tmp = 0
	if (t_2 <= -2e+238) or not (t_2 <= 5e+242):
		tmp = t_3
	else:
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if ((t_2 <= -2e+238) || !(t_2 <= 5e+242))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * t_3))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	tmp = 0.0;
	if ((t_2 <= -2e+238) || ~((t_2 <= 5e+242)))
		tmp = t_3;
	else
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e+238], N[Not[LessEqual[t$95$2, 5e+242]], $MachinePrecision]], t$95$3, N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -2.0000000000000001e238 or 5.0000000000000004e242 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.7%

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

   3. Taylor expanded in y around inf 81.6%

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

   if -2.0000000000000001e238 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000004e242

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -2 \cdot 10^{+238} \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+242}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a + \left(z \cdot \left(x + y\right) - y \cdot b\right) \cdot \frac{1}{t_1}\\ t_3 := \left(z + a\right) - b\\ t_4 := \frac{a}{\frac{t_1}{y + t}}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-73}:\\ \;\;\;\;t_4 + \frac{x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+73}:\\ \;\;\;\;z + t_4\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ a (* (- (* z (+ x y)) (* y b)) (/ 1.0 t_1))))
        (t_3 (- (+ z a) b))
        (t_4 (/ a (/ t_1 (+ y t)))))
   (if (<= y -6.2e+45)
     t_3
     (if (<= y -5.5e-203)
       (/ (- (* (+ y t) a) (* y b)) t_1)
       (if (<= y 9.5e-73)
         (+ t_4 (/ (* x z) (+ x t)))
         (if (<= y 4e+23)
           t_2
           (if (<= y 4.9e+73) (+ z t_4) (if (<= y 2.85e+124) t_2 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 + (((z * (x + y)) - (y * b)) * (1.0 / t_1));
	double t_3 = (z + a) - b;
	double t_4 = a / (t_1 / (y + t));
	double tmp;
	if (y <= -6.2e+45) {
		tmp = t_3;
	} else if (y <= -5.5e-203) {
		tmp = (((y + t) * a) - (y * b)) / t_1;
	} else if (y <= 9.5e-73) {
		tmp = t_4 + ((x * z) / (x + t));
	} else if (y <= 4e+23) {
		tmp = t_2;
	} else if (y <= 4.9e+73) {
		tmp = z + t_4;
	} else if (y <= 2.85e+124) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a + (((z * (x + y)) - (y * b)) * (1.0d0 / t_1))
    t_3 = (z + a) - b
    t_4 = a / (t_1 / (y + t))
    if (y <= (-6.2d+45)) then
        tmp = t_3
    else if (y <= (-5.5d-203)) then
        tmp = (((y + t) * a) - (y * b)) / t_1
    else if (y <= 9.5d-73) then
        tmp = t_4 + ((x * z) / (x + t))
    else if (y <= 4d+23) then
        tmp = t_2
    else if (y <= 4.9d+73) then
        tmp = z + t_4
    else if (y <= 2.85d+124) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a + (((z * (x + y)) - (y * b)) * (1.0 / t_1));
	double t_3 = (z + a) - b;
	double t_4 = a / (t_1 / (y + t));
	double tmp;
	if (y <= -6.2e+45) {
		tmp = t_3;
	} else if (y <= -5.5e-203) {
		tmp = (((y + t) * a) - (y * b)) / t_1;
	} else if (y <= 9.5e-73) {
		tmp = t_4 + ((x * z) / (x + t));
	} else if (y <= 4e+23) {
		tmp = t_2;
	} else if (y <= 4.9e+73) {
		tmp = z + t_4;
	} else if (y <= 2.85e+124) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a + (((z * (x + y)) - (y * b)) * (1.0 / t_1))
	t_3 = (z + a) - b
	t_4 = a / (t_1 / (y + t))
	tmp = 0
	if y <= -6.2e+45:
		tmp = t_3
	elif y <= -5.5e-203:
		tmp = (((y + t) * a) - (y * b)) / t_1
	elif y <= 9.5e-73:
		tmp = t_4 + ((x * z) / (x + t))
	elif y <= 4e+23:
		tmp = t_2
	elif y <= 4.9e+73:
		tmp = z + t_4
	elif y <= 2.85e+124:
		tmp = t_2
	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(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) * Float64(1.0 / t_1)))
	t_3 = Float64(Float64(z + a) - b)
	t_4 = Float64(a / Float64(t_1 / Float64(y + t)))
	tmp = 0.0
	if (y <= -6.2e+45)
		tmp = t_3;
	elseif (y <= -5.5e-203)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / t_1);
	elseif (y <= 9.5e-73)
		tmp = Float64(t_4 + Float64(Float64(x * z) / Float64(x + t)));
	elseif (y <= 4e+23)
		tmp = t_2;
	elseif (y <= 4.9e+73)
		tmp = Float64(z + t_4);
	elseif (y <= 2.85e+124)
		tmp = t_2;
	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 + (((z * (x + y)) - (y * b)) * (1.0 / t_1));
	t_3 = (z + a) - b;
	t_4 = a / (t_1 / (y + t));
	tmp = 0.0;
	if (y <= -6.2e+45)
		tmp = t_3;
	elseif (y <= -5.5e-203)
		tmp = (((y + t) * a) - (y * b)) / t_1;
	elseif (y <= 9.5e-73)
		tmp = t_4 + ((x * z) / (x + t));
	elseif (y <= 4e+23)
		tmp = t_2;
	elseif (y <= 4.9e+73)
		tmp = z + t_4;
	elseif (y <= 2.85e+124)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$4 = N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+45], t$95$3, If[LessEqual[y, -5.5e-203], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 9.5e-73], N[(t$95$4 + N[(N[(x * z), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+23], t$95$2, If[LessEqual[y, 4.9e+73], N[(z + t$95$4), $MachinePrecision], If[LessEqual[y, 2.85e+124], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.19999999999999975e45 or 2.85000000000000011e124 < y

   1. Initial program 35.8%

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

   3. Taylor expanded in y around inf 80.9%

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

   if -6.19999999999999975e45 < y < -5.5000000000000002e-203

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0 76.2%

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

      1. *-commutative 76.2%

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

   5. Simplified 76.2%

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

   if -5.5000000000000002e-203 < y < 9.50000000000000005e-73

   1. Initial program 86.1%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. associate--l+ 86.2%

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

      2. associate-/l* 93.0%

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

      3. associate-+r+ 93.0%

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

      4. div-sub 93.0%

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

      5. +-commutative 93.0%

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

      6. *-commutative 93.0%

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

      7. associate-+r+ 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in y around 0 85.7%

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

   if 9.50000000000000005e-73 < y < 3.9999999999999997e23 or 4.8999999999999999e73 < y < 2.85000000000000011e124

   1. Initial program 87.0%

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

   3. Taylor expanded in z around inf 87.0%

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

      1. associate--l+ 87.0%

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

      2. associate-/l* 94.6%

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

      3. associate-+r+ 94.6%

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

      4. div-sub 94.7%

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

      5. +-commutative 94.7%

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

      6. *-commutative 94.7%

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

      7. associate-+r+ 94.7%

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

   5. Simplified 94.7%

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

      1. div-inv 94.5%

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

      2. +-commutative 94.5%

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

      3. +-commutative 94.5%

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

   7. Applied egg-rr 94.5%

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

   8. Taylor expanded in t around inf 85.9%

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

   if 3.9999999999999997e23 < y < 4.8999999999999999e73

   1. Initial program 68.9%

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

   3. Taylor expanded in z around inf 68.9%

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

      1. associate--l+ 68.9%

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

      2. associate-/l* 79.3%

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

      3. associate-+r+ 79.3%

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

      4. div-sub 79.3%

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

      5. +-commutative 79.3%

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

      6. *-commutative 79.3%

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

      7. associate-+r+ 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in x around inf 89.1%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \frac{x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+23}:\\ \;\;\;\;a + \left(z \cdot \left(x + y\right) - y \cdot b\right) \cdot \frac{1}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+73}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+124}:\\ \;\;\;\;a + \left(z \cdot \left(x + y\right) - y \cdot b\right) \cdot \frac{1}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z + \frac{a}{\frac{t_1}{y + t}}\\ \mathbf{if}\;x \leq -8 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.38 \cdot 10^{+73}:\\ \;\;\;\;a + \frac{z}{\frac{t_1}{x + y}}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{t_1}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;a + \left(z \cdot \left(x + y\right) - y \cdot b\right) \cdot \frac{1}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (+ z (/ a (/ t_1 (+ y t))))))
   (if (<= x -8e+175)
     t_2
     (if (<= x -1.38e+73)
       (+ a (/ z (/ t_1 (+ x y))))
       (if (<= x -6.2e+62)
         (/ (- (* (+ y t) a) (* y b)) t_1)
         (if (<= x 4.1e+40)
           (+ a (* (- (* z (+ x y)) (* y b)) (/ 1.0 t_1)))
           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 / (t_1 / (y + t)));
	double tmp;
	if (x <= -8e+175) {
		tmp = t_2;
	} else if (x <= -1.38e+73) {
		tmp = a + (z / (t_1 / (x + y)));
	} else if (x <= -6.2e+62) {
		tmp = (((y + t) * a) - (y * b)) / t_1;
	} else if (x <= 4.1e+40) {
		tmp = a + (((z * (x + y)) - (y * b)) * (1.0 / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z + (a / (t_1 / (y + t)))
    if (x <= (-8d+175)) then
        tmp = t_2
    else if (x <= (-1.38d+73)) then
        tmp = a + (z / (t_1 / (x + y)))
    else if (x <= (-6.2d+62)) then
        tmp = (((y + t) * a) - (y * b)) / t_1
    else if (x <= 4.1d+40) then
        tmp = a + (((z * (x + y)) - (y * b)) * (1.0d0 / t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z + (a / (t_1 / (y + t)));
	double tmp;
	if (x <= -8e+175) {
		tmp = t_2;
	} else if (x <= -1.38e+73) {
		tmp = a + (z / (t_1 / (x + y)));
	} else if (x <= -6.2e+62) {
		tmp = (((y + t) * a) - (y * b)) / t_1;
	} else if (x <= 4.1e+40) {
		tmp = a + (((z * (x + y)) - (y * b)) * (1.0 / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z + (a / (t_1 / (y + t)))
	tmp = 0
	if x <= -8e+175:
		tmp = t_2
	elif x <= -1.38e+73:
		tmp = a + (z / (t_1 / (x + y)))
	elif x <= -6.2e+62:
		tmp = (((y + t) * a) - (y * b)) / t_1
	elif x <= 4.1e+40:
		tmp = a + (((z * (x + y)) - (y * b)) * (1.0 / t_1))
	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(z + Float64(a / Float64(t_1 / Float64(y + t))))
	tmp = 0.0
	if (x <= -8e+175)
		tmp = t_2;
	elseif (x <= -1.38e+73)
		tmp = Float64(a + Float64(z / Float64(t_1 / Float64(x + y))));
	elseif (x <= -6.2e+62)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / t_1);
	elseif (x <= 4.1e+40)
		tmp = Float64(a + Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) * Float64(1.0 / t_1)));
	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 / (t_1 / (y + t)));
	tmp = 0.0;
	if (x <= -8e+175)
		tmp = t_2;
	elseif (x <= -1.38e+73)
		tmp = a + (z / (t_1 / (x + y)));
	elseif (x <= -6.2e+62)
		tmp = (((y + t) * a) - (y * b)) / t_1;
	elseif (x <= 4.1e+40)
		tmp = a + (((z * (x + y)) - (y * b)) * (1.0 / t_1));
	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[(z + N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+175], t$95$2, If[LessEqual[x, -1.38e+73], N[(a + N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e+62], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x, 4.1e+40], N[(a + N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.9999999999999995e175 or 4.1000000000000002e40 < x

   1. Initial program 57.8%

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

   3. Taylor expanded in z around inf 57.8%

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

      1. associate--l+ 57.8%

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

      2. associate-/l* 61.6%

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

      3. associate-+r+ 61.6%

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

      4. div-sub 61.6%

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

      5. +-commutative 61.6%

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

      6. *-commutative 61.6%

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

      7. associate-+r+ 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in x around inf 80.3%

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

   if -7.9999999999999995e175 < x < -1.38000000000000007e73

   1. Initial program 52.5%

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

   3. Taylor expanded in z around inf 52.5%

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

      1. associate--l+ 52.5%

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

      2. associate-/l* 62.9%

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

      3. associate-+r+ 62.9%

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

      4. div-sub 62.9%

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

      5. +-commutative 62.9%

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

      6. *-commutative 62.9%

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

      7. associate-+r+ 62.9%

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

   5. Simplified 62.9%

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

      1. div-inv 62.9%

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

      2. +-commutative 62.9%

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

      3. +-commutative 62.9%

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

   7. Applied egg-rr 62.9%

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

   8. Taylor expanded in z around inf 54.2%

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

      1. associate-/l* 85.7%

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

      2. +-commutative 85.7%

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

      3. +-commutative 85.7%

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

      4. associate-+l+ 85.7%

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

      5. +-commutative 85.7%

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

      6. +-commutative 85.7%

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

   10. Simplified 85.7%

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

   11. Taylor expanded in t around inf 80.2%

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

   if -1.38000000000000007e73 < x < -6.20000000000000029e62

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 99.2%

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

      1. *-commutative 99.2%

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

   5. Simplified 99.2%

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

   if -6.20000000000000029e62 < x < 4.1000000000000002e40

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf 75.4%

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

      1. associate--l+ 75.4%

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

      2. associate-/l* 83.9%

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

      3. associate-+r+ 83.9%

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

      4. div-sub 83.9%

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

      5. +-commutative 83.9%

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

      6. *-commutative 83.9%

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

      7. associate-+r+ 83.9%

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

   5. Simplified 83.9%

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

      1. div-inv 83.8%

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

      2. +-commutative 83.8%

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

      3. +-commutative 83.8%

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

   7. Applied egg-rr 83.8%

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

   8. Taylor expanded in t around inf 78.0%

      \[\leadsto \color{blue}{a} + \left(z \cdot \left(y + x\right) - y \cdot b\right) \cdot \frac{1}{y + \left(x + t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+175}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;x \leq -1.38 \cdot 10^{+73}:\\ \;\;\;\;a + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;a + \left(z \cdot \left(x + y\right) - y \cdot b\right) \cdot \frac{1}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + \frac{y}{\frac{t}{z}}\right) - \frac{b}{\frac{t}{y}}\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-44}:\\ \;\;\;\;z + \frac{a}{\frac{t_2}{y + t}}\\ \mathbf{elif}\;t \leq 4.35 \cdot 10^{+15}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t_2}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a (/ y (/ t z))) (/ b (/ t y)))) (t_2 (+ y (+ x t))))
   (if (<= t -7e+77)
     t_1
     (if (<= t 7e-44)
       (+ z (/ a (/ t_2 (+ y t))))
       (if (<= t 4.35e+15)
         (/ (+ (* z (+ x y)) (* y (- a b))) (+ x y))
         (if (<= t 1.3e+97)
           (- (+ z a) b)
           (if (<= t 4e+146) t_1 (+ a (/ z (/ t_2 (+ x y)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + (y / (t / z))) - (b / (t / y));
	double t_2 = y + (x + t);
	double tmp;
	if (t <= -7e+77) {
		tmp = t_1;
	} else if (t <= 7e-44) {
		tmp = z + (a / (t_2 / (y + t)));
	} else if (t <= 4.35e+15) {
		tmp = ((z * (x + y)) + (y * (a - b))) / (x + y);
	} else if (t <= 1.3e+97) {
		tmp = (z + a) - b;
	} else if (t <= 4e+146) {
		tmp = t_1;
	} else {
		tmp = a + (z / (t_2 / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a + (y / (t / z))) - (b / (t / y))
    t_2 = y + (x + t)
    if (t <= (-7d+77)) then
        tmp = t_1
    else if (t <= 7d-44) then
        tmp = z + (a / (t_2 / (y + t)))
    else if (t <= 4.35d+15) then
        tmp = ((z * (x + y)) + (y * (a - b))) / (x + y)
    else if (t <= 1.3d+97) then
        tmp = (z + a) - b
    else if (t <= 4d+146) then
        tmp = t_1
    else
        tmp = a + (z / (t_2 / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + (y / (t / z))) - (b / (t / y));
	double t_2 = y + (x + t);
	double tmp;
	if (t <= -7e+77) {
		tmp = t_1;
	} else if (t <= 7e-44) {
		tmp = z + (a / (t_2 / (y + t)));
	} else if (t <= 4.35e+15) {
		tmp = ((z * (x + y)) + (y * (a - b))) / (x + y);
	} else if (t <= 1.3e+97) {
		tmp = (z + a) - b;
	} else if (t <= 4e+146) {
		tmp = t_1;
	} else {
		tmp = a + (z / (t_2 / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + (y / (t / z))) - (b / (t / y))
	t_2 = y + (x + t)
	tmp = 0
	if t <= -7e+77:
		tmp = t_1
	elif t <= 7e-44:
		tmp = z + (a / (t_2 / (y + t)))
	elif t <= 4.35e+15:
		tmp = ((z * (x + y)) + (y * (a - b))) / (x + y)
	elif t <= 1.3e+97:
		tmp = (z + a) - b
	elif t <= 4e+146:
		tmp = t_1
	else:
		tmp = a + (z / (t_2 / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + Float64(y / Float64(t / z))) - Float64(b / Float64(t / y)))
	t_2 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (t <= -7e+77)
		tmp = t_1;
	elseif (t <= 7e-44)
		tmp = Float64(z + Float64(a / Float64(t_2 / Float64(y + t))));
	elseif (t <= 4.35e+15)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) + Float64(y * Float64(a - b))) / Float64(x + y));
	elseif (t <= 1.3e+97)
		tmp = Float64(Float64(z + a) - b);
	elseif (t <= 4e+146)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(z / Float64(t_2 / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + (y / (t / z))) - (b / (t / y));
	t_2 = y + (x + t);
	tmp = 0.0;
	if (t <= -7e+77)
		tmp = t_1;
	elseif (t <= 7e-44)
		tmp = z + (a / (t_2 / (y + t)));
	elseif (t <= 4.35e+15)
		tmp = ((z * (x + y)) + (y * (a - b))) / (x + y);
	elseif (t <= 1.3e+97)
		tmp = (z + a) - b;
	elseif (t <= 4e+146)
		tmp = t_1;
	else
		tmp = a + (z / (t_2 / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+77], t$95$1, If[LessEqual[t, 7e-44], N[(z + N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.35e+15], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+97], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 4e+146], t$95$1, N[(a + N[(z / N[(t$95$2 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.0000000000000003e77 or 1.3e97 < t < 3.99999999999999973e146

   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 t around inf 69.7%

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

      1. +-commutative 69.7%

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

      2. associate-+l+ 69.7%

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

      3. associate-/l* 69.8%

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

      4. associate-/l* 70.0%

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

      5. +-commutative 70.0%

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

      6. associate-/l* 75.1%

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

      7. +-commutative 75.1%

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

      8. associate-/l* 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in x around 0 70.1%

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

      1. associate-/l* 72.4%

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

      2. associate-/l* 80.5%

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

   8. Simplified 80.5%

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

   if -7.0000000000000003e77 < t < 6.9999999999999995e-44

   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 inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. associate-/l* 69.9%

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

      3. associate-+r+ 69.9%

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

      4. div-sub 69.9%

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

      5. +-commutative 69.9%

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

      6. *-commutative 69.9%

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

      7. associate-+r+ 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in x around inf 74.0%

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

   if 6.9999999999999995e-44 < t < 4.35e15

   1. Initial program 94.3%

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

   3. Taylor expanded in t around 0 81.4%

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

      1. sub-neg 81.4%

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

      2. mul-1-neg 81.4%

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

      3. +-commutative 81.4%

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

      4. associate-+r+ 81.4%

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

      5. +-commutative 81.4%

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

      6. associate-*r* 81.4%

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

      7. distribute-rgt-in 81.4%

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

      8. mul-1-neg 81.4%

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

      9. +-commutative 81.4%

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

      10. +-commutative 81.4%

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

   5. Simplified 81.4%

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

   if 4.35e15 < t < 1.3e97

   1. Initial program 40.1%

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

   3. Taylor expanded in y around inf 71.4%

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

   if 3.99999999999999973e146 < t

   1. Initial program 64.3%

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

   3. Taylor expanded in z around inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. associate-/l* 78.3%

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

      3. associate-+r+ 78.3%

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

      4. div-sub 78.4%

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

      5. +-commutative 78.4%

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

      6. *-commutative 78.4%

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

      7. associate-+r+ 78.4%

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

   5. Simplified 78.4%

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

      1. div-inv 78.3%

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

      2. +-commutative 78.3%

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

      3. +-commutative 78.3%

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

   7. Applied egg-rr 78.3%

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

   8. Taylor expanded in z around inf 69.2%

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

      1. associate-/l* 83.3%

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

      2. +-commutative 83.3%

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

      3. +-commutative 83.3%

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

      4. associate-+l+ 83.3%

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

      5. +-commutative 83.3%

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

      6. +-commutative 83.3%

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

   10. Simplified 83.3%

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

   11. Taylor expanded in t around inf 79.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+77}:\\ \;\;\;\;\left(a + \frac{y}{\frac{t}{z}}\right) - \frac{b}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-44}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;t \leq 4.35 \cdot 10^{+15}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+146}:\\ \;\;\;\;\left(a + \frac{y}{\frac{t}{z}}\right) - \frac{b}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z + \frac{a}{\frac{t_1}{y + t}}\\ t_3 := a + \frac{z}{\frac{t_1}{x + y}}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+24}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5400000:\\ \;\;\;\;\frac{-b}{\frac{t_1}{y}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ z (/ a (/ t_1 (+ y t)))))
        (t_3 (+ a (/ z (/ t_1 (+ x y))))))
   (if (<= t -2.6e+24)
     t_3
     (if (<= t 6.5e-41)
       t_2
       (if (<= t 5400000.0)
         (/ (- b) (/ t_1 y))
         (if (<= t 1.45e+98) t_2 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 = z + (a / (t_1 / (y + t)));
	double t_3 = a + (z / (t_1 / (x + y)));
	double tmp;
	if (t <= -2.6e+24) {
		tmp = t_3;
	} else if (t <= 6.5e-41) {
		tmp = t_2;
	} else if (t <= 5400000.0) {
		tmp = -b / (t_1 / y);
	} else if (t <= 1.45e+98) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z + (a / (t_1 / (y + t)))
    t_3 = a + (z / (t_1 / (x + y)))
    if (t <= (-2.6d+24)) then
        tmp = t_3
    else if (t <= 6.5d-41) then
        tmp = t_2
    else if (t <= 5400000.0d0) then
        tmp = -b / (t_1 / y)
    else if (t <= 1.45d+98) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z + (a / (t_1 / (y + t)));
	double t_3 = a + (z / (t_1 / (x + y)));
	double tmp;
	if (t <= -2.6e+24) {
		tmp = t_3;
	} else if (t <= 6.5e-41) {
		tmp = t_2;
	} else if (t <= 5400000.0) {
		tmp = -b / (t_1 / y);
	} else if (t <= 1.45e+98) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z + (a / (t_1 / (y + t)))
	t_3 = a + (z / (t_1 / (x + y)))
	tmp = 0
	if t <= -2.6e+24:
		tmp = t_3
	elif t <= 6.5e-41:
		tmp = t_2
	elif t <= 5400000.0:
		tmp = -b / (t_1 / y)
	elif t <= 1.45e+98:
		tmp = t_2
	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(z + Float64(a / Float64(t_1 / Float64(y + t))))
	t_3 = Float64(a + Float64(z / Float64(t_1 / Float64(x + y))))
	tmp = 0.0
	if (t <= -2.6e+24)
		tmp = t_3;
	elseif (t <= 6.5e-41)
		tmp = t_2;
	elseif (t <= 5400000.0)
		tmp = Float64(Float64(-b) / Float64(t_1 / y));
	elseif (t <= 1.45e+98)
		tmp = t_2;
	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 = z + (a / (t_1 / (y + t)));
	t_3 = a + (z / (t_1 / (x + y)));
	tmp = 0.0;
	if (t <= -2.6e+24)
		tmp = t_3;
	elseif (t <= 6.5e-41)
		tmp = t_2;
	elseif (t <= 5400000.0)
		tmp = -b / (t_1 / y);
	elseif (t <= 1.45e+98)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+24], t$95$3, If[LessEqual[t, 6.5e-41], t$95$2, If[LessEqual[t, 5400000.0], N[((-b) / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+98], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5999999999999998e24 or 1.45000000000000005e98 < t

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 70.8%

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

      1. associate--l+ 70.8%

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

      2. associate-/l* 82.4%

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

      3. associate-+r+ 82.4%

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

      4. div-sub 82.4%

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

      5. +-commutative 82.4%

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

      6. *-commutative 82.4%

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

      7. associate-+r+ 82.4%

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

   5. Simplified 82.4%

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

      1. div-inv 82.4%

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

      2. +-commutative 82.4%

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

      3. +-commutative 82.4%

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

   7. Applied egg-rr 82.4%

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

   8. Taylor expanded in z around inf 72.2%

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

      1. associate-/l* 81.4%

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

      2. +-commutative 81.4%

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

      3. +-commutative 81.4%

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

      4. associate-+l+ 81.4%

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

      5. +-commutative 81.4%

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

      6. +-commutative 81.4%

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

   10. Simplified 81.4%

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

   11. Taylor expanded in t around inf 77.7%

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

   if -2.5999999999999998e24 < t < 6.5000000000000004e-41 or 5.4e6 < t < 1.45000000000000005e98

   1. Initial program 64.8%

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

   3. Taylor expanded in z around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-/l* 68.4%

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

      3. associate-+r+ 68.4%

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

      4. div-sub 68.4%

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

      5. +-commutative 68.4%

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

      6. *-commutative 68.4%

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

      7. associate-+r+ 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around inf 72.1%

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

   if 6.5000000000000004e-41 < t < 5.4e6

   1. Initial program 91.2%

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

   3. Taylor expanded in b around inf 73.3%

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

      1. mul-1-neg 73.3%

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

      2. associate-/l* 73.6%

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

      3. distribute-neg-frac 73.6%

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

      4. +-commutative 73.6%

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

      5. associate-+r+ 73.6%

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

      6. +-commutative 73.6%

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

      7. associate-+l+ 73.6%

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

   5. Simplified 73.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+24}:\\ \;\;\;\;a + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-41}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;t \leq 5400000:\\ \;\;\;\;\frac{-b}{\frac{y + \left(x + t\right)}{y}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+98}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z + \frac{a}{\frac{t_1}{y + t}}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+76}:\\ \;\;\;\;\left(a + \frac{y}{\frac{t}{z}}\right) - \frac{b}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5400000:\\ \;\;\;\;\frac{-b}{\frac{t_1}{y}}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t_1}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (+ z (/ a (/ t_1 (+ y t))))))
   (if (<= t -8.5e+76)
     (- (+ a (/ y (/ t z))) (/ b (/ t y)))
     (if (<= t 6.5e-41)
       t_2
       (if (<= t 5400000.0)
         (/ (- b) (/ t_1 y))
         (if (<= t 9.6e+99) t_2 (+ a (/ z (/ t_1 (+ x y))))))))))

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 / (t_1 / (y + t)));
	double tmp;
	if (t <= -8.5e+76) {
		tmp = (a + (y / (t / z))) - (b / (t / y));
	} else if (t <= 6.5e-41) {
		tmp = t_2;
	} else if (t <= 5400000.0) {
		tmp = -b / (t_1 / y);
	} else if (t <= 9.6e+99) {
		tmp = t_2;
	} else {
		tmp = a + (z / (t_1 / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z + (a / (t_1 / (y + t)))
    if (t <= (-8.5d+76)) then
        tmp = (a + (y / (t / z))) - (b / (t / y))
    else if (t <= 6.5d-41) then
        tmp = t_2
    else if (t <= 5400000.0d0) then
        tmp = -b / (t_1 / y)
    else if (t <= 9.6d+99) then
        tmp = t_2
    else
        tmp = a + (z / (t_1 / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z + (a / (t_1 / (y + t)));
	double tmp;
	if (t <= -8.5e+76) {
		tmp = (a + (y / (t / z))) - (b / (t / y));
	} else if (t <= 6.5e-41) {
		tmp = t_2;
	} else if (t <= 5400000.0) {
		tmp = -b / (t_1 / y);
	} else if (t <= 9.6e+99) {
		tmp = t_2;
	} else {
		tmp = a + (z / (t_1 / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z + (a / (t_1 / (y + t)))
	tmp = 0
	if t <= -8.5e+76:
		tmp = (a + (y / (t / z))) - (b / (t / y))
	elif t <= 6.5e-41:
		tmp = t_2
	elif t <= 5400000.0:
		tmp = -b / (t_1 / y)
	elif t <= 9.6e+99:
		tmp = t_2
	else:
		tmp = a + (z / (t_1 / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z + Float64(a / Float64(t_1 / Float64(y + t))))
	tmp = 0.0
	if (t <= -8.5e+76)
		tmp = Float64(Float64(a + Float64(y / Float64(t / z))) - Float64(b / Float64(t / y)));
	elseif (t <= 6.5e-41)
		tmp = t_2;
	elseif (t <= 5400000.0)
		tmp = Float64(Float64(-b) / Float64(t_1 / y));
	elseif (t <= 9.6e+99)
		tmp = t_2;
	else
		tmp = Float64(a + Float64(z / Float64(t_1 / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z + (a / (t_1 / (y + t)));
	tmp = 0.0;
	if (t <= -8.5e+76)
		tmp = (a + (y / (t / z))) - (b / (t / y));
	elseif (t <= 6.5e-41)
		tmp = t_2;
	elseif (t <= 5400000.0)
		tmp = -b / (t_1 / y);
	elseif (t <= 9.6e+99)
		tmp = t_2;
	else
		tmp = a + (z / (t_1 / (x + y)));
	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[(z + N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+76], N[(N[(a + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-41], t$95$2, If[LessEqual[t, 5400000.0], N[((-b) / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+99], t$95$2, N[(a + N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.49999999999999992e76

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-+l+ 69.0%

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

      3. associate-/l* 69.1%

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

      4. associate-/l* 69.4%

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

      5. +-commutative 69.4%

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

      6. associate-/l* 75.5%

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

      7. +-commutative 75.5%

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

      8. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in x around 0 67.6%

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

      1. associate-/l* 70.4%

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

      2. associate-/l* 80.0%

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

   8. Simplified 80.0%

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

   if -8.49999999999999992e76 < t < 6.5000000000000004e-41 or 5.4e6 < t < 9.6000000000000005e99

   1. Initial program 66.0%

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

   3. Taylor expanded in z around inf 66.0%

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

      1. associate--l+ 66.0%

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

      2. associate-/l* 69.3%

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

      3. associate-+r+ 69.3%

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

      4. div-sub 69.3%

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

      5. +-commutative 69.3%

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

      6. *-commutative 69.3%

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

      7. associate-+r+ 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in x around inf 73.3%

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

   if 6.5000000000000004e-41 < t < 5.4e6

   1. Initial program 91.2%

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

   3. Taylor expanded in b around inf 73.3%

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

      1. mul-1-neg 73.3%

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

      2. associate-/l* 73.6%

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

      3. distribute-neg-frac 73.6%

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

      4. +-commutative 73.6%

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

      5. associate-+r+ 73.6%

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

      6. +-commutative 73.6%

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

      7. associate-+l+ 73.6%

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

   5. Simplified 73.6%

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

   if 9.6000000000000005e99 < t

   1. Initial program 67.3%

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

   3. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. associate-/l* 82.0%

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

      3. associate-+r+ 82.0%

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

      4. div-sub 82.1%

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

      5. +-commutative 82.1%

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

      6. *-commutative 82.1%

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

      7. associate-+r+ 82.1%

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

   5. Simplified 82.1%

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

      1. div-inv 82.0%

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

      2. +-commutative 82.0%

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

      3. +-commutative 82.0%

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

   7. Applied egg-rr 82.0%

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

   8. Taylor expanded in z around inf 64.8%

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

      1. associate-/l* 77.3%

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

      2. +-commutative 77.3%

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

      3. +-commutative 77.3%

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

      4. associate-+l+ 77.3%

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

      5. +-commutative 77.3%

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

      6. +-commutative 77.3%

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

   10. Simplified 77.3%

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

   11. Taylor expanded in t around inf 74.8%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+76}:\\ \;\;\;\;\left(a + \frac{y}{\frac{t}{z}}\right) - \frac{b}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-41}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;t \leq 5400000:\\ \;\;\;\;\frac{-b}{\frac{y + \left(x + t\right)}{y}}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+99}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+78}:\\ \;\;\;\;\left(a + \frac{y}{\frac{t}{z}}\right) - \frac{b}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-41}:\\ \;\;\;\;z + \frac{a}{\frac{t_2}{y + t}}\\ \mathbf{elif}\;t \leq 7800000000000:\\ \;\;\;\;\frac{y \cdot t_1}{t_2}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t_2}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ y (+ x t))))
   (if (<= t -4.8e+78)
     (- (+ a (/ y (/ t z))) (/ b (/ t y)))
     (if (<= t 6.1e-41)
       (+ z (/ a (/ t_2 (+ y t))))
       (if (<= t 7800000000000.0)
         (/ (* y t_1) t_2)
         (if (<= t 5.2e+103) t_1 (+ a (/ z (/ t_2 (+ x y))))))))))

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 (t <= -4.8e+78) {
		tmp = (a + (y / (t / z))) - (b / (t / y));
	} else if (t <= 6.1e-41) {
		tmp = z + (a / (t_2 / (y + t)));
	} else if (t <= 7800000000000.0) {
		tmp = (y * t_1) / t_2;
	} else if (t <= 5.2e+103) {
		tmp = t_1;
	} else {
		tmp = a + (z / (t_2 / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    if (t <= (-4.8d+78)) then
        tmp = (a + (y / (t / z))) - (b / (t / y))
    else if (t <= 6.1d-41) then
        tmp = z + (a / (t_2 / (y + t)))
    else if (t <= 7800000000000.0d0) then
        tmp = (y * t_1) / t_2
    else if (t <= 5.2d+103) then
        tmp = t_1
    else
        tmp = a + (z / (t_2 / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double tmp;
	if (t <= -4.8e+78) {
		tmp = (a + (y / (t / z))) - (b / (t / y));
	} else if (t <= 6.1e-41) {
		tmp = z + (a / (t_2 / (y + t)));
	} else if (t <= 7800000000000.0) {
		tmp = (y * t_1) / t_2;
	} else if (t <= 5.2e+103) {
		tmp = t_1;
	} else {
		tmp = a + (z / (t_2 / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	tmp = 0
	if t <= -4.8e+78:
		tmp = (a + (y / (t / z))) - (b / (t / y))
	elif t <= 6.1e-41:
		tmp = z + (a / (t_2 / (y + t)))
	elif t <= 7800000000000.0:
		tmp = (y * t_1) / t_2
	elif t <= 5.2e+103:
		tmp = t_1
	else:
		tmp = a + (z / (t_2 / (x + y)))
	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 (t <= -4.8e+78)
		tmp = Float64(Float64(a + Float64(y / Float64(t / z))) - Float64(b / Float64(t / y)));
	elseif (t <= 6.1e-41)
		tmp = Float64(z + Float64(a / Float64(t_2 / Float64(y + t))));
	elseif (t <= 7800000000000.0)
		tmp = Float64(Float64(y * t_1) / t_2);
	elseif (t <= 5.2e+103)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(z / Float64(t_2 / Float64(x + y))));
	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 (t <= -4.8e+78)
		tmp = (a + (y / (t / z))) - (b / (t / y));
	elseif (t <= 6.1e-41)
		tmp = z + (a / (t_2 / (y + t)));
	elseif (t <= 7800000000000.0)
		tmp = (y * t_1) / t_2;
	elseif (t <= 5.2e+103)
		tmp = t_1;
	else
		tmp = a + (z / (t_2 / (x + y)));
	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[t, -4.8e+78], N[(N[(a + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.1e-41], N[(z + N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7800000000000.0], N[(N[(y * t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t, 5.2e+103], t$95$1, N[(a + N[(z / N[(t$95$2 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.7999999999999997e78

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-+l+ 69.0%

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

      3. associate-/l* 69.1%

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

      4. associate-/l* 69.4%

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

      5. +-commutative 69.4%

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

      6. associate-/l* 75.5%

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

      7. +-commutative 75.5%

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

      8. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in x around 0 67.6%

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

      1. associate-/l* 70.4%

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

      2. associate-/l* 80.0%

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

   8. Simplified 80.0%

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

   if -4.7999999999999997e78 < t < 6.0999999999999999e-41

   1. Initial program 67.8%

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

   3. Taylor expanded in z around inf 67.8%

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

      1. associate--l+ 67.8%

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

      2. associate-/l* 70.2%

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

      3. associate-+r+ 70.2%

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

      4. div-sub 70.2%

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

      5. +-commutative 70.2%

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

      6. *-commutative 70.2%

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

      7. associate-+r+ 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in x around inf 74.2%

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

   if 6.0999999999999999e-41 < t < 7.8e12

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf 77.2%

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

   if 7.8e12 < t < 5.2000000000000003e103

   1. Initial program 52.0%

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

   3. Taylor expanded in y around inf 62.8%

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

   if 5.2000000000000003e103 < t

   1. Initial program 66.5%

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

   3. Taylor expanded in z around inf 66.5%

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

      1. associate--l+ 66.5%

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

      2. associate-/l* 81.6%

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

      3. associate-+r+ 81.6%

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

      4. div-sub 81.6%

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

      5. +-commutative 81.6%

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

      6. *-commutative 81.6%

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

      7. associate-+r+ 81.6%

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

   5. Simplified 81.6%

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

      1. div-inv 81.6%

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

      2. +-commutative 81.6%

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

      3. +-commutative 81.6%

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

   7. Applied egg-rr 81.6%

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

   8. Taylor expanded in z around inf 66.5%

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

      1. associate-/l* 79.3%

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

      2. +-commutative 79.3%

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

      3. +-commutative 79.3%

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

      4. associate-+l+ 79.3%

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

      5. +-commutative 79.3%

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

      6. +-commutative 79.3%

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

   10. Simplified 79.3%

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

   11. Taylor expanded in t around inf 76.8%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+78}:\\ \;\;\;\;\left(a + \frac{y}{\frac{t}{z}}\right) - \frac{b}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-41}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;t \leq 7800000000000:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+103}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+78}:\\ \;\;\;\;\left(a + \frac{y}{\frac{t}{z}}\right) - \frac{b}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-41}:\\ \;\;\;\;z + \frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{t_1}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+103}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t_1}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= t -5.5e+78)
     (- (+ a (/ y (/ t z))) (/ b (/ t y)))
     (if (<= t 4.2e-41)
       (+ z (/ a (/ t_1 (+ y t))))
       (if (<= t 1.42e+17)
         (/ (- (* (+ y t) a) (* y b)) t_1)
         (if (<= t 4.6e+103) (- (+ z a) b) (+ a (/ z (/ t_1 (+ x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (t <= -5.5e+78) {
		tmp = (a + (y / (t / z))) - (b / (t / y));
	} else if (t <= 4.2e-41) {
		tmp = z + (a / (t_1 / (y + t)));
	} else if (t <= 1.42e+17) {
		tmp = (((y + t) * a) - (y * b)) / t_1;
	} else if (t <= 4.6e+103) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (z / (t_1 / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (t <= (-5.5d+78)) then
        tmp = (a + (y / (t / z))) - (b / (t / y))
    else if (t <= 4.2d-41) then
        tmp = z + (a / (t_1 / (y + t)))
    else if (t <= 1.42d+17) then
        tmp = (((y + t) * a) - (y * b)) / t_1
    else if (t <= 4.6d+103) then
        tmp = (z + a) - b
    else
        tmp = a + (z / (t_1 / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (t <= -5.5e+78) {
		tmp = (a + (y / (t / z))) - (b / (t / y));
	} else if (t <= 4.2e-41) {
		tmp = z + (a / (t_1 / (y + t)));
	} else if (t <= 1.42e+17) {
		tmp = (((y + t) * a) - (y * b)) / t_1;
	} else if (t <= 4.6e+103) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (z / (t_1 / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if t <= -5.5e+78:
		tmp = (a + (y / (t / z))) - (b / (t / y))
	elif t <= 4.2e-41:
		tmp = z + (a / (t_1 / (y + t)))
	elif t <= 1.42e+17:
		tmp = (((y + t) * a) - (y * b)) / t_1
	elif t <= 4.6e+103:
		tmp = (z + a) - b
	else:
		tmp = a + (z / (t_1 / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (t <= -5.5e+78)
		tmp = Float64(Float64(a + Float64(y / Float64(t / z))) - Float64(b / Float64(t / y)));
	elseif (t <= 4.2e-41)
		tmp = Float64(z + Float64(a / Float64(t_1 / Float64(y + t))));
	elseif (t <= 1.42e+17)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / t_1);
	elseif (t <= 4.6e+103)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(z / Float64(t_1 / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (t <= -5.5e+78)
		tmp = (a + (y / (t / z))) - (b / (t / y));
	elseif (t <= 4.2e-41)
		tmp = z + (a / (t_1 / (y + t)));
	elseif (t <= 1.42e+17)
		tmp = (((y + t) * a) - (y * b)) / t_1;
	elseif (t <= 4.6e+103)
		tmp = (z + a) - b;
	else
		tmp = a + (z / (t_1 / (x + y)));
	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[LessEqual[t, -5.5e+78], N[(N[(a + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-41], N[(z + N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.42e+17], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 4.6e+103], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.4999999999999997e78

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-+l+ 69.0%

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

      3. associate-/l* 69.1%

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

      4. associate-/l* 69.4%

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

      5. +-commutative 69.4%

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

      6. associate-/l* 75.5%

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

      7. +-commutative 75.5%

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

      8. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in x around 0 67.6%

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

      1. associate-/l* 70.4%

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

      2. associate-/l* 80.0%

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

   8. Simplified 80.0%

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

   if -5.4999999999999997e78 < t < 4.20000000000000025e-41

   1. Initial program 67.8%

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

   3. Taylor expanded in z around inf 67.8%

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

      1. associate--l+ 67.8%

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

      2. associate-/l* 70.2%

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

      3. associate-+r+ 70.2%

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

      4. div-sub 70.2%

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

      5. +-commutative 70.2%

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

      6. *-commutative 70.2%

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

      7. associate-+r+ 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in x around inf 74.2%

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

   if 4.20000000000000025e-41 < t < 1.42e17

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 75.9%

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

      1. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   if 1.42e17 < t < 4.60000000000000017e103

   1. Initial program 43.5%

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

   3. Taylor expanded in y around inf 67.6%

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

   if 4.60000000000000017e103 < t

   1. Initial program 66.5%

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

   3. Taylor expanded in z around inf 66.5%

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

      1. associate--l+ 66.5%

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

      2. associate-/l* 81.6%

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

      3. associate-+r+ 81.6%

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

      4. div-sub 81.6%

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

      5. +-commutative 81.6%

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

      6. *-commutative 81.6%

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

      7. associate-+r+ 81.6%

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

   5. Simplified 81.6%

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

      1. div-inv 81.6%

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

      2. +-commutative 81.6%

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

      3. +-commutative 81.6%

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

   7. Applied egg-rr 81.6%

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

   8. Taylor expanded in z around inf 66.5%

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

      1. associate-/l* 79.3%

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

      2. +-commutative 79.3%

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

      3. +-commutative 79.3%

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

      4. associate-+l+ 79.3%

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

      5. +-commutative 79.3%

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

      6. +-commutative 79.3%

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

   10. Simplified 79.3%

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

   11. Taylor expanded in t around inf 76.8%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+78}:\\ \;\;\;\;\left(a + \frac{y}{\frac{t}{z}}\right) - \frac{b}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-41}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+103}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{if}\;t \leq -1.82 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-225}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (/ a (/ (+ y (+ x t)) (+ y t)))))
   (if (<= t -1.82e+59)
     t_2
     (if (<= t -6.2e-303)
       t_1
       (if (<= t 7.8e-225) z (if (<= t 4.2e+90) 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 / ((y + (x + t)) / (y + t));
	double tmp;
	if (t <= -1.82e+59) {
		tmp = t_2;
	} else if (t <= -6.2e-303) {
		tmp = t_1;
	} else if (t <= 7.8e-225) {
		tmp = z;
	} else if (t <= 4.2e+90) {
		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 / ((y + (x + t)) / (y + t))
    if (t <= (-1.82d+59)) then
        tmp = t_2
    else if (t <= (-6.2d-303)) then
        tmp = t_1
    else if (t <= 7.8d-225) then
        tmp = z
    else if (t <= 4.2d+90) 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 / ((y + (x + t)) / (y + t));
	double tmp;
	if (t <= -1.82e+59) {
		tmp = t_2;
	} else if (t <= -6.2e-303) {
		tmp = t_1;
	} else if (t <= 7.8e-225) {
		tmp = z;
	} else if (t <= 4.2e+90) {
		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 / ((y + (x + t)) / (y + t))
	tmp = 0
	if t <= -1.82e+59:
		tmp = t_2
	elif t <= -6.2e-303:
		tmp = t_1
	elif t <= 7.8e-225:
		tmp = z
	elif t <= 4.2e+90:
		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(Float64(y + Float64(x + t)) / Float64(y + t)))
	tmp = 0.0
	if (t <= -1.82e+59)
		tmp = t_2;
	elseif (t <= -6.2e-303)
		tmp = t_1;
	elseif (t <= 7.8e-225)
		tmp = z;
	elseif (t <= 4.2e+90)
		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 / ((y + (x + t)) / (y + t));
	tmp = 0.0;
	if (t <= -1.82e+59)
		tmp = t_2;
	elseif (t <= -6.2e-303)
		tmp = t_1;
	elseif (t <= 7.8e-225)
		tmp = z;
	elseif (t <= 4.2e+90)
		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[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.82e+59], t$95$2, If[LessEqual[t, -6.2e-303], t$95$1, If[LessEqual[t, 7.8e-225], z, If[LessEqual[t, 4.2e+90], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.82000000000000008e59 or 4.19999999999999961e90 < t

   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 a around inf 42.0%

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

      1. associate-/l* 61.2%

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

      2. associate-+r+ 61.2%

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

   5. Simplified 61.2%

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

   if -1.82000000000000008e59 < t < -6.2000000000000002e-303 or 7.8000000000000001e-225 < t < 4.19999999999999961e90

   1. Initial program 67.3%

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

   3. Taylor expanded in y around inf 66.2%

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

   if -6.2000000000000002e-303 < t < 7.8000000000000001e-225

   1. Initial program 62.5%

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

   3. Taylor expanded in x around inf 74.3%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.82 \cdot 10^{+59}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-303}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-225}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+90}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-222}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{+87}:\\ \;\;\;\;a + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -3.9e+28)
     t_1
     (if (<= y 6e-222)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 1.72e+87) (+ a (/ z (/ (+ y (+ x t)) (+ x y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.9e+28) {
		tmp = t_1;
	} else if (y <= 6e-222) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.72e+87) {
		tmp = a + (z / ((y + (x + t)) / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-3.9d+28)) then
        tmp = t_1
    else if (y <= 6d-222) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 1.72d+87) then
        tmp = a + (z / ((y + (x + t)) / (x + y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.9e+28) {
		tmp = t_1;
	} else if (y <= 6e-222) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.72e+87) {
		tmp = a + (z / ((y + (x + t)) / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -3.9e+28:
		tmp = t_1
	elif y <= 6e-222:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 1.72e+87:
		tmp = a + (z / ((y + (x + t)) / (x + y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.9e+28)
		tmp = t_1;
	elseif (y <= 6e-222)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 1.72e+87)
		tmp = Float64(a + Float64(z / Float64(Float64(y + Float64(x + t)) / Float64(x + y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.9e+28)
		tmp = t_1;
	elseif (y <= 6e-222)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 1.72e+87)
		tmp = a + (z / ((y + (x + t)) / (x + y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.9e+28], t$95$1, If[LessEqual[y, 6e-222], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.72e+87], N[(a + N[(z / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8999999999999999e28 or 1.72000000000000008e87 < y

   1. Initial program 37.8%

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

   3. Taylor expanded in y around inf 80.2%

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

   if -3.8999999999999999e28 < y < 6.00000000000000059e-222

   1. Initial program 91.2%

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

   3. Taylor expanded in y around 0 67.8%

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

   if 6.00000000000000059e-222 < y < 1.72000000000000008e87

   1. Initial program 82.7%

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

   3. Taylor expanded in z around inf 82.7%

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

      1. associate--l+ 82.7%

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

      2. associate-/l* 90.6%

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

      3. associate-+r+ 90.6%

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

      4. div-sub 90.6%

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

      5. +-commutative 90.6%

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

      6. *-commutative 90.6%

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

      7. associate-+r+ 90.6%

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

   5. Simplified 90.6%

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

      1. div-inv 90.5%

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

      2. +-commutative 90.5%

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

      3. +-commutative 90.5%

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

   7. Applied egg-rr 90.5%

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

   8. Taylor expanded in z around inf 72.9%

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

      1. associate-/l* 80.7%

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

      2. +-commutative 80.7%

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

      3. +-commutative 80.7%

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

      4. associate-+l+ 80.7%

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

      5. +-commutative 80.7%

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

      6. +-commutative 80.7%

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

   10. Simplified 80.7%

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

   11. Taylor expanded in t around inf 66.7%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+28}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-222}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{+87}:\\ \;\;\;\;a + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -1.82 \cdot 10^{+59}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-225}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - \frac{x}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -1.82e+59)
     a
     (if (<= t -1.95e-303)
       t_1
       (if (<= t 1.32e-225)
         z
         (if (<= t 4.8e+128) t_1 (* a (- 1.0 (/ x t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -1.82e+59) {
		tmp = a;
	} else if (t <= -1.95e-303) {
		tmp = t_1;
	} else if (t <= 1.32e-225) {
		tmp = z;
	} else if (t <= 4.8e+128) {
		tmp = t_1;
	} else {
		tmp = a * (1.0 - (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-1.82d+59)) then
        tmp = a
    else if (t <= (-1.95d-303)) then
        tmp = t_1
    else if (t <= 1.32d-225) then
        tmp = z
    else if (t <= 4.8d+128) then
        tmp = t_1
    else
        tmp = a * (1.0d0 - (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -1.82e+59) {
		tmp = a;
	} else if (t <= -1.95e-303) {
		tmp = t_1;
	} else if (t <= 1.32e-225) {
		tmp = z;
	} else if (t <= 4.8e+128) {
		tmp = t_1;
	} else {
		tmp = a * (1.0 - (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -1.82e+59:
		tmp = a
	elif t <= -1.95e-303:
		tmp = t_1
	elif t <= 1.32e-225:
		tmp = z
	elif t <= 4.8e+128:
		tmp = t_1
	else:
		tmp = a * (1.0 - (x / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -1.82e+59)
		tmp = a;
	elseif (t <= -1.95e-303)
		tmp = t_1;
	elseif (t <= 1.32e-225)
		tmp = z;
	elseif (t <= 4.8e+128)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(1.0 - Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -1.82e+59)
		tmp = a;
	elseif (t <= -1.95e-303)
		tmp = t_1;
	elseif (t <= 1.32e-225)
		tmp = z;
	elseif (t <= 4.8e+128)
		tmp = t_1;
	else
		tmp = a * (1.0 - (x / t));
	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[t, -1.82e+59], a, If[LessEqual[t, -1.95e-303], t$95$1, If[LessEqual[t, 1.32e-225], z, If[LessEqual[t, 4.8e+128], t$95$1, N[(a * N[(1.0 - N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.82000000000000008e59

   1. Initial program 72.6%

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

   3. Taylor expanded in t around inf 62.0%

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

   if -1.82000000000000008e59 < t < -1.95e-303 or 1.32e-225 < t < 4.8000000000000004e128

   1. Initial program 67.4%

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

   3. Taylor expanded in y around inf 65.0%

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

   if -1.95e-303 < t < 1.32e-225

   1. Initial program 62.5%

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

   3. Taylor expanded in x around inf 74.3%

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

   if 4.8000000000000004e128 < t

   1. Initial program 68.1%

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

   3. Taylor expanded in t around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. associate-+l+ 67.7%

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

      3. associate-/l* 67.7%

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

      4. associate-/l* 68.0%

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

      5. +-commutative 68.0%

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

      6. associate-/l* 76.7%

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

      7. +-commutative 76.7%

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

      8. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in a around inf 58.3%

      \[\leadsto \color{blue}{a \cdot \left(1 - \frac{x}{t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.82 \cdot 10^{+59}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-303}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-225}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+128}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - \frac{x}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -1.82 \cdot 10^{+59}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-225}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -1.82e+59)
     a
     (if (<= t -7.5e-303)
       t_1
       (if (<= t 8e-225) z (if (<= t 3.8e+106) t_1 a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -1.82e+59) {
		tmp = a;
	} else if (t <= -7.5e-303) {
		tmp = t_1;
	} else if (t <= 8e-225) {
		tmp = z;
	} else if (t <= 3.8e+106) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-1.82d+59)) then
        tmp = a
    else if (t <= (-7.5d-303)) then
        tmp = t_1
    else if (t <= 8d-225) then
        tmp = z
    else if (t <= 3.8d+106) then
        tmp = t_1
    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 t_1 = (z + a) - b;
	double tmp;
	if (t <= -1.82e+59) {
		tmp = a;
	} else if (t <= -7.5e-303) {
		tmp = t_1;
	} else if (t <= 8e-225) {
		tmp = z;
	} else if (t <= 3.8e+106) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -1.82e+59:
		tmp = a
	elif t <= -7.5e-303:
		tmp = t_1
	elif t <= 8e-225:
		tmp = z
	elif t <= 3.8e+106:
		tmp = t_1
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -1.82e+59)
		tmp = a;
	elseif (t <= -7.5e-303)
		tmp = t_1;
	elseif (t <= 8e-225)
		tmp = z;
	elseif (t <= 3.8e+106)
		tmp = t_1;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -1.82e+59)
		tmp = a;
	elseif (t <= -7.5e-303)
		tmp = t_1;
	elseif (t <= 8e-225)
		tmp = z;
	elseif (t <= 3.8e+106)
		tmp = t_1;
	else
		tmp = a;
	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[t, -1.82e+59], a, If[LessEqual[t, -7.5e-303], t$95$1, If[LessEqual[t, 8e-225], z, If[LessEqual[t, 3.8e+106], t$95$1, a]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.82000000000000008e59 or 3.7999999999999998e106 < t

   1. Initial program 70.3%

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

   3. Taylor expanded in t around inf 60.3%

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

   if -1.82000000000000008e59 < t < -7.49999999999999972e-303 or 7.9999999999999997e-225 < t < 3.7999999999999998e106

   1. Initial program 67.8%

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

   3. Taylor expanded in y around inf 65.4%

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

   if -7.49999999999999972e-303 < t < 7.9999999999999997e-225

   1. Initial program 62.5%

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

   3. Taylor expanded in x around inf 74.3%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.82 \cdot 10^{+59}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-303}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-225}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+106}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+41} \lor \neg \left(y \leq 1.4 \cdot 10^{+40}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.4e+41) (not (<= y 1.4e+40)))
   (- (+ z a) b)
   (/ (+ (* t a) (* x z)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.4e+41) || !(y <= 1.4e+40)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.4d+41)) .or. (.not. (y <= 1.4d+40))) then
        tmp = (z + a) - b
    else
        tmp = ((t * a) + (x * z)) / (x + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.4e+41) || !(y <= 1.4e+40)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.4e+41) or not (y <= 1.4e+40):
		tmp = (z + a) - b
	else:
		tmp = ((t * a) + (x * z)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.4e+41) || !(y <= 1.4e+40))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.4e+41) || ~((y <= 1.4e+40)))
		tmp = (z + a) - b;
	else
		tmp = ((t * a) + (x * z)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.4e+41], N[Not[LessEqual[y, 1.4e+40]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.40000000000000019e41 or 1.4000000000000001e40 < y

   1. Initial program 39.8%

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

   3. Taylor expanded in y around inf 76.2%

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

   if -6.40000000000000019e41 < y < 1.4000000000000001e40

   1. Initial program 89.6%

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

   3. Taylor expanded in y around 0 64.9%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+41} \lor \neg \left(y \leq 1.4 \cdot 10^{+40}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+24}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+34}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.2e+24) a (if (<= t 1.3e+34) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.2e+24) {
		tmp = a;
	} else if (t <= 1.3e+34) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9.2d+24)) then
        tmp = a
    else if (t <= 1.3d+34) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.2e+24) {
		tmp = a;
	} else if (t <= 1.3e+34) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.2e+24:
		tmp = a
	elif t <= 1.3e+34:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.2e+24)
		tmp = a;
	elseif (t <= 1.3e+34)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.2e+24)
		tmp = a;
	elseif (t <= 1.3e+34)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.2e+24], a, If[LessEqual[t, 1.3e+34], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -9.1999999999999996e24 or 1.29999999999999999e34 < t

   1. Initial program 67.0%

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

   3. Taylor expanded in t around inf 57.0%

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

   if -9.1999999999999996e24 < t < 1.29999999999999999e34

   1. Initial program 69.6%

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

   3. Taylor expanded in x around inf 45.9%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+24}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+34}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.2% 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 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 t around inf 36.0%

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

4. Final simplification 36.0%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.4% 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 2024018 
(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)))