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

Percentage Accurate: 59.5% → 87.8%

Time: 18.5s

Alternatives: 19

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.5% 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: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \left(y + t\right) \cdot a\\ t_3 := \frac{\left(t_2 + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{+284} \lor \neg \left(t_3 \leq 10^{+264}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right) + \frac{t_2}{t_1}\right) - \frac{y \cdot b}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (* (+ y t) a))
        (t_3 (/ (- (+ t_2 (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_3 -1e+284) (not (<= t_3 1e+264)))
     (- (+ z a) b)
     (- (+ (* z (+ (/ x t_1) (/ y t_1))) (/ t_2 t_1)) (/ (* y b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = (y + t) * a;
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_3 <= -1e+284) || !(t_3 <= 1e+264)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / 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 = t + (x + y)
    t_2 = (y + t) * a
    t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t))
    if ((t_3 <= (-1d+284)) .or. (.not. (t_3 <= 1d+264))) then
        tmp = (z + a) - b
    else
        tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / 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 = t + (x + y);
	double t_2 = (y + t) * a;
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_3 <= -1e+284) || !(t_3 <= 1e+264)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = (y + t) * a
	t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_3 <= -1e+284) or not (t_3 <= 1e+264):
		tmp = (z + a) - b
	else:
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(Float64(y + t) * a)
	t_3 = Float64(Float64(Float64(t_2 + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_3 <= -1e+284) || !(t_3 <= 1e+264))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))) + Float64(t_2 / t_1)) - Float64(Float64(y * b) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = (y + t) * a;
	t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_3 <= -1e+284) || ~((t_3 <= 1e+264)))
		tmp = (z + a) - b;
	else
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$3, -1e+284], N[Not[LessEqual[t$95$3, 1e+264]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.00000000000000008e284 or 1.00000000000000004e264 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.6%

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

   2. Taylor expanded in y around inf 74.9%

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

   if -1.00000000000000008e284 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000004e264

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 98.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+284} \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+264}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \frac{\left(y + t\right) \cdot a}{t + \left(x + y\right)}\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \end{array} \]

Alternative 2: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+290} \lor \neg \left(t_1 \leq 10^{+264}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 -4e+290) (not (<= t_1 1e+264))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -4e+290) || !(t_1 <= 1e+264)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t))
    if ((t_1 <= (-4d+290)) .or. (.not. (t_1 <= 1d+264))) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -4e+290) || !(t_1 <= 1e+264)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -4e+290) or not (t_1 <= 1e+264):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= -4e+290) || !(t_1 <= 1e+264))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -4e+290) || ~((t_1 <= 1e+264)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+290], N[Not[LessEqual[t$95$1, 1e+264]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.00000000000000025e290 or 1.00000000000000004e264 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.8%

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

   2. Taylor expanded in y around inf 74.4%

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

   if -4.00000000000000025e290 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000004e264

   1. Initial program 98.6%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -4 \cdot 10^{+290} \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+264}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 3: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{y + \left(x + t\right)}{a - b}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-129}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 0.029:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+35}:\\ \;\;\;\;\frac{a}{\frac{t + \left(x + y\right)}{y + t}}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+83}:\\ \;\;\;\;z + a \cdot \left(\frac{t}{x} + \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (/ (+ y (+ x t)) (- a b)))) (t_2 (- (+ z a) b)))
   (if (<= y -1.8e+124)
     t_2
     (if (<= y -1.15e+87)
       t_1
       (if (<= y -4.2e-81)
         t_2
         (if (<= y 5.4e-129)
           (+ a (/ x (/ (+ x t) z)))
           (if (<= y 0.029)
             (+ z (/ (* y a) (+ x y)))
             (if (<= y 3.3e+35)
               (/ a (/ (+ t (+ x y)) (+ y t)))
               (if (<= y 8.8e+83)
                 (+ z (* a (+ (/ t x) (/ y x))))
                 (if (<= y 1.2e+103)
                   (/ y (/ (+ x y) (- a b)))
                   (if (<= y 8.2e+132) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / ((y + (x + t)) / (a - b));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.8e+124) {
		tmp = t_2;
	} else if (y <= -1.15e+87) {
		tmp = t_1;
	} else if (y <= -4.2e-81) {
		tmp = t_2;
	} else if (y <= 5.4e-129) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 0.029) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 3.3e+35) {
		tmp = a / ((t + (x + y)) / (y + t));
	} else if (y <= 8.8e+83) {
		tmp = z + (a * ((t / x) + (y / x)));
	} else if (y <= 1.2e+103) {
		tmp = y / ((x + y) / (a - b));
	} else if (y <= 8.2e+132) {
		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 = y / ((y + (x + t)) / (a - b))
    t_2 = (z + a) - b
    if (y <= (-1.8d+124)) then
        tmp = t_2
    else if (y <= (-1.15d+87)) then
        tmp = t_1
    else if (y <= (-4.2d-81)) then
        tmp = t_2
    else if (y <= 5.4d-129) then
        tmp = a + (x / ((x + t) / z))
    else if (y <= 0.029d0) then
        tmp = z + ((y * a) / (x + y))
    else if (y <= 3.3d+35) then
        tmp = a / ((t + (x + y)) / (y + t))
    else if (y <= 8.8d+83) then
        tmp = z + (a * ((t / x) + (y / x)))
    else if (y <= 1.2d+103) then
        tmp = y / ((x + y) / (a - b))
    else if (y <= 8.2d+132) 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 = y / ((y + (x + t)) / (a - b));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.8e+124) {
		tmp = t_2;
	} else if (y <= -1.15e+87) {
		tmp = t_1;
	} else if (y <= -4.2e-81) {
		tmp = t_2;
	} else if (y <= 5.4e-129) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 0.029) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 3.3e+35) {
		tmp = a / ((t + (x + y)) / (y + t));
	} else if (y <= 8.8e+83) {
		tmp = z + (a * ((t / x) + (y / x)));
	} else if (y <= 1.2e+103) {
		tmp = y / ((x + y) / (a - b));
	} else if (y <= 8.2e+132) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y / ((y + (x + t)) / (a - b))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -1.8e+124:
		tmp = t_2
	elif y <= -1.15e+87:
		tmp = t_1
	elif y <= -4.2e-81:
		tmp = t_2
	elif y <= 5.4e-129:
		tmp = a + (x / ((x + t) / z))
	elif y <= 0.029:
		tmp = z + ((y * a) / (x + y))
	elif y <= 3.3e+35:
		tmp = a / ((t + (x + y)) / (y + t))
	elif y <= 8.8e+83:
		tmp = z + (a * ((t / x) + (y / x)))
	elif y <= 1.2e+103:
		tmp = y / ((x + y) / (a - b))
	elif y <= 8.2e+132:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(Float64(y + Float64(x + t)) / Float64(a - b)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.8e+124)
		tmp = t_2;
	elseif (y <= -1.15e+87)
		tmp = t_1;
	elseif (y <= -4.2e-81)
		tmp = t_2;
	elseif (y <= 5.4e-129)
		tmp = Float64(a + Float64(x / Float64(Float64(x + t) / z)));
	elseif (y <= 0.029)
		tmp = Float64(z + Float64(Float64(y * a) / Float64(x + y)));
	elseif (y <= 3.3e+35)
		tmp = Float64(a / Float64(Float64(t + Float64(x + y)) / Float64(y + t)));
	elseif (y <= 8.8e+83)
		tmp = Float64(z + Float64(a * Float64(Float64(t / x) + Float64(y / x))));
	elseif (y <= 1.2e+103)
		tmp = Float64(y / Float64(Float64(x + y) / Float64(a - b)));
	elseif (y <= 8.2e+132)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y / ((y + (x + t)) / (a - b));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.8e+124)
		tmp = t_2;
	elseif (y <= -1.15e+87)
		tmp = t_1;
	elseif (y <= -4.2e-81)
		tmp = t_2;
	elseif (y <= 5.4e-129)
		tmp = a + (x / ((x + t) / z));
	elseif (y <= 0.029)
		tmp = z + ((y * a) / (x + y));
	elseif (y <= 3.3e+35)
		tmp = a / ((t + (x + y)) / (y + t));
	elseif (y <= 8.8e+83)
		tmp = z + (a * ((t / x) + (y / x)));
	elseif (y <= 1.2e+103)
		tmp = y / ((x + y) / (a - b));
	elseif (y <= 8.2e+132)
		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[(y / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.8e+124], t$95$2, If[LessEqual[y, -1.15e+87], t$95$1, If[LessEqual[y, -4.2e-81], t$95$2, If[LessEqual[y, 5.4e-129], N[(a + N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.029], N[(z + N[(N[(y * a), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+35], N[(a / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e+83], N[(z + N[(a * N[(N[(t / x), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+103], N[(y / N[(N[(x + y), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+132], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.79999999999999993e124 or -1.1500000000000001e87 < y < -4.1999999999999998e-81 or 8.19999999999999983e132 < y

   1. Initial program 48.9%

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

   2. Taylor expanded in y around inf 75.0%

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

   if -1.79999999999999993e124 < y < -1.1500000000000001e87 or 1.1999999999999999e103 < y < 8.19999999999999983e132

   1. Initial program 62.5%

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

   2. Taylor expanded in y around inf 55.6%

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

   3. Taylor expanded in z around 0 51.6%

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

      1. associate-/l* 85.1%

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

      2. +-commutative 85.1%

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

      3. +-commutative 85.1%

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

      4. associate-+l+ 85.1%

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

      5. +-commutative 85.1%

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

   5. Simplified 85.1%

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

   if -4.1999999999999998e-81 < y < 5.39999999999999998e-129

   1. Initial program 80.2%

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

   2. Taylor expanded in a around 0 89.3%

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

      1. associate--l+ 89.3%

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

      2. +-commutative 89.3%

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

      3. +-commutative 89.3%

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

      4. +-commutative 89.3%

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

      5. div-sub 89.3%

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

      6. +-commutative 89.3%

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

      7. *-commutative 89.3%

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

      8. +-commutative 89.3%

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

   4. Simplified 89.3%

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

   5. Taylor expanded in y around 0 74.8%

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

      1. associate-/l* 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in y around inf 63.9%

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

   if 5.39999999999999998e-129 < y < 0.0290000000000000015

   1. Initial program 74.6%

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

   2. Taylor expanded in a around 0 80.4%

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

      1. associate--l+ 80.4%

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

      2. +-commutative 80.4%

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

      3. +-commutative 80.4%

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

      4. +-commutative 80.4%

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

      5. div-sub 80.4%

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

      6. +-commutative 80.4%

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

      7. *-commutative 80.4%

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

      8. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in y around 0 63.4%

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

      1. associate-/l* 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in t around 0 69.3%

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

   if 0.0290000000000000015 < y < 3.3000000000000002e35

   1. Initial program 34.5%

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

   2. Taylor expanded in a around inf 34.5%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   if 3.3000000000000002e35 < y < 8.79999999999999995e83

   1. Initial program 68.7%

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

   2. Taylor expanded in x around inf 57.7%

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

      1. associate--r+ 57.7%

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

      2. sub-neg 57.7%

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

      3. mul-1-neg 57.7%

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

      4. associate-+r+ 57.7%

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

      5. +-commutative 57.7%

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

      6. associate--l+ 57.7%

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

   4. Simplified 88.8%

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

   5. Taylor expanded in a around inf 88.5%

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

   if 8.79999999999999995e83 < y < 1.1999999999999999e103

   1. Initial program 1.8%

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

   2. Taylor expanded in y around inf 1.9%

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

   3. Taylor expanded in z around 0 2.1%

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

      1. associate-/l* 50.4%

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

      2. +-commutative 50.4%

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

      3. +-commutative 50.4%

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

      4. associate-+l+ 50.4%

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

      5. +-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in t around 0 51.8%

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

      1. associate-/l* 100.0%

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

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y}{\frac{x + y}{a - b}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+124}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{\frac{y + \left(x + t\right)}{a - b}}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-129}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 0.029:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+35}:\\ \;\;\;\;\frac{a}{\frac{t + \left(x + y\right)}{y + t}}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+83}:\\ \;\;\;\;z + a \cdot \left(\frac{t}{x} + \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+132}:\\ \;\;\;\;\frac{y}{\frac{y + \left(x + t\right)}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 4: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + a \cdot \left(\frac{t}{x} + \frac{y}{x}\right)\\ t_2 := a + \frac{z \cdot \left(x + y\right) - y \cdot b}{t + \left(x + y\right)}\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-10}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (* a (+ (/ t x) (/ y x)))))
        (t_2 (+ a (/ (- (* z (+ x y)) (* y b)) (+ t (+ x y))))))
   (if (<= x -5.6e+199)
     t_1
     (if (<= x -2.25e-29)
       (+ a (/ x (/ (+ x t) z)))
       (if (<= x 2.95e-64)
         t_2
         (if (<= x 2.15e-10) (- (+ z a) b) (if (<= x 1.5e+130) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a * ((t / x) + (y / x)));
	double t_2 = a + (((z * (x + y)) - (y * b)) / (t + (x + y)));
	double tmp;
	if (x <= -5.6e+199) {
		tmp = t_1;
	} else if (x <= -2.25e-29) {
		tmp = a + (x / ((x + t) / z));
	} else if (x <= 2.95e-64) {
		tmp = t_2;
	} else if (x <= 2.15e-10) {
		tmp = (z + a) - b;
	} else if (x <= 1.5e+130) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + (a * ((t / x) + (y / x)))
    t_2 = a + (((z * (x + y)) - (y * b)) / (t + (x + y)))
    if (x <= (-5.6d+199)) then
        tmp = t_1
    else if (x <= (-2.25d-29)) then
        tmp = a + (x / ((x + t) / z))
    else if (x <= 2.95d-64) then
        tmp = t_2
    else if (x <= 2.15d-10) then
        tmp = (z + a) - b
    else if (x <= 1.5d+130) then
        tmp = t_2
    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 * ((t / x) + (y / x)));
	double t_2 = a + (((z * (x + y)) - (y * b)) / (t + (x + y)));
	double tmp;
	if (x <= -5.6e+199) {
		tmp = t_1;
	} else if (x <= -2.25e-29) {
		tmp = a + (x / ((x + t) / z));
	} else if (x <= 2.95e-64) {
		tmp = t_2;
	} else if (x <= 2.15e-10) {
		tmp = (z + a) - b;
	} else if (x <= 1.5e+130) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (a * ((t / x) + (y / x)))
	t_2 = a + (((z * (x + y)) - (y * b)) / (t + (x + y)))
	tmp = 0
	if x <= -5.6e+199:
		tmp = t_1
	elif x <= -2.25e-29:
		tmp = a + (x / ((x + t) / z))
	elif x <= 2.95e-64:
		tmp = t_2
	elif x <= 2.15e-10:
		tmp = (z + a) - b
	elif x <= 1.5e+130:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(a * Float64(Float64(t / x) + Float64(y / x))))
	t_2 = Float64(a + Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / Float64(t + Float64(x + y))))
	tmp = 0.0
	if (x <= -5.6e+199)
		tmp = t_1;
	elseif (x <= -2.25e-29)
		tmp = Float64(a + Float64(x / Float64(Float64(x + t) / z)));
	elseif (x <= 2.95e-64)
		tmp = t_2;
	elseif (x <= 2.15e-10)
		tmp = Float64(Float64(z + a) - b);
	elseif (x <= 1.5e+130)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (a * ((t / x) + (y / x)));
	t_2 = a + (((z * (x + y)) - (y * b)) / (t + (x + y)));
	tmp = 0.0;
	if (x <= -5.6e+199)
		tmp = t_1;
	elseif (x <= -2.25e-29)
		tmp = a + (x / ((x + t) / z));
	elseif (x <= 2.95e-64)
		tmp = t_2;
	elseif (x <= 2.15e-10)
		tmp = (z + a) - b;
	elseif (x <= 1.5e+130)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(a * N[(N[(t / x), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.6e+199], t$95$1, If[LessEqual[x, -2.25e-29], N[(a + N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.95e-64], t$95$2, If[LessEqual[x, 2.15e-10], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[x, 1.5e+130], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.6000000000000002e199 or 1.5e130 < x

   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. Taylor expanded in x around inf 59.0%

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

      1. associate--r+ 59.0%

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

      2. sub-neg 59.0%

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

      3. mul-1-neg 59.0%

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

      4. associate-+r+ 59.0%

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

      5. +-commutative 59.0%

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

      6. associate--l+ 61.1%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in a around inf 78.4%

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

   if -5.6000000000000002e199 < x < -2.2499999999999999e-29

   1. Initial program 65.0%

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

   2. Taylor expanded in a around 0 72.8%

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

      1. associate--l+ 72.8%

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

      2. +-commutative 72.8%

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

      3. +-commutative 72.8%

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

      4. +-commutative 72.8%

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

      5. div-sub 72.8%

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

      6. +-commutative 72.8%

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

      7. *-commutative 72.8%

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

      8. +-commutative 72.8%

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

   4. Simplified 72.8%

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

   5. Taylor expanded in y around 0 71.1%

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

      1. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in y around inf 67.5%

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

   if -2.2499999999999999e-29 < x < 2.94999999999999997e-64 or 2.15000000000000007e-10 < x < 1.5e130

   1. Initial program 66.9%

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

   2. Taylor expanded in a around 0 79.9%

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

      1. associate--l+ 79.9%

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

      2. +-commutative 79.9%

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

      3. +-commutative 79.9%

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

      4. +-commutative 79.9%

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

      5. div-sub 79.9%

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

      6. +-commutative 79.9%

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

      7. *-commutative 79.9%

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

      8. +-commutative 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in y around inf 75.8%

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

   if 2.94999999999999997e-64 < x < 2.15000000000000007e-10

   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. Taylor expanded in y around inf 77.9%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+199}:\\ \;\;\;\;z + a \cdot \left(\frac{t}{x} + \frac{y}{x}\right)\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-64}:\\ \;\;\;\;a + \frac{z \cdot \left(x + y\right) - y \cdot b}{t + \left(x + y\right)}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-10}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+130}:\\ \;\;\;\;a + \frac{z \cdot \left(x + y\right) - y \cdot b}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{t}{x} + \frac{y}{x}\right)\\ \end{array} \]

Alternative 5: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 0.016:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+33}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+93}:\\ \;\;\;\;z + a \cdot \left(\frac{t}{x} + \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+122}:\\ \;\;\;\;\frac{-b}{\frac{t + \left(x + y\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4.2e+123)
     t_1
     (if (<= y -5e+111)
       (/ a (/ (+ x y) y))
       (if (<= y -6.5e-79)
         t_1
         (if (<= y 1.1e-127)
           (+ a (/ x (/ (+ x t) z)))
           (if (<= y 0.016)
             (+ z (/ (* y a) (+ x y)))
             (if (<= y 2.3e+33)
               a
               (if (<= y 2.7e+93)
                 (+ z (* a (+ (/ t x) (/ y x))))
                 (if (<= y 4.1e+122)
                   (/ (- b) (/ (+ t (+ x y)) 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 <= -4.2e+123) {
		tmp = t_1;
	} else if (y <= -5e+111) {
		tmp = a / ((x + y) / y);
	} else if (y <= -6.5e-79) {
		tmp = t_1;
	} else if (y <= 1.1e-127) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 0.016) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 2.3e+33) {
		tmp = a;
	} else if (y <= 2.7e+93) {
		tmp = z + (a * ((t / x) + (y / x)));
	} else if (y <= 4.1e+122) {
		tmp = -b / ((t + (x + y)) / 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 <= (-4.2d+123)) then
        tmp = t_1
    else if (y <= (-5d+111)) then
        tmp = a / ((x + y) / y)
    else if (y <= (-6.5d-79)) then
        tmp = t_1
    else if (y <= 1.1d-127) then
        tmp = a + (x / ((x + t) / z))
    else if (y <= 0.016d0) then
        tmp = z + ((y * a) / (x + y))
    else if (y <= 2.3d+33) then
        tmp = a
    else if (y <= 2.7d+93) then
        tmp = z + (a * ((t / x) + (y / x)))
    else if (y <= 4.1d+122) then
        tmp = -b / ((t + (x + y)) / 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 <= -4.2e+123) {
		tmp = t_1;
	} else if (y <= -5e+111) {
		tmp = a / ((x + y) / y);
	} else if (y <= -6.5e-79) {
		tmp = t_1;
	} else if (y <= 1.1e-127) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 0.016) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 2.3e+33) {
		tmp = a;
	} else if (y <= 2.7e+93) {
		tmp = z + (a * ((t / x) + (y / x)));
	} else if (y <= 4.1e+122) {
		tmp = -b / ((t + (x + y)) / 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 <= -4.2e+123:
		tmp = t_1
	elif y <= -5e+111:
		tmp = a / ((x + y) / y)
	elif y <= -6.5e-79:
		tmp = t_1
	elif y <= 1.1e-127:
		tmp = a + (x / ((x + t) / z))
	elif y <= 0.016:
		tmp = z + ((y * a) / (x + y))
	elif y <= 2.3e+33:
		tmp = a
	elif y <= 2.7e+93:
		tmp = z + (a * ((t / x) + (y / x)))
	elif y <= 4.1e+122:
		tmp = -b / ((t + (x + y)) / 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 <= -4.2e+123)
		tmp = t_1;
	elseif (y <= -5e+111)
		tmp = Float64(a / Float64(Float64(x + y) / y));
	elseif (y <= -6.5e-79)
		tmp = t_1;
	elseif (y <= 1.1e-127)
		tmp = Float64(a + Float64(x / Float64(Float64(x + t) / z)));
	elseif (y <= 0.016)
		tmp = Float64(z + Float64(Float64(y * a) / Float64(x + y)));
	elseif (y <= 2.3e+33)
		tmp = a;
	elseif (y <= 2.7e+93)
		tmp = Float64(z + Float64(a * Float64(Float64(t / x) + Float64(y / x))));
	elseif (y <= 4.1e+122)
		tmp = Float64(Float64(-b) / Float64(Float64(t + Float64(x + y)) / 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 <= -4.2e+123)
		tmp = t_1;
	elseif (y <= -5e+111)
		tmp = a / ((x + y) / y);
	elseif (y <= -6.5e-79)
		tmp = t_1;
	elseif (y <= 1.1e-127)
		tmp = a + (x / ((x + t) / z));
	elseif (y <= 0.016)
		tmp = z + ((y * a) / (x + y));
	elseif (y <= 2.3e+33)
		tmp = a;
	elseif (y <= 2.7e+93)
		tmp = z + (a * ((t / x) + (y / x)));
	elseif (y <= 4.1e+122)
		tmp = -b / ((t + (x + y)) / 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, -4.2e+123], t$95$1, If[LessEqual[y, -5e+111], N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-79], t$95$1, If[LessEqual[y, 1.1e-127], N[(a + N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.016], N[(z + N[(N[(y * a), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+33], a, If[LessEqual[y, 2.7e+93], N[(z + N[(a * N[(N[(t / x), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+122], N[((-b) / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -4.19999999999999988e123 or -4.9999999999999997e111 < y < -6.5000000000000003e-79 or 4.1000000000000002e122 < y

   1. Initial program 49.8%

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

   2. Taylor expanded in y around inf 74.9%

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

   if -4.19999999999999988e123 < y < -4.9999999999999997e111

   1. Initial program 61.9%

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

   2. Taylor expanded in a around inf 61.9%

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

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in t around 0 99.7%

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

      1. +-commutative 99.7%

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

   7. Simplified 99.7%

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

   if -6.5000000000000003e-79 < y < 1.1000000000000001e-127

   1. Initial program 80.2%

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

   2. Taylor expanded in a around 0 89.3%

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

      1. associate--l+ 89.3%

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

      2. +-commutative 89.3%

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

      3. +-commutative 89.3%

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

      4. +-commutative 89.3%

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

      5. div-sub 89.3%

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

      6. +-commutative 89.3%

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

      7. *-commutative 89.3%

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

      8. +-commutative 89.3%

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

   4. Simplified 89.3%

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

   5. Taylor expanded in y around 0 74.8%

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

      1. associate-/l* 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in y around inf 63.9%

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

   if 1.1000000000000001e-127 < y < 0.016

   1. Initial program 74.6%

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

   2. Taylor expanded in a around 0 80.4%

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

      1. associate--l+ 80.4%

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

      2. +-commutative 80.4%

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

      3. +-commutative 80.4%

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

      4. +-commutative 80.4%

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

      5. div-sub 80.4%

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

      6. +-commutative 80.4%

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

      7. *-commutative 80.4%

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

      8. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in y around 0 63.4%

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

      1. associate-/l* 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in t around 0 69.3%

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

   if 0.016 < y < 2.30000000000000011e33

   1. Initial program 34.5%

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

   2. Taylor expanded in t around inf 86.2%

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

   if 2.30000000000000011e33 < y < 2.6999999999999999e93

   1. Initial program 68.7%

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

   2. Taylor expanded in x around inf 57.7%

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

      1. associate--r+ 57.7%

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

      2. sub-neg 57.7%

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

      3. mul-1-neg 57.7%

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

      4. associate-+r+ 57.7%

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

      5. +-commutative 57.7%

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

      6. associate--l+ 57.7%

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

   4. Simplified 88.8%

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

   5. Taylor expanded in a around inf 88.5%

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

   if 2.6999999999999999e93 < y < 4.1000000000000002e122

   1. Initial program 58.5%

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

   2. Taylor expanded in b around inf 38.5%

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

      1. mul-1-neg 38.5%

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

      2. associate-/l* 65.5%

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

      3. distribute-neg-frac 65.5%

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

      4. +-commutative 65.5%

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

   4. Simplified 65.5%

      \[\leadsto \color{blue}{\frac{-b}{\frac{t + \left(y + x\right)}{y}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-79}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 0.016:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+33}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+93}:\\ \;\;\;\;z + a \cdot \left(\frac{t}{x} + \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+122}:\\ \;\;\;\;\frac{-b}{\frac{t + \left(x + y\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 6: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := t + \left(x + y\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-128}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-7}:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+33}:\\ \;\;\;\;\frac{a}{\frac{t_2}{y + t}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+95}:\\ \;\;\;\;z + a \cdot \left(\frac{t}{x} + \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+132}:\\ \;\;\;\;\frac{-b}{\frac{t_2}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ t (+ x y))))
   (if (<= y -4.2e+123)
     t_1
     (if (<= y -5e+111)
       (/ a (/ (+ x y) y))
       (if (<= y -6.5e-79)
         t_1
         (if (<= y 6.6e-128)
           (+ a (/ x (/ (+ x t) z)))
           (if (<= y 6.4e-7)
             (+ z (/ (* y a) (+ x y)))
             (if (<= y 1.1e+33)
               (/ a (/ t_2 (+ y t)))
               (if (<= y 1.2e+95)
                 (+ z (* a (+ (/ t x) (/ y x))))
                 (if (<= y 8.2e+132) (/ (- b) (/ t_2 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 t_2 = t + (x + y);
	double tmp;
	if (y <= -4.2e+123) {
		tmp = t_1;
	} else if (y <= -5e+111) {
		tmp = a / ((x + y) / y);
	} else if (y <= -6.5e-79) {
		tmp = t_1;
	} else if (y <= 6.6e-128) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 6.4e-7) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 1.1e+33) {
		tmp = a / (t_2 / (y + t));
	} else if (y <= 1.2e+95) {
		tmp = z + (a * ((t / x) + (y / x)));
	} else if (y <= 8.2e+132) {
		tmp = -b / (t_2 / 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) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = t + (x + y)
    if (y <= (-4.2d+123)) then
        tmp = t_1
    else if (y <= (-5d+111)) then
        tmp = a / ((x + y) / y)
    else if (y <= (-6.5d-79)) then
        tmp = t_1
    else if (y <= 6.6d-128) then
        tmp = a + (x / ((x + t) / z))
    else if (y <= 6.4d-7) then
        tmp = z + ((y * a) / (x + y))
    else if (y <= 1.1d+33) then
        tmp = a / (t_2 / (y + t))
    else if (y <= 1.2d+95) then
        tmp = z + (a * ((t / x) + (y / x)))
    else if (y <= 8.2d+132) then
        tmp = -b / (t_2 / 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 t_2 = t + (x + y);
	double tmp;
	if (y <= -4.2e+123) {
		tmp = t_1;
	} else if (y <= -5e+111) {
		tmp = a / ((x + y) / y);
	} else if (y <= -6.5e-79) {
		tmp = t_1;
	} else if (y <= 6.6e-128) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 6.4e-7) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 1.1e+33) {
		tmp = a / (t_2 / (y + t));
	} else if (y <= 1.2e+95) {
		tmp = z + (a * ((t / x) + (y / x)));
	} else if (y <= 8.2e+132) {
		tmp = -b / (t_2 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = t + (x + y)
	tmp = 0
	if y <= -4.2e+123:
		tmp = t_1
	elif y <= -5e+111:
		tmp = a / ((x + y) / y)
	elif y <= -6.5e-79:
		tmp = t_1
	elif y <= 6.6e-128:
		tmp = a + (x / ((x + t) / z))
	elif y <= 6.4e-7:
		tmp = z + ((y * a) / (x + y))
	elif y <= 1.1e+33:
		tmp = a / (t_2 / (y + t))
	elif y <= 1.2e+95:
		tmp = z + (a * ((t / x) + (y / x)))
	elif y <= 8.2e+132:
		tmp = -b / (t_2 / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (y <= -4.2e+123)
		tmp = t_1;
	elseif (y <= -5e+111)
		tmp = Float64(a / Float64(Float64(x + y) / y));
	elseif (y <= -6.5e-79)
		tmp = t_1;
	elseif (y <= 6.6e-128)
		tmp = Float64(a + Float64(x / Float64(Float64(x + t) / z)));
	elseif (y <= 6.4e-7)
		tmp = Float64(z + Float64(Float64(y * a) / Float64(x + y)));
	elseif (y <= 1.1e+33)
		tmp = Float64(a / Float64(t_2 / Float64(y + t)));
	elseif (y <= 1.2e+95)
		tmp = Float64(z + Float64(a * Float64(Float64(t / x) + Float64(y / x))));
	elseif (y <= 8.2e+132)
		tmp = Float64(Float64(-b) / Float64(t_2 / 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;
	t_2 = t + (x + y);
	tmp = 0.0;
	if (y <= -4.2e+123)
		tmp = t_1;
	elseif (y <= -5e+111)
		tmp = a / ((x + y) / y);
	elseif (y <= -6.5e-79)
		tmp = t_1;
	elseif (y <= 6.6e-128)
		tmp = a + (x / ((x + t) / z));
	elseif (y <= 6.4e-7)
		tmp = z + ((y * a) / (x + y));
	elseif (y <= 1.1e+33)
		tmp = a / (t_2 / (y + t));
	elseif (y <= 1.2e+95)
		tmp = z + (a * ((t / x) + (y / x)));
	elseif (y <= 8.2e+132)
		tmp = -b / (t_2 / 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]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+123], t$95$1, If[LessEqual[y, -5e+111], N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-79], t$95$1, If[LessEqual[y, 6.6e-128], N[(a + N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-7], N[(z + N[(N[(y * a), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+33], N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+95], N[(z + N[(a * N[(N[(t / x), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+132], N[((-b) / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -4.19999999999999988e123 or -4.9999999999999997e111 < y < -6.5000000000000003e-79 or 8.19999999999999983e132 < y

   1. Initial program 49.3%

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

   2. Taylor expanded in y around inf 74.6%

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

   if -4.19999999999999988e123 < y < -4.9999999999999997e111

   1. Initial program 61.9%

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

   2. Taylor expanded in a around inf 61.9%

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

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in t around 0 99.7%

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

      1. +-commutative 99.7%

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

   7. Simplified 99.7%

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

   if -6.5000000000000003e-79 < y < 6.6e-128

   1. Initial program 80.2%

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

   2. Taylor expanded in a around 0 89.3%

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

      1. associate--l+ 89.3%

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

      2. +-commutative 89.3%

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

      3. +-commutative 89.3%

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

      4. +-commutative 89.3%

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

      5. div-sub 89.3%

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

      6. +-commutative 89.3%

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

      7. *-commutative 89.3%

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

      8. +-commutative 89.3%

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

   4. Simplified 89.3%

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

   5. Taylor expanded in y around 0 74.8%

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

      1. associate-/l* 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in y around inf 63.9%

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

   if 6.6e-128 < y < 6.4000000000000001e-7

   1. Initial program 74.6%

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

   2. Taylor expanded in a around 0 80.4%

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

      1. associate--l+ 80.4%

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

      2. +-commutative 80.4%

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

      3. +-commutative 80.4%

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

      4. +-commutative 80.4%

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

      5. div-sub 80.4%

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

      6. +-commutative 80.4%

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

      7. *-commutative 80.4%

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

      8. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in y around 0 63.4%

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

      1. associate-/l* 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in t around 0 69.3%

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

   if 6.4000000000000001e-7 < y < 1.09999999999999997e33

   1. Initial program 34.5%

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

   2. Taylor expanded in a around inf 34.5%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   if 1.09999999999999997e33 < y < 1.2e95

   1. Initial program 68.7%

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

   2. Taylor expanded in x around inf 57.7%

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

      1. associate--r+ 57.7%

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

      2. sub-neg 57.7%

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

      3. mul-1-neg 57.7%

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

      4. associate-+r+ 57.7%

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

      5. +-commutative 57.7%

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

      6. associate--l+ 57.7%

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

   4. Simplified 88.8%

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

   5. Taylor expanded in a around inf 88.5%

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

   if 1.2e95 < y < 8.19999999999999983e132

   1. Initial program 60.3%

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

   2. Taylor expanded in b around inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. associate-/l* 79.7%

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

      3. distribute-neg-frac 79.7%

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

      4. +-commutative 79.7%

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

   4. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{-b}{\frac{t + \left(y + x\right)}{y}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-79}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-128}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-7}:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+33}:\\ \;\;\;\;\frac{a}{\frac{t + \left(x + y\right)}{y + t}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+95}:\\ \;\;\;\;z + a \cdot \left(\frac{t}{x} + \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+132}:\\ \;\;\;\;\frac{-b}{\frac{t + \left(x + y\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 7: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{y}{\frac{t_1}{a - b}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+124}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{+36}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-114}:\\ \;\;\;\;a - \frac{y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-230}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+65}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ y (/ t_1 (- a b)))) (t_3 (- (+ z a) b)))
   (if (<= y -1.3e+124)
     t_3
     (if (<= y -1.08e+87)
       t_2
       (if (<= y -1.16e+36)
         (+ z a)
         (if (<= y -7.8e-114)
           (- a (/ (* y b) t_1))
           (if (<= y 3.2e-230)
             (/ (+ (* t a) (* x z)) (+ x t))
             (if (<= y 4.2e+65)
               (+ a (/ x (/ (+ x t) z)))
               (if (<= y 2.1e+133) 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 = y / (t_1 / (a - b));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -1.3e+124) {
		tmp = t_3;
	} else if (y <= -1.08e+87) {
		tmp = t_2;
	} else if (y <= -1.16e+36) {
		tmp = z + a;
	} else if (y <= -7.8e-114) {
		tmp = a - ((y * b) / t_1);
	} else if (y <= 3.2e-230) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.2e+65) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 2.1e+133) {
		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 = y / (t_1 / (a - b))
    t_3 = (z + a) - b
    if (y <= (-1.3d+124)) then
        tmp = t_3
    else if (y <= (-1.08d+87)) then
        tmp = t_2
    else if (y <= (-1.16d+36)) then
        tmp = z + a
    else if (y <= (-7.8d-114)) then
        tmp = a - ((y * b) / t_1)
    else if (y <= 3.2d-230) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 4.2d+65) then
        tmp = a + (x / ((x + t) / z))
    else if (y <= 2.1d+133) 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 = y / (t_1 / (a - b));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -1.3e+124) {
		tmp = t_3;
	} else if (y <= -1.08e+87) {
		tmp = t_2;
	} else if (y <= -1.16e+36) {
		tmp = z + a;
	} else if (y <= -7.8e-114) {
		tmp = a - ((y * b) / t_1);
	} else if (y <= 3.2e-230) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.2e+65) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 2.1e+133) {
		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 = y / (t_1 / (a - b))
	t_3 = (z + a) - b
	tmp = 0
	if y <= -1.3e+124:
		tmp = t_3
	elif y <= -1.08e+87:
		tmp = t_2
	elif y <= -1.16e+36:
		tmp = z + a
	elif y <= -7.8e-114:
		tmp = a - ((y * b) / t_1)
	elif y <= 3.2e-230:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 4.2e+65:
		tmp = a + (x / ((x + t) / z))
	elif y <= 2.1e+133:
		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(y / Float64(t_1 / Float64(a - b)))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.3e+124)
		tmp = t_3;
	elseif (y <= -1.08e+87)
		tmp = t_2;
	elseif (y <= -1.16e+36)
		tmp = Float64(z + a);
	elseif (y <= -7.8e-114)
		tmp = Float64(a - Float64(Float64(y * b) / t_1));
	elseif (y <= 3.2e-230)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 4.2e+65)
		tmp = Float64(a + Float64(x / Float64(Float64(x + t) / z)));
	elseif (y <= 2.1e+133)
		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 = y / (t_1 / (a - b));
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.3e+124)
		tmp = t_3;
	elseif (y <= -1.08e+87)
		tmp = t_2;
	elseif (y <= -1.16e+36)
		tmp = z + a;
	elseif (y <= -7.8e-114)
		tmp = a - ((y * b) / t_1);
	elseif (y <= 3.2e-230)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 4.2e+65)
		tmp = a + (x / ((x + t) / z));
	elseif (y <= 2.1e+133)
		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[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.3e+124], t$95$3, If[LessEqual[y, -1.08e+87], t$95$2, If[LessEqual[y, -1.16e+36], N[(z + a), $MachinePrecision], If[LessEqual[y, -7.8e-114], N[(a - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-230], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+65], N[(a + N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+133], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.3e124 or 2.1e133 < y

   1. Initial program 38.8%

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

   2. Taylor expanded in y around inf 83.8%

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

   if -1.3e124 < y < -1.08000000000000007e87 or 4.19999999999999983e65 < y < 2.1e133

   1. Initial program 60.3%

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

   2. Taylor expanded in y around inf 54.8%

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

   3. Taylor expanded in z around 0 48.4%

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

      1. associate-/l* 78.7%

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

      2. +-commutative 78.7%

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

      3. +-commutative 78.7%

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

      4. associate-+l+ 78.7%

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

      5. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   if -1.08000000000000007e87 < y < -1.15999999999999998e36

   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. Taylor expanded in y around inf 69.0%

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

   3. Taylor expanded in b around 0 79.2%

      \[\leadsto \color{blue}{a + z} \]
   4. Step-by-step derivation

      1. +-commutative 79.2%

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

   5. Simplified 79.2%

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

   if -1.15999999999999998e36 < y < -7.80000000000000003e-114

   1. Initial program 73.8%

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

   2. Taylor expanded in a around 0 93.3%

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

      1. associate--l+ 93.3%

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

      2. +-commutative 93.3%

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

      3. +-commutative 93.3%

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

      4. +-commutative 93.3%

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

      5. div-sub 93.3%

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

      6. +-commutative 93.3%

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

      7. *-commutative 93.3%

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

      8. +-commutative 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in y around inf 80.2%

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

   6. Taylor expanded in z around 0 67.3%

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

      1. associate-*r/ 67.3%

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

      2. mul-1-neg 67.3%

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

      3. *-commutative 67.3%

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

      4. distribute-lft-neg-in 67.3%

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

      5. neg-mul-1 67.3%

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

      6. *-commutative 67.3%

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

      7. neg-mul-1 67.3%

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

      8. +-commutative 67.3%

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

      9. +-commutative 67.3%

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

      10. associate-+l+ 67.3%

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

      11. +-commutative 67.3%

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

   8. Simplified 67.3%

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

   if -7.80000000000000003e-114 < y < 3.2e-230

   1. Initial program 82.9%

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

   2. Taylor expanded in y around 0 71.9%

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

   if 3.2e-230 < y < 4.19999999999999983e65

   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. Taylor expanded in a around 0 85.0%

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

      1. associate--l+ 85.0%

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

      2. +-commutative 85.0%

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

      3. +-commutative 85.0%

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

      4. +-commutative 85.0%

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

      5. div-sub 85.0%

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

      6. +-commutative 85.0%

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

      7. *-commutative 85.0%

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

      8. +-commutative 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in y around 0 71.0%

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

      1. associate-/l* 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around inf 62.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+124}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{\frac{y + \left(x + t\right)}{a - b}}\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{+36}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-114}:\\ \;\;\;\;a - \frac{y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-230}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+65}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+133}:\\ \;\;\;\;\frac{y}{\frac{y + \left(x + t\right)}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 8: 63.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{y + \left(x + t\right)}{a - b}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-225}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{+59}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (/ (+ y (+ x t)) (- a b)))) (t_2 (- (+ z a) b)))
   (if (<= y -1.85e+126)
     t_2
     (if (<= y -2.6e+87)
       t_1
       (if (<= y -6.6e-80)
         t_2
         (if (<= y 3.4e-225)
           (/ (+ (* t a) (* x z)) (+ x t))
           (if (<= y 1.62e+59)
             (+ a (/ x (/ (+ x t) z)))
             (if (<= y 8.2e+132) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / ((y + (x + t)) / (a - b));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.85e+126) {
		tmp = t_2;
	} else if (y <= -2.6e+87) {
		tmp = t_1;
	} else if (y <= -6.6e-80) {
		tmp = t_2;
	} else if (y <= 3.4e-225) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.62e+59) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 8.2e+132) {
		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 = y / ((y + (x + t)) / (a - b))
    t_2 = (z + a) - b
    if (y <= (-1.85d+126)) then
        tmp = t_2
    else if (y <= (-2.6d+87)) then
        tmp = t_1
    else if (y <= (-6.6d-80)) then
        tmp = t_2
    else if (y <= 3.4d-225) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 1.62d+59) then
        tmp = a + (x / ((x + t) / z))
    else if (y <= 8.2d+132) 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 = y / ((y + (x + t)) / (a - b));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.85e+126) {
		tmp = t_2;
	} else if (y <= -2.6e+87) {
		tmp = t_1;
	} else if (y <= -6.6e-80) {
		tmp = t_2;
	} else if (y <= 3.4e-225) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.62e+59) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 8.2e+132) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y / ((y + (x + t)) / (a - b))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -1.85e+126:
		tmp = t_2
	elif y <= -2.6e+87:
		tmp = t_1
	elif y <= -6.6e-80:
		tmp = t_2
	elif y <= 3.4e-225:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 1.62e+59:
		tmp = a + (x / ((x + t) / z))
	elif y <= 8.2e+132:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(Float64(y + Float64(x + t)) / Float64(a - b)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.85e+126)
		tmp = t_2;
	elseif (y <= -2.6e+87)
		tmp = t_1;
	elseif (y <= -6.6e-80)
		tmp = t_2;
	elseif (y <= 3.4e-225)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 1.62e+59)
		tmp = Float64(a + Float64(x / Float64(Float64(x + t) / z)));
	elseif (y <= 8.2e+132)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y / ((y + (x + t)) / (a - b));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.85e+126)
		tmp = t_2;
	elseif (y <= -2.6e+87)
		tmp = t_1;
	elseif (y <= -6.6e-80)
		tmp = t_2;
	elseif (y <= 3.4e-225)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 1.62e+59)
		tmp = a + (x / ((x + t) / z));
	elseif (y <= 8.2e+132)
		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[(y / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.85e+126], t$95$2, If[LessEqual[y, -2.6e+87], t$95$1, If[LessEqual[y, -6.6e-80], t$95$2, If[LessEqual[y, 3.4e-225], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.62e+59], N[(a + N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+132], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.8499999999999999e126 or -2.59999999999999998e87 < y < -6.5999999999999999e-80 or 8.19999999999999983e132 < y

   1. Initial program 48.9%

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

   2. Taylor expanded in y around inf 75.0%

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

   if -1.8499999999999999e126 < y < -2.59999999999999998e87 or 1.6200000000000001e59 < y < 8.19999999999999983e132

   1. Initial program 60.3%

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

   2. Taylor expanded in y around inf 54.8%

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

   3. Taylor expanded in z around 0 48.4%

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

      1. associate-/l* 78.7%

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

      2. +-commutative 78.7%

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

      3. +-commutative 78.7%

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

      4. associate-+l+ 78.7%

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

      5. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   if -6.5999999999999999e-80 < y < 3.3999999999999999e-225

   1. Initial program 82.8%

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

   2. Taylor expanded in y around 0 69.7%

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

   if 3.3999999999999999e-225 < y < 1.6200000000000001e59

   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. Taylor expanded in a around 0 85.0%

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

      1. associate--l+ 85.0%

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

      2. +-commutative 85.0%

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

      3. +-commutative 85.0%

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

      4. +-commutative 85.0%

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

      5. div-sub 85.0%

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

      6. +-commutative 85.0%

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

      7. *-commutative 85.0%

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

      8. +-commutative 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in y around 0 71.0%

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

      1. associate-/l* 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around inf 62.7%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+126}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{\frac{y + \left(x + t\right)}{a - b}}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-80}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-225}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{+59}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+132}:\\ \;\;\;\;\frac{y}{\frac{y + \left(x + t\right)}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 9: 63.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-128}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+123}:\\ \;\;\;\;\frac{-b}{\frac{t + \left(x + y\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -7.8e+124)
     t_1
     (if (<= y -1.5e+111)
       (/ a (/ (+ x y) y))
       (if (<= y -3.6e-88)
         t_1
         (if (<= y 2.3e-128)
           (+ a (/ x (/ (+ x t) z)))
           (if (<= y 2.5e+101)
             (+ z (/ (* y a) (+ x y)))
             (if (<= y 2e+123) (/ (- b) (/ (+ t (+ x y)) 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 <= -7.8e+124) {
		tmp = t_1;
	} else if (y <= -1.5e+111) {
		tmp = a / ((x + y) / y);
	} else if (y <= -3.6e-88) {
		tmp = t_1;
	} else if (y <= 2.3e-128) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 2.5e+101) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 2e+123) {
		tmp = -b / ((t + (x + y)) / 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 <= (-7.8d+124)) then
        tmp = t_1
    else if (y <= (-1.5d+111)) then
        tmp = a / ((x + y) / y)
    else if (y <= (-3.6d-88)) then
        tmp = t_1
    else if (y <= 2.3d-128) then
        tmp = a + (x / ((x + t) / z))
    else if (y <= 2.5d+101) then
        tmp = z + ((y * a) / (x + y))
    else if (y <= 2d+123) then
        tmp = -b / ((t + (x + y)) / 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 <= -7.8e+124) {
		tmp = t_1;
	} else if (y <= -1.5e+111) {
		tmp = a / ((x + y) / y);
	} else if (y <= -3.6e-88) {
		tmp = t_1;
	} else if (y <= 2.3e-128) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 2.5e+101) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 2e+123) {
		tmp = -b / ((t + (x + y)) / 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 <= -7.8e+124:
		tmp = t_1
	elif y <= -1.5e+111:
		tmp = a / ((x + y) / y)
	elif y <= -3.6e-88:
		tmp = t_1
	elif y <= 2.3e-128:
		tmp = a + (x / ((x + t) / z))
	elif y <= 2.5e+101:
		tmp = z + ((y * a) / (x + y))
	elif y <= 2e+123:
		tmp = -b / ((t + (x + y)) / 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 <= -7.8e+124)
		tmp = t_1;
	elseif (y <= -1.5e+111)
		tmp = Float64(a / Float64(Float64(x + y) / y));
	elseif (y <= -3.6e-88)
		tmp = t_1;
	elseif (y <= 2.3e-128)
		tmp = Float64(a + Float64(x / Float64(Float64(x + t) / z)));
	elseif (y <= 2.5e+101)
		tmp = Float64(z + Float64(Float64(y * a) / Float64(x + y)));
	elseif (y <= 2e+123)
		tmp = Float64(Float64(-b) / Float64(Float64(t + Float64(x + y)) / 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 <= -7.8e+124)
		tmp = t_1;
	elseif (y <= -1.5e+111)
		tmp = a / ((x + y) / y);
	elseif (y <= -3.6e-88)
		tmp = t_1;
	elseif (y <= 2.3e-128)
		tmp = a + (x / ((x + t) / z));
	elseif (y <= 2.5e+101)
		tmp = z + ((y * a) / (x + y));
	elseif (y <= 2e+123)
		tmp = -b / ((t + (x + y)) / 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, -7.8e+124], t$95$1, If[LessEqual[y, -1.5e+111], N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.6e-88], t$95$1, If[LessEqual[y, 2.3e-128], N[(a + N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+101], N[(z + N[(N[(y * a), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+123], N[((-b) / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.8000000000000001e124 or -1.5e111 < y < -3.5999999999999999e-88 or 1.99999999999999996e123 < y

   1. Initial program 49.8%

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

   2. Taylor expanded in y around inf 74.9%

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

   if -7.8000000000000001e124 < y < -1.5e111

   1. Initial program 61.9%

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

   2. Taylor expanded in a around inf 61.9%

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

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in t around 0 99.7%

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

      1. +-commutative 99.7%

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

   7. Simplified 99.7%

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

   if -3.5999999999999999e-88 < y < 2.3000000000000001e-128

   1. Initial program 80.2%

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

   2. Taylor expanded in a around 0 89.3%

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

      1. associate--l+ 89.3%

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

      2. +-commutative 89.3%

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

      3. +-commutative 89.3%

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

      4. +-commutative 89.3%

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

      5. div-sub 89.3%

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

      6. +-commutative 89.3%

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

      7. *-commutative 89.3%

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

      8. +-commutative 89.3%

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

   4. Simplified 89.3%

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

   5. Taylor expanded in y around 0 74.8%

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

      1. associate-/l* 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in y around inf 63.9%

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

   if 2.3000000000000001e-128 < y < 2.49999999999999994e101

   1. Initial program 65.8%

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

   2. Taylor expanded in a around 0 81.3%

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

      1. associate--l+ 81.3%

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

      2. +-commutative 81.3%

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

      3. +-commutative 81.3%

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

      4. +-commutative 81.3%

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

      5. div-sub 81.3%

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

      6. +-commutative 81.3%

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

      7. *-commutative 81.3%

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

      8. +-commutative 81.3%

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

   4. Simplified 81.3%

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

   5. Taylor expanded in y around 0 68.9%

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

      1. associate-/l* 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in t around 0 64.5%

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

   if 2.49999999999999994e101 < y < 1.99999999999999996e123

   1. Initial program 58.5%

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

   2. Taylor expanded in b around inf 38.5%

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

      1. mul-1-neg 38.5%

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

      2. associate-/l* 65.5%

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

      3. distribute-neg-frac 65.5%

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

      4. +-commutative 65.5%

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

   4. Simplified 65.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+124}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-88}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-128}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+123}:\\ \;\;\;\;\frac{-b}{\frac{t + \left(x + y\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 0.0028:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ a (/ x (/ (+ x t) z)))))
   (if (<= y -4.2e+123)
     t_1
     (if (<= y -5e+111)
       (/ a (/ (+ x y) y))
       (if (<= y -6.5e-79)
         t_1
         (if (<= y 2.9e-127)
           t_2
           (if (<= y 0.0028)
             (+ z (/ (* y a) (+ x y)))
             (if (<= y 4.4e+101) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (x / ((x + t) / z));
	double tmp;
	if (y <= -4.2e+123) {
		tmp = t_1;
	} else if (y <= -5e+111) {
		tmp = a / ((x + y) / y);
	} else if (y <= -6.5e-79) {
		tmp = t_1;
	} else if (y <= 2.9e-127) {
		tmp = t_2;
	} else if (y <= 0.0028) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 4.4e+101) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a + (x / ((x + t) / z))
    if (y <= (-4.2d+123)) then
        tmp = t_1
    else if (y <= (-5d+111)) then
        tmp = a / ((x + y) / y)
    else if (y <= (-6.5d-79)) then
        tmp = t_1
    else if (y <= 2.9d-127) then
        tmp = t_2
    else if (y <= 0.0028d0) then
        tmp = z + ((y * a) / (x + y))
    else if (y <= 4.4d+101) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (x / ((x + t) / z));
	double tmp;
	if (y <= -4.2e+123) {
		tmp = t_1;
	} else if (y <= -5e+111) {
		tmp = a / ((x + y) / y);
	} else if (y <= -6.5e-79) {
		tmp = t_1;
	} else if (y <= 2.9e-127) {
		tmp = t_2;
	} else if (y <= 0.0028) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 4.4e+101) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a + (x / ((x + t) / z))
	tmp = 0
	if y <= -4.2e+123:
		tmp = t_1
	elif y <= -5e+111:
		tmp = a / ((x + y) / y)
	elif y <= -6.5e-79:
		tmp = t_1
	elif y <= 2.9e-127:
		tmp = t_2
	elif y <= 0.0028:
		tmp = z + ((y * a) / (x + y))
	elif y <= 4.4e+101:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a + Float64(x / Float64(Float64(x + t) / z)))
	tmp = 0.0
	if (y <= -4.2e+123)
		tmp = t_1;
	elseif (y <= -5e+111)
		tmp = Float64(a / Float64(Float64(x + y) / y));
	elseif (y <= -6.5e-79)
		tmp = t_1;
	elseif (y <= 2.9e-127)
		tmp = t_2;
	elseif (y <= 0.0028)
		tmp = Float64(z + Float64(Float64(y * a) / Float64(x + y)));
	elseif (y <= 4.4e+101)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a + (x / ((x + t) / z));
	tmp = 0.0;
	if (y <= -4.2e+123)
		tmp = t_1;
	elseif (y <= -5e+111)
		tmp = a / ((x + y) / y);
	elseif (y <= -6.5e-79)
		tmp = t_1;
	elseif (y <= 2.9e-127)
		tmp = t_2;
	elseif (y <= 0.0028)
		tmp = z + ((y * a) / (x + y));
	elseif (y <= 4.4e+101)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+123], t$95$1, If[LessEqual[y, -5e+111], N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-79], t$95$1, If[LessEqual[y, 2.9e-127], t$95$2, If[LessEqual[y, 0.0028], N[(z + N[(N[(y * a), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+101], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.19999999999999988e123 or -4.9999999999999997e111 < y < -6.5000000000000003e-79 or 4.4000000000000001e101 < y

   1. Initial program 51.1%

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

   2. Taylor expanded in y around inf 73.6%

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

   if -4.19999999999999988e123 < y < -4.9999999999999997e111

   1. Initial program 61.9%

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

   2. Taylor expanded in a around inf 61.9%

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

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in t around 0 99.7%

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

      1. +-commutative 99.7%

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

   7. Simplified 99.7%

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

   if -6.5000000000000003e-79 < y < 2.9e-127 or 0.00279999999999999997 < y < 4.4000000000000001e101

   1. Initial program 74.6%

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

   2. Taylor expanded in a around 0 86.5%

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

      1. associate--l+ 86.5%

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

      2. +-commutative 86.5%

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

      3. +-commutative 86.5%

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

      4. +-commutative 86.5%

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

      5. div-sub 86.5%

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

      6. +-commutative 86.5%

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

      7. *-commutative 86.5%

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

      8. +-commutative 86.5%

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

   4. Simplified 86.5%

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

   5. Taylor expanded in y around 0 74.6%

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

      1. associate-/l* 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in y around inf 62.9%

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

   if 2.9e-127 < y < 0.00279999999999999997

   1. Initial program 74.6%

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

   2. Taylor expanded in a around 0 80.4%

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

      1. associate--l+ 80.4%

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

      2. +-commutative 80.4%

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

      3. +-commutative 80.4%

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

      4. +-commutative 80.4%

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

      5. div-sub 80.4%

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

      6. +-commutative 80.4%

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

      7. *-commutative 80.4%

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

      8. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in y around 0 63.4%

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

      1. associate-/l* 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in t around 0 69.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-79}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-127}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 0.0028:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+101}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-127}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+95}:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+124}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4.2e+123)
     t_1
     (if (<= y -5e+111)
       (/ a (/ (+ x y) y))
       (if (<= y -5.5e-86)
         t_1
         (if (<= y 4.5e-127)
           (+ a (/ x (/ (+ x t) z)))
           (if (<= y 2.4e+95)
             (+ z (/ (* y a) (+ x y)))
             (if (<= y 1.22e+124) (/ y (/ (+ x y) (- a b))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.2e+123) {
		tmp = t_1;
	} else if (y <= -5e+111) {
		tmp = a / ((x + y) / y);
	} else if (y <= -5.5e-86) {
		tmp = t_1;
	} else if (y <= 4.5e-127) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 2.4e+95) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 1.22e+124) {
		tmp = y / ((x + y) / (a - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-4.2d+123)) then
        tmp = t_1
    else if (y <= (-5d+111)) then
        tmp = a / ((x + y) / y)
    else if (y <= (-5.5d-86)) then
        tmp = t_1
    else if (y <= 4.5d-127) then
        tmp = a + (x / ((x + t) / z))
    else if (y <= 2.4d+95) then
        tmp = z + ((y * a) / (x + y))
    else if (y <= 1.22d+124) then
        tmp = y / ((x + y) / (a - b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.2e+123) {
		tmp = t_1;
	} else if (y <= -5e+111) {
		tmp = a / ((x + y) / y);
	} else if (y <= -5.5e-86) {
		tmp = t_1;
	} else if (y <= 4.5e-127) {
		tmp = a + (x / ((x + t) / z));
	} else if (y <= 2.4e+95) {
		tmp = z + ((y * a) / (x + y));
	} else if (y <= 1.22e+124) {
		tmp = y / ((x + y) / (a - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -4.2e+123:
		tmp = t_1
	elif y <= -5e+111:
		tmp = a / ((x + y) / y)
	elif y <= -5.5e-86:
		tmp = t_1
	elif y <= 4.5e-127:
		tmp = a + (x / ((x + t) / z))
	elif y <= 2.4e+95:
		tmp = z + ((y * a) / (x + y))
	elif y <= 1.22e+124:
		tmp = y / ((x + y) / (a - b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4.2e+123)
		tmp = t_1;
	elseif (y <= -5e+111)
		tmp = Float64(a / Float64(Float64(x + y) / y));
	elseif (y <= -5.5e-86)
		tmp = t_1;
	elseif (y <= 4.5e-127)
		tmp = Float64(a + Float64(x / Float64(Float64(x + t) / z)));
	elseif (y <= 2.4e+95)
		tmp = Float64(z + Float64(Float64(y * a) / Float64(x + y)));
	elseif (y <= 1.22e+124)
		tmp = Float64(y / Float64(Float64(x + y) / Float64(a - b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -4.2e+123)
		tmp = t_1;
	elseif (y <= -5e+111)
		tmp = a / ((x + y) / y);
	elseif (y <= -5.5e-86)
		tmp = t_1;
	elseif (y <= 4.5e-127)
		tmp = a + (x / ((x + t) / z));
	elseif (y <= 2.4e+95)
		tmp = z + ((y * a) / (x + y));
	elseif (y <= 1.22e+124)
		tmp = y / ((x + y) / (a - b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4.2e+123], t$95$1, If[LessEqual[y, -5e+111], N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.5e-86], t$95$1, If[LessEqual[y, 4.5e-127], N[(a + N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+95], N[(z + N[(N[(y * a), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e+124], N[(y / N[(N[(x + y), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.19999999999999988e123 or -4.9999999999999997e111 < y < -5.5e-86 or 1.22e124 < y

   1. Initial program 49.8%

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

   2. Taylor expanded in y around inf 74.9%

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

   if -4.19999999999999988e123 < y < -4.9999999999999997e111

   1. Initial program 61.9%

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

   2. Taylor expanded in a around inf 61.9%

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

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in t around 0 99.7%

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

      1. +-commutative 99.7%

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

   7. Simplified 99.7%

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

   if -5.5e-86 < y < 4.4999999999999999e-127

   1. Initial program 80.2%

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

   2. Taylor expanded in a around 0 89.3%

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

      1. associate--l+ 89.3%

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

      2. +-commutative 89.3%

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

      3. +-commutative 89.3%

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

      4. +-commutative 89.3%

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

      5. div-sub 89.3%

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

      6. +-commutative 89.3%

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

      7. *-commutative 89.3%

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

      8. +-commutative 89.3%

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

   4. Simplified 89.3%

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

   5. Taylor expanded in y around 0 74.8%

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

      1. associate-/l* 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in y around inf 63.9%

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

   if 4.4999999999999999e-127 < y < 2.4e95

   1. Initial program 65.8%

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

   2. Taylor expanded in a around 0 81.3%

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

      1. associate--l+ 81.3%

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

      2. +-commutative 81.3%

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

      3. +-commutative 81.3%

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

      4. +-commutative 81.3%

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

      5. div-sub 81.3%

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

      6. +-commutative 81.3%

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

      7. *-commutative 81.3%

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

      8. +-commutative 81.3%

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

   4. Simplified 81.3%

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

   5. Taylor expanded in y around 0 68.9%

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

      1. associate-/l* 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in t around 0 64.5%

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

   if 2.4e95 < y < 1.22e124

   1. Initial program 58.5%

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

   2. Taylor expanded in y around inf 45.6%

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

   3. Taylor expanded in z around 0 45.4%

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

      1. associate-/l* 72.6%

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

      2. +-commutative 72.6%

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

      3. +-commutative 72.6%

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

      4. associate-+l+ 72.6%

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

      5. +-commutative 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in t around 0 45.5%

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

      1. associate-/l* 59.6%

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

   8. Simplified 59.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{x + y}{a - b}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-127}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+95}:\\ \;\;\;\;z + \frac{y \cdot a}{x + y}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+124}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 12: 64.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-87} \lor \neg \left(y \leq 4.4 \cdot 10^{+101}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4.2e+123)
     t_1
     (if (<= y -5e+111)
       (/ a (/ (+ x y) y))
       (if (or (<= y -1.2e-87) (not (<= y 4.4e+101)))
         t_1
         (+ a (/ x (/ (+ x t) z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.2e+123) {
		tmp = t_1;
	} else if (y <= -5e+111) {
		tmp = a / ((x + y) / y);
	} else if ((y <= -1.2e-87) || !(y <= 4.4e+101)) {
		tmp = t_1;
	} else {
		tmp = a + (x / ((x + t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-4.2d+123)) then
        tmp = t_1
    else if (y <= (-5d+111)) then
        tmp = a / ((x + y) / y)
    else if ((y <= (-1.2d-87)) .or. (.not. (y <= 4.4d+101))) then
        tmp = t_1
    else
        tmp = a + (x / ((x + t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.2e+123) {
		tmp = t_1;
	} else if (y <= -5e+111) {
		tmp = a / ((x + y) / y);
	} else if ((y <= -1.2e-87) || !(y <= 4.4e+101)) {
		tmp = t_1;
	} else {
		tmp = a + (x / ((x + t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -4.2e+123:
		tmp = t_1
	elif y <= -5e+111:
		tmp = a / ((x + y) / y)
	elif (y <= -1.2e-87) or not (y <= 4.4e+101):
		tmp = t_1
	else:
		tmp = a + (x / ((x + t) / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4.2e+123)
		tmp = t_1;
	elseif (y <= -5e+111)
		tmp = Float64(a / Float64(Float64(x + y) / y));
	elseif ((y <= -1.2e-87) || !(y <= 4.4e+101))
		tmp = t_1;
	else
		tmp = Float64(a + Float64(x / Float64(Float64(x + t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -4.2e+123)
		tmp = t_1;
	elseif (y <= -5e+111)
		tmp = a / ((x + y) / y);
	elseif ((y <= -1.2e-87) || ~((y <= 4.4e+101)))
		tmp = t_1;
	else
		tmp = a + (x / ((x + t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4.2e+123], t$95$1, If[LessEqual[y, -5e+111], N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.2e-87], N[Not[LessEqual[y, 4.4e+101]], $MachinePrecision]], t$95$1, N[(a + N[(x / N[(N[(x + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.19999999999999988e123 or -4.9999999999999997e111 < y < -1.2e-87 or 4.4000000000000001e101 < y

   1. Initial program 51.1%

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

   2. Taylor expanded in y around inf 73.6%

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

   if -4.19999999999999988e123 < y < -4.9999999999999997e111

   1. Initial program 61.9%

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

   2. Taylor expanded in a around inf 61.9%

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

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in t around 0 99.7%

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

      1. +-commutative 99.7%

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

   7. Simplified 99.7%

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

   if -1.2e-87 < y < 4.4000000000000001e101

   1. Initial program 74.6%

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

   2. Taylor expanded in a around 0 85.4%

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

      1. associate--l+ 85.4%

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

      2. +-commutative 85.4%

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

      3. +-commutative 85.4%

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

      4. +-commutative 85.4%

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

      5. div-sub 85.4%

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

      6. +-commutative 85.4%

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

      7. *-commutative 85.4%

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

      8. +-commutative 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in y around 0 72.6%

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

      1. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in y around inf 60.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-87} \lor \neg \left(y \leq 4.4 \cdot 10^{+101}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{x}{\frac{x + t}{z}}\\ \end{array} \]

Alternative 13: 59.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{a}{1 + \frac{x}{t}}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-277}:\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (/ a (+ 1.0 (/ x t)))))
   (if (<= t -1.3e+196)
     t_2
     (if (<= t -1.8e-238)
       t_1
       (if (<= t -8.8e-277)
         (- z (/ (* y b) x))
         (if (<= t 8.8e+104) 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 / (1.0 + (x / t));
	double tmp;
	if (t <= -1.3e+196) {
		tmp = t_2;
	} else if (t <= -1.8e-238) {
		tmp = t_1;
	} else if (t <= -8.8e-277) {
		tmp = z - ((y * b) / x);
	} else if (t <= 8.8e+104) {
		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 / (1.0d0 + (x / t))
    if (t <= (-1.3d+196)) then
        tmp = t_2
    else if (t <= (-1.8d-238)) then
        tmp = t_1
    else if (t <= (-8.8d-277)) then
        tmp = z - ((y * b) / x)
    else if (t <= 8.8d+104) 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 / (1.0 + (x / t));
	double tmp;
	if (t <= -1.3e+196) {
		tmp = t_2;
	} else if (t <= -1.8e-238) {
		tmp = t_1;
	} else if (t <= -8.8e-277) {
		tmp = z - ((y * b) / x);
	} else if (t <= 8.8e+104) {
		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 / (1.0 + (x / t))
	tmp = 0
	if t <= -1.3e+196:
		tmp = t_2
	elif t <= -1.8e-238:
		tmp = t_1
	elif t <= -8.8e-277:
		tmp = z - ((y * b) / x)
	elif t <= 8.8e+104:
		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(1.0 + Float64(x / t)))
	tmp = 0.0
	if (t <= -1.3e+196)
		tmp = t_2;
	elseif (t <= -1.8e-238)
		tmp = t_1;
	elseif (t <= -8.8e-277)
		tmp = Float64(z - Float64(Float64(y * b) / x));
	elseif (t <= 8.8e+104)
		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 / (1.0 + (x / t));
	tmp = 0.0;
	if (t <= -1.3e+196)
		tmp = t_2;
	elseif (t <= -1.8e-238)
		tmp = t_1;
	elseif (t <= -8.8e-277)
		tmp = z - ((y * b) / x);
	elseif (t <= 8.8e+104)
		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[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+196], t$95$2, If[LessEqual[t, -1.8e-238], t$95$1, If[LessEqual[t, -8.8e-277], N[(z - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e+104], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.30000000000000006e196 or 8.80000000000000002e104 < t

   1. Initial program 57.1%

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

   2. Taylor expanded in a around inf 35.9%

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

      1. associate-/l* 65.6%

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

      2. +-commutative 65.6%

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

   4. Simplified 65.6%

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

   5. Taylor expanded in t around inf 64.6%

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

   if -1.30000000000000006e196 < t < -1.80000000000000005e-238 or -8.79999999999999983e-277 < t < 8.80000000000000002e104

   1. Initial program 63.2%

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

   2. Taylor expanded in y around inf 65.4%

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

   if -1.80000000000000005e-238 < t < -8.79999999999999983e-277

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 99.8%

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

      1. associate--r+ 99.8%

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

      2. sub-neg 99.8%

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

      3. mul-1-neg 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate--l+ 99.8%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in b around inf 84.7%

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

      1. associate-*r/ 84.7%

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

      2. mul-1-neg 84.7%

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

      3. *-commutative 84.7%

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

      4. distribute-lft-neg-in 84.7%

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

      5. neg-mul-1 84.7%

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

      6. *-commutative 84.7%

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

      7. neg-mul-1 84.7%

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

   7. Simplified 84.7%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+196}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-238}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-277}:\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+104}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \end{array} \]

Alternative 14: 59.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.82 \cdot 10^{+196} \lor \neg \left(t \leq 1.9 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.82e+196) (not (<= t 1.9e+102)))
   (/ a (+ 1.0 (/ x t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.82e+196) || !(t <= 1.9e+102)) {
		tmp = a / (1.0 + (x / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.82d+196)) .or. (.not. (t <= 1.9d+102))) then
        tmp = a / (1.0d0 + (x / t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.82e+196) || !(t <= 1.9e+102)) {
		tmp = a / (1.0 + (x / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.82e+196) or not (t <= 1.9e+102):
		tmp = a / (1.0 + (x / t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.82e+196) || !(t <= 1.9e+102))
		tmp = Float64(a / Float64(1.0 + Float64(x / t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.82e+196) || ~((t <= 1.9e+102)))
		tmp = a / (1.0 + (x / t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.82e+196], N[Not[LessEqual[t, 1.9e+102]], $MachinePrecision]], N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.82e196 or 1.89999999999999989e102 < t

   1. Initial program 57.1%

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

   2. Taylor expanded in a around inf 35.9%

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

      1. associate-/l* 65.6%

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

      2. +-commutative 65.6%

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

   4. Simplified 65.6%

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

   5. Taylor expanded in t around inf 64.6%

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

   if -1.82e196 < t < 1.89999999999999989e102

   1. Initial program 64.5%

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

   2. Taylor expanded in y around inf 63.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.82 \cdot 10^{+196} \lor \neg \left(t \leq 1.9 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 15: 57.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.2 \cdot 10^{+99}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= t 4.2e+99) (- (+ z a) b) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 4.2e+99) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 4.2d+99) then
        tmp = (z + a) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 4.2e+99) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 4.2e+99:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 4.2e+99)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 4.2e+99)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 4.2e+99], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if t < 4.2000000000000002e99

   1. Initial program 63.2%

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

   2. Taylor expanded in y around inf 61.2%

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

   if 4.2000000000000002e99 < t

   1. Initial program 60.4%

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

   2. Taylor expanded in t around inf 47.0%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.2 \cdot 10^{+99}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16: 42.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-16}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-96}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.05e-16) a (if (<= t 1.25e-96) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.05e-16) {
		tmp = a;
	} else if (t <= 1.25e-96) {
		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 <= (-2.05d-16)) then
        tmp = a
    else if (t <= 1.25d-96) 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 <= -2.05e-16) {
		tmp = a;
	} else if (t <= 1.25e-96) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.05e-16:
		tmp = a
	elif t <= 1.25e-96:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.05e-16)
		tmp = a;
	elseif (t <= 1.25e-96)
		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 <= -2.05e-16)
		tmp = a;
	elseif (t <= 1.25e-96)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.05e-16], a, If[LessEqual[t, 1.25e-96], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -2.05000000000000003e-16 or 1.24999999999999999e-96 < t

   1. Initial program 62.3%

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

   2. Taylor expanded in t around inf 43.1%

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

   if -2.05000000000000003e-16 < t < 1.24999999999999999e-96

   1. Initial program 63.3%

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

   2. Taylor expanded in x around inf 47.9%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-16}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-96}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 17: 50.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+153}:\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b -9.5e+153) (- b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+153) {
		tmp = -b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.5d+153)) then
        tmp = -b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+153) {
		tmp = -b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e+153:
		tmp = -b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e+153)
		tmp = Float64(-b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e+153)
		tmp = -b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e+153], (-b), N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.4999999999999995e153

   1. Initial program 49.0%

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

   2. Taylor expanded in y around inf 51.7%

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

   3. Taylor expanded in b around inf 36.1%

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

      1. neg-mul-1 36.1%

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

   5. Simplified 36.1%

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

   if -9.4999999999999995e153 < b

   1. Initial program 64.9%

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

   2. Taylor expanded in y around inf 55.2%

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

   3. Taylor expanded in b around 0 52.0%

      \[\leadsto \color{blue}{a + z} \]
   4. Step-by-step derivation

      1. +-commutative 52.0%

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

   5. Simplified 52.0%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+153}:\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 18: 51.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+152}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b -7e+152) (- a b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e+152) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7d+152)) then
        tmp = a - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e+152) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7e+152:
		tmp = a - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7e+152)
		tmp = Float64(a - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7e+152)
		tmp = a - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7e+152], N[(a - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.99999999999999963e152

   1. Initial program 49.0%

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

   2. Taylor expanded in y around inf 51.7%

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

   3. Taylor expanded in z around 0 46.2%

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

   if -6.99999999999999963e152 < b

   1. Initial program 64.9%

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

   2. Taylor expanded in y around inf 55.2%

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

   3. Taylor expanded in b around 0 52.0%

      \[\leadsto \color{blue}{a + z} \]
   4. Step-by-step derivation

      1. +-commutative 52.0%

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

   5. Simplified 52.0%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+152}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 19: 32.4% 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 62.8%

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

2. Taylor expanded in t around inf 31.5%

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

3. Final simplification 31.5%

   \[\leadsto a \]

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 2023310 
(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)))