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

Percentage Accurate: 59.9% → 88.0%

Time: 14.7s

Alternatives: 17

Speedup: 0.8×

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: 59.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 5 \cdot 10^{+235}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_1\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+235)))
     (- (+ z a) b)
     (/ (- (fma (+ x y) z t_1) (* y b)) (+ x (+ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = ((((x + y) * z) + t_1) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+235)) {
		tmp = (z + a) - b;
	} else {
		tmp = (fma((x + y), z, t_1) - (y * b)) / (x + (y + t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+235))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(fma(Float64(x + y), z, t_1) - Float64(y * b)) / Float64(x + Float64(y + t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+235]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $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)) < -inf.0 or 5.00000000000000027e235 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in y around inf 72.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000027e235

   1. Initial program 99.7%

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

      1. fma-define 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+235}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, a \cdot \left(y + t\right)\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+235}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+235))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+235)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+235)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+235):
		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(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+235))
		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 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+235)))
		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[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+235]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.00000000000000027e235 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in y around inf 72.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000027e235

   1. Initial program 99.7%

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

4. Final simplification 88.7%

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

Alternative 3: 63.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-73}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-208}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t\_1}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+33}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{t\_1}{y}}{a + \left(z - b\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= y -4.4e-73)
     (- (+ z a) b)
     (if (<= y -7e-208)
       (/ (- (* a (+ y t)) (* y b)) t_1)
       (if (<= y 4.6e-67)
         (/ (+ (* x z) (* t a)) (+ x t))
         (if (<= y 2.7e+33)
           (* (+ y t) (/ a t_1))
           (/ 1.0 (/ (/ t_1 y) (+ a (- z b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (y <= -4.4e-73) {
		tmp = (z + a) - b;
	} else if (y <= -7e-208) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else if (y <= 4.6e-67) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 2.7e+33) {
		tmp = (y + t) * (a / t_1);
	} else {
		tmp = 1.0 / ((t_1 / y) / (a + (z - 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) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (y <= (-4.4d-73)) then
        tmp = (z + a) - b
    else if (y <= (-7d-208)) then
        tmp = ((a * (y + t)) - (y * b)) / t_1
    else if (y <= 4.6d-67) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 2.7d+33) then
        tmp = (y + t) * (a / t_1)
    else
        tmp = 1.0d0 / ((t_1 / y) / (a + (z - 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 t_1 = y + (x + t);
	double tmp;
	if (y <= -4.4e-73) {
		tmp = (z + a) - b;
	} else if (y <= -7e-208) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else if (y <= 4.6e-67) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 2.7e+33) {
		tmp = (y + t) * (a / t_1);
	} else {
		tmp = 1.0 / ((t_1 / y) / (a + (z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if y <= -4.4e-73:
		tmp = (z + a) - b
	elif y <= -7e-208:
		tmp = ((a * (y + t)) - (y * b)) / t_1
	elif y <= 4.6e-67:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 2.7e+33:
		tmp = (y + t) * (a / t_1)
	else:
		tmp = 1.0 / ((t_1 / y) / (a + (z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -4.4e-73)
		tmp = Float64(Float64(z + a) - b);
	elseif (y <= -7e-208)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_1);
	elseif (y <= 4.6e-67)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 2.7e+33)
		tmp = Float64(Float64(y + t) * Float64(a / t_1));
	else
		tmp = Float64(1.0 / Float64(Float64(t_1 / y) / Float64(a + Float64(z - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (y <= -4.4e-73)
		tmp = (z + a) - b;
	elseif (y <= -7e-208)
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	elseif (y <= 4.6e-67)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 2.7e+33)
		tmp = (y + t) * (a / t_1);
	else
		tmp = 1.0 / ((t_1 / y) / (a + (z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e-73], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -7e-208], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 4.6e-67], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+33], N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(t$95$1 / y), $MachinePrecision] / N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.4e-73

   1. Initial program 44.9%

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

   3. Taylor expanded in y around inf 74.3%

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

   if -4.4e-73 < y < -6.99999999999999982e-208

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0 63.7%

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

      1. +-commutative 63.7%

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

      2. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   if -6.99999999999999982e-208 < y < 4.6000000000000001e-67

   1. Initial program 82.3%

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

   3. Taylor expanded in y around 0 66.0%

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

   if 4.6000000000000001e-67 < y < 2.69999999999999991e33

   1. Initial program 72.0%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. associate-/l* 73.4%

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

      2. +-commutative 73.4%

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

      3. +-commutative 73.4%

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

      4. associate-+r+ 73.4%

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

   5. Simplified 73.4%

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

      1. associate-*r/ 49.5%

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

      2. *-commutative 49.5%

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

      3. +-commutative 49.5%

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

      4. associate-+l+ 49.5%

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

      5. +-commutative 49.5%

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

   7. Applied egg-rr 49.5%

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

      1. associate-/l* 75.6%

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

   9. Simplified 75.6%

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

   if 2.69999999999999991e33 < y

   1. Initial program 45.4%

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

   3. Taylor expanded in y around inf 41.1%

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

      1. clear-num 41.0%

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

      2. inv-pow 41.0%

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

      3. +-commutative 41.0%

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

      4. associate--l+ 41.0%

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

   5. Applied egg-rr 41.0%

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

      1. unpow-1 41.0%

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

      2. associate-/r* 81.2%

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

   7. Simplified 81.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-73}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-208}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+33}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{if}\;y \leq -8800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-143}:\\ \;\;\;\;\frac{\left(y \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{x \cdot z}{a \cdot \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ (/ (+ y (+ x t)) y) (+ a (- z b))))))
   (if (<= y -8800000000000.0)
     t_1
     (if (<= y -8.2e-143)
       (/ (- (+ (* y a) (* (+ x y) z)) (* y b)) (+ x y))
       (if (<= y 2.95e+35)
         (* a (+ (/ t (+ x t)) (/ (* x z) (* a (+ x t)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 / (((y + (x + t)) / y) / (a + (z - b)));
	double tmp;
	if (y <= -8800000000000.0) {
		tmp = t_1;
	} else if (y <= -8.2e-143) {
		tmp = (((y * a) + ((x + y) * z)) - (y * b)) / (x + y);
	} else if (y <= 2.95e+35) {
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / (((y + (x + t)) / y) / (a + (z - b)))
    if (y <= (-8800000000000.0d0)) then
        tmp = t_1
    else if (y <= (-8.2d-143)) then
        tmp = (((y * a) + ((x + y) * z)) - (y * b)) / (x + y)
    else if (y <= 2.95d+35) then
        tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 / (((y + (x + t)) / y) / (a + (z - b)));
	double tmp;
	if (y <= -8800000000000.0) {
		tmp = t_1;
	} else if (y <= -8.2e-143) {
		tmp = (((y * a) + ((x + y) * z)) - (y * b)) / (x + y);
	} else if (y <= 2.95e+35) {
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 / (((y + (x + t)) / y) / (a + (z - b)))
	tmp = 0
	if y <= -8800000000000.0:
		tmp = t_1
	elif y <= -8.2e-143:
		tmp = (((y * a) + ((x + y) * z)) - (y * b)) / (x + y)
	elif y <= 2.95e+35:
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 / Float64(Float64(Float64(y + Float64(x + t)) / y) / Float64(a + Float64(z - b))))
	tmp = 0.0
	if (y <= -8800000000000.0)
		tmp = t_1;
	elseif (y <= -8.2e-143)
		tmp = Float64(Float64(Float64(Float64(y * a) + Float64(Float64(x + y) * z)) - Float64(y * b)) / Float64(x + y));
	elseif (y <= 2.95e+35)
		tmp = Float64(a * Float64(Float64(t / Float64(x + t)) + Float64(Float64(x * z) / Float64(a * Float64(x + t)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 / (((y + (x + t)) / y) / (a + (z - b)));
	tmp = 0.0;
	if (y <= -8800000000000.0)
		tmp = t_1;
	elseif (y <= -8.2e-143)
		tmp = (((y * a) + ((x + y) * z)) - (y * b)) / (x + y);
	elseif (y <= 2.95e+35)
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 / N[(N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8800000000000.0], t$95$1, If[LessEqual[y, -8.2e-143], N[(N[(N[(N[(y * a), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e+35], N[(a * N[(N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / N[(a * N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.8e12 or 2.94999999999999993e35 < y

   1. Initial program 40.5%

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

   3. Taylor expanded in y around inf 35.0%

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

      1. clear-num 34.9%

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

      2. inv-pow 34.9%

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

      3. +-commutative 34.9%

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

      4. associate--l+ 34.9%

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

   5. Applied egg-rr 34.9%

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

      1. unpow-1 34.9%

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

      2. associate-/r* 80.0%

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

   7. Simplified 80.0%

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

   if -8.8e12 < y < -8.2e-143

   1. Initial program 84.2%

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

   3. Taylor expanded in t around 0 79.1%

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

   if -8.2e-143 < y < 2.94999999999999993e35

   1. Initial program 79.2%

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

   3. Taylor expanded in a around inf 80.4%

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

      1. associate-+r+ 80.4%

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

      2. +-commutative 80.4%

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

      3. +-commutative 80.4%

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

      4. associate-+r+ 80.4%

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

      5. +-commutative 80.4%

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

      6. associate-+r+ 80.4%

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

      7. +-commutative 80.4%

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

      8. +-commutative 80.4%

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

      9. associate-+r+ 80.4%

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

      10. associate-/r* 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in y around 0 64.0%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8800000000000:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-143}:\\ \;\;\;\;\frac{\left(y \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{x \cdot z}{a \cdot \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -1.04 \cdot 10^{-81}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t\_1}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{x \cdot z}{a \cdot \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{t\_1}{y}}{a + \left(z - b\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= y -1.04e-81)
     (- (+ z a) b)
     (if (<= y -9.8e-175)
       (/ (- (* a (+ y t)) (* y b)) t_1)
       (if (<= y 2.1e+35)
         (* a (+ (/ t (+ x t)) (/ (* x z) (* a (+ x t)))))
         (/ 1.0 (/ (/ t_1 y) (+ a (- z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (y <= -1.04e-81) {
		tmp = (z + a) - b;
	} else if (y <= -9.8e-175) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else if (y <= 2.1e+35) {
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	} else {
		tmp = 1.0 / ((t_1 / y) / (a + (z - 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) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (y <= (-1.04d-81)) then
        tmp = (z + a) - b
    else if (y <= (-9.8d-175)) then
        tmp = ((a * (y + t)) - (y * b)) / t_1
    else if (y <= 2.1d+35) then
        tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))))
    else
        tmp = 1.0d0 / ((t_1 / y) / (a + (z - 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 t_1 = y + (x + t);
	double tmp;
	if (y <= -1.04e-81) {
		tmp = (z + a) - b;
	} else if (y <= -9.8e-175) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else if (y <= 2.1e+35) {
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	} else {
		tmp = 1.0 / ((t_1 / y) / (a + (z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if y <= -1.04e-81:
		tmp = (z + a) - b
	elif y <= -9.8e-175:
		tmp = ((a * (y + t)) - (y * b)) / t_1
	elif y <= 2.1e+35:
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))))
	else:
		tmp = 1.0 / ((t_1 / y) / (a + (z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -1.04e-81)
		tmp = Float64(Float64(z + a) - b);
	elseif (y <= -9.8e-175)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_1);
	elseif (y <= 2.1e+35)
		tmp = Float64(a * Float64(Float64(t / Float64(x + t)) + Float64(Float64(x * z) / Float64(a * Float64(x + t)))));
	else
		tmp = Float64(1.0 / Float64(Float64(t_1 / y) / Float64(a + Float64(z - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (y <= -1.04e-81)
		tmp = (z + a) - b;
	elseif (y <= -9.8e-175)
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	elseif (y <= 2.1e+35)
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	else
		tmp = 1.0 / ((t_1 / y) / (a + (z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.04e-81], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -9.8e-175], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.1e+35], N[(a * N[(N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / N[(a * N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(t$95$1 / y), $MachinePrecision] / N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.04e-81

   1. Initial program 44.9%

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

   3. Taylor expanded in y around inf 74.3%

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

   if -1.04e-81 < y < -9.79999999999999996e-175

   1. Initial program 87.1%

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

   3. Taylor expanded in z around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   if -9.79999999999999996e-175 < y < 2.0999999999999999e35

   1. Initial program 79.2%

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

   3. Taylor expanded in a around inf 80.5%

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

      1. associate-+r+ 80.5%

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

      2. +-commutative 80.5%

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

      3. +-commutative 80.5%

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

      4. associate-+r+ 80.5%

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

      5. +-commutative 80.5%

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

      6. associate-+r+ 80.5%

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

      7. +-commutative 80.5%

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

      8. +-commutative 80.5%

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

      9. associate-+r+ 80.5%

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

      10. associate-/r* 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in y around 0 66.3%

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

   if 2.0999999999999999e35 < y

   1. Initial program 46.1%

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

   3. Taylor expanded in y around inf 41.7%

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

      1. clear-num 41.7%

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

      2. inv-pow 41.7%

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

      3. +-commutative 41.7%

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

      4. associate--l+ 41.7%

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

   5. Applied egg-rr 41.7%

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

      1. unpow-1 41.7%

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

      2. associate-/r* 82.6%

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

   7. Simplified 82.6%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{-81}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{x \cdot z}{a \cdot \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := x + \left(y + t\right)\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_2}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_2}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ x (+ y t))))
   (if (<= a -1.2e+100)
     (* a (/ (+ y t) t_2))
     (if (<= a -5.2e-243)
       t_1
       (if (<= a 2.8e-52)
         (* z (/ (+ x y) t_2))
         (if (<= a 2e+41) t_1 (* (+ y t) (/ a (+ y (+ x t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = x + (y + t);
	double tmp;
	if (a <= -1.2e+100) {
		tmp = a * ((y + t) / t_2);
	} else if (a <= -5.2e-243) {
		tmp = t_1;
	} else if (a <= 2.8e-52) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 2e+41) {
		tmp = t_1;
	} else {
		tmp = (y + t) * (a / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = x + (y + t)
    if (a <= (-1.2d+100)) then
        tmp = a * ((y + t) / t_2)
    else if (a <= (-5.2d-243)) then
        tmp = t_1
    else if (a <= 2.8d-52) then
        tmp = z * ((x + y) / t_2)
    else if (a <= 2d+41) then
        tmp = t_1
    else
        tmp = (y + t) * (a / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = x + (y + t);
	double tmp;
	if (a <= -1.2e+100) {
		tmp = a * ((y + t) / t_2);
	} else if (a <= -5.2e-243) {
		tmp = t_1;
	} else if (a <= 2.8e-52) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 2e+41) {
		tmp = t_1;
	} else {
		tmp = (y + t) * (a / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = x + (y + t)
	tmp = 0
	if a <= -1.2e+100:
		tmp = a * ((y + t) / t_2)
	elif a <= -5.2e-243:
		tmp = t_1
	elif a <= 2.8e-52:
		tmp = z * ((x + y) / t_2)
	elif a <= 2e+41:
		tmp = t_1
	else:
		tmp = (y + t) * (a / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(x + Float64(y + t))
	tmp = 0.0
	if (a <= -1.2e+100)
		tmp = Float64(a * Float64(Float64(y + t) / t_2));
	elseif (a <= -5.2e-243)
		tmp = t_1;
	elseif (a <= 2.8e-52)
		tmp = Float64(z * Float64(Float64(x + y) / t_2));
	elseif (a <= 2e+41)
		tmp = t_1;
	else
		tmp = Float64(Float64(y + t) * Float64(a / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = x + (y + t);
	tmp = 0.0;
	if (a <= -1.2e+100)
		tmp = a * ((y + t) / t_2);
	elseif (a <= -5.2e-243)
		tmp = t_1;
	elseif (a <= 2.8e-52)
		tmp = z * ((x + y) / t_2);
	elseif (a <= 2e+41)
		tmp = t_1;
	else
		tmp = (y + t) * (a / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e+100], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.2e-243], t$95$1, If[LessEqual[a, 2.8e-52], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+41], t$95$1, N[(N[(y + t), $MachinePrecision] * N[(a / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.20000000000000006e100

   1. Initial program 48.0%

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

   3. Taylor expanded in a around inf 30.7%

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

      1. associate-/l* 68.6%

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

      2. +-commutative 68.6%

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

      3. +-commutative 68.6%

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

      4. associate-+r+ 68.6%

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

   5. Simplified 68.6%

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

   if -1.20000000000000006e100 < a < -5.1999999999999995e-243 or 2.79999999999999995e-52 < a < 2.00000000000000001e41

   1. Initial program 63.9%

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

   3. Taylor expanded in y around inf 65.3%

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

   if -5.1999999999999995e-243 < a < 2.79999999999999995e-52

   1. Initial program 75.6%

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

   3. Taylor expanded in z around inf 40.9%

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

      1. associate-/l* 60.3%

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

      2. +-commutative 60.3%

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

      3. +-commutative 60.3%

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

      4. associate-+r+ 60.3%

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

   5. Simplified 60.3%

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

   if 2.00000000000000001e41 < a

   1. Initial program 56.7%

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

   3. Taylor expanded in a around inf 44.8%

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

      1. associate-/l* 76.6%

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

      2. +-commutative 76.6%

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

      3. +-commutative 76.6%

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

      4. associate-+r+ 76.6%

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

   5. Simplified 76.6%

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

      1. associate-*r/ 44.8%

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

      2. *-commutative 44.8%

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

      3. +-commutative 44.8%

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

      4. associate-+l+ 44.8%

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

      5. +-commutative 44.8%

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

   7. Applied egg-rr 44.8%

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

      1. associate-/l* 78.2%

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

   9. Simplified 78.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-243}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+41}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := x + \left(y + t\right)\\ t_3 := a \cdot \frac{y + t}{t\_2}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+99}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-51}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_2}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ x (+ y t))) (t_3 (* a (/ (+ y t) t_2))))
   (if (<= a -4e+99)
     t_3
     (if (<= a -3.7e-241)
       t_1
       (if (<= a 1.2e-51)
         (* z (/ (+ x y) t_2))
         (if (<= a 3.05e+41) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = x + (y + t);
	double t_3 = a * ((y + t) / t_2);
	double tmp;
	if (a <= -4e+99) {
		tmp = t_3;
	} else if (a <= -3.7e-241) {
		tmp = t_1;
	} else if (a <= 1.2e-51) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 3.05e+41) {
		tmp = t_1;
	} 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 = (z + a) - b
    t_2 = x + (y + t)
    t_3 = a * ((y + t) / t_2)
    if (a <= (-4d+99)) then
        tmp = t_3
    else if (a <= (-3.7d-241)) then
        tmp = t_1
    else if (a <= 1.2d-51) then
        tmp = z * ((x + y) / t_2)
    else if (a <= 3.05d+41) then
        tmp = t_1
    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 = (z + a) - b;
	double t_2 = x + (y + t);
	double t_3 = a * ((y + t) / t_2);
	double tmp;
	if (a <= -4e+99) {
		tmp = t_3;
	} else if (a <= -3.7e-241) {
		tmp = t_1;
	} else if (a <= 1.2e-51) {
		tmp = z * ((x + y) / t_2);
	} else if (a <= 3.05e+41) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = x + (y + t)
	t_3 = a * ((y + t) / t_2)
	tmp = 0
	if a <= -4e+99:
		tmp = t_3
	elif a <= -3.7e-241:
		tmp = t_1
	elif a <= 1.2e-51:
		tmp = z * ((x + y) / t_2)
	elif a <= 3.05e+41:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(a * Float64(Float64(y + t) / t_2))
	tmp = 0.0
	if (a <= -4e+99)
		tmp = t_3;
	elseif (a <= -3.7e-241)
		tmp = t_1;
	elseif (a <= 1.2e-51)
		tmp = Float64(z * Float64(Float64(x + y) / t_2));
	elseif (a <= 3.05e+41)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = x + (y + t);
	t_3 = a * ((y + t) / t_2);
	tmp = 0.0;
	if (a <= -4e+99)
		tmp = t_3;
	elseif (a <= -3.7e-241)
		tmp = t_1;
	elseif (a <= 1.2e-51)
		tmp = z * ((x + y) / t_2);
	elseif (a <= 3.05e+41)
		tmp = t_1;
	else
		tmp = t_3;
	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[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+99], t$95$3, If[LessEqual[a, -3.7e-241], t$95$1, If[LessEqual[a, 1.2e-51], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.05e+41], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.9999999999999999e99 or 3.04999999999999999e41 < a

   1. Initial program 52.5%

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

   3. Taylor expanded in a around inf 38.0%

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

      1. associate-/l* 72.7%

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

      2. +-commutative 72.7%

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

      3. +-commutative 72.7%

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

      4. associate-+r+ 72.7%

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

   5. Simplified 72.7%

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

   if -3.9999999999999999e99 < a < -3.6999999999999999e-241 or 1.2e-51 < a < 3.04999999999999999e41

   1. Initial program 63.9%

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

   3. Taylor expanded in y around inf 65.3%

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

   if -3.6999999999999999e-241 < a < 1.2e-51

   1. Initial program 75.6%

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

   3. Taylor expanded in z around inf 40.9%

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

      1. associate-/l* 60.3%

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

      2. +-commutative 60.3%

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

      3. +-commutative 60.3%

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

      4. associate-+r+ 60.3%

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

   5. Simplified 60.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-241}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-51}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+41}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{-200}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-65}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+33}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{t\_1}{y}}{a + \left(z - b\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= y -5.6e-200)
     (- (+ z a) b)
     (if (<= y 6.7e-65)
       (/ (+ (* x z) (* t a)) (+ x t))
       (if (<= y 2.35e+33)
         (* (+ y t) (/ a t_1))
         (/ 1.0 (/ (/ t_1 y) (+ a (- z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (y <= -5.6e-200) {
		tmp = (z + a) - b;
	} else if (y <= 6.7e-65) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 2.35e+33) {
		tmp = (y + t) * (a / t_1);
	} else {
		tmp = 1.0 / ((t_1 / y) / (a + (z - 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) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (y <= (-5.6d-200)) then
        tmp = (z + a) - b
    else if (y <= 6.7d-65) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 2.35d+33) then
        tmp = (y + t) * (a / t_1)
    else
        tmp = 1.0d0 / ((t_1 / y) / (a + (z - 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 t_1 = y + (x + t);
	double tmp;
	if (y <= -5.6e-200) {
		tmp = (z + a) - b;
	} else if (y <= 6.7e-65) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 2.35e+33) {
		tmp = (y + t) * (a / t_1);
	} else {
		tmp = 1.0 / ((t_1 / y) / (a + (z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if y <= -5.6e-200:
		tmp = (z + a) - b
	elif y <= 6.7e-65:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 2.35e+33:
		tmp = (y + t) * (a / t_1)
	else:
		tmp = 1.0 / ((t_1 / y) / (a + (z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -5.6e-200)
		tmp = Float64(Float64(z + a) - b);
	elseif (y <= 6.7e-65)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 2.35e+33)
		tmp = Float64(Float64(y + t) * Float64(a / t_1));
	else
		tmp = Float64(1.0 / Float64(Float64(t_1 / y) / Float64(a + Float64(z - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (y <= -5.6e-200)
		tmp = (z + a) - b;
	elseif (y <= 6.7e-65)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 2.35e+33)
		tmp = (y + t) * (a / t_1);
	else
		tmp = 1.0 / ((t_1 / y) / (a + (z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e-200], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, 6.7e-65], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e+33], N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(t$95$1 / y), $MachinePrecision] / N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.60000000000000013e-200

   1. Initial program 54.1%

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

   3. Taylor expanded in y around inf 67.4%

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

   if -5.60000000000000013e-200 < y < 6.7000000000000004e-65

   1. Initial program 81.9%

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

   3. Taylor expanded in y around 0 66.2%

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

   if 6.7000000000000004e-65 < y < 2.3499999999999999e33

   1. Initial program 72.0%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. associate-/l* 73.4%

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

      2. +-commutative 73.4%

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

      3. +-commutative 73.4%

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

      4. associate-+r+ 73.4%

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

   5. Simplified 73.4%

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

      1. associate-*r/ 49.5%

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

      2. *-commutative 49.5%

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

      3. +-commutative 49.5%

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

      4. associate-+l+ 49.5%

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

      5. +-commutative 49.5%

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

   7. Applied egg-rr 49.5%

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

      1. associate-/l* 75.6%

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

   9. Simplified 75.6%

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

   if 2.3499999999999999e33 < y

   1. Initial program 45.4%

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

   3. Taylor expanded in y around inf 41.1%

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

      1. clear-num 41.0%

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

      2. inv-pow 41.0%

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

      3. +-commutative 41.0%

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

      4. associate--l+ 41.0%

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

   5. Applied egg-rr 41.0%

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

      1. unpow-1 41.0%

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

      2. associate-/r* 81.2%

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

   7. Simplified 81.2%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-200}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-65}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+33}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{-200}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+33}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= y -6.4e-200)
     (- (+ z a) b)
     (if (<= y 4.6e-67)
       (/ (+ (* x z) (* t a)) (+ x t))
       (if (<= y 2.25e+33)
         (* (+ y t) (/ a t_1))
         (* y (* (+ a (- z b)) (/ 1.0 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (y <= -6.4e-200) {
		tmp = (z + a) - b;
	} else if (y <= 4.6e-67) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 2.25e+33) {
		tmp = (y + t) * (a / t_1);
	} else {
		tmp = y * ((a + (z - b)) * (1.0 / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (y <= (-6.4d-200)) then
        tmp = (z + a) - b
    else if (y <= 4.6d-67) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 2.25d+33) then
        tmp = (y + t) * (a / t_1)
    else
        tmp = y * ((a + (z - b)) * (1.0d0 / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (y <= -6.4e-200) {
		tmp = (z + a) - b;
	} else if (y <= 4.6e-67) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 2.25e+33) {
		tmp = (y + t) * (a / t_1);
	} else {
		tmp = y * ((a + (z - b)) * (1.0 / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if y <= -6.4e-200:
		tmp = (z + a) - b
	elif y <= 4.6e-67:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 2.25e+33:
		tmp = (y + t) * (a / t_1)
	else:
		tmp = y * ((a + (z - b)) * (1.0 / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -6.4e-200)
		tmp = Float64(Float64(z + a) - b);
	elseif (y <= 4.6e-67)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 2.25e+33)
		tmp = Float64(Float64(y + t) * Float64(a / t_1));
	else
		tmp = Float64(y * Float64(Float64(a + Float64(z - b)) * Float64(1.0 / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (y <= -6.4e-200)
		tmp = (z + a) - b;
	elseif (y <= 4.6e-67)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 2.25e+33)
		tmp = (y + t) * (a / t_1);
	else
		tmp = y * ((a + (z - b)) * (1.0 / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e-200], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, 4.6e-67], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+33], N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.39999999999999965e-200

   1. Initial program 54.1%

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

   3. Taylor expanded in y around inf 67.4%

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

   if -6.39999999999999965e-200 < y < 4.6000000000000001e-67

   1. Initial program 81.9%

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

   3. Taylor expanded in y around 0 66.2%

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

   if 4.6000000000000001e-67 < y < 2.25e33

   1. Initial program 72.0%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. associate-/l* 73.4%

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

      2. +-commutative 73.4%

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

      3. +-commutative 73.4%

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

      4. associate-+r+ 73.4%

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

   5. Simplified 73.4%

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

      1. associate-*r/ 49.5%

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

      2. *-commutative 49.5%

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

      3. +-commutative 49.5%

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

      4. associate-+l+ 49.5%

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

      5. +-commutative 49.5%

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

   7. Applied egg-rr 49.5%

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

      1. associate-/l* 75.6%

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

   9. Simplified 75.6%

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

   if 2.25e33 < y

   1. Initial program 45.4%

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

   3. Taylor expanded in y around inf 41.1%

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

      1. div-inv 40.8%

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

      2. associate--l+ 40.8%

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

      3. +-commutative 40.8%

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

   5. Applied egg-rr 40.8%

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

      1. associate-*l* 77.8%

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

   7. Simplified 77.8%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-200}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+33}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+30}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.8e-200)
     t_1
     (if (<= y 4.3e-68)
       (/ (+ (* x z) (* t a)) (+ x t))
       (if (<= y 1.95e+30) (* (+ y t) (/ a (+ y (+ x t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.8e-200) {
		tmp = t_1;
	} else if (y <= 4.3e-68) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 1.95e+30) {
		tmp = (y + t) * (a / (y + (x + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.8d-200)) then
        tmp = t_1
    else if (y <= 4.3d-68) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 1.95d+30) then
        tmp = (y + t) * (a / (y + (x + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.8e-200) {
		tmp = t_1;
	} else if (y <= 4.3e-68) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 1.95e+30) {
		tmp = (y + t) * (a / (y + (x + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.8e-200:
		tmp = t_1
	elif y <= 4.3e-68:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 1.95e+30:
		tmp = (y + t) * (a / (y + (x + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.8e-200)
		tmp = t_1;
	elseif (y <= 4.3e-68)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 1.95e+30)
		tmp = Float64(Float64(y + t) * Float64(a / Float64(y + Float64(x + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.8e-200)
		tmp = t_1;
	elseif (y <= 4.3e-68)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 1.95e+30)
		tmp = (y + t) * (a / (y + (x + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.8e-200], t$95$1, If[LessEqual[y, 4.3e-68], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+30], N[(N[(y + t), $MachinePrecision] * N[(a / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.80000000000000007e-200 or 1.95000000000000005e30 < y

   1. Initial program 50.8%

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

   3. Taylor expanded in y around inf 70.7%

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

   if -2.80000000000000007e-200 < y < 4.3000000000000001e-68

   1. Initial program 81.9%

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

   3. Taylor expanded in y around 0 66.2%

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

   if 4.3000000000000001e-68 < y < 1.95000000000000005e30

   1. Initial program 74.7%

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

   3. Taylor expanded in a around inf 49.2%

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

      1. associate-/l* 69.8%

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

      2. +-commutative 69.8%

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

      3. +-commutative 69.8%

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

      4. associate-+r+ 69.8%

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

   5. Simplified 69.8%

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

      1. associate-*r/ 49.2%

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

      2. *-commutative 49.2%

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

      3. +-commutative 49.2%

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

      4. associate-+l+ 49.2%

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

      5. +-commutative 49.2%

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

   7. Applied egg-rr 49.2%

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

      1. associate-/l* 72.4%

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

   9. Simplified 72.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-200}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+30}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+98} \lor \neg \left(a \leq 3.3 \cdot 10^{+41}\right):\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.75e+98) (not (<= a 3.3e+41)))
   (* a (/ (+ y t) (+ x (+ y t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.75e+98) || !(a <= 3.3e+41)) {
		tmp = a * ((y + t) / (x + (y + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.75d+98)) .or. (.not. (a <= 3.3d+41))) then
        tmp = a * ((y + t) / (x + (y + t)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.75e+98) || !(a <= 3.3e+41)) {
		tmp = a * ((y + t) / (x + (y + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.75e+98) or not (a <= 3.3e+41):
		tmp = a * ((y + t) / (x + (y + t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.75e+98) || !(a <= 3.3e+41))
		tmp = Float64(a * Float64(Float64(y + t) / Float64(x + Float64(y + t))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.75e+98) || ~((a <= 3.3e+41)))
		tmp = a * ((y + t) / (x + (y + t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.75e+98], N[Not[LessEqual[a, 3.3e+41]], $MachinePrecision]], N[(a * N[(N[(y + t), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.75e98 or 3.3e41 < a

   1. Initial program 52.5%

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

   3. Taylor expanded in a around inf 38.0%

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

      1. associate-/l* 72.7%

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

      2. +-commutative 72.7%

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

      3. +-commutative 72.7%

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

      4. associate-+r+ 72.7%

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

   5. Simplified 72.7%

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

   if -1.75e98 < a < 3.3e41

   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. Add Preprocessing

   3. Taylor expanded in y around inf 56.8%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+98} \lor \neg \left(a \leq 3.3 \cdot 10^{+41}\right):\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+223}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+82}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4e+223) a (if (<= t 4.7e+82) (- (+ z a) b) (* a (/ t (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4e+223) {
		tmp = a;
	} else if (t <= 4.7e+82) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4d+223)) then
        tmp = a
    else if (t <= 4.7d+82) then
        tmp = (z + a) - b
    else
        tmp = a * (t / (x + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4e+223) {
		tmp = a;
	} else if (t <= 4.7e+82) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4e+223:
		tmp = a
	elif t <= 4.7e+82:
		tmp = (z + a) - b
	else:
		tmp = a * (t / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4e+223)
		tmp = a;
	elseif (t <= 4.7e+82)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(t / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4e+223)
		tmp = a;
	elseif (t <= 4.7e+82)
		tmp = (z + a) - b;
	else
		tmp = a * (t / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4e+223], a, If[LessEqual[t, 4.7e+82], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.00000000000000019e223

   1. Initial program 53.2%

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

   3. Taylor expanded in t around inf 69.6%

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

   if -4.00000000000000019e223 < t < 4.7e82

   1. Initial program 66.7%

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

   3. Taylor expanded in y around inf 60.9%

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

   if 4.7e82 < t

   1. Initial program 49.1%

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

   3. Taylor expanded in a around inf 36.1%

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

      1. associate-/l* 66.6%

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

      2. +-commutative 66.6%

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

      3. +-commutative 66.6%

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

      4. associate-+r+ 66.6%

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

   5. Simplified 66.6%

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

      1. associate-*r/ 36.1%

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

      2. *-commutative 36.1%

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

      3. +-commutative 36.1%

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

      4. associate-+l+ 36.1%

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

      5. +-commutative 36.1%

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

   7. Applied egg-rr 36.1%

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

      1. associate-/l* 60.5%

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

   9. Simplified 60.5%

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

   10. Taylor expanded in y around 0 37.7%

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

       1. associate-/l* 64.7%

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

       2. +-commutative 64.7%

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

   12. Simplified 64.7%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+223}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+82}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+223}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+83}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.25e+223) a (if (<= t 5.6e+83) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.25e+223) {
		tmp = a;
	} else if (t <= 5.6e+83) {
		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 <= (-2.25d+223)) then
        tmp = a
    else if (t <= 5.6d+83) 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 <= -2.25e+223) {
		tmp = a;
	} else if (t <= 5.6e+83) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.25e+223:
		tmp = a
	elif t <= 5.6e+83:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.25e+223)
		tmp = a;
	elseif (t <= 5.6e+83)
		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 <= -2.25e+223)
		tmp = a;
	elseif (t <= 5.6e+83)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.25e+223], a, If[LessEqual[t, 5.6e+83], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -2.25e223 or 5.6000000000000001e83 < t

   1. Initial program 50.0%

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

   3. Taylor expanded in t around inf 60.7%

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

   if -2.25e223 < t < 5.6000000000000001e83

   1. Initial program 66.7%

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

   3. Taylor expanded in y around inf 60.9%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+223}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+83}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+104}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+25}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.5e+104) z (if (<= z 4.2e+25) (- a b) (- z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.5e+104) {
		tmp = z;
	} else if (z <= 4.2e+25) {
		tmp = a - b;
	} else {
		tmp = z - 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 (z <= (-7.5d+104)) then
        tmp = z
    else if (z <= 4.2d+25) then
        tmp = a - b
    else
        tmp = z - 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 (z <= -7.5e+104) {
		tmp = z;
	} else if (z <= 4.2e+25) {
		tmp = a - b;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.5e+104:
		tmp = z
	elif z <= 4.2e+25:
		tmp = a - b
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.5e+104)
		tmp = z;
	elseif (z <= 4.2e+25)
		tmp = Float64(a - b);
	else
		tmp = Float64(z - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7.5e+104)
		tmp = z;
	elseif (z <= 4.2e+25)
		tmp = a - b;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.5e+104], z, If[LessEqual[z, 4.2e+25], N[(a - b), $MachinePrecision], N[(z - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5000000000000002e104

   1. Initial program 52.3%

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

   3. Taylor expanded in x around inf 47.6%

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

   if -7.5000000000000002e104 < z < 4.1999999999999998e25

   1. Initial program 67.4%

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

   3. Taylor expanded in y around inf 57.7%

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

   4. Taylor expanded in z around 0 54.9%

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

   if 4.1999999999999998e25 < z

   1. Initial program 55.7%

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

   3. Taylor expanded in y around inf 60.8%

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

   4. Taylor expanded in a around 0 58.7%

      \[\leadsto \color{blue}{z - b} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 48.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+106}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+26}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8e+106) z (if (<= z 1.25e+26) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8e+106) {
		tmp = z;
	} else if (z <= 1.25e+26) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-8d+106)) then
        tmp = z
    else if (z <= 1.25d+26) then
        tmp = a - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8e+106) {
		tmp = z;
	} else if (z <= 1.25e+26) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8e+106:
		tmp = z
	elif z <= 1.25e+26:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8e+106)
		tmp = z;
	elseif (z <= 1.25e+26)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8e+106)
		tmp = z;
	elseif (z <= 1.25e+26)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8e+106], z, If[LessEqual[z, 1.25e+26], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000073e106 or 1.25e26 < z

   1. Initial program 54.4%

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

   3. Taylor expanded in x around inf 53.1%

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

   if -8.00000000000000073e106 < z < 1.25e26

   1. Initial program 67.4%

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

   3. Taylor expanded in y around inf 57.7%

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

   4. Taylor expanded in z around 0 54.9%

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

Alternative 16: 44.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+104}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+26}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e+104) z (if (<= z 5e+26) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+104) {
		tmp = z;
	} else if (z <= 5e+26) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.15d+104)) then
        tmp = z
    else if (z <= 5d+26) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+104) {
		tmp = z;
	} else if (z <= 5e+26) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.15e+104:
		tmp = z
	elif z <= 5e+26:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e+104)
		tmp = z;
	elseif (z <= 5e+26)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.15e+104)
		tmp = z;
	elseif (z <= 5e+26)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e+104], z, If[LessEqual[z, 5e+26], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999992e104 or 5.0000000000000001e26 < z

   1. Initial program 53.9%

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

   3. Taylor expanded in x around inf 53.7%

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

   if -1.14999999999999992e104 < z < 5.0000000000000001e26

   1. Initial program 67.6%

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

   3. Taylor expanded in t around inf 47.4%

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

Alternative 17: 32.8% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. Add Preprocessing

3. Taylor expanded in t around inf 37.0%

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

Developer Target 1: 82.3% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024165 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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