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

Percentage Accurate: 60.4% → 88.0%

Time: 13.2s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 5 \cdot 10^{+284}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot t\_3\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+284)))
     t_3
     (/ (+ (* t a) (+ (* x z) (* y t_3))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+284)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+284)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1
	t_3 = (z + a) - b
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+284):
		tmp = t_3
	else:
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+284))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * t_3))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+284)))
		tmp = t_3;
	else
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+284]], $MachinePrecision]], t$95$3, N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.9999999999999999e284 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.1%

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

   3. Taylor expanded in y around inf 75.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999999e284

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 99.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+284}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot a + x \cdot z}{x + t}\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{1}{\frac{\frac{t\_2}{y}}{a + \left(z - b\right)}}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+156}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+111}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-137}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-265}:\\ \;\;\;\;\left(z + \frac{y \cdot a}{x}\right) - \frac{y \cdot b}{x}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+49}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* t a) (* x z)) (+ x t)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ 1.0 (/ (/ t_2 y) (+ a (- z b))))))
   (if (<= y -2.7e+156)
     t_3
     (if (<= y -5.2e+111)
       (- (+ z a) b)
       (if (<= y -6e-137)
         t_3
         (if (<= y -1.15e-226)
           t_1
           (if (<= y -2.1e-265)
             (- (+ z (/ (* y a) x)) (/ (* y b) x))
             (if (<= y 1.7e-135)
               t_1
               (if (<= y 1.3e+49)
                 (/ (- (* z (+ x y)) (* y b)) t_2)
                 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x * z)) / (x + t);
	double t_2 = y + (x + t);
	double t_3 = 1.0 / ((t_2 / y) / (a + (z - b)));
	double tmp;
	if (y <= -2.7e+156) {
		tmp = t_3;
	} else if (y <= -5.2e+111) {
		tmp = (z + a) - b;
	} else if (y <= -6e-137) {
		tmp = t_3;
	} else if (y <= -1.15e-226) {
		tmp = t_1;
	} else if (y <= -2.1e-265) {
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	} else if (y <= 1.7e-135) {
		tmp = t_1;
	} else if (y <= 1.3e+49) {
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((t * a) + (x * z)) / (x + t)
    t_2 = y + (x + t)
    t_3 = 1.0d0 / ((t_2 / y) / (a + (z - b)))
    if (y <= (-2.7d+156)) then
        tmp = t_3
    else if (y <= (-5.2d+111)) then
        tmp = (z + a) - b
    else if (y <= (-6d-137)) then
        tmp = t_3
    else if (y <= (-1.15d-226)) then
        tmp = t_1
    else if (y <= (-2.1d-265)) then
        tmp = (z + ((y * a) / x)) - ((y * b) / x)
    else if (y <= 1.7d-135) then
        tmp = t_1
    else if (y <= 1.3d+49) then
        tmp = ((z * (x + y)) - (y * b)) / t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x * z)) / (x + t);
	double t_2 = y + (x + t);
	double t_3 = 1.0 / ((t_2 / y) / (a + (z - b)));
	double tmp;
	if (y <= -2.7e+156) {
		tmp = t_3;
	} else if (y <= -5.2e+111) {
		tmp = (z + a) - b;
	} else if (y <= -6e-137) {
		tmp = t_3;
	} else if (y <= -1.15e-226) {
		tmp = t_1;
	} else if (y <= -2.1e-265) {
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	} else if (y <= 1.7e-135) {
		tmp = t_1;
	} else if (y <= 1.3e+49) {
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t * a) + (x * z)) / (x + t)
	t_2 = y + (x + t)
	t_3 = 1.0 / ((t_2 / y) / (a + (z - b)))
	tmp = 0
	if y <= -2.7e+156:
		tmp = t_3
	elif y <= -5.2e+111:
		tmp = (z + a) - b
	elif y <= -6e-137:
		tmp = t_3
	elif y <= -1.15e-226:
		tmp = t_1
	elif y <= -2.1e-265:
		tmp = (z + ((y * a) / x)) - ((y * b) / x)
	elif y <= 1.7e-135:
		tmp = t_1
	elif y <= 1.3e+49:
		tmp = ((z * (x + y)) - (y * b)) / t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(1.0 / Float64(Float64(t_2 / y) / Float64(a + Float64(z - b))))
	tmp = 0.0
	if (y <= -2.7e+156)
		tmp = t_3;
	elseif (y <= -5.2e+111)
		tmp = Float64(Float64(z + a) - b);
	elseif (y <= -6e-137)
		tmp = t_3;
	elseif (y <= -1.15e-226)
		tmp = t_1;
	elseif (y <= -2.1e-265)
		tmp = Float64(Float64(z + Float64(Float64(y * a) / x)) - Float64(Float64(y * b) / x));
	elseif (y <= 1.7e-135)
		tmp = t_1;
	elseif (y <= 1.3e+49)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t * a) + (x * z)) / (x + t);
	t_2 = y + (x + t);
	t_3 = 1.0 / ((t_2 / y) / (a + (z - b)));
	tmp = 0.0;
	if (y <= -2.7e+156)
		tmp = t_3;
	elseif (y <= -5.2e+111)
		tmp = (z + a) - b;
	elseif (y <= -6e-137)
		tmp = t_3;
	elseif (y <= -1.15e-226)
		tmp = t_1;
	elseif (y <= -2.1e-265)
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	elseif (y <= 1.7e-135)
		tmp = t_1;
	elseif (y <= 1.3e+49)
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 / N[(N[(t$95$2 / y), $MachinePrecision] / N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+156], t$95$3, If[LessEqual[y, -5.2e+111], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -6e-137], t$95$3, If[LessEqual[y, -1.15e-226], t$95$1, If[LessEqual[y, -2.1e-265], N[(N[(z + N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-135], t$95$1, If[LessEqual[y, 1.3e+49], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7e156 or -5.1999999999999997e111 < y < -5.9999999999999996e-137 or 1.29999999999999994e49 < y

   1. Initial program 45.7%

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

   3. Taylor expanded in y around inf 39.4%

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

      1. clear-num 39.3%

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

      2. inv-pow 39.3%

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

      3. associate-+l+ 39.3%

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

      4. +-commutative 39.3%

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

      5. associate--l+ 39.3%

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

   5. Applied egg-rr 39.3%

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

      1. unpow-1 39.3%

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

      2. associate-/r* 82.6%

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

      3. associate-+r+ 82.6%

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

      4. +-commutative 82.6%

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

      5. associate-+r+ 82.6%

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

   7. Simplified 82.6%

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

   if -2.7e156 < y < -5.1999999999999997e111

   1. Initial program 31.3%

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

   3. Taylor expanded in y around inf 84.2%

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

   if -5.9999999999999996e-137 < y < -1.15e-226 or -2.10000000000000004e-265 < y < 1.69999999999999995e-135

   1. Initial program 79.7%

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

   3. Taylor expanded in y around 0 68.4%

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

   if -1.15e-226 < y < -2.10000000000000004e-265

   1. Initial program 65.4%

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

   3. Taylor expanded in x around inf 64.5%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 55.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 82.0%

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

   if 1.69999999999999995e-135 < y < 1.29999999999999994e49

   1. Initial program 77.9%

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

   3. Taylor expanded in a around 0 59.3%

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

      1. +-commutative 59.3%

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

      2. *-commutative 59.3%

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

   5. Simplified 59.3%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+156}:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+111}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-137}:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-226}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-265}:\\ \;\;\;\;\left(z + \frac{y \cdot a}{x}\right) - \frac{y \cdot b}{x}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+49}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot a + x \cdot z}{x + t}\\ t_2 := \frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+111}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{-137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-265}:\\ \;\;\;\;\left(z + \frac{y \cdot a}{x}\right) - \frac{y \cdot b}{x}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* t a) (* x z)) (+ x t)))
        (t_2 (/ 1.0 (/ (/ (+ y (+ x t)) y) (+ a (- z b))))))
   (if (<= y -3.7e+164)
     t_2
     (if (<= y -5.2e+111)
       (- (+ z a) b)
       (if (<= y -8.1e-137)
         t_2
         (if (<= y -1.15e-226)
           t_1
           (if (<= y -2.1e-265)
             (- (+ z (/ (* y a) x)) (/ (* y b) x))
             (if (<= y 1.55e-78) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x * z)) / (x + t);
	double t_2 = 1.0 / (((y + (x + t)) / y) / (a + (z - b)));
	double tmp;
	if (y <= -3.7e+164) {
		tmp = t_2;
	} else if (y <= -5.2e+111) {
		tmp = (z + a) - b;
	} else if (y <= -8.1e-137) {
		tmp = t_2;
	} else if (y <= -1.15e-226) {
		tmp = t_1;
	} else if (y <= -2.1e-265) {
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	} else if (y <= 1.55e-78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((t * a) + (x * z)) / (x + t)
    t_2 = 1.0d0 / (((y + (x + t)) / y) / (a + (z - b)))
    if (y <= (-3.7d+164)) then
        tmp = t_2
    else if (y <= (-5.2d+111)) then
        tmp = (z + a) - b
    else if (y <= (-8.1d-137)) then
        tmp = t_2
    else if (y <= (-1.15d-226)) then
        tmp = t_1
    else if (y <= (-2.1d-265)) then
        tmp = (z + ((y * a) / x)) - ((y * b) / x)
    else if (y <= 1.55d-78) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x * z)) / (x + t);
	double t_2 = 1.0 / (((y + (x + t)) / y) / (a + (z - b)));
	double tmp;
	if (y <= -3.7e+164) {
		tmp = t_2;
	} else if (y <= -5.2e+111) {
		tmp = (z + a) - b;
	} else if (y <= -8.1e-137) {
		tmp = t_2;
	} else if (y <= -1.15e-226) {
		tmp = t_1;
	} else if (y <= -2.1e-265) {
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	} else if (y <= 1.55e-78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t * a) + (x * z)) / (x + t)
	t_2 = 1.0 / (((y + (x + t)) / y) / (a + (z - b)))
	tmp = 0
	if y <= -3.7e+164:
		tmp = t_2
	elif y <= -5.2e+111:
		tmp = (z + a) - b
	elif y <= -8.1e-137:
		tmp = t_2
	elif y <= -1.15e-226:
		tmp = t_1
	elif y <= -2.1e-265:
		tmp = (z + ((y * a) / x)) - ((y * b) / x)
	elif y <= 1.55e-78:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t))
	t_2 = Float64(1.0 / Float64(Float64(Float64(y + Float64(x + t)) / y) / Float64(a + Float64(z - b))))
	tmp = 0.0
	if (y <= -3.7e+164)
		tmp = t_2;
	elseif (y <= -5.2e+111)
		tmp = Float64(Float64(z + a) - b);
	elseif (y <= -8.1e-137)
		tmp = t_2;
	elseif (y <= -1.15e-226)
		tmp = t_1;
	elseif (y <= -2.1e-265)
		tmp = Float64(Float64(z + Float64(Float64(y * a) / x)) - Float64(Float64(y * b) / x));
	elseif (y <= 1.55e-78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t * a) + (x * z)) / (x + t);
	t_2 = 1.0 / (((y + (x + t)) / y) / (a + (z - b)));
	tmp = 0.0;
	if (y <= -3.7e+164)
		tmp = t_2;
	elseif (y <= -5.2e+111)
		tmp = (z + a) - b;
	elseif (y <= -8.1e-137)
		tmp = t_2;
	elseif (y <= -1.15e-226)
		tmp = t_1;
	elseif (y <= -2.1e-265)
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	elseif (y <= 1.55e-78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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, -3.7e+164], t$95$2, If[LessEqual[y, -5.2e+111], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -8.1e-137], t$95$2, If[LessEqual[y, -1.15e-226], t$95$1, If[LessEqual[y, -2.1e-265], N[(N[(z + N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-78], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.7000000000000001e164 or -5.1999999999999997e111 < y < -8.1000000000000003e-137 or 1.55000000000000009e-78 < y

   1. Initial program 51.7%

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

   3. Taylor expanded in y around inf 41.4%

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

      1. clear-num 41.2%

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

      2. inv-pow 41.2%

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

      3. associate-+l+ 41.2%

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

      4. +-commutative 41.2%

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

      5. associate--l+ 41.2%

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

   5. Applied egg-rr 41.2%

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

      1. unpow-1 41.2%

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

      2. associate-/r* 77.2%

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

      3. associate-+r+ 77.2%

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

      4. +-commutative 77.2%

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

      5. associate-+r+ 77.2%

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

   7. Simplified 77.2%

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

   if -3.7000000000000001e164 < y < -5.1999999999999997e111

   1. Initial program 31.3%

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

   3. Taylor expanded in y around inf 84.2%

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

   if -8.1000000000000003e-137 < y < -1.15e-226 or -2.10000000000000004e-265 < y < 1.55000000000000009e-78

   1. Initial program 78.4%

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

   3. Taylor expanded in y around 0 64.9%

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

   if -1.15e-226 < y < -2.10000000000000004e-265

   1. Initial program 65.4%

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

   3. Taylor expanded in x around inf 64.5%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 55.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 82.0%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+164}:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+111}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{-137}:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-226}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-265}:\\ \;\;\;\;\left(z + \frac{y \cdot a}{x}\right) - \frac{y \cdot b}{x}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-78}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{1}{\frac{\frac{t\_1}{y}}{a + \left(z - b\right)}}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+111}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{-137} \lor \neg \left(y \leq 4200000000\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + z \cdot \left(x + y\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ 1.0 (/ (/ t_1 y) (+ a (- z b))))))
   (if (<= y -4.5e+162)
     t_2
     (if (<= y -5.2e+111)
       (- (+ z a) b)
       (if (or (<= y -8.1e-137) (not (<= y 4200000000.0)))
         t_2
         (/ (+ (* (+ y t) a) (* z (+ x y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = 1.0 / ((t_1 / y) / (a + (z - b)));
	double tmp;
	if (y <= -4.5e+162) {
		tmp = t_2;
	} else if (y <= -5.2e+111) {
		tmp = (z + a) - b;
	} else if ((y <= -8.1e-137) || !(y <= 4200000000.0)) {
		tmp = t_2;
	} else {
		tmp = (((y + t) * a) + (z * (x + y))) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = 1.0d0 / ((t_1 / y) / (a + (z - b)))
    if (y <= (-4.5d+162)) then
        tmp = t_2
    else if (y <= (-5.2d+111)) then
        tmp = (z + a) - b
    else if ((y <= (-8.1d-137)) .or. (.not. (y <= 4200000000.0d0))) then
        tmp = t_2
    else
        tmp = (((y + t) * a) + (z * (x + y))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = 1.0 / ((t_1 / y) / (a + (z - b)));
	double tmp;
	if (y <= -4.5e+162) {
		tmp = t_2;
	} else if (y <= -5.2e+111) {
		tmp = (z + a) - b;
	} else if ((y <= -8.1e-137) || !(y <= 4200000000.0)) {
		tmp = t_2;
	} else {
		tmp = (((y + t) * a) + (z * (x + y))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = 1.0 / ((t_1 / y) / (a + (z - b)))
	tmp = 0
	if y <= -4.5e+162:
		tmp = t_2
	elif y <= -5.2e+111:
		tmp = (z + a) - b
	elif (y <= -8.1e-137) or not (y <= 4200000000.0):
		tmp = t_2
	else:
		tmp = (((y + t) * a) + (z * (x + y))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(1.0 / Float64(Float64(t_1 / y) / Float64(a + Float64(z - b))))
	tmp = 0.0
	if (y <= -4.5e+162)
		tmp = t_2;
	elseif (y <= -5.2e+111)
		tmp = Float64(Float64(z + a) - b);
	elseif ((y <= -8.1e-137) || !(y <= 4200000000.0))
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = 1.0 / ((t_1 / y) / (a + (z - b)));
	tmp = 0.0;
	if (y <= -4.5e+162)
		tmp = t_2;
	elseif (y <= -5.2e+111)
		tmp = (z + a) - b;
	elseif ((y <= -8.1e-137) || ~((y <= 4200000000.0)))
		tmp = t_2;
	else
		tmp = (((y + t) * a) + (z * (x + y))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[(N[(t$95$1 / y), $MachinePrecision] / N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+162], t$95$2, If[LessEqual[y, -5.2e+111], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[Or[LessEqual[y, -8.1e-137], N[Not[LessEqual[y, 4200000000.0]], $MachinePrecision]], t$95$2, N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.49999999999999972e162 or -5.1999999999999997e111 < y < -8.1000000000000003e-137 or 4.2e9 < y

   1. Initial program 48.9%

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

   3. Taylor expanded in y around inf 41.0%

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

      1. clear-num 40.9%

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

      2. inv-pow 40.9%

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

      3. associate-+l+ 40.9%

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

      4. +-commutative 40.9%

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

      5. associate--l+ 40.9%

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

   5. Applied egg-rr 40.9%

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

      1. unpow-1 40.9%

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

      2. associate-/r* 81.6%

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

      3. associate-+r+ 81.6%

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

      4. +-commutative 81.6%

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

      5. associate-+r+ 81.6%

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

   7. Simplified 81.6%

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

   if -4.49999999999999972e162 < y < -5.1999999999999997e111

   1. Initial program 31.3%

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

   3. Taylor expanded in y around inf 84.2%

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

   if -8.1000000000000003e-137 < y < 4.2e9

   1. Initial program 76.2%

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

   3. Taylor expanded in b around 0 67.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+162}:\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+111}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{-137} \lor \neg \left(y \leq 4200000000\right):\\ \;\;\;\;\frac{1}{\frac{\frac{y + \left(x + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + z \cdot \left(x + y\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-139}:\\ \;\;\;\;\frac{y \cdot t\_1}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-226}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-265}:\\ \;\;\;\;\left(z + \frac{y \cdot a}{x}\right) - \frac{y \cdot b}{x}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-157}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (/ (+ (* t a) (* x z)) (+ x t))))
   (if (<= y -5e+111)
     t_1
     (if (<= y -3.05e-139)
       (/ (* y t_1) (+ y (+ x t)))
       (if (<= y -1.18e-226)
         t_2
         (if (<= y -2.1e-265)
           (- (+ z (/ (* y a) x)) (/ (* y b) x))
           (if (<= y 3.1e-157) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = ((t * a) + (x * z)) / (x + t);
	double tmp;
	if (y <= -5e+111) {
		tmp = t_1;
	} else if (y <= -3.05e-139) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (y <= -1.18e-226) {
		tmp = t_2;
	} else if (y <= -2.1e-265) {
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	} else if (y <= 3.1e-157) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = ((t * a) + (x * z)) / (x + t)
    if (y <= (-5d+111)) then
        tmp = t_1
    else if (y <= (-3.05d-139)) then
        tmp = (y * t_1) / (y + (x + t))
    else if (y <= (-1.18d-226)) then
        tmp = t_2
    else if (y <= (-2.1d-265)) then
        tmp = (z + ((y * a) / x)) - ((y * b) / x)
    else if (y <= 3.1d-157) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = ((t * a) + (x * z)) / (x + t);
	double tmp;
	if (y <= -5e+111) {
		tmp = t_1;
	} else if (y <= -3.05e-139) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (y <= -1.18e-226) {
		tmp = t_2;
	} else if (y <= -2.1e-265) {
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	} else if (y <= 3.1e-157) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = ((t * a) + (x * z)) / (x + t)
	tmp = 0
	if y <= -5e+111:
		tmp = t_1
	elif y <= -3.05e-139:
		tmp = (y * t_1) / (y + (x + t))
	elif y <= -1.18e-226:
		tmp = t_2
	elif y <= -2.1e-265:
		tmp = (z + ((y * a) / x)) - ((y * b) / x)
	elif y <= 3.1e-157:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t))
	tmp = 0.0
	if (y <= -5e+111)
		tmp = t_1;
	elseif (y <= -3.05e-139)
		tmp = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)));
	elseif (y <= -1.18e-226)
		tmp = t_2;
	elseif (y <= -2.1e-265)
		tmp = Float64(Float64(z + Float64(Float64(y * a) / x)) - Float64(Float64(y * b) / x));
	elseif (y <= 3.1e-157)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = ((t * a) + (x * z)) / (x + t);
	tmp = 0.0;
	if (y <= -5e+111)
		tmp = t_1;
	elseif (y <= -3.05e-139)
		tmp = (y * t_1) / (y + (x + t));
	elseif (y <= -1.18e-226)
		tmp = t_2;
	elseif (y <= -2.1e-265)
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	elseif (y <= 3.1e-157)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+111], t$95$1, If[LessEqual[y, -3.05e-139], N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.18e-226], t$95$2, If[LessEqual[y, -2.1e-265], N[(N[(z + N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-157], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.9999999999999997e111 or 3.0999999999999998e-157 < y

   1. Initial program 44.4%

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

   3. Taylor expanded in y around inf 72.3%

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

   if -4.9999999999999997e111 < y < -3.0499999999999999e-139

   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 y around inf 62.9%

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

   if -3.0499999999999999e-139 < y < -1.1799999999999999e-226 or -2.10000000000000004e-265 < y < 3.0999999999999998e-157

   1. Initial program 81.1%

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

   3. Taylor expanded in y around 0 68.8%

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

   if -1.1799999999999999e-226 < y < -2.10000000000000004e-265

   1. Initial program 65.4%

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

   3. Taylor expanded in x around inf 64.5%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 55.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 82.0%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-139}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-226}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-265}:\\ \;\;\;\;\left(z + \frac{y \cdot a}{x}\right) - \frac{y \cdot b}{x}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-157}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-121}:\\ \;\;\;\;y \cdot \frac{z - b}{y + t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+194}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* a (/ (+ y t) (+ t (+ x y))))))
   (if (<= a -2e+32)
     t_2
     (if (<= a -1.9e-131)
       t_1
       (if (<= a -6.1e-299)
         (* z (/ (+ x y) (+ y (+ x t))))
         (if (<= a 2.55e-121)
           (* y (/ (- z b) (+ y t)))
           (if (<= a 2.7e+194) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (t + (x + y)));
	double tmp;
	if (a <= -2e+32) {
		tmp = t_2;
	} else if (a <= -1.9e-131) {
		tmp = t_1;
	} else if (a <= -6.1e-299) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else if (a <= 2.55e-121) {
		tmp = y * ((z - b) / (y + t));
	} else if (a <= 2.7e+194) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a * ((y + t) / (t + (x + y)))
    if (a <= (-2d+32)) then
        tmp = t_2
    else if (a <= (-1.9d-131)) then
        tmp = t_1
    else if (a <= (-6.1d-299)) then
        tmp = z * ((x + y) / (y + (x + t)))
    else if (a <= 2.55d-121) then
        tmp = y * ((z - b) / (y + t))
    else if (a <= 2.7d+194) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (t + (x + y)));
	double tmp;
	if (a <= -2e+32) {
		tmp = t_2;
	} else if (a <= -1.9e-131) {
		tmp = t_1;
	} else if (a <= -6.1e-299) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else if (a <= 2.55e-121) {
		tmp = y * ((z - b) / (y + t));
	} else if (a <= 2.7e+194) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a * ((y + t) / (t + (x + y)))
	tmp = 0
	if a <= -2e+32:
		tmp = t_2
	elif a <= -1.9e-131:
		tmp = t_1
	elif a <= -6.1e-299:
		tmp = z * ((x + y) / (y + (x + t)))
	elif a <= 2.55e-121:
		tmp = y * ((z - b) / (y + t))
	elif a <= 2.7e+194:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a * Float64(Float64(y + t) / Float64(t + Float64(x + y))))
	tmp = 0.0
	if (a <= -2e+32)
		tmp = t_2;
	elseif (a <= -1.9e-131)
		tmp = t_1;
	elseif (a <= -6.1e-299)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	elseif (a <= 2.55e-121)
		tmp = Float64(y * Float64(Float64(z - b) / Float64(y + t)));
	elseif (a <= 2.7e+194)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a * ((y + t) / (t + (x + y)));
	tmp = 0.0;
	if (a <= -2e+32)
		tmp = t_2;
	elseif (a <= -1.9e-131)
		tmp = t_1;
	elseif (a <= -6.1e-299)
		tmp = z * ((x + y) / (y + (x + t)));
	elseif (a <= 2.55e-121)
		tmp = y * ((z - b) / (y + t));
	elseif (a <= 2.7e+194)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+32], t$95$2, If[LessEqual[a, -1.9e-131], t$95$1, If[LessEqual[a, -6.1e-299], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.55e-121], N[(y * N[(N[(z - b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+194], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.00000000000000011e32 or 2.7000000000000002e194 < a

   1. Initial program 49.6%

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

   3. Taylor expanded in a around inf 36.5%

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

      1. associate-/l* 73.2%

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

      2. +-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -2.00000000000000011e32 < a < -1.89999999999999997e-131 or 2.5499999999999999e-121 < a < 2.7000000000000002e194

   1. Initial program 64.9%

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

   3. Taylor expanded in y around inf 65.4%

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

   if -1.89999999999999997e-131 < a < -6.10000000000000034e-299

   1. Initial program 65.7%

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

   3. Taylor expanded in z around inf 39.2%

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

      1. associate-/l* 70.8%

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

      2. +-commutative 70.8%

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

      3. +-commutative 70.8%

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

      4. associate-+r+ 70.8%

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

      5. +-commutative 70.8%

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

      6. associate-+l+ 70.8%

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

   5. Simplified 70.8%

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

   if -6.10000000000000034e-299 < a < 2.5499999999999999e-121

   1. Initial program 62.4%

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

   3. Taylor expanded in y around inf 39.3%

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

   4. Taylor expanded in x around 0 41.3%

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

   5. Taylor expanded in a around 0 41.3%

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

      1. associate-/l* 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-131}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-121}:\\ \;\;\;\;y \cdot \frac{z - b}{y + t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+194}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{-137}:\\ \;\;\;\;\left(a + \left(z - b\right)\right) \cdot \frac{y}{y + t}\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-265}:\\ \;\;\;\;\left(z + \frac{y \cdot a}{x}\right) - \frac{y \cdot b}{x}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* t a) (* x z)) (+ x t))))
   (if (<= y -7.8e-137)
     (* (+ a (- z b)) (/ y (+ y t)))
     (if (<= y -1.18e-226)
       t_1
       (if (<= y -1.7e-265)
         (- (+ z (/ (* y a) x)) (/ (* y b) x))
         (if (<= y 3.7e-160) t_1 (- (+ z a) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x * z)) / (x + t);
	double tmp;
	if (y <= -7.8e-137) {
		tmp = (a + (z - b)) * (y / (y + t));
	} else if (y <= -1.18e-226) {
		tmp = t_1;
	} else if (y <= -1.7e-265) {
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	} else if (y <= 3.7e-160) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = ((t * a) + (x * z)) / (x + t)
    if (y <= (-7.8d-137)) then
        tmp = (a + (z - b)) * (y / (y + t))
    else if (y <= (-1.18d-226)) then
        tmp = t_1
    else if (y <= (-1.7d-265)) then
        tmp = (z + ((y * a) / x)) - ((y * b) / x)
    else if (y <= 3.7d-160) then
        tmp = t_1
    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 t_1 = ((t * a) + (x * z)) / (x + t);
	double tmp;
	if (y <= -7.8e-137) {
		tmp = (a + (z - b)) * (y / (y + t));
	} else if (y <= -1.18e-226) {
		tmp = t_1;
	} else if (y <= -1.7e-265) {
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	} else if (y <= 3.7e-160) {
		tmp = t_1;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t * a) + (x * z)) / (x + t)
	tmp = 0
	if y <= -7.8e-137:
		tmp = (a + (z - b)) * (y / (y + t))
	elif y <= -1.18e-226:
		tmp = t_1
	elif y <= -1.7e-265:
		tmp = (z + ((y * a) / x)) - ((y * b) / x)
	elif y <= 3.7e-160:
		tmp = t_1
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t))
	tmp = 0.0
	if (y <= -7.8e-137)
		tmp = Float64(Float64(a + Float64(z - b)) * Float64(y / Float64(y + t)));
	elseif (y <= -1.18e-226)
		tmp = t_1;
	elseif (y <= -1.7e-265)
		tmp = Float64(Float64(z + Float64(Float64(y * a) / x)) - Float64(Float64(y * b) / x));
	elseif (y <= 3.7e-160)
		tmp = t_1;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t * a) + (x * z)) / (x + t);
	tmp = 0.0;
	if (y <= -7.8e-137)
		tmp = (a + (z - b)) * (y / (y + t));
	elseif (y <= -1.18e-226)
		tmp = t_1;
	elseif (y <= -1.7e-265)
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	elseif (y <= 3.7e-160)
		tmp = t_1;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e-137], N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] * N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.18e-226], t$95$1, If[LessEqual[y, -1.7e-265], N[(N[(z + N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-160], t$95$1, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.7999999999999999e-137

   1. Initial program 49.9%

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

   3. Taylor expanded in y around inf 39.5%

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

   4. Taylor expanded in x around 0 34.6%

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

      1. associate-/l* 65.0%

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

      2. +-commutative 65.0%

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

      3. associate--l+ 65.0%

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

   6. Applied egg-rr 65.0%

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

      1. associate-*r/ 34.6%

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

      2. associate-*l/ 66.9%

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

      3. associate-+r- 66.8%

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

      4. +-commutative 66.8%

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

      5. associate--l+ 66.8%

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

   8. Simplified 66.8%

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

   if -7.7999999999999999e-137 < y < -1.1799999999999999e-226 or -1.7e-265 < y < 3.69999999999999977e-160

   1. Initial program 81.1%

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

   3. Taylor expanded in y around 0 68.8%

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

   if -1.1799999999999999e-226 < y < -1.7e-265

   1. Initial program 65.4%

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

   3. Taylor expanded in x around inf 64.5%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 55.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 82.0%

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

   if 3.69999999999999977e-160 < y

   1. Initial program 53.0%

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

   3. Taylor expanded in y around inf 68.4%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-137}:\\ \;\;\;\;\left(a + \left(z - b\right)\right) \cdot \frac{y}{y + t}\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-226}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-265}:\\ \;\;\;\;\left(z + \frac{y \cdot a}{x}\right) - \frac{y \cdot b}{x}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-160}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-131}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+97}:\\ \;\;\;\;\left(a + \left(z - b\right)\right) \cdot \frac{y}{y + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ (+ y t) (+ t (+ x y))))))
   (if (<= a -1.55e+32)
     t_1
     (if (<= a -1.15e-131)
       (- (+ z a) b)
       (if (<= a -4e-300)
         (* z (/ (+ x y) (+ y (+ x t))))
         (if (<= a 9e+97) (* (+ a (- z b)) (/ y (+ y t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * ((y + t) / (t + (x + y)));
	double tmp;
	if (a <= -1.55e+32) {
		tmp = t_1;
	} else if (a <= -1.15e-131) {
		tmp = (z + a) - b;
	} else if (a <= -4e-300) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else if (a <= 9e+97) {
		tmp = (a + (z - b)) * (y / (y + 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 = a * ((y + t) / (t + (x + y)))
    if (a <= (-1.55d+32)) then
        tmp = t_1
    else if (a <= (-1.15d-131)) then
        tmp = (z + a) - b
    else if (a <= (-4d-300)) then
        tmp = z * ((x + y) / (y + (x + t)))
    else if (a <= 9d+97) then
        tmp = (a + (z - b)) * (y / (y + 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 = a * ((y + t) / (t + (x + y)));
	double tmp;
	if (a <= -1.55e+32) {
		tmp = t_1;
	} else if (a <= -1.15e-131) {
		tmp = (z + a) - b;
	} else if (a <= -4e-300) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else if (a <= 9e+97) {
		tmp = (a + (z - b)) * (y / (y + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * ((y + t) / (t + (x + y)))
	tmp = 0
	if a <= -1.55e+32:
		tmp = t_1
	elif a <= -1.15e-131:
		tmp = (z + a) - b
	elif a <= -4e-300:
		tmp = z * ((x + y) / (y + (x + t)))
	elif a <= 9e+97:
		tmp = (a + (z - b)) * (y / (y + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(Float64(y + t) / Float64(t + Float64(x + y))))
	tmp = 0.0
	if (a <= -1.55e+32)
		tmp = t_1;
	elseif (a <= -1.15e-131)
		tmp = Float64(Float64(z + a) - b);
	elseif (a <= -4e-300)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	elseif (a <= 9e+97)
		tmp = Float64(Float64(a + Float64(z - b)) * Float64(y / Float64(y + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * ((y + t) / (t + (x + y)));
	tmp = 0.0;
	if (a <= -1.55e+32)
		tmp = t_1;
	elseif (a <= -1.15e-131)
		tmp = (z + a) - b;
	elseif (a <= -4e-300)
		tmp = z * ((x + y) / (y + (x + t)));
	elseif (a <= 9e+97)
		tmp = (a + (z - b)) * (y / (y + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(N[(y + t), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e+32], t$95$1, If[LessEqual[a, -1.15e-131], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[a, -4e-300], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+97], N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] * N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.54999999999999997e32 or 8.99999999999999952e97 < a

   1. Initial program 48.8%

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

   3. Taylor expanded in a around inf 34.3%

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

      1. associate-/l* 69.5%

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

      2. +-commutative 69.5%

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

   5. Simplified 69.5%

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

   if -1.54999999999999997e32 < a < -1.15000000000000011e-131

   1. Initial program 76.0%

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

   3. Taylor expanded in y around inf 72.4%

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

   if -1.15000000000000011e-131 < a < -4.0000000000000001e-300

   1. Initial program 65.7%

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

   3. Taylor expanded in z around inf 39.2%

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

      1. associate-/l* 70.8%

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

      2. +-commutative 70.8%

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

      3. +-commutative 70.8%

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

      4. associate-+r+ 70.8%

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

      5. +-commutative 70.8%

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

      6. associate-+l+ 70.8%

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

   5. Simplified 70.8%

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

   if -4.0000000000000001e-300 < a < 8.99999999999999952e97

   1. Initial program 62.7%

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

   3. Taylor expanded in y around inf 37.5%

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

   4. Taylor expanded in x around 0 37.9%

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

      1. associate-/l* 61.1%

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

      2. +-commutative 61.1%

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

      3. associate--l+ 61.1%

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

   6. Applied egg-rr 61.1%

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

      1. associate-*r/ 37.9%

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

      2. associate-*l/ 64.5%

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

      3. associate-+r- 64.5%

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

      4. +-commutative 64.5%

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

      5. associate--l+ 64.5%

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

   8. Simplified 64.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-131}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+97}:\\ \;\;\;\;\left(a + \left(z - b\right)\right) \cdot \frac{y}{y + t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z - b}{y + t}\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* a (/ (+ y t) (+ t (+ x y))))))
   (if (<= a -2e+32)
     t_2
     (if (<= a -4.2e-297)
       t_1
       (if (<= a 5.4e-122)
         (* y (/ (- z b) (+ y t)))
         (if (<= a 1.52e+193) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (t + (x + y)));
	double tmp;
	if (a <= -2e+32) {
		tmp = t_2;
	} else if (a <= -4.2e-297) {
		tmp = t_1;
	} else if (a <= 5.4e-122) {
		tmp = y * ((z - b) / (y + t));
	} else if (a <= 1.52e+193) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a * ((y + t) / (t + (x + y)))
    if (a <= (-2d+32)) then
        tmp = t_2
    else if (a <= (-4.2d-297)) then
        tmp = t_1
    else if (a <= 5.4d-122) then
        tmp = y * ((z - b) / (y + t))
    else if (a <= 1.52d+193) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (t + (x + y)));
	double tmp;
	if (a <= -2e+32) {
		tmp = t_2;
	} else if (a <= -4.2e-297) {
		tmp = t_1;
	} else if (a <= 5.4e-122) {
		tmp = y * ((z - b) / (y + t));
	} else if (a <= 1.52e+193) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a * ((y + t) / (t + (x + y)))
	tmp = 0
	if a <= -2e+32:
		tmp = t_2
	elif a <= -4.2e-297:
		tmp = t_1
	elif a <= 5.4e-122:
		tmp = y * ((z - b) / (y + t))
	elif a <= 1.52e+193:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a * Float64(Float64(y + t) / Float64(t + Float64(x + y))))
	tmp = 0.0
	if (a <= -2e+32)
		tmp = t_2;
	elseif (a <= -4.2e-297)
		tmp = t_1;
	elseif (a <= 5.4e-122)
		tmp = Float64(y * Float64(Float64(z - b) / Float64(y + t)));
	elseif (a <= 1.52e+193)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a * ((y + t) / (t + (x + y)));
	tmp = 0.0;
	if (a <= -2e+32)
		tmp = t_2;
	elseif (a <= -4.2e-297)
		tmp = t_1;
	elseif (a <= 5.4e-122)
		tmp = y * ((z - b) / (y + t));
	elseif (a <= 1.52e+193)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+32], t$95$2, If[LessEqual[a, -4.2e-297], t$95$1, If[LessEqual[a, 5.4e-122], N[(y * N[(N[(z - b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.52e+193], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.00000000000000011e32 or 1.52e193 < a

   1. Initial program 49.6%

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

   3. Taylor expanded in a around inf 36.5%

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

      1. associate-/l* 73.2%

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

      2. +-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -2.00000000000000011e32 < a < -4.20000000000000027e-297 or 5.40000000000000019e-122 < a < 1.52e193

   1. Initial program 65.1%

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

   3. Taylor expanded in y around inf 62.3%

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

   if -4.20000000000000027e-297 < a < 5.40000000000000019e-122

   1. Initial program 62.4%

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

   3. Taylor expanded in y around inf 39.3%

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

   4. Taylor expanded in x around 0 41.3%

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

   5. Taylor expanded in a around 0 41.3%

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

      1. associate-/l* 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-297}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z - b}{y + t}\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{+193}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-137}:\\ \;\;\;\;\left(a + \left(z - b\right)\right) \cdot \frac{y}{y + t}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-157}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.5e-137)
   (* (+ a (- z b)) (/ y (+ y t)))
   (if (<= y 3.1e-157) (/ (+ (* t a) (* x z)) (+ x t)) (- (+ z a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.5e-137) {
		tmp = (a + (z - b)) * (y / (y + t));
	} else if (y <= 3.1e-157) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7.5d-137)) then
        tmp = (a + (z - b)) * (y / (y + t))
    else if (y <= 3.1d-157) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.5e-137) {
		tmp = (a + (z - b)) * (y / (y + t));
	} else if (y <= 3.1e-157) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.5e-137:
		tmp = (a + (z - b)) * (y / (y + t))
	elif y <= 3.1e-157:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.5e-137)
		tmp = Float64(Float64(a + Float64(z - b)) * Float64(y / Float64(y + t)));
	elseif (y <= 3.1e-157)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.5e-137)
		tmp = (a + (z - b)) * (y / (y + t));
	elseif (y <= 3.1e-157)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.5e-137], N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] * N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-157], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999995e-137

   1. Initial program 49.9%

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

   3. Taylor expanded in y around inf 39.5%

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

   4. Taylor expanded in x around 0 34.6%

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

      1. associate-/l* 65.0%

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

      2. +-commutative 65.0%

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

      3. associate--l+ 65.0%

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

   6. Applied egg-rr 65.0%

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

      1. associate-*r/ 34.6%

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

      2. associate-*l/ 66.9%

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

      3. associate-+r- 66.8%

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

      4. +-commutative 66.8%

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

      5. associate--l+ 66.8%

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

   8. Simplified 66.8%

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

   if -7.4999999999999995e-137 < y < 3.0999999999999998e-157

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 64.8%

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

   if 3.0999999999999998e-157 < y

   1. Initial program 53.0%

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

   3. Taylor expanded in y around inf 68.4%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-137}:\\ \;\;\;\;\left(a + \left(z - b\right)\right) \cdot \frac{y}{y + t}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-157}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+95} \lor \neg \left(b \leq 2 \cdot 10^{+161}\right):\\ \;\;\;\;b \cdot \frac{y}{\left(-y\right) - \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8e+95) (not (<= b 2e+161)))
   (* b (/ y (- (- y) (+ x t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8e+95) || !(b <= 2e+161)) {
		tmp = b * (y / (-y - (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-8d+95)) .or. (.not. (b <= 2d+161))) then
        tmp = b * (y / (-y - (x + t)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8e+95) || !(b <= 2e+161)) {
		tmp = b * (y / (-y - (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -8e+95) or not (b <= 2e+161):
		tmp = b * (y / (-y - (x + t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8e+95) || !(b <= 2e+161))
		tmp = Float64(b * Float64(y / Float64(Float64(-y) - Float64(x + t))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -8e+95) || ~((b <= 2e+161)))
		tmp = b * (y / (-y - (x + t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8e+95], N[Not[LessEqual[b, 2e+161]], $MachinePrecision]], N[(b * N[(y / N[((-y) - N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.00000000000000016e95 or 2.0000000000000001e161 < b

   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 b around inf 30.5%

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

      1. mul-1-neg 30.5%

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

      2. associate-/l* 58.3%

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

      3. distribute-rgt-neg-in 58.3%

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

      4. mul-1-neg 58.3%

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

      5. associate-*r/ 58.3%

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

      6. neg-mul-1 58.3%

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

      7. +-commutative 58.3%

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

      8. associate-+r+ 58.3%

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

      9. +-commutative 58.3%

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

      10. associate-+l+ 58.3%

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

   5. Simplified 58.3%

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

   if -8.00000000000000016e95 < b < 2.0000000000000001e161

   1. Initial program 62.5%

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

   3. Taylor expanded in y around inf 65.6%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+95} \lor \neg \left(b \leq 2 \cdot 10^{+161}\right):\\ \;\;\;\;b \cdot \frac{y}{\left(-y\right) - \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+223} \lor \neg \left(b \leq 2.4 \cdot 10^{+190}\right):\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.4e+223) (not (<= b 2.4e+190))) (- b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.4e+223) || !(b <= 2.4e+190)) {
		tmp = -b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.4d+223)) .or. (.not. (b <= 2.4d+190))) then
        tmp = -b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.4e+223) || !(b <= 2.4e+190)) {
		tmp = -b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.4e+223) or not (b <= 2.4e+190):
		tmp = -b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.4e+223) || !(b <= 2.4e+190))
		tmp = Float64(-b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.4e+223) || ~((b <= 2.4e+190)))
		tmp = -b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.4e+223], N[Not[LessEqual[b, 2.4e+190]], $MachinePrecision]], (-b), N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.3999999999999999e223 or 2.3999999999999999e190 < b

   1. Initial program 40.3%

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

   3. Taylor expanded in b around inf 26.7%

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

      1. associate-*r* 26.7%

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

      2. neg-mul-1 26.7%

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

      3. *-commutative 26.7%

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

   5. Simplified 26.7%

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

   6. Taylor expanded in y around inf 41.9%

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

      1. neg-mul-1 41.9%

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

   8. Simplified 41.9%

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

   if -4.3999999999999999e223 < b < 2.3999999999999999e190

   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 59.5%

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

   4. Taylor expanded in b around 0 56.2%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+223} \lor \neg \left(b \leq 2.4 \cdot 10^{+190}\right):\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{+219}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+185}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.75e+219) (- a b) (if (<= b 2.6e+185) (+ z a) (- z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.75e+219) {
		tmp = a - b;
	} else if (b <= 2.6e+185) {
		tmp = z + a;
	} 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 (b <= (-2.75d+219)) then
        tmp = a - b
    else if (b <= 2.6d+185) then
        tmp = z + a
    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 (b <= -2.75e+219) {
		tmp = a - b;
	} else if (b <= 2.6e+185) {
		tmp = z + a;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.75e+219:
		tmp = a - b
	elif b <= 2.6e+185:
		tmp = z + a
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.75e+219)
		tmp = Float64(a - b);
	elseif (b <= 2.6e+185)
		tmp = Float64(z + a);
	else
		tmp = Float64(z - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.75e+219)
		tmp = a - b;
	elseif (b <= 2.6e+185)
		tmp = z + a;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.75e+219], N[(a - b), $MachinePrecision], If[LessEqual[b, 2.6e+185], N[(z + a), $MachinePrecision], N[(z - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.74999999999999986e219

   1. Initial program 35.9%

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

   3. Taylor expanded in z around 0 26.5%

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

      1. *-commutative 26.5%

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

   5. Simplified 26.5%

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

   6. Taylor expanded in y around inf 54.5%

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

   if -2.74999999999999986e219 < b < 2.60000000000000001e185

   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 59.5%

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

   4. Taylor expanded in b around 0 56.2%

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

   if 2.60000000000000001e185 < b

   1. Initial program 43.2%

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

   3. Taylor expanded in y around inf 37.5%

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

   4. Taylor expanded in a around 0 37.5%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{+219}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+185}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+222}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+188}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.25e+222) (- a b) (if (<= b 2.5e+188) (+ z a) (- b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.25e+222) {
		tmp = a - b;
	} else if (b <= 2.5e+188) {
		tmp = z + a;
	} else {
		tmp = -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 (b <= (-2.25d+222)) then
        tmp = a - b
    else if (b <= 2.5d+188) then
        tmp = z + a
    else
        tmp = -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 (b <= -2.25e+222) {
		tmp = a - b;
	} else if (b <= 2.5e+188) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.25e+222:
		tmp = a - b
	elif b <= 2.5e+188:
		tmp = z + a
	else:
		tmp = -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.25e+222)
		tmp = Float64(a - b);
	elseif (b <= 2.5e+188)
		tmp = Float64(z + a);
	else
		tmp = Float64(-b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.25e+222)
		tmp = a - b;
	elseif (b <= 2.5e+188)
		tmp = z + a;
	else
		tmp = -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.25e+222], N[(a - b), $MachinePrecision], If[LessEqual[b, 2.5e+188], N[(z + a), $MachinePrecision], (-b)]]

Derivation

1. Split input into 3 regimes

2. if b < -2.24999999999999994e222

   1. Initial program 35.9%

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

   3. Taylor expanded in z around 0 26.5%

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

      1. *-commutative 26.5%

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

   5. Simplified 26.5%

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

   6. Taylor expanded in y around inf 54.5%

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

   if -2.24999999999999994e222 < b < 2.5000000000000001e188

   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 59.5%

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

   4. Taylor expanded in b around 0 56.2%

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

   if 2.5000000000000001e188 < b

   1. Initial program 43.2%

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

   3. Taylor expanded in b around inf 29.9%

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

      1. associate-*r* 29.9%

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

      2. neg-mul-1 29.9%

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

      3. *-commutative 29.9%

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

   5. Simplified 29.9%

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

   6. Taylor expanded in y around inf 37.2%

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

      1. neg-mul-1 37.2%

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

   8. Simplified 37.2%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+222}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+188}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-19}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-156}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.8e-19) a (if (<= a 3.3e-156) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.8e-19) {
		tmp = a;
	} else if (a <= 3.3e-156) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-7.8d-19)) then
        tmp = a
    else if (a <= 3.3d-156) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.8e-19) {
		tmp = a;
	} else if (a <= 3.3e-156) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.8e-19:
		tmp = a
	elif a <= 3.3e-156:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.8e-19)
		tmp = a;
	elseif (a <= 3.3e-156)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -7.8e-19)
		tmp = a;
	elseif (a <= 3.3e-156)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.8e-19], a, If[LessEqual[a, 3.3e-156], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -7.7999999999999999e-19 or 3.2999999999999999e-156 < a

   1. Initial program 56.8%

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

   3. Taylor expanded in t around inf 44.2%

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

   if -7.7999999999999999e-19 < a < 3.2999999999999999e-156

   1. Initial program 64.3%

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

   3. Taylor expanded in x around inf 44.3%

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

Alternative 16: 57.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+145}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.35e+145) a (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.35e+145) {
		tmp = a;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.35d+145)) then
        tmp = a
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.35e+145) {
		tmp = a;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.35e+145:
		tmp = a
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.35e+145)
		tmp = a;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.35e+145)
		tmp = a;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.35e+145], a, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3500000000000001e145

   1. Initial program 53.0%

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

   3. Taylor expanded in t around inf 59.3%

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

   if -2.3500000000000001e145 < t

   1. Initial program 60.9%

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

   3. Taylor expanded in y around inf 60.4%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+145}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.2% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.8%

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

3. Taylor expanded in t around inf 31.4%

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

Developer target: 82.1% 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 2024088 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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