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

Percentage Accurate: 59.8% → 88.3%

Time: 18.5s

Alternatives: 23

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.8% 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: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \left(x + y\right)\\ t_3 := \frac{\left(t_2 + \left(y + t\right) \cdot a\right) - y \cdot b}{t_1}\\ t_4 := \frac{y}{t_1}\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{+278}:\\ \;\;\;\;a + z \cdot \left(\frac{x}{t_1} + t_4\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+201}:\\ \;\;\;\;a \cdot \left(t_4 + \frac{t}{t_1}\right) + \frac{t_2 - y \cdot b}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - \frac{b}{\frac{x}{y} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (* z (+ x y)))
        (t_3 (/ (- (+ t_2 (* (+ y t) a)) (* y b)) t_1))
        (t_4 (/ y t_1)))
   (if (<= t_3 -5e+278)
     (+ a (* z (+ (/ x t_1) t_4)))
     (if (<= t_3 2e+201)
       (+ (* a (+ t_4 (/ t t_1))) (/ (- t_2 (* y b)) t_1))
       (- (+ z (/ a (/ (+ x y) y))) (/ b (+ (/ x y) 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * (x + y);
	double t_3 = ((t_2 + ((y + t) * a)) - (y * b)) / t_1;
	double t_4 = y / t_1;
	double tmp;
	if (t_3 <= -5e+278) {
		tmp = a + (z * ((x / t_1) + t_4));
	} else if (t_3 <= 2e+201) {
		tmp = (a * (t_4 + (t / t_1))) + ((t_2 - (y * b)) / t_1);
	} else {
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * (x + y)
    t_3 = ((t_2 + ((y + t) * a)) - (y * b)) / t_1
    t_4 = y / t_1
    if (t_3 <= (-5d+278)) then
        tmp = a + (z * ((x / t_1) + t_4))
    else if (t_3 <= 2d+201) then
        tmp = (a * (t_4 + (t / t_1))) + ((t_2 - (y * b)) / t_1)
    else
        tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * (x + y);
	double t_3 = ((t_2 + ((y + t) * a)) - (y * b)) / t_1;
	double t_4 = y / t_1;
	double tmp;
	if (t_3 <= -5e+278) {
		tmp = a + (z * ((x / t_1) + t_4));
	} else if (t_3 <= 2e+201) {
		tmp = (a * (t_4 + (t / t_1))) + ((t_2 - (y * b)) / t_1);
	} else {
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * (x + y)
	t_3 = ((t_2 + ((y + t) * a)) - (y * b)) / t_1
	t_4 = y / t_1
	tmp = 0
	if t_3 <= -5e+278:
		tmp = a + (z * ((x / t_1) + t_4))
	elif t_3 <= 2e+201:
		tmp = (a * (t_4 + (t / t_1))) + ((t_2 - (y * b)) / t_1)
	else:
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(x + y))
	t_3 = Float64(Float64(Float64(t_2 + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	t_4 = Float64(y / t_1)
	tmp = 0.0
	if (t_3 <= -5e+278)
		tmp = Float64(a + Float64(z * Float64(Float64(x / t_1) + t_4)));
	elseif (t_3 <= 2e+201)
		tmp = Float64(Float64(a * Float64(t_4 + Float64(t / t_1))) + Float64(Float64(t_2 - Float64(y * b)) / t_1));
	else
		tmp = Float64(Float64(z + Float64(a / Float64(Float64(x + y) / y))) - Float64(b / Float64(Float64(x / y) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * (x + y);
	t_3 = ((t_2 + ((y + t) * a)) - (y * b)) / t_1;
	t_4 = y / t_1;
	tmp = 0.0;
	if (t_3 <= -5e+278)
		tmp = a + (z * ((x / t_1) + t_4));
	elseif (t_3 <= 2e+201)
		tmp = (a * (t_4 + (t / t_1))) + ((t_2 - (y * b)) / t_1);
	else
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(y / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+278], N[(a + N[(z * N[(N[(x / t$95$1), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+201], N[(N[(a * N[(t$95$4 + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.00000000000000029e278

   1. Initial program 8.8%

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

   2. Taylor expanded in z around 0 52.4%

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

      1. associate--l+ 52.4%

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

      2. associate-+r+ 52.4%

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

      3. associate-+r+ 52.4%

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

      4. div-sub 52.4%

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

      5. *-commutative 52.4%

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

      6. associate-+r+ 52.4%

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

   4. Simplified 52.4%

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

   5. Taylor expanded in t around inf 80.9%

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

   if -5.00000000000000029e278 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000008e201

   1. Initial program 99.7%

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

   2. Taylor expanded in a around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. div-sub 99.8%

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

      6. +-commutative 99.8%

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

      7. *-commutative 99.8%

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

      8. associate-+r+ 99.8%

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

   4. Simplified 99.8%

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

   if 2.00000000000000008e201 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 15.0%

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

   2. Taylor expanded in z around 0 33.4%

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

      1. associate--l+ 33.4%

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

      2. associate-+r+ 33.4%

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

      3. associate-+r+ 33.4%

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

      4. div-sub 33.4%

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

      5. *-commutative 33.4%

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

      6. associate-+r+ 33.4%

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

   4. Simplified 33.4%

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

   5. Taylor expanded in x around inf 30.2%

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

   6. Taylor expanded in t around 0 31.9%

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

      1. associate-/l* 46.6%

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

      2. +-commutative 46.6%

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

      3. associate-/l* 74.6%

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

      4. +-commutative 74.6%

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

   8. Simplified 74.6%

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

   9. Taylor expanded in y around 0 74.6%

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

       1. +-commutative 74.6%

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

   11. Simplified 74.6%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+278}:\\ \;\;\;\;a + z \cdot \left(\frac{x}{y + \left(x + t\right)} + \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+201}:\\ \;\;\;\;a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right) + \frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - \frac{b}{\frac{x}{y} + 1}\\ \end{array} \]

Alternative 2: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+278}:\\ \;\;\;\;a + z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+201}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - \frac{b}{\frac{x}{y} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) t_1)))
   (if (<= t_2 -5e+278)
     (+ a (* z (+ (/ x t_1) (/ y t_1))))
     (if (<= t_2 2e+201)
       t_2
       (- (+ z (/ a (/ (+ x y) y))) (/ b (+ (/ x y) 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -5e+278) {
		tmp = a + (z * ((x / t_1) + (y / t_1)));
	} else if (t_2 <= 2e+201) {
		tmp = t_2;
	} else {
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1
    if (t_2 <= (-5d+278)) then
        tmp = a + (z * ((x / t_1) + (y / t_1)))
    else if (t_2 <= 2d+201) then
        tmp = t_2
    else
        tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -5e+278) {
		tmp = a + (z * ((x / t_1) + (y / t_1)));
	} else if (t_2 <= 2e+201) {
		tmp = t_2;
	} else {
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1
	tmp = 0
	if t_2 <= -5e+278:
		tmp = a + (z * ((x / t_1) + (y / t_1)))
	elif t_2 <= 2e+201:
		tmp = t_2
	else:
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= -5e+278)
		tmp = Float64(a + Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))));
	elseif (t_2 <= 2e+201)
		tmp = t_2;
	else
		tmp = Float64(Float64(z + Float64(a / Float64(Float64(x + y) / y))) - Float64(b / Float64(Float64(x / y) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_2 <= -5e+278)
		tmp = a + (z * ((x / t_1) + (y / t_1)));
	elseif (t_2 <= 2e+201)
		tmp = t_2;
	else
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0));
	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[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+278], N[(a + N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+201], t$95$2, N[(N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.00000000000000029e278

   1. Initial program 8.8%

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

   2. Taylor expanded in z around 0 52.4%

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

      1. associate--l+ 52.4%

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

      2. associate-+r+ 52.4%

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

      3. associate-+r+ 52.4%

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

      4. div-sub 52.4%

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

      5. *-commutative 52.4%

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

      6. associate-+r+ 52.4%

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

   4. Simplified 52.4%

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

   5. Taylor expanded in t around inf 80.9%

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

   if -5.00000000000000029e278 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000008e201

   1. Initial program 99.7%

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

   if 2.00000000000000008e201 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 15.0%

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

   2. Taylor expanded in z around 0 33.4%

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

      1. associate--l+ 33.4%

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

      2. associate-+r+ 33.4%

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

      3. associate-+r+ 33.4%

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

      4. div-sub 33.4%

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

      5. *-commutative 33.4%

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

      6. associate-+r+ 33.4%

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

   4. Simplified 33.4%

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

   5. Taylor expanded in x around inf 30.2%

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

   6. Taylor expanded in t around 0 31.9%

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

      1. associate-/l* 46.6%

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

      2. +-commutative 46.6%

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

      3. associate-/l* 74.6%

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

      4. +-commutative 74.6%

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

   8. Simplified 74.6%

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

   9. Taylor expanded in y around 0 74.6%

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

       1. +-commutative 74.6%

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

   11. Simplified 74.6%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+278}:\\ \;\;\;\;a + z \cdot \left(\frac{x}{y + \left(x + t\right)} + \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+201}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - \frac{b}{\frac{x}{y} + 1}\\ \end{array} \]

Alternative 3: 64.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+166}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+118}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t + \left(x + y\right)}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-106}:\\ \;\;\;\;z - \frac{b}{\frac{x + y}{y}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-105}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (* y (- a b)) (+ x y))))
        (t_2 (- (+ z a) (/ (* y b) (+ y t)))))
   (if (<= t -7e+166)
     (+ a (* z (/ (+ x y) t)))
     (if (<= t -9e+118)
       (* (+ y t) (/ a (+ t (+ x y))))
       (if (<= t -5e-23)
         t_2
         (if (<= t -2.5e-106)
           (- z (/ b (/ (+ x y) y)))
           (if (<= t 1.4e-266)
             t_1
             (if (<= t 7.5e-105)
               (- (+ z a) b)
               (if (<= t 2.2e+31)
                 t_1
                 (if (<= t 7.5e+150) t_2 (+ a (/ z (/ t (+ x y))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - ((y * b) / (y + t));
	double tmp;
	if (t <= -7e+166) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= -9e+118) {
		tmp = (y + t) * (a / (t + (x + y)));
	} else if (t <= -5e-23) {
		tmp = t_2;
	} else if (t <= -2.5e-106) {
		tmp = z - (b / ((x + y) / y));
	} else if (t <= 1.4e-266) {
		tmp = t_1;
	} else if (t <= 7.5e-105) {
		tmp = (z + a) - b;
	} else if (t <= 2.2e+31) {
		tmp = t_1;
	} else if (t <= 7.5e+150) {
		tmp = t_2;
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + ((y * (a - b)) / (x + y))
    t_2 = (z + a) - ((y * b) / (y + t))
    if (t <= (-7d+166)) then
        tmp = a + (z * ((x + y) / t))
    else if (t <= (-9d+118)) then
        tmp = (y + t) * (a / (t + (x + y)))
    else if (t <= (-5d-23)) then
        tmp = t_2
    else if (t <= (-2.5d-106)) then
        tmp = z - (b / ((x + y) / y))
    else if (t <= 1.4d-266) then
        tmp = t_1
    else if (t <= 7.5d-105) then
        tmp = (z + a) - b
    else if (t <= 2.2d+31) then
        tmp = t_1
    else if (t <= 7.5d+150) then
        tmp = t_2
    else
        tmp = a + (z / (t / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - ((y * b) / (y + t));
	double tmp;
	if (t <= -7e+166) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= -9e+118) {
		tmp = (y + t) * (a / (t + (x + y)));
	} else if (t <= -5e-23) {
		tmp = t_2;
	} else if (t <= -2.5e-106) {
		tmp = z - (b / ((x + y) / y));
	} else if (t <= 1.4e-266) {
		tmp = t_1;
	} else if (t <= 7.5e-105) {
		tmp = (z + a) - b;
	} else if (t <= 2.2e+31) {
		tmp = t_1;
	} else if (t <= 7.5e+150) {
		tmp = t_2;
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + ((y * (a - b)) / (x + y))
	t_2 = (z + a) - ((y * b) / (y + t))
	tmp = 0
	if t <= -7e+166:
		tmp = a + (z * ((x + y) / t))
	elif t <= -9e+118:
		tmp = (y + t) * (a / (t + (x + y)))
	elif t <= -5e-23:
		tmp = t_2
	elif t <= -2.5e-106:
		tmp = z - (b / ((x + y) / y))
	elif t <= 1.4e-266:
		tmp = t_1
	elif t <= 7.5e-105:
		tmp = (z + a) - b
	elif t <= 2.2e+31:
		tmp = t_1
	elif t <= 7.5e+150:
		tmp = t_2
	else:
		tmp = a + (z / (t / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)))
	t_2 = Float64(Float64(z + a) - Float64(Float64(y * b) / Float64(y + t)))
	tmp = 0.0
	if (t <= -7e+166)
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / t)));
	elseif (t <= -9e+118)
		tmp = Float64(Float64(y + t) * Float64(a / Float64(t + Float64(x + y))));
	elseif (t <= -5e-23)
		tmp = t_2;
	elseif (t <= -2.5e-106)
		tmp = Float64(z - Float64(b / Float64(Float64(x + y) / y)));
	elseif (t <= 1.4e-266)
		tmp = t_1;
	elseif (t <= 7.5e-105)
		tmp = Float64(Float64(z + a) - b);
	elseif (t <= 2.2e+31)
		tmp = t_1;
	elseif (t <= 7.5e+150)
		tmp = t_2;
	else
		tmp = Float64(a + Float64(z / Float64(t / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + ((y * (a - b)) / (x + y));
	t_2 = (z + a) - ((y * b) / (y + t));
	tmp = 0.0;
	if (t <= -7e+166)
		tmp = a + (z * ((x + y) / t));
	elseif (t <= -9e+118)
		tmp = (y + t) * (a / (t + (x + y)));
	elseif (t <= -5e-23)
		tmp = t_2;
	elseif (t <= -2.5e-106)
		tmp = z - (b / ((x + y) / y));
	elseif (t <= 1.4e-266)
		tmp = t_1;
	elseif (t <= 7.5e-105)
		tmp = (z + a) - b;
	elseif (t <= 2.2e+31)
		tmp = t_1;
	elseif (t <= 7.5e+150)
		tmp = t_2;
	else
		tmp = a + (z / (t / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+166], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e+118], N[(N[(y + t), $MachinePrecision] * N[(a / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-23], t$95$2, If[LessEqual[t, -2.5e-106], N[(z - N[(b / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-266], t$95$1, If[LessEqual[t, 7.5e-105], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 2.2e+31], t$95$1, If[LessEqual[t, 7.5e+150], t$95$2, N[(a + N[(z / N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -6.9999999999999997e166

   1. Initial program 42.3%

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

   2. Taylor expanded in z around 0 55.4%

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

      1. associate--l+ 55.4%

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

      2. associate-+r+ 55.4%

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

      3. associate-+r+ 55.4%

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

      4. div-sub 55.4%

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

      5. *-commutative 55.4%

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

      6. associate-+r+ 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in t around inf 76.5%

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

   6. Taylor expanded in t around inf 70.1%

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

      1. +-commutative 70.1%

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

   8. Simplified 70.1%

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

   if -6.9999999999999997e166 < t < -9.00000000000000004e118

   1. Initial program 41.0%

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

   2. Taylor expanded in a around inf 40.8%

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

      1. associate-/l* 87.7%

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

      2. associate-+r+ 87.7%

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

   4. Simplified 87.7%

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

      1. associate-/r/ 86.8%

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

      2. associate-+l+ 86.8%

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

      3. +-commutative 86.8%

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

   6. Applied egg-rr 86.8%

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

   if -9.00000000000000004e118 < t < -5.0000000000000002e-23 or 2.2000000000000001e31 < t < 7.4999999999999998e150

   1. Initial program 66.4%

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

   2. Taylor expanded in z around 0 80.0%

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

      1. associate--l+ 80.0%

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

      2. associate-+r+ 80.0%

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

      3. associate-+r+ 80.0%

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

      4. div-sub 80.0%

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

      5. *-commutative 80.0%

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

      6. associate-+r+ 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in x around inf 71.7%

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

   6. Taylor expanded in x around 0 69.0%

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

      1. *-commutative 69.0%

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

      2. +-commutative 69.0%

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

   8. Simplified 69.0%

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

   if -5.0000000000000002e-23 < t < -2.49999999999999991e-106

   1. Initial program 55.4%

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

   2. Taylor expanded in z around 0 65.1%

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

      1. associate--l+ 65.1%

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

      2. associate-+r+ 65.1%

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

      3. associate-+r+ 65.1%

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

      4. div-sub 65.1%

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

      5. *-commutative 65.1%

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

      6. associate-+r+ 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in x around inf 65.1%

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

   6. Taylor expanded in t around 0 54.9%

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

      1. associate-/l* 55.1%

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

      2. +-commutative 55.1%

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

      3. associate-/l* 89.9%

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

      4. +-commutative 89.9%

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

   8. Simplified 89.9%

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

   9. Taylor expanded in z around inf 88.0%

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

   if -2.49999999999999991e-106 < t < 1.4e-266 or 7.5000000000000006e-105 < t < 2.2000000000000001e31

   1. Initial program 71.5%

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

   2. Taylor expanded in z around 0 83.5%

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

      1. associate--l+ 83.5%

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

      2. associate-+r+ 83.5%

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

      3. associate-+r+ 83.5%

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

      4. div-sub 83.5%

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

      5. *-commutative 83.5%

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

      6. associate-+r+ 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in x around inf 82.0%

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

   6. Taylor expanded in t around 0 82.0%

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

      1. distribute-rgt-out-- 82.2%

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

      2. +-commutative 82.2%

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

   8. Simplified 82.2%

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

   if 1.4e-266 < t < 7.5000000000000006e-105

   1. Initial program 47.9%

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

   2. Taylor expanded in y around inf 77.6%

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

   if 7.4999999999999998e150 < t

   1. Initial program 44.5%

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

   2. Taylor expanded in z around 0 55.7%

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

      1. associate--l+ 55.7%

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

      2. associate-+r+ 55.7%

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

      3. associate-+r+ 55.7%

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

      4. div-sub 55.8%

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

      5. *-commutative 55.8%

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

      6. associate-+r+ 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in t around inf 80.3%

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

   6. Taylor expanded in t around inf 62.4%

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

      1. associate-/l* 74.5%

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

      2. +-commutative 74.5%

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

   8. Simplified 74.5%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+166}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+118}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t + \left(x + y\right)}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-23}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-106}:\\ \;\;\;\;z - \frac{b}{\frac{x + y}{y}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-266}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-105}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+31}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+150}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \]

Alternative 4: 80.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a + z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+120}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;t \leq -540000000000 \lor \neg \left(t \leq 6.5 \cdot 10^{+31}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - \frac{b}{\frac{x}{y} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (+ a (* z (+ (/ x t_1) (/ y t_1))))))
   (if (<= t -1.26e+159)
     t_2
     (if (<= t -8.5e+120)
       (/ a (/ t_1 (+ y t)))
       (if (or (<= t -540000000000.0) (not (<= t 6.5e+31)))
         t_2
         (- (+ z (/ a (/ (+ x y) y))) (/ b (+ (/ x y) 1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a + (z * ((x / t_1) + (y / t_1)));
	double tmp;
	if (t <= -1.26e+159) {
		tmp = t_2;
	} else if (t <= -8.5e+120) {
		tmp = a / (t_1 / (y + t));
	} else if ((t <= -540000000000.0) || !(t <= 6.5e+31)) {
		tmp = t_2;
	} else {
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0));
	}
	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 = a + (z * ((x / t_1) + (y / t_1)))
    if (t <= (-1.26d+159)) then
        tmp = t_2
    else if (t <= (-8.5d+120)) then
        tmp = a / (t_1 / (y + t))
    else if ((t <= (-540000000000.0d0)) .or. (.not. (t <= 6.5d+31))) then
        tmp = t_2
    else
        tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a + (z * ((x / t_1) + (y / t_1)));
	double tmp;
	if (t <= -1.26e+159) {
		tmp = t_2;
	} else if (t <= -8.5e+120) {
		tmp = a / (t_1 / (y + t));
	} else if ((t <= -540000000000.0) || !(t <= 6.5e+31)) {
		tmp = t_2;
	} else {
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a + (z * ((x / t_1) + (y / t_1)))
	tmp = 0
	if t <= -1.26e+159:
		tmp = t_2
	elif t <= -8.5e+120:
		tmp = a / (t_1 / (y + t))
	elif (t <= -540000000000.0) or not (t <= 6.5e+31):
		tmp = t_2
	else:
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a + Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))))
	tmp = 0.0
	if (t <= -1.26e+159)
		tmp = t_2;
	elseif (t <= -8.5e+120)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif ((t <= -540000000000.0) || !(t <= 6.5e+31))
		tmp = t_2;
	else
		tmp = Float64(Float64(z + Float64(a / Float64(Float64(x + y) / y))) - Float64(b / Float64(Float64(x / y) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a + (z * ((x / t_1) + (y / t_1)));
	tmp = 0.0;
	if (t <= -1.26e+159)
		tmp = t_2;
	elseif (t <= -8.5e+120)
		tmp = a / (t_1 / (y + t));
	elseif ((t <= -540000000000.0) || ~((t <= 6.5e+31)))
		tmp = t_2;
	else
		tmp = (z + (a / ((x + y) / y))) - (b / ((x / y) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+159], t$95$2, If[LessEqual[t, -8.5e+120], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -540000000000.0], N[Not[LessEqual[t, 6.5e+31]], $MachinePrecision]], t$95$2, N[(N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2599999999999999e159 or -8.50000000000000026e120 < t < -5.4e11 or 6.5000000000000004e31 < t

   1. Initial program 52.5%

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

   2. Taylor expanded in z around 0 65.0%

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

      1. associate--l+ 65.0%

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

      2. associate-+r+ 65.0%

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

      3. associate-+r+ 65.0%

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

      4. div-sub 65.0%

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

      5. *-commutative 65.0%

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

      6. associate-+r+ 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in t around inf 76.9%

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

   if -1.2599999999999999e159 < t < -8.50000000000000026e120

   1. Initial program 41.0%

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

   2. Taylor expanded in a around inf 40.8%

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

      1. associate-/l* 87.7%

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

      2. associate-+r+ 87.7%

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

   4. Simplified 87.7%

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

   if -5.4e11 < t < 6.5000000000000004e31

   1. Initial program 62.3%

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

   2. Taylor expanded in z around 0 77.2%

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

      1. associate--l+ 77.2%

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

      2. associate-+r+ 77.2%

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

      3. associate-+r+ 77.2%

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

      4. div-sub 77.2%

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

      5. *-commutative 77.2%

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

      6. associate-+r+ 77.2%

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

   4. Simplified 77.2%

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

   5. Taylor expanded in x around inf 75.4%

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

   6. Taylor expanded in t around 0 73.1%

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

      1. associate-/l* 79.8%

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

      2. +-commutative 79.8%

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

      3. associate-/l* 95.0%

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

      4. +-commutative 95.0%

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

   8. Simplified 95.0%

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

   9. Taylor expanded in y around 0 95.0%

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

       1. +-commutative 95.0%

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

   11. Simplified 95.0%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+159}:\\ \;\;\;\;a + z \cdot \left(\frac{x}{y + \left(x + t\right)} + \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+120}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;t \leq -540000000000 \lor \neg \left(t \leq 6.5 \cdot 10^{+31}\right):\\ \;\;\;\;a + z \cdot \left(\frac{x}{y + \left(x + t\right)} + \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - \frac{b}{\frac{x}{y} + 1}\\ \end{array} \]

Alternative 5: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y}{y}\\ t_2 := \left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+160}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+120}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t + \left(x + y\right)}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-106}:\\ \;\;\;\;z - \frac{b}{t_1}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-266}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+31}:\\ \;\;\;\;\left(z + \frac{a}{t_1}\right) - b\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x y) y)) (t_2 (- (+ z a) (/ (* y b) (+ y t)))))
   (if (<= t -4.5e+160)
     (+ a (* z (/ (+ x y) t)))
     (if (<= t -2.5e+120)
       (* (+ y t) (/ a (+ t (+ x y))))
       (if (<= t -2.7e-29)
         t_2
         (if (<= t -3e-106)
           (- z (/ b t_1))
           (if (<= t 1.35e-266)
             (+ z (/ (* y (- a b)) (+ x y)))
             (if (<= t 1.9e+31)
               (- (+ z (/ a t_1)) b)
               (if (<= t 5e+154) t_2 (+ a (/ z (/ t (+ x y)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) / y;
	double t_2 = (z + a) - ((y * b) / (y + t));
	double tmp;
	if (t <= -4.5e+160) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= -2.5e+120) {
		tmp = (y + t) * (a / (t + (x + y)));
	} else if (t <= -2.7e-29) {
		tmp = t_2;
	} else if (t <= -3e-106) {
		tmp = z - (b / t_1);
	} else if (t <= 1.35e-266) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (t <= 1.9e+31) {
		tmp = (z + (a / t_1)) - b;
	} else if (t <= 5e+154) {
		tmp = t_2;
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + y) / y
    t_2 = (z + a) - ((y * b) / (y + t))
    if (t <= (-4.5d+160)) then
        tmp = a + (z * ((x + y) / t))
    else if (t <= (-2.5d+120)) then
        tmp = (y + t) * (a / (t + (x + y)))
    else if (t <= (-2.7d-29)) then
        tmp = t_2
    else if (t <= (-3d-106)) then
        tmp = z - (b / t_1)
    else if (t <= 1.35d-266) then
        tmp = z + ((y * (a - b)) / (x + y))
    else if (t <= 1.9d+31) then
        tmp = (z + (a / t_1)) - b
    else if (t <= 5d+154) then
        tmp = t_2
    else
        tmp = a + (z / (t / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) / y;
	double t_2 = (z + a) - ((y * b) / (y + t));
	double tmp;
	if (t <= -4.5e+160) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= -2.5e+120) {
		tmp = (y + t) * (a / (t + (x + y)));
	} else if (t <= -2.7e-29) {
		tmp = t_2;
	} else if (t <= -3e-106) {
		tmp = z - (b / t_1);
	} else if (t <= 1.35e-266) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (t <= 1.9e+31) {
		tmp = (z + (a / t_1)) - b;
	} else if (t <= 5e+154) {
		tmp = t_2;
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) / y
	t_2 = (z + a) - ((y * b) / (y + t))
	tmp = 0
	if t <= -4.5e+160:
		tmp = a + (z * ((x + y) / t))
	elif t <= -2.5e+120:
		tmp = (y + t) * (a / (t + (x + y)))
	elif t <= -2.7e-29:
		tmp = t_2
	elif t <= -3e-106:
		tmp = z - (b / t_1)
	elif t <= 1.35e-266:
		tmp = z + ((y * (a - b)) / (x + y))
	elif t <= 1.9e+31:
		tmp = (z + (a / t_1)) - b
	elif t <= 5e+154:
		tmp = t_2
	else:
		tmp = a + (z / (t / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) / y)
	t_2 = Float64(Float64(z + a) - Float64(Float64(y * b) / Float64(y + t)))
	tmp = 0.0
	if (t <= -4.5e+160)
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / t)));
	elseif (t <= -2.5e+120)
		tmp = Float64(Float64(y + t) * Float64(a / Float64(t + Float64(x + y))));
	elseif (t <= -2.7e-29)
		tmp = t_2;
	elseif (t <= -3e-106)
		tmp = Float64(z - Float64(b / t_1));
	elseif (t <= 1.35e-266)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	elseif (t <= 1.9e+31)
		tmp = Float64(Float64(z + Float64(a / t_1)) - b);
	elseif (t <= 5e+154)
		tmp = t_2;
	else
		tmp = Float64(a + Float64(z / Float64(t / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) / y;
	t_2 = (z + a) - ((y * b) / (y + t));
	tmp = 0.0;
	if (t <= -4.5e+160)
		tmp = a + (z * ((x + y) / t));
	elseif (t <= -2.5e+120)
		tmp = (y + t) * (a / (t + (x + y)));
	elseif (t <= -2.7e-29)
		tmp = t_2;
	elseif (t <= -3e-106)
		tmp = z - (b / t_1);
	elseif (t <= 1.35e-266)
		tmp = z + ((y * (a - b)) / (x + y));
	elseif (t <= 1.9e+31)
		tmp = (z + (a / t_1)) - b;
	elseif (t <= 5e+154)
		tmp = t_2;
	else
		tmp = a + (z / (t / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+160], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.5e+120], N[(N[(y + t), $MachinePrecision] * N[(a / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.7e-29], t$95$2, If[LessEqual[t, -3e-106], N[(z - N[(b / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-266], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+31], N[(N[(z + N[(a / t$95$1), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 5e+154], t$95$2, N[(a + N[(z / N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -4.4999999999999998e160

   1. Initial program 42.3%

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

   2. Taylor expanded in z around 0 55.4%

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

      1. associate--l+ 55.4%

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

      2. associate-+r+ 55.4%

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

      3. associate-+r+ 55.4%

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

      4. div-sub 55.4%

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

      5. *-commutative 55.4%

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

      6. associate-+r+ 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in t around inf 76.5%

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

   6. Taylor expanded in t around inf 70.1%

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

      1. +-commutative 70.1%

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

   8. Simplified 70.1%

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

   if -4.4999999999999998e160 < t < -2.50000000000000009e120

   1. Initial program 41.0%

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

   2. Taylor expanded in a around inf 40.8%

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

      1. associate-/l* 87.7%

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

      2. associate-+r+ 87.7%

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

   4. Simplified 87.7%

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

      1. associate-/r/ 86.8%

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

      2. associate-+l+ 86.8%

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

      3. +-commutative 86.8%

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

   6. Applied egg-rr 86.8%

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

   if -2.50000000000000009e120 < t < -2.70000000000000023e-29 or 1.9000000000000001e31 < t < 5.00000000000000004e154

   1. Initial program 66.4%

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

   2. Taylor expanded in z around 0 80.0%

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

      1. associate--l+ 80.0%

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

      2. associate-+r+ 80.0%

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

      3. associate-+r+ 80.0%

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

      4. div-sub 80.0%

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

      5. *-commutative 80.0%

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

      6. associate-+r+ 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in x around inf 71.7%

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

   6. Taylor expanded in x around 0 69.0%

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

      1. *-commutative 69.0%

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

      2. +-commutative 69.0%

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

   8. Simplified 69.0%

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

   if -2.70000000000000023e-29 < t < -3.00000000000000019e-106

   1. Initial program 55.4%

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

   2. Taylor expanded in z around 0 65.1%

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

      1. associate--l+ 65.1%

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

      2. associate-+r+ 65.1%

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

      3. associate-+r+ 65.1%

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

      4. div-sub 65.1%

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

      5. *-commutative 65.1%

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

      6. associate-+r+ 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in x around inf 65.1%

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

   6. Taylor expanded in t around 0 54.9%

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

      1. associate-/l* 55.1%

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

      2. +-commutative 55.1%

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

      3. associate-/l* 89.9%

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

      4. +-commutative 89.9%

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

   8. Simplified 89.9%

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

   9. Taylor expanded in z around inf 88.0%

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

   if -3.00000000000000019e-106 < t < 1.34999999999999998e-266

   1. Initial program 73.0%

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

   2. Taylor expanded in z around 0 83.5%

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

      1. associate--l+ 83.5%

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

      2. associate-+r+ 83.5%

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

      3. associate-+r+ 83.5%

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

      4. div-sub 83.4%

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

      5. *-commutative 83.4%

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

      6. associate-+r+ 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in x around inf 83.5%

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

   6. Taylor expanded in t around 0 83.5%

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

      1. distribute-rgt-out-- 83.5%

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

      2. +-commutative 83.5%

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

   8. Simplified 83.5%

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

   if 1.34999999999999998e-266 < t < 1.9000000000000001e31

   1. Initial program 54.2%

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

   2. Taylor expanded in z around 0 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-+r+ 74.2%

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

      3. associate-+r+ 74.2%

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

      4. div-sub 74.2%

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

      5. *-commutative 74.2%

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

      6. associate-+r+ 74.2%

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

   4. Simplified 74.2%

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

   5. Taylor expanded in x around inf 70.0%

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

   6. Taylor expanded in t around 0 68.3%

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

      1. associate-/l* 78.4%

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

      2. +-commutative 78.4%

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

      3. associate-/l* 93.9%

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

      4. +-commutative 93.9%

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

   8. Simplified 93.9%

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

   9. Taylor expanded in y around inf 78.8%

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

   if 5.00000000000000004e154 < t

   1. Initial program 44.5%

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

   2. Taylor expanded in z around 0 55.7%

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

      1. associate--l+ 55.7%

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

      2. associate-+r+ 55.7%

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

      3. associate-+r+ 55.7%

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

      4. div-sub 55.8%

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

      5. *-commutative 55.8%

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

      6. associate-+r+ 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in t around inf 80.3%

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

   6. Taylor expanded in t around inf 62.4%

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

      1. associate-/l* 74.5%

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

      2. +-commutative 74.5%

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

   8. Simplified 74.5%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+160}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+120}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t + \left(x + y\right)}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-29}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-106}:\\ \;\;\;\;z - \frac{b}{\frac{x + y}{y}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-266}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+31}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - b\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \]

Alternative 6: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y}{y}\\ t_2 := \left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{if}\;t \leq -2 \cdot 10^{+159}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+119}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-107}:\\ \;\;\;\;z - \frac{b}{t_1}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-266}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+31}:\\ \;\;\;\;\left(z + \frac{a}{t_1}\right) - b\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x y) y)) (t_2 (- (+ z a) (/ (* y b) (+ y t)))))
   (if (<= t -2e+159)
     (+ a (* z (/ (+ x y) t)))
     (if (<= t -9e+119)
       (/ a (/ (+ y (+ x t)) (+ y t)))
       (if (<= t -8.6e-23)
         t_2
         (if (<= t -8.5e-107)
           (- z (/ b t_1))
           (if (<= t 1.25e-266)
             (+ z (/ (* y (- a b)) (+ x y)))
             (if (<= t 5.8e+31)
               (- (+ z (/ a t_1)) b)
               (if (<= t 1.6e+154) t_2 (+ a (/ z (/ t (+ x y)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) / y;
	double t_2 = (z + a) - ((y * b) / (y + t));
	double tmp;
	if (t <= -2e+159) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= -9e+119) {
		tmp = a / ((y + (x + t)) / (y + t));
	} else if (t <= -8.6e-23) {
		tmp = t_2;
	} else if (t <= -8.5e-107) {
		tmp = z - (b / t_1);
	} else if (t <= 1.25e-266) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (t <= 5.8e+31) {
		tmp = (z + (a / t_1)) - b;
	} else if (t <= 1.6e+154) {
		tmp = t_2;
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + y) / y
    t_2 = (z + a) - ((y * b) / (y + t))
    if (t <= (-2d+159)) then
        tmp = a + (z * ((x + y) / t))
    else if (t <= (-9d+119)) then
        tmp = a / ((y + (x + t)) / (y + t))
    else if (t <= (-8.6d-23)) then
        tmp = t_2
    else if (t <= (-8.5d-107)) then
        tmp = z - (b / t_1)
    else if (t <= 1.25d-266) then
        tmp = z + ((y * (a - b)) / (x + y))
    else if (t <= 5.8d+31) then
        tmp = (z + (a / t_1)) - b
    else if (t <= 1.6d+154) then
        tmp = t_2
    else
        tmp = a + (z / (t / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) / y;
	double t_2 = (z + a) - ((y * b) / (y + t));
	double tmp;
	if (t <= -2e+159) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= -9e+119) {
		tmp = a / ((y + (x + t)) / (y + t));
	} else if (t <= -8.6e-23) {
		tmp = t_2;
	} else if (t <= -8.5e-107) {
		tmp = z - (b / t_1);
	} else if (t <= 1.25e-266) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (t <= 5.8e+31) {
		tmp = (z + (a / t_1)) - b;
	} else if (t <= 1.6e+154) {
		tmp = t_2;
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) / y
	t_2 = (z + a) - ((y * b) / (y + t))
	tmp = 0
	if t <= -2e+159:
		tmp = a + (z * ((x + y) / t))
	elif t <= -9e+119:
		tmp = a / ((y + (x + t)) / (y + t))
	elif t <= -8.6e-23:
		tmp = t_2
	elif t <= -8.5e-107:
		tmp = z - (b / t_1)
	elif t <= 1.25e-266:
		tmp = z + ((y * (a - b)) / (x + y))
	elif t <= 5.8e+31:
		tmp = (z + (a / t_1)) - b
	elif t <= 1.6e+154:
		tmp = t_2
	else:
		tmp = a + (z / (t / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) / y)
	t_2 = Float64(Float64(z + a) - Float64(Float64(y * b) / Float64(y + t)))
	tmp = 0.0
	if (t <= -2e+159)
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / t)));
	elseif (t <= -9e+119)
		tmp = Float64(a / Float64(Float64(y + Float64(x + t)) / Float64(y + t)));
	elseif (t <= -8.6e-23)
		tmp = t_2;
	elseif (t <= -8.5e-107)
		tmp = Float64(z - Float64(b / t_1));
	elseif (t <= 1.25e-266)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	elseif (t <= 5.8e+31)
		tmp = Float64(Float64(z + Float64(a / t_1)) - b);
	elseif (t <= 1.6e+154)
		tmp = t_2;
	else
		tmp = Float64(a + Float64(z / Float64(t / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) / y;
	t_2 = (z + a) - ((y * b) / (y + t));
	tmp = 0.0;
	if (t <= -2e+159)
		tmp = a + (z * ((x + y) / t));
	elseif (t <= -9e+119)
		tmp = a / ((y + (x + t)) / (y + t));
	elseif (t <= -8.6e-23)
		tmp = t_2;
	elseif (t <= -8.5e-107)
		tmp = z - (b / t_1);
	elseif (t <= 1.25e-266)
		tmp = z + ((y * (a - b)) / (x + y));
	elseif (t <= 5.8e+31)
		tmp = (z + (a / t_1)) - b;
	elseif (t <= 1.6e+154)
		tmp = t_2;
	else
		tmp = a + (z / (t / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+159], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e+119], N[(a / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.6e-23], t$95$2, If[LessEqual[t, -8.5e-107], N[(z - N[(b / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-266], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+31], N[(N[(z + N[(a / t$95$1), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 1.6e+154], t$95$2, N[(a + N[(z / N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.9999999999999999e159

   1. Initial program 42.3%

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

   2. Taylor expanded in z around 0 55.4%

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

      1. associate--l+ 55.4%

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

      2. associate-+r+ 55.4%

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

      3. associate-+r+ 55.4%

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

      4. div-sub 55.4%

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

      5. *-commutative 55.4%

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

      6. associate-+r+ 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in t around inf 76.5%

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

   6. Taylor expanded in t around inf 70.1%

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

      1. +-commutative 70.1%

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

   8. Simplified 70.1%

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

   if -1.9999999999999999e159 < t < -9.00000000000000039e119

   1. Initial program 41.0%

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

   2. Taylor expanded in a around inf 40.8%

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

      1. associate-/l* 87.7%

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

      2. associate-+r+ 87.7%

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

   4. Simplified 87.7%

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

   if -9.00000000000000039e119 < t < -8.60000000000000004e-23 or 5.8000000000000001e31 < t < 1.6e154

   1. Initial program 66.4%

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

   2. Taylor expanded in z around 0 80.0%

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

      1. associate--l+ 80.0%

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

      2. associate-+r+ 80.0%

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

      3. associate-+r+ 80.0%

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

      4. div-sub 80.0%

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

      5. *-commutative 80.0%

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

      6. associate-+r+ 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in x around inf 71.7%

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

   6. Taylor expanded in x around 0 69.0%

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

      1. *-commutative 69.0%

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

      2. +-commutative 69.0%

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

   8. Simplified 69.0%

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

   if -8.60000000000000004e-23 < t < -8.49999999999999956e-107

   1. Initial program 55.4%

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

   2. Taylor expanded in z around 0 65.1%

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

      1. associate--l+ 65.1%

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

      2. associate-+r+ 65.1%

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

      3. associate-+r+ 65.1%

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

      4. div-sub 65.1%

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

      5. *-commutative 65.1%

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

      6. associate-+r+ 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in x around inf 65.1%

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

   6. Taylor expanded in t around 0 54.9%

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

      1. associate-/l* 55.1%

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

      2. +-commutative 55.1%

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

      3. associate-/l* 89.9%

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

      4. +-commutative 89.9%

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

   8. Simplified 89.9%

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

   9. Taylor expanded in z around inf 88.0%

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

   if -8.49999999999999956e-107 < t < 1.24999999999999998e-266

   1. Initial program 73.0%

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

   2. Taylor expanded in z around 0 83.5%

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

      1. associate--l+ 83.5%

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

      2. associate-+r+ 83.5%

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

      3. associate-+r+ 83.5%

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

      4. div-sub 83.4%

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

      5. *-commutative 83.4%

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

      6. associate-+r+ 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in x around inf 83.5%

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

   6. Taylor expanded in t around 0 83.5%

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

      1. distribute-rgt-out-- 83.5%

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

      2. +-commutative 83.5%

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

   8. Simplified 83.5%

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

   if 1.24999999999999998e-266 < t < 5.8000000000000001e31

   1. Initial program 54.2%

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

   2. Taylor expanded in z around 0 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-+r+ 74.2%

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

      3. associate-+r+ 74.2%

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

      4. div-sub 74.2%

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

      5. *-commutative 74.2%

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

      6. associate-+r+ 74.2%

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

   4. Simplified 74.2%

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

   5. Taylor expanded in x around inf 70.0%

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

   6. Taylor expanded in t around 0 68.3%

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

      1. associate-/l* 78.4%

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

      2. +-commutative 78.4%

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

      3. associate-/l* 93.9%

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

      4. +-commutative 93.9%

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

   8. Simplified 93.9%

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

   9. Taylor expanded in y around inf 78.8%

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

   if 1.6e154 < t

   1. Initial program 44.5%

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

   2. Taylor expanded in z around 0 55.7%

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

      1. associate--l+ 55.7%

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

      2. associate-+r+ 55.7%

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

      3. associate-+r+ 55.7%

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

      4. div-sub 55.8%

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

      5. *-commutative 55.8%

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

      6. associate-+r+ 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in t around inf 80.3%

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

   6. Taylor expanded in t around inf 62.4%

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

      1. associate-/l* 74.5%

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

      2. +-commutative 74.5%

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

   8. Simplified 74.5%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+159}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+119}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-23}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-107}:\\ \;\;\;\;z - \frac{b}{\frac{x + y}{y}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-266}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+31}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - b\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \]

Alternative 7: 71.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(z + \frac{a}{\frac{x + y}{y}}\right) - b\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-106}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (- (* (+ y t) a) (* y b)) (+ y (+ x t)))))
        (t_2 (- (+ z (/ a (/ (+ x y) y))) b)))
   (if (<= y -2.4e+73)
     t_2
     (if (<= y 2.55e-288)
       t_1
       (if (<= y 2.3e-106)
         (/ (+ (* t a) (* x z)) (+ x t))
         (if (<= y 4e+106) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((((y + t) * a) - (y * b)) / (y + (x + t)));
	double t_2 = (z + (a / ((x + y) / y))) - b;
	double tmp;
	if (y <= -2.4e+73) {
		tmp = t_2;
	} else if (y <= 2.55e-288) {
		tmp = t_1;
	} else if (y <= 2.3e-106) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4e+106) {
		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 + ((((y + t) * a) - (y * b)) / (y + (x + t)))
    t_2 = (z + (a / ((x + y) / y))) - b
    if (y <= (-2.4d+73)) then
        tmp = t_2
    else if (y <= 2.55d-288) then
        tmp = t_1
    else if (y <= 2.3d-106) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 4d+106) 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 + ((((y + t) * a) - (y * b)) / (y + (x + t)));
	double t_2 = (z + (a / ((x + y) / y))) - b;
	double tmp;
	if (y <= -2.4e+73) {
		tmp = t_2;
	} else if (y <= 2.55e-288) {
		tmp = t_1;
	} else if (y <= 2.3e-106) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + ((((y + t) * a) - (y * b)) / (y + (x + t)))
	t_2 = (z + (a / ((x + y) / y))) - b
	tmp = 0
	if y <= -2.4e+73:
		tmp = t_2
	elif y <= 2.55e-288:
		tmp = t_1
	elif y <= 2.3e-106:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 4e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / Float64(y + Float64(x + t))))
	t_2 = Float64(Float64(z + Float64(a / Float64(Float64(x + y) / y))) - b)
	tmp = 0.0
	if (y <= -2.4e+73)
		tmp = t_2;
	elseif (y <= 2.55e-288)
		tmp = t_1;
	elseif (y <= 2.3e-106)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 4e+106)
		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 + ((((y + t) * a) - (y * b)) / (y + (x + t)));
	t_2 = (z + (a / ((x + y) / y))) - b;
	tmp = 0.0;
	if (y <= -2.4e+73)
		tmp = t_2;
	elseif (y <= 2.55e-288)
		tmp = t_1;
	elseif (y <= 2.3e-106)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 4e+106)
		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[(z + N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.4e+73], t$95$2, If[LessEqual[y, 2.55e-288], t$95$1, If[LessEqual[y, 2.3e-106], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+106], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000002e73 or 4.00000000000000036e106 < y

   1. Initial program 33.5%

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

   2. Taylor expanded in z around 0 49.2%

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

      1. associate--l+ 49.2%

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

      2. associate-+r+ 49.2%

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

      3. associate-+r+ 49.2%

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

      4. div-sub 49.2%

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

      5. *-commutative 49.2%

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

      6. associate-+r+ 49.2%

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

   4. Simplified 49.2%

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

   5. Taylor expanded in x around inf 41.9%

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

   6. Taylor expanded in t around 0 43.6%

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

      1. associate-/l* 60.8%

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

      2. +-commutative 60.8%

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

      3. associate-/l* 86.9%

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

      4. +-commutative 86.9%

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

   8. Simplified 86.9%

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

   9. Taylor expanded in y around inf 82.0%

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

   if -2.40000000000000002e73 < y < 2.54999999999999997e-288 or 2.3000000000000001e-106 < y < 4.00000000000000036e106

   1. Initial program 71.3%

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

   2. Taylor expanded in z around 0 84.0%

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

      1. associate--l+ 84.0%

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

      2. associate-+r+ 84.0%

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

      3. associate-+r+ 84.0%

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

      4. div-sub 84.0%

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

      5. *-commutative 84.0%

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

      6. associate-+r+ 84.0%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in x around inf 72.5%

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

   if 2.54999999999999997e-288 < y < 2.3000000000000001e-106

   1. Initial program 77.8%

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

   2. Taylor expanded in y around 0 77.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - b\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-288}:\\ \;\;\;\;z + \frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-106}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+106}:\\ \;\;\;\;z + \frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - b\\ \end{array} \]

Alternative 8: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + \frac{a}{\frac{x + y}{y}}\right) - y \cdot \frac{b}{x + y}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+187}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z (/ a (/ (+ x y) y))) (* y (/ b (+ x y))))))
   (if (<= t -9.5e+187)
     (+ a (* z (/ (+ x y) t)))
     (if (<= t 7e+31)
       t_1
       (if (<= t 3.6e+77)
         (- (+ z a) (/ (* y b) (+ y t)))
         (if (<= t 8e+180) t_1 (+ a (/ z (/ t (+ x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (a / ((x + y) / y))) - (y * (b / (x + y)));
	double tmp;
	if (t <= -9.5e+187) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= 7e+31) {
		tmp = t_1;
	} else if (t <= 3.6e+77) {
		tmp = (z + a) - ((y * b) / (y + t));
	} else if (t <= 8e+180) {
		tmp = t_1;
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + (a / ((x + y) / y))) - (y * (b / (x + y)))
    if (t <= (-9.5d+187)) then
        tmp = a + (z * ((x + y) / t))
    else if (t <= 7d+31) then
        tmp = t_1
    else if (t <= 3.6d+77) then
        tmp = (z + a) - ((y * b) / (y + t))
    else if (t <= 8d+180) then
        tmp = t_1
    else
        tmp = a + (z / (t / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (a / ((x + y) / y))) - (y * (b / (x + y)));
	double tmp;
	if (t <= -9.5e+187) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= 7e+31) {
		tmp = t_1;
	} else if (t <= 3.6e+77) {
		tmp = (z + a) - ((y * b) / (y + t));
	} else if (t <= 8e+180) {
		tmp = t_1;
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (a / ((x + y) / y))) - (y * (b / (x + y)))
	tmp = 0
	if t <= -9.5e+187:
		tmp = a + (z * ((x + y) / t))
	elif t <= 7e+31:
		tmp = t_1
	elif t <= 3.6e+77:
		tmp = (z + a) - ((y * b) / (y + t))
	elif t <= 8e+180:
		tmp = t_1
	else:
		tmp = a + (z / (t / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(a / Float64(Float64(x + y) / y))) - Float64(y * Float64(b / Float64(x + y))))
	tmp = 0.0
	if (t <= -9.5e+187)
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / t)));
	elseif (t <= 7e+31)
		tmp = t_1;
	elseif (t <= 3.6e+77)
		tmp = Float64(Float64(z + a) - Float64(Float64(y * b) / Float64(y + t)));
	elseif (t <= 8e+180)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(z / Float64(t / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (a / ((x + y) / y))) - (y * (b / (x + y)));
	tmp = 0.0;
	if (t <= -9.5e+187)
		tmp = a + (z * ((x + y) / t));
	elseif (t <= 7e+31)
		tmp = t_1;
	elseif (t <= 3.6e+77)
		tmp = (z + a) - ((y * b) / (y + t));
	elseif (t <= 8e+180)
		tmp = t_1;
	else
		tmp = a + (z / (t / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+187], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+31], t$95$1, If[LessEqual[t, 3.6e+77], N[(N[(z + a), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+180], t$95$1, N[(a + N[(z / N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.4999999999999996e187

   1. Initial program 40.8%

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

   2. Taylor expanded in z around 0 52.2%

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

      1. associate--l+ 52.2%

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

      2. associate-+r+ 52.2%

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

      3. associate-+r+ 52.2%

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

      4. div-sub 52.2%

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

      5. *-commutative 52.2%

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

      6. associate-+r+ 52.2%

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

   4. Simplified 52.2%

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

   5. Taylor expanded in t around inf 80.4%

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

   6. Taylor expanded in t around inf 76.6%

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

      1. +-commutative 76.6%

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

   8. Simplified 76.6%

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

   if -9.4999999999999996e187 < t < 7e31 or 3.5999999999999998e77 < t < 8.0000000000000001e180

   1. Initial program 59.0%

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

   2. Taylor expanded in z around 0 73.1%

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

      1. associate--l+ 73.1%

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

      2. associate-+r+ 73.1%

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

      3. associate-+r+ 73.1%

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

      4. div-sub 73.1%

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

      5. *-commutative 73.1%

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

      6. associate-+r+ 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in x around inf 69.7%

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

   6. Taylor expanded in t around 0 64.7%

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

      1. associate-/l* 72.6%

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

      2. +-commutative 72.6%

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

      3. associate-/l* 86.4%

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

      4. +-commutative 86.4%

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

   8. Simplified 86.4%

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

      1. associate-/r/ 84.8%

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

   10. Applied egg-rr 84.8%

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

   if 7e31 < t < 3.5999999999999998e77

   1. Initial program 85.7%

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

   2. Taylor expanded in z around 0 93.0%

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

      1. associate--l+ 93.0%

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

      2. associate-+r+ 93.0%

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

      3. associate-+r+ 93.0%

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

      4. div-sub 93.0%

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

      5. *-commutative 93.0%

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

      6. associate-+r+ 93.0%

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

   4. Simplified 93.0%

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

   5. Taylor expanded in x around inf 78.8%

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

   6. Taylor expanded in x around 0 82.7%

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

      1. *-commutative 82.7%

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

      2. +-commutative 82.7%

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

   8. Simplified 82.7%

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

   if 8.0000000000000001e180 < t

   1. Initial program 48.5%

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

   2. Taylor expanded in z around 0 61.0%

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

      1. associate--l+ 61.0%

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

      2. associate-+r+ 61.0%

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

      3. associate-+r+ 61.0%

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

      4. div-sub 61.0%

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

      5. *-commutative 61.0%

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

      6. associate-+r+ 61.0%

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

   4. Simplified 61.0%

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

   5. Taylor expanded in t around inf 80.9%

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

   6. Taylor expanded in t around inf 61.1%

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

      1. associate-/l* 74.4%

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

      2. +-commutative 74.4%

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

   8. Simplified 74.4%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+187}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+31}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - y \cdot \frac{b}{x + y}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+180}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - y \cdot \frac{b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \]

Alternative 9: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+189}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+31}:\\ \;\;\;\;t_1 - \frac{b}{\frac{x}{y} + 1}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+180}:\\ \;\;\;\;t_1 - y \cdot \frac{b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ a (/ (+ x y) y)))))
   (if (<= t -2.9e+189)
     (+ a (* z (/ (+ x y) t)))
     (if (<= t 4.8e+31)
       (- t_1 (/ b (+ (/ x y) 1.0)))
       (if (<= t 3.6e+77)
         (- (+ z a) (/ (* y b) (+ y t)))
         (if (<= t 1.9e+180)
           (- t_1 (* y (/ b (+ x y))))
           (+ a (/ z (/ t (+ x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a / ((x + y) / y));
	double tmp;
	if (t <= -2.9e+189) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= 4.8e+31) {
		tmp = t_1 - (b / ((x / y) + 1.0));
	} else if (t <= 3.6e+77) {
		tmp = (z + a) - ((y * b) / (y + t));
	} else if (t <= 1.9e+180) {
		tmp = t_1 - (y * (b / (x + y)));
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (a / ((x + y) / y))
    if (t <= (-2.9d+189)) then
        tmp = a + (z * ((x + y) / t))
    else if (t <= 4.8d+31) then
        tmp = t_1 - (b / ((x / y) + 1.0d0))
    else if (t <= 3.6d+77) then
        tmp = (z + a) - ((y * b) / (y + t))
    else if (t <= 1.9d+180) then
        tmp = t_1 - (y * (b / (x + y)))
    else
        tmp = a + (z / (t / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a / ((x + y) / y));
	double tmp;
	if (t <= -2.9e+189) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= 4.8e+31) {
		tmp = t_1 - (b / ((x / y) + 1.0));
	} else if (t <= 3.6e+77) {
		tmp = (z + a) - ((y * b) / (y + t));
	} else if (t <= 1.9e+180) {
		tmp = t_1 - (y * (b / (x + y)));
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (a / ((x + y) / y))
	tmp = 0
	if t <= -2.9e+189:
		tmp = a + (z * ((x + y) / t))
	elif t <= 4.8e+31:
		tmp = t_1 - (b / ((x / y) + 1.0))
	elif t <= 3.6e+77:
		tmp = (z + a) - ((y * b) / (y + t))
	elif t <= 1.9e+180:
		tmp = t_1 - (y * (b / (x + y)))
	else:
		tmp = a + (z / (t / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(a / Float64(Float64(x + y) / y)))
	tmp = 0.0
	if (t <= -2.9e+189)
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / t)));
	elseif (t <= 4.8e+31)
		tmp = Float64(t_1 - Float64(b / Float64(Float64(x / y) + 1.0)));
	elseif (t <= 3.6e+77)
		tmp = Float64(Float64(z + a) - Float64(Float64(y * b) / Float64(y + t)));
	elseif (t <= 1.9e+180)
		tmp = Float64(t_1 - Float64(y * Float64(b / Float64(x + y))));
	else
		tmp = Float64(a + Float64(z / Float64(t / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (a / ((x + y) / y));
	tmp = 0.0;
	if (t <= -2.9e+189)
		tmp = a + (z * ((x + y) / t));
	elseif (t <= 4.8e+31)
		tmp = t_1 - (b / ((x / y) + 1.0));
	elseif (t <= 3.6e+77)
		tmp = (z + a) - ((y * b) / (y + t));
	elseif (t <= 1.9e+180)
		tmp = t_1 - (y * (b / (x + y)));
	else
		tmp = a + (z / (t / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+189], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+31], N[(t$95$1 - N[(b / N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+77], N[(N[(z + a), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+180], N[(t$95$1 - N[(y * N[(b / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z / N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.90000000000000019e189

   1. Initial program 40.8%

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

   2. Taylor expanded in z around 0 52.2%

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

      1. associate--l+ 52.2%

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

      2. associate-+r+ 52.2%

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

      3. associate-+r+ 52.2%

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

      4. div-sub 52.2%

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

      5. *-commutative 52.2%

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

      6. associate-+r+ 52.2%

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

   4. Simplified 52.2%

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

   5. Taylor expanded in t around inf 80.4%

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

   6. Taylor expanded in t around inf 76.6%

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

      1. +-commutative 76.6%

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

   8. Simplified 76.6%

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

   if -2.90000000000000019e189 < t < 4.79999999999999965e31

   1. Initial program 61.4%

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

   2. Taylor expanded in z around 0 75.4%

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

      1. associate--l+ 75.4%

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

      2. associate-+r+ 75.4%

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

      3. associate-+r+ 75.4%

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

      4. div-sub 75.3%

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

      5. *-commutative 75.3%

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

      6. associate-+r+ 75.3%

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

   4. Simplified 75.3%

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

   5. Taylor expanded in x around inf 72.2%

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

   6. Taylor expanded in t around 0 66.1%

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

      1. associate-/l* 73.1%

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

      2. +-commutative 73.1%

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

      3. associate-/l* 86.6%

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

      4. +-commutative 86.6%

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

   8. Simplified 86.6%

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

   9. Taylor expanded in y around 0 86.7%

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

       1. +-commutative 86.7%

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

   11. Simplified 86.7%

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

   if 4.79999999999999965e31 < t < 3.5999999999999998e77

   1. Initial program 85.7%

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

   2. Taylor expanded in z around 0 93.0%

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

      1. associate--l+ 93.0%

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

      2. associate-+r+ 93.0%

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

      3. associate-+r+ 93.0%

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

      4. div-sub 93.0%

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

      5. *-commutative 93.0%

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

      6. associate-+r+ 93.0%

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

   4. Simplified 93.0%

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

   5. Taylor expanded in x around inf 78.8%

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

   6. Taylor expanded in x around 0 82.7%

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

      1. *-commutative 82.7%

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

      2. +-commutative 82.7%

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

   8. Simplified 82.7%

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

   if 3.5999999999999998e77 < t < 1.9e180

   1. Initial program 37.1%

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

   2. Taylor expanded in z around 0 53.1%

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

      1. associate--l+ 53.1%

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

      2. associate-+r+ 53.1%

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

      3. associate-+r+ 53.1%

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

      4. div-sub 53.1%

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

      5. *-commutative 53.1%

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

      6. associate-+r+ 53.1%

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

   4. Simplified 53.1%

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

   5. Taylor expanded in x around inf 47.5%

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

   6. Taylor expanded in t around 0 52.2%

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

      1. associate-/l* 68.0%

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

      2. +-commutative 68.0%

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

      3. associate-/l* 84.1%

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

      4. +-commutative 84.1%

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

   8. Simplified 84.1%

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

      1. associate-/r/ 84.2%

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

   10. Applied egg-rr 84.2%

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

   if 1.9e180 < t

   1. Initial program 48.5%

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

   2. Taylor expanded in z around 0 61.0%

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

      1. associate--l+ 61.0%

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

      2. associate-+r+ 61.0%

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

      3. associate-+r+ 61.0%

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

      4. div-sub 61.0%

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

      5. *-commutative 61.0%

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

      6. associate-+r+ 61.0%

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

   4. Simplified 61.0%

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

   5. Taylor expanded in t around inf 80.9%

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

   6. Taylor expanded in t around inf 61.1%

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

      1. associate-/l* 74.4%

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

      2. +-commutative 74.4%

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

   8. Simplified 74.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+189}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+31}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - \frac{b}{\frac{x}{y} + 1}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;\left(z + a\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+180}:\\ \;\;\;\;\left(z + \frac{a}{\frac{x + y}{y}}\right) - y \cdot \frac{b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \]

Alternative 10: 61.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \frac{b}{\frac{x + y}{y}}\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{-5}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+96}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t + \left(x + y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (/ b (/ (+ x y) y)))))
   (if (<= a -5.4e-5)
     (+ z a)
     (if (<= a 9.2e+46)
       t_1
       (if (<= a 3e+96)
         (+ a (/ y (/ (+ y t) z)))
         (if (<= a 2.1e+109) t_1 (* (+ y t) (/ a (+ t (+ x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (b / ((x + y) / y));
	double tmp;
	if (a <= -5.4e-5) {
		tmp = z + a;
	} else if (a <= 9.2e+46) {
		tmp = t_1;
	} else if (a <= 3e+96) {
		tmp = a + (y / ((y + t) / z));
	} else if (a <= 2.1e+109) {
		tmp = t_1;
	} else {
		tmp = (y + t) * (a / (t + (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z - (b / ((x + y) / y))
    if (a <= (-5.4d-5)) then
        tmp = z + a
    else if (a <= 9.2d+46) then
        tmp = t_1
    else if (a <= 3d+96) then
        tmp = a + (y / ((y + t) / z))
    else if (a <= 2.1d+109) then
        tmp = t_1
    else
        tmp = (y + t) * (a / (t + (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (b / ((x + y) / y));
	double tmp;
	if (a <= -5.4e-5) {
		tmp = z + a;
	} else if (a <= 9.2e+46) {
		tmp = t_1;
	} else if (a <= 3e+96) {
		tmp = a + (y / ((y + t) / z));
	} else if (a <= 2.1e+109) {
		tmp = t_1;
	} else {
		tmp = (y + t) * (a / (t + (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - (b / ((x + y) / y))
	tmp = 0
	if a <= -5.4e-5:
		tmp = z + a
	elif a <= 9.2e+46:
		tmp = t_1
	elif a <= 3e+96:
		tmp = a + (y / ((y + t) / z))
	elif a <= 2.1e+109:
		tmp = t_1
	else:
		tmp = (y + t) * (a / (t + (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(b / Float64(Float64(x + y) / y)))
	tmp = 0.0
	if (a <= -5.4e-5)
		tmp = Float64(z + a);
	elseif (a <= 9.2e+46)
		tmp = t_1;
	elseif (a <= 3e+96)
		tmp = Float64(a + Float64(y / Float64(Float64(y + t) / z)));
	elseif (a <= 2.1e+109)
		tmp = t_1;
	else
		tmp = Float64(Float64(y + t) * Float64(a / Float64(t + Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z - (b / ((x + y) / y));
	tmp = 0.0;
	if (a <= -5.4e-5)
		tmp = z + a;
	elseif (a <= 9.2e+46)
		tmp = t_1;
	elseif (a <= 3e+96)
		tmp = a + (y / ((y + t) / z));
	elseif (a <= 2.1e+109)
		tmp = t_1;
	else
		tmp = (y + t) * (a / (t + (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(b / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.4e-5], N[(z + a), $MachinePrecision], If[LessEqual[a, 9.2e+46], t$95$1, If[LessEqual[a, 3e+96], N[(a + N[(y / N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+109], t$95$1, N[(N[(y + t), $MachinePrecision] * N[(a / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.3999999999999998e-5

   1. Initial program 51.2%

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

   2. Taylor expanded in z around 0 62.0%

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

      1. associate--l+ 62.0%

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

      2. associate-+r+ 62.0%

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

      3. associate-+r+ 62.0%

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

      4. div-sub 62.0%

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

      5. *-commutative 62.0%

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

      6. associate-+r+ 62.0%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in t around inf 74.1%

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

   6. Taylor expanded in x around inf 68.3%

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

   if -5.3999999999999998e-5 < a < 9.2000000000000002e46 or 3e96 < a < 2.1000000000000001e109

   1. Initial program 66.9%

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

   2. Taylor expanded in z around 0 84.2%

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

      1. associate--l+ 84.2%

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

      2. associate-+r+ 84.2%

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

      3. associate-+r+ 84.2%

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

      4. div-sub 84.2%

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

      5. *-commutative 84.2%

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

      6. associate-+r+ 84.2%

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

   4. Simplified 84.2%

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

   5. Taylor expanded in x around inf 65.1%

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

   6. Taylor expanded in t around 0 56.1%

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

      1. associate-/l* 56.1%

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

      2. +-commutative 56.1%

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

      3. associate-/l* 67.2%

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

      4. +-commutative 67.2%

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

   8. Simplified 67.2%

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

   9. Taylor expanded in z around inf 63.9%

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

   if 9.2000000000000002e46 < a < 3e96

   1. Initial program 67.7%

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

   2. Taylor expanded in z around 0 67.9%

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

      1. associate--l+ 67.9%

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

      2. associate-+r+ 67.9%

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

      3. associate-+r+ 67.9%

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

      4. div-sub 67.9%

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

      5. *-commutative 67.9%

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

      6. associate-+r+ 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in t around inf 82.8%

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

   6. Taylor expanded in x around 0 82.8%

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

      1. associate-/l* 82.8%

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

      2. +-commutative 82.8%

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

   8. Simplified 82.8%

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

   if 2.1000000000000001e109 < a

   1. Initial program 28.4%

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

   2. Taylor expanded in a around inf 26.5%

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

      1. associate-/l* 82.5%

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

      2. associate-+r+ 82.5%

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

   4. Simplified 82.5%

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

      1. associate-/r/ 80.3%

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

      2. associate-+l+ 80.3%

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

      3. +-commutative 80.3%

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

   6. Applied egg-rr 80.3%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-5}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;z - \frac{b}{\frac{x + y}{y}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+96}:\\ \;\;\;\;a + \frac{y}{\frac{y + t}{z}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+109}:\\ \;\;\;\;z - \frac{b}{\frac{x + y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t + \left(x + y\right)}\\ \end{array} \]

Alternative 11: 61.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-5}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;a \leq 60000:\\ \;\;\;\;z - \frac{b}{\frac{x + y}{y}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+109}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t + \left(x + y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1e-5)
   (+ z a)
   (if (<= a 60000.0)
     (- z (/ b (/ (+ x y) y)))
     (if (<= a 2e+109)
       (+ z (/ (* y (- a b)) (+ x y)))
       (* (+ y t) (/ a (+ t (+ x y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1e-5) {
		tmp = z + a;
	} else if (a <= 60000.0) {
		tmp = z - (b / ((x + y) / y));
	} else if (a <= 2e+109) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else {
		tmp = (y + t) * (a / (t + (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1d-5)) then
        tmp = z + a
    else if (a <= 60000.0d0) then
        tmp = z - (b / ((x + y) / y))
    else if (a <= 2d+109) then
        tmp = z + ((y * (a - b)) / (x + y))
    else
        tmp = (y + t) * (a / (t + (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1e-5) {
		tmp = z + a;
	} else if (a <= 60000.0) {
		tmp = z - (b / ((x + y) / y));
	} else if (a <= 2e+109) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else {
		tmp = (y + t) * (a / (t + (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1e-5:
		tmp = z + a
	elif a <= 60000.0:
		tmp = z - (b / ((x + y) / y))
	elif a <= 2e+109:
		tmp = z + ((y * (a - b)) / (x + y))
	else:
		tmp = (y + t) * (a / (t + (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1e-5)
		tmp = Float64(z + a);
	elseif (a <= 60000.0)
		tmp = Float64(z - Float64(b / Float64(Float64(x + y) / y)));
	elseif (a <= 2e+109)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	else
		tmp = Float64(Float64(y + t) * Float64(a / Float64(t + Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1e-5)
		tmp = z + a;
	elseif (a <= 60000.0)
		tmp = z - (b / ((x + y) / y));
	elseif (a <= 2e+109)
		tmp = z + ((y * (a - b)) / (x + y));
	else
		tmp = (y + t) * (a / (t + (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1e-5], N[(z + a), $MachinePrecision], If[LessEqual[a, 60000.0], N[(z - N[(b / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+109], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + t), $MachinePrecision] * N[(a / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.00000000000000008e-5

   1. Initial program 51.2%

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

   2. Taylor expanded in z around 0 62.0%

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

      1. associate--l+ 62.0%

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

      2. associate-+r+ 62.0%

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

      3. associate-+r+ 62.0%

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

      4. div-sub 62.0%

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

      5. *-commutative 62.0%

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

      6. associate-+r+ 62.0%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in t around inf 74.1%

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

   6. Taylor expanded in x around inf 68.3%

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

   if -1.00000000000000008e-5 < a < 6e4

   1. Initial program 65.2%

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

   2. Taylor expanded in z around 0 83.9%

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

      1. associate--l+ 83.9%

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

      2. associate-+r+ 83.9%

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

      3. associate-+r+ 83.9%

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

      4. div-sub 83.9%

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

      5. *-commutative 83.9%

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

      6. associate-+r+ 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in x around inf 62.6%

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

   6. Taylor expanded in t around 0 52.6%

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

      1. associate-/l* 52.6%

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

      2. +-commutative 52.6%

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

      3. associate-/l* 64.2%

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

      4. +-commutative 64.2%

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

   8. Simplified 64.2%

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

   9. Taylor expanded in z around inf 63.5%

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

   if 6e4 < a < 1.99999999999999996e109

   1. Initial program 75.2%

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

   2. Taylor expanded in z around 0 78.6%

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

      1. associate--l+ 78.6%

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

      2. associate-+r+ 78.6%

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

      3. associate-+r+ 78.6%

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

      4. div-sub 78.6%

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

      5. *-commutative 78.6%

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

      6. associate-+r+ 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in x around inf 78.6%

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

   6. Taylor expanded in t around 0 74.8%

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

      1. distribute-rgt-out-- 74.8%

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

      2. +-commutative 74.8%

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

   8. Simplified 74.8%

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

   if 1.99999999999999996e109 < a

   1. Initial program 28.4%

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

   2. Taylor expanded in a around inf 26.5%

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

      1. associate-/l* 82.5%

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

      2. associate-+r+ 82.5%

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

   4. Simplified 82.5%

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

      1. associate-/r/ 80.3%

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

      2. associate-+l+ 80.3%

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

      3. +-commutative 80.3%

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

   6. Applied egg-rr 80.3%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-5}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;a \leq 60000:\\ \;\;\;\;z - \frac{b}{\frac{x + y}{y}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+109}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t + \left(x + y\right)}\\ \end{array} \]

Alternative 12: 62.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+169} \lor \neg \left(t \leq 2.6 \cdot 10^{+152}\right):\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.8e+169) (not (<= t 2.6e+152)))
   (+ a (* z (/ (+ x y) t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.8e+169) || !(t <= 2.6e+152)) {
		tmp = a + (z * ((x + y) / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.8d+169)) .or. (.not. (t <= 2.6d+152))) then
        tmp = a + (z * ((x + y) / t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.8e+169) || !(t <= 2.6e+152)) {
		tmp = a + (z * ((x + y) / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.8e+169) or not (t <= 2.6e+152):
		tmp = a + (z * ((x + y) / t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.8e+169) || !(t <= 2.6e+152))
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.8e+169) || ~((t <= 2.6e+152)))
		tmp = a + (z * ((x + y) / t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.8e+169], N[Not[LessEqual[t, 2.6e+152]], $MachinePrecision]], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8000000000000002e169 or 2.6000000000000001e152 < t

   1. Initial program 43.6%

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

   2. Taylor expanded in z around 0 55.6%

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

      1. associate--l+ 55.6%

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

      2. associate-+r+ 55.6%

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

      3. associate-+r+ 55.6%

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

      4. div-sub 55.6%

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

      5. *-commutative 55.6%

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

      6. associate-+r+ 55.6%

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

   4. Simplified 55.6%

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

   5. Taylor expanded in t around inf 78.7%

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

   6. Taylor expanded in t around inf 72.6%

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

      1. +-commutative 72.6%

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

   8. Simplified 72.6%

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

   if -2.8000000000000002e169 < t < 2.6000000000000001e152

   1. Initial program 62.1%

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

   2. Taylor expanded in y around inf 63.3%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+169} \lor \neg \left(t \leq 2.6 \cdot 10^{+152}\right):\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 13: 59.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-6} \lor \neg \left(a \leq 6.5 \cdot 10^{+16}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b}{\frac{x + y}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -8e-6) (not (<= a 6.5e+16))) (+ z a) (- z (/ b (/ (+ x y) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8e-6) || !(a <= 6.5e+16)) {
		tmp = z + a;
	} else {
		tmp = z - (b / ((x + y) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-8d-6)) .or. (.not. (a <= 6.5d+16))) then
        tmp = z + a
    else
        tmp = z - (b / ((x + y) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8e-6) || !(a <= 6.5e+16)) {
		tmp = z + a;
	} else {
		tmp = z - (b / ((x + y) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -8e-6) or not (a <= 6.5e+16):
		tmp = z + a
	else:
		tmp = z - (b / ((x + y) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -8e-6) || !(a <= 6.5e+16))
		tmp = Float64(z + a);
	else
		tmp = Float64(z - Float64(b / Float64(Float64(x + y) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -8e-6) || ~((a <= 6.5e+16)))
		tmp = z + a;
	else
		tmp = z - (b / ((x + y) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -8e-6], N[Not[LessEqual[a, 6.5e+16]], $MachinePrecision]], N[(z + a), $MachinePrecision], N[(z - N[(b / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.99999999999999964e-6 or 6.5e16 < a

   1. Initial program 46.9%

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

   2. Taylor expanded in z around 0 54.7%

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

      1. associate--l+ 54.7%

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

      2. associate-+r+ 54.7%

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

      3. associate-+r+ 54.7%

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

      4. div-sub 54.7%

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

      5. *-commutative 54.7%

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

      6. associate-+r+ 54.7%

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

   4. Simplified 54.7%

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

   5. Taylor expanded in t around inf 69.5%

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

   6. Taylor expanded in x around inf 65.4%

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

   if -7.99999999999999964e-6 < a < 6.5e16

   1. Initial program 66.0%

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

   2. Taylor expanded in z around 0 84.2%

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

      1. associate--l+ 84.2%

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

      2. associate-+r+ 84.2%

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

      3. associate-+r+ 84.2%

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

      4. div-sub 84.2%

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

      5. *-commutative 84.2%

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

      6. associate-+r+ 84.2%

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

   4. Simplified 84.2%

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

   5. Taylor expanded in x around inf 63.4%

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

   6. Taylor expanded in t around 0 53.6%

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

      1. associate-/l* 53.6%

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

      2. +-commutative 53.6%

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

      3. associate-/l* 65.0%

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

      4. +-commutative 65.0%

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

   8. Simplified 65.0%

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

   9. Taylor expanded in z around inf 63.6%

      \[\leadsto \color{blue}{z} - \frac{b}{\frac{y + x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-6} \lor \neg \left(a \leq 6.5 \cdot 10^{+16}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b}{\frac{x + y}{y}}\\ \end{array} \]

Alternative 14: 62.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+160}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+148}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.1e+160)
   (+ a (* z (/ (+ x y) t)))
   (if (<= t 1.16e+148) (- (+ z a) b) (+ a (/ z (/ t (+ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.1e+160) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= 1.16e+148) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.1d+160)) then
        tmp = a + (z * ((x + y) / t))
    else if (t <= 1.16d+148) then
        tmp = (z + a) - b
    else
        tmp = a + (z / (t / (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.1e+160) {
		tmp = a + (z * ((x + y) / t));
	} else if (t <= 1.16e+148) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (z / (t / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.1e+160:
		tmp = a + (z * ((x + y) / t))
	elif t <= 1.16e+148:
		tmp = (z + a) - b
	else:
		tmp = a + (z / (t / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.1e+160)
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / t)));
	elseif (t <= 1.16e+148)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(z / Float64(t / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.1e+160)
		tmp = a + (z * ((x + y) / t));
	elseif (t <= 1.16e+148)
		tmp = (z + a) - b;
	else
		tmp = a + (z / (t / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.1e+160], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e+148], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(z / N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.09999999999999998e160

   1. Initial program 42.3%

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

   2. Taylor expanded in z around 0 55.4%

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

      1. associate--l+ 55.4%

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

      2. associate-+r+ 55.4%

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

      3. associate-+r+ 55.4%

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

      4. div-sub 55.4%

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

      5. *-commutative 55.4%

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

      6. associate-+r+ 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in t around inf 76.5%

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

   6. Taylor expanded in t around inf 70.1%

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

      1. +-commutative 70.1%

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

   8. Simplified 70.1%

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

   if -4.09999999999999998e160 < t < 1.1599999999999999e148

   1. Initial program 62.1%

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

   2. Taylor expanded in y around inf 63.3%

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

   if 1.1599999999999999e148 < t

   1. Initial program 44.5%

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

   2. Taylor expanded in z around 0 55.7%

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

      1. associate--l+ 55.7%

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

      2. associate-+r+ 55.7%

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

      3. associate-+r+ 55.7%

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

      4. div-sub 55.8%

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

      5. *-commutative 55.8%

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

      6. associate-+r+ 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in t around inf 80.3%

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

   6. Taylor expanded in t around inf 62.4%

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

      1. associate-/l* 74.5%

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

      2. +-commutative 74.5%

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

   8. Simplified 74.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+160}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+148}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \end{array} \]

Alternative 15: 59.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+164} \lor \neg \left(t \leq 3.2 \cdot 10^{+152}\right):\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6e+164) (not (<= t 3.2e+152)))
   (+ a (/ y (/ t z)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6e+164) || !(t <= 3.2e+152)) {
		tmp = a + (y / (t / z));
	} 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 <= (-6d+164)) .or. (.not. (t <= 3.2d+152))) then
        tmp = a + (y / (t / z))
    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 <= -6e+164) || !(t <= 3.2e+152)) {
		tmp = a + (y / (t / z));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6e+164) or not (t <= 3.2e+152):
		tmp = a + (y / (t / z))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6e+164) || !(t <= 3.2e+152))
		tmp = Float64(a + Float64(y / Float64(t / z)));
	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 <= -6e+164) || ~((t <= 3.2e+152)))
		tmp = a + (y / (t / z));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6e+164], N[Not[LessEqual[t, 3.2e+152]], $MachinePrecision]], N[(a + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.00000000000000001e164 or 3.20000000000000005e152 < t

   1. Initial program 43.6%

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

   2. Taylor expanded in z around 0 55.6%

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

      1. associate--l+ 55.6%

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

      2. associate-+r+ 55.6%

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

      3. associate-+r+ 55.6%

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

      4. div-sub 55.6%

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

      5. *-commutative 55.6%

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

      6. associate-+r+ 55.6%

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

   4. Simplified 55.6%

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

   5. Taylor expanded in t around inf 78.7%

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

   6. Taylor expanded in t around inf 60.5%

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

      1. associate-/l* 72.6%

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

      2. +-commutative 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in y around inf 52.6%

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

       1. associate-/l* 59.7%

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

   11. Simplified 59.7%

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

   if -6.00000000000000001e164 < t < 3.20000000000000005e152

   1. Initial program 62.1%

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

   2. Taylor expanded in y around inf 63.3%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+164} \lor \neg \left(t \leq 3.2 \cdot 10^{+152}\right):\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 16: 60.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+161}:\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+182}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5e+161)
   (+ a (/ y (/ t z)))
   (if (<= t 5.5e+182) (- (+ z a) b) (+ a (/ z (/ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5e+161) {
		tmp = a + (y / (t / z));
	} else if (t <= 5.5e+182) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (z / (t / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5d+161)) then
        tmp = a + (y / (t / z))
    else if (t <= 5.5d+182) then
        tmp = (z + a) - b
    else
        tmp = a + (z / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5e+161) {
		tmp = a + (y / (t / z));
	} else if (t <= 5.5e+182) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (z / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5e+161:
		tmp = a + (y / (t / z))
	elif t <= 5.5e+182:
		tmp = (z + a) - b
	else:
		tmp = a + (z / (t / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5e+161)
		tmp = Float64(a + Float64(y / Float64(t / z)));
	elseif (t <= 5.5e+182)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(z / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5e+161)
		tmp = a + (y / (t / z));
	elseif (t <= 5.5e+182)
		tmp = (z + a) - b;
	else
		tmp = a + (z / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5e+161], N[(a + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+182], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.9999999999999997e161

   1. Initial program 42.3%

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

   2. Taylor expanded in z around 0 55.4%

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

      1. associate--l+ 55.4%

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

      2. associate-+r+ 55.4%

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

      3. associate-+r+ 55.4%

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

      4. div-sub 55.4%

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

      5. *-commutative 55.4%

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

      6. associate-+r+ 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in t around inf 76.5%

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

   6. Taylor expanded in t around inf 57.9%

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

      1. associate-/l* 70.1%

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

      2. +-commutative 70.1%

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

   8. Simplified 70.1%

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

   9. Taylor expanded in y around inf 49.7%

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

       1. associate-/l* 59.0%

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

   11. Simplified 59.0%

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

   if -4.9999999999999997e161 < t < 5.49999999999999977e182

   1. Initial program 61.2%

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

   2. Taylor expanded in y around inf 63.2%

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

   if 5.49999999999999977e182 < t

   1. Initial program 47.2%

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

   2. Taylor expanded in z around 0 59.9%

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

      1. associate--l+ 59.9%

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

      2. associate-+r+ 59.9%

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

      3. associate-+r+ 59.9%

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

      4. div-sub 60.0%

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

      5. *-commutative 60.0%

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

      6. associate-+r+ 60.0%

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

   4. Simplified 60.0%

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

   5. Taylor expanded in t around inf 80.3%

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

   6. Taylor expanded in t around inf 60.0%

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

      1. associate-/l* 73.8%

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

      2. +-commutative 73.8%

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

   8. Simplified 73.8%

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

   9. Taylor expanded in y around 0 63.3%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+161}:\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+182}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x}}\\ \end{array} \]

Alternative 17: 60.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.58 \cdot 10^{+165}:\\ \;\;\;\;a + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+182}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.58e+165)
   (+ a (/ z (/ t y)))
   (if (<= t 7.6e+182) (- (+ z a) b) (+ a (/ z (/ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.58e+165) {
		tmp = a + (z / (t / y));
	} else if (t <= 7.6e+182) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (z / (t / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.58d+165)) then
        tmp = a + (z / (t / y))
    else if (t <= 7.6d+182) then
        tmp = (z + a) - b
    else
        tmp = a + (z / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.58e+165) {
		tmp = a + (z / (t / y));
	} else if (t <= 7.6e+182) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (z / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.58e+165:
		tmp = a + (z / (t / y))
	elif t <= 7.6e+182:
		tmp = (z + a) - b
	else:
		tmp = a + (z / (t / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.58e+165)
		tmp = Float64(a + Float64(z / Float64(t / y)));
	elseif (t <= 7.6e+182)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(z / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.58e+165)
		tmp = a + (z / (t / y));
	elseif (t <= 7.6e+182)
		tmp = (z + a) - b;
	else
		tmp = a + (z / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.58e+165], N[(a + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e+182], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.58000000000000007e165

   1. Initial program 42.3%

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

   2. Taylor expanded in z around 0 55.4%

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

      1. associate--l+ 55.4%

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

      2. associate-+r+ 55.4%

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

      3. associate-+r+ 55.4%

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

      4. div-sub 55.4%

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

      5. *-commutative 55.4%

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

      6. associate-+r+ 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in t around inf 76.5%

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

   6. Taylor expanded in t around inf 57.9%

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

      1. associate-/l* 70.1%

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

      2. +-commutative 70.1%

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

   8. Simplified 70.1%

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

   9. Taylor expanded in y around inf 59.0%

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

   if -1.58000000000000007e165 < t < 7.60000000000000025e182

   1. Initial program 61.2%

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

   2. Taylor expanded in y around inf 63.2%

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

   if 7.60000000000000025e182 < t

   1. Initial program 47.2%

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

   2. Taylor expanded in z around 0 59.9%

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

      1. associate--l+ 59.9%

         \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right)} \]

      2. associate-+r+ 59.9%

         \[\leadsto z \cdot \left(\frac{x}{\color{blue}{\left(t + x\right) + y}} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

      3. associate-+r+ 59.9%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\color{blue}{\left(t + x\right) + y}}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

      4. div-sub 60.0%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \color{blue}{\frac{a \cdot \left(t + y\right) - b \cdot y}{t + \left(x + y\right)}} \]

      5. *-commutative 60.0%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - \color{blue}{y \cdot b}}{t + \left(x + y\right)} \]

      6. associate-+r+ 60.0%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\color{blue}{\left(t + x\right) + y}} \]

   4. Simplified 60.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\left(t + x\right) + y}} \]

   5. Taylor expanded in t around inf 80.3%

      \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \color{blue}{a} \]

   6. Taylor expanded in t around inf 60.0%

      \[\leadsto \color{blue}{\frac{z \cdot \left(x + y\right)}{t}} + a \]
   7. Step-by-step derivation

      1. associate-/l* 73.8%

         \[\leadsto \color{blue}{\frac{z}{\frac{t}{x + y}}} + a \]

      2. +-commutative 73.8%

         \[\leadsto \frac{z}{\frac{t}{\color{blue}{y + x}}} + a \]

   8. Simplified 73.8%

      \[\leadsto \color{blue}{\frac{z}{\frac{t}{y + x}}} + a \]

   9. Taylor expanded in y around 0 63.3%

      \[\leadsto \frac{z}{\color{blue}{\frac{t}{x}}} + a \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.58 \cdot 10^{+165}:\\ \;\;\;\;a + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+182}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x}}\\ \end{array} \]

Alternative 18: 59.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+117}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+183}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.06e+117)
   (/ a (+ 1.0 (/ x t)))
   (if (<= t 1.95e+183) (- (+ z a) b) (+ a (/ z (/ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.06e+117) {
		tmp = a / (1.0 + (x / t));
	} else if (t <= 1.95e+183) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (z / (t / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.06d+117)) then
        tmp = a / (1.0d0 + (x / t))
    else if (t <= 1.95d+183) then
        tmp = (z + a) - b
    else
        tmp = a + (z / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.06e+117) {
		tmp = a / (1.0 + (x / t));
	} else if (t <= 1.95e+183) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (z / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.06e+117:
		tmp = a / (1.0 + (x / t))
	elif t <= 1.95e+183:
		tmp = (z + a) - b
	else:
		tmp = a + (z / (t / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.06e+117)
		tmp = Float64(a / Float64(1.0 + Float64(x / t)));
	elseif (t <= 1.95e+183)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(z / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.06e+117)
		tmp = a / (1.0 + (x / t));
	elseif (t <= 1.95e+183)
		tmp = (z + a) - b;
	else
		tmp = a + (z / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.06e+117], N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+183], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.06e117

   1. Initial program 42.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in a around inf 26.0%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)}} \]
   3. Step-by-step derivation

      1. associate-/l* 62.7%

         \[\leadsto \color{blue}{\frac{a}{\frac{t + \left(x + y\right)}{t + y}}} \]

      2. associate-+r+ 62.7%

         \[\leadsto \frac{a}{\frac{\color{blue}{\left(t + x\right) + y}}{t + y}} \]

   4. Simplified 62.7%

      \[\leadsto \color{blue}{\frac{a}{\frac{\left(t + x\right) + y}{t + y}}} \]

   5. Taylor expanded in t around inf 60.4%

      \[\leadsto \frac{a}{\color{blue}{1 + \frac{x}{t}}} \]

   if -1.06e117 < t < 1.9499999999999999e183

   1. Initial program 62.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in y around inf 64.2%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if 1.9499999999999999e183 < t

   1. Initial program 47.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in z around 0 59.9%

      \[\leadsto \color{blue}{\left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)}\right) - \frac{b \cdot y}{t + \left(x + y\right)}} \]
   3. Step-by-step derivation

      1. associate--l+ 59.9%

         \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right)} \]

      2. associate-+r+ 59.9%

         \[\leadsto z \cdot \left(\frac{x}{\color{blue}{\left(t + x\right) + y}} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

      3. associate-+r+ 59.9%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\color{blue}{\left(t + x\right) + y}}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

      4. div-sub 60.0%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \color{blue}{\frac{a \cdot \left(t + y\right) - b \cdot y}{t + \left(x + y\right)}} \]

      5. *-commutative 60.0%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - \color{blue}{y \cdot b}}{t + \left(x + y\right)} \]

      6. associate-+r+ 60.0%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\color{blue}{\left(t + x\right) + y}} \]

   4. Simplified 60.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\left(t + x\right) + y}} \]

   5. Taylor expanded in t around inf 80.3%

      \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \color{blue}{a} \]

   6. Taylor expanded in t around inf 60.0%

      \[\leadsto \color{blue}{\frac{z \cdot \left(x + y\right)}{t}} + a \]
   7. Step-by-step derivation

      1. associate-/l* 73.8%

         \[\leadsto \color{blue}{\frac{z}{\frac{t}{x + y}}} + a \]

      2. +-commutative 73.8%

         \[\leadsto \frac{z}{\frac{t}{\color{blue}{y + x}}} + a \]

   8. Simplified 73.8%

      \[\leadsto \color{blue}{\frac{z}{\frac{t}{y + x}}} + a \]

   9. Taylor expanded in y around 0 63.3%

      \[\leadsto \frac{z}{\color{blue}{\frac{t}{x}}} + a \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+117}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+183}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x}}\\ \end{array} \]

Alternative 19: 57.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+119}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+190}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.1e+119) (+ z a) (if (<= x 7e+190) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.1e+119) {
		tmp = z + a;
	} else if (x <= 7e+190) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.1d+119)) then
        tmp = z + a
    else if (x <= 7d+190) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.1e+119) {
		tmp = z + a;
	} else if (x <= 7e+190) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.1e+119:
		tmp = z + a
	elif x <= 7e+190:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.1e+119)
		tmp = Float64(z + a);
	elseif (x <= 7e+190)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.1e+119)
		tmp = z + a;
	elseif (x <= 7e+190)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.1e+119], N[(z + a), $MachinePrecision], If[LessEqual[x, 7e+190], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 3 regimes

2. if x < -2.09999999999999983e119

   1. Initial program 49.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in z around 0 70.7%

      \[\leadsto \color{blue}{\left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)}\right) - \frac{b \cdot y}{t + \left(x + y\right)}} \]
   3. Step-by-step derivation

      1. associate--l+ 70.7%

         \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right)} \]

      2. associate-+r+ 70.7%

         \[\leadsto z \cdot \left(\frac{x}{\color{blue}{\left(t + x\right) + y}} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

      3. associate-+r+ 70.7%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\color{blue}{\left(t + x\right) + y}}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

      4. div-sub 70.7%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \color{blue}{\frac{a \cdot \left(t + y\right) - b \cdot y}{t + \left(x + y\right)}} \]

      5. *-commutative 70.7%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - \color{blue}{y \cdot b}}{t + \left(x + y\right)} \]

      6. associate-+r+ 70.7%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\color{blue}{\left(t + x\right) + y}} \]

   4. Simplified 70.7%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\left(t + x\right) + y}} \]

   5. Taylor expanded in t around inf 57.9%

      \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \color{blue}{a} \]

   6. Taylor expanded in x around inf 45.0%

      \[\leadsto \color{blue}{z} + a \]

   if -2.09999999999999983e119 < x < 6.9999999999999997e190

   1. Initial program 60.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in y around inf 63.4%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if 6.9999999999999997e190 < x

   1. Initial program 45.3%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in x around inf 63.1%

      \[\leadsto \color{blue}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+119}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+190}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 20: 50.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+231} \lor \neg \left(y \leq 8.2 \cdot 10^{+219}\right):\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.55e+231) (not (<= y 8.2e+219))) (- a b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.55e+231) || !(y <= 8.2e+219)) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.55d+231)) .or. (.not. (y <= 8.2d+219))) then
        tmp = a - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.55e+231) || !(y <= 8.2e+219)) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.55e+231) or not (y <= 8.2e+219):
		tmp = a - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.55e+231) || !(y <= 8.2e+219))
		tmp = Float64(a - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.55e+231) || ~((y <= 8.2e+219)))
		tmp = a - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.55e+231], N[Not[LessEqual[y, 8.2e+219]], $MachinePrecision]], N[(a - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.54999999999999995e231 or 8.1999999999999996e219 < y

   1. Initial program 20.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in z around 0 33.7%

      \[\leadsto \color{blue}{\left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)}\right) - \frac{b \cdot y}{t + \left(x + y\right)}} \]
   3. Step-by-step derivation

      1. associate--l+ 33.7%

         \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right)} \]

      2. associate-+r+ 33.7%

         \[\leadsto z \cdot \left(\frac{x}{\color{blue}{\left(t + x\right) + y}} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

      3. associate-+r+ 33.7%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\color{blue}{\left(t + x\right) + y}}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

      4. div-sub 33.7%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \color{blue}{\frac{a \cdot \left(t + y\right) - b \cdot y}{t + \left(x + y\right)}} \]

      5. *-commutative 33.7%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - \color{blue}{y \cdot b}}{t + \left(x + y\right)} \]

      6. associate-+r+ 33.7%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\color{blue}{\left(t + x\right) + y}} \]

   4. Simplified 33.7%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\left(t + x\right) + y}} \]

   5. Taylor expanded in x around inf 28.5%

      \[\leadsto \color{blue}{z} + \frac{a \cdot \left(t + y\right) - y \cdot b}{\left(t + x\right) + y} \]

   6. Taylor expanded in z around 0 20.2%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}} \]
   7. Step-by-step derivation

      1. div-sub 20.2%

         \[\leadsto \color{blue}{\frac{a \cdot \left(t + y\right) - b \cdot y}{t + \left(x + y\right)}} \]

      2. *-commutative 20.2%

         \[\leadsto \frac{\color{blue}{\left(t + y\right) \cdot a} - b \cdot y}{t + \left(x + y\right)} \]

      3. +-commutative 20.2%

         \[\leadsto \frac{\color{blue}{\left(y + t\right)} \cdot a - b \cdot y}{t + \left(x + y\right)} \]

      4. *-commutative 20.2%

         \[\leadsto \frac{\left(y + t\right) \cdot a - \color{blue}{y \cdot b}}{t + \left(x + y\right)} \]

      5. +-commutative 20.2%

         \[\leadsto \frac{\left(y + t\right) \cdot a - y \cdot b}{t + \color{blue}{\left(y + x\right)}} \]

   8. Simplified 20.2%

      \[\leadsto \color{blue}{\frac{\left(y + t\right) \cdot a - y \cdot b}{t + \left(y + x\right)}} \]

   9. Taylor expanded in y around inf 77.4%

      \[\leadsto \color{blue}{a - b} \]

   if -1.54999999999999995e231 < y < 8.1999999999999996e219

   1. Initial program 62.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in z around 0 76.3%

      \[\leadsto \color{blue}{\left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)}\right) - \frac{b \cdot y}{t + \left(x + y\right)}} \]
   3. Step-by-step derivation

      1. associate--l+ 76.3%

         \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right)} \]

      2. associate-+r+ 76.3%

         \[\leadsto z \cdot \left(\frac{x}{\color{blue}{\left(t + x\right) + y}} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

      3. associate-+r+ 76.3%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\color{blue}{\left(t + x\right) + y}}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

      4. div-sub 76.3%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \color{blue}{\frac{a \cdot \left(t + y\right) - b \cdot y}{t + \left(x + y\right)}} \]

      5. *-commutative 76.3%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - \color{blue}{y \cdot b}}{t + \left(x + y\right)} \]

      6. associate-+r+ 76.3%

         \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\color{blue}{\left(t + x\right) + y}} \]

   4. Simplified 76.3%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\left(t + x\right) + y}} \]

   5. Taylor expanded in t around inf 68.8%

      \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \color{blue}{a} \]

   6. Taylor expanded in x around inf 54.7%

      \[\leadsto \color{blue}{z} + a \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+231} \lor \neg \left(y \leq 8.2 \cdot 10^{+219}\right):\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 21: 44.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+23}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+76}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.5e+23) z (if (<= x 1.2e+76) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.5e+23) {
		tmp = z;
	} else if (x <= 1.2e+76) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6.5d+23)) then
        tmp = z
    else if (x <= 1.2d+76) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.5e+23) {
		tmp = z;
	} else if (x <= 1.2e+76) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.5e+23:
		tmp = z
	elif x <= 1.2e+76:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.5e+23)
		tmp = z;
	elseif (x <= 1.2e+76)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.5e+23)
		tmp = z;
	elseif (x <= 1.2e+76)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.5e+23], z, If[LessEqual[x, 1.2e+76], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4999999999999996e23 or 1.2e76 < x

   1. Initial program 49.3%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in x around inf 47.0%

      \[\leadsto \color{blue}{z} \]

   if -6.4999999999999996e23 < x < 1.2e76

   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. Taylor expanded in t around inf 50.7%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+23}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+76}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 22: 51.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ z + a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ z a))

C

double code(double x, double y, double z, double t, double a, double b) {
	return z + 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 = z + a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return z + a;
}

Python

def code(x, y, z, t, a, b):
	return z + a

Julia

function code(x, y, z, t, a, b)
	return Float64(z + a)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = z + a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(z + a), $MachinePrecision]

Derivation

1. Initial program 57.0%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

2. Taylor expanded in z around 0 70.3%

   \[\leadsto \color{blue}{\left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)}\right) - \frac{b \cdot y}{t + \left(x + y\right)}} \]
3. Step-by-step derivation

   1. associate--l+ 70.3%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right)} \]

   2. associate-+r+ 70.3%

      \[\leadsto z \cdot \left(\frac{x}{\color{blue}{\left(t + x\right) + y}} + \frac{y}{t + \left(x + y\right)}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

   3. associate-+r+ 70.3%

      \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\color{blue}{\left(t + x\right) + y}}\right) + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}\right) \]

   4. div-sub 70.3%

      \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \color{blue}{\frac{a \cdot \left(t + y\right) - b \cdot y}{t + \left(x + y\right)}} \]

   5. *-commutative 70.3%

      \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - \color{blue}{y \cdot b}}{t + \left(x + y\right)} \]

   6. associate-+r+ 70.3%

      \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\color{blue}{\left(t + x\right) + y}} \]

4. Simplified 70.3%

   \[\leadsto \color{blue}{z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{\left(t + x\right) + y}} \]

5. Taylor expanded in t around inf 66.1%

   \[\leadsto z \cdot \left(\frac{x}{\left(t + x\right) + y} + \frac{y}{\left(t + x\right) + y}\right) + \color{blue}{a} \]

6. Taylor expanded in x around inf 53.3%

   \[\leadsto \color{blue}{z} + a \]

7. Final simplification 53.3%

   \[\leadsto z + a \]

Alternative 23: 32.6% 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 57.0%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

2. Taylor expanded in t around inf 32.9%

   \[\leadsto \color{blue}{a} \]

3. Final simplification 32.9%

   \[\leadsto a \]

Developer target: 81.7% 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 2023322 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1.0 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b)))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))