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

Percentage Accurate: 60.3% → 86.7%

Time: 14.4s

Alternatives: 24

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.3% 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: 86.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(y + t\right) \cdot a\\ t_3 := \frac{\left(t\_2 + z \cdot \left(x + y\right)\right) - y \cdot b}{t\_1}\\ t_4 := t + \left(x + y\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_1} + \left(\mathsf{fma}\left(z, \frac{x + y}{a \cdot t\_1}, \frac{y}{t\_1}\right) - \frac{b}{t\_1} \cdot \frac{y}{a}\right)\right)\\ \mathbf{elif}\;t\_3 \leq 10^{+259}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t\_4} + \frac{y}{t\_4}\right) + \frac{t\_2}{t\_4}\right) - \frac{y \cdot b}{t\_4}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (* (+ y t) a))
        (t_3 (/ (- (+ t_2 (* z (+ x y))) (* y b)) t_1))
        (t_4 (+ t (+ x y))))
   (if (<= t_3 (- INFINITY))
     (*
      a
      (+
       (/ t t_1)
       (- (fma z (/ (+ x y) (* a t_1)) (/ y t_1)) (* (/ b t_1) (/ y a)))))
     (if (<= t_3 1e+259)
       (- (+ (* z (+ (/ x t_4) (/ y t_4))) (/ t_2 t_4)) (/ (* y b) t_4))
       (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (y + t) * a;
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / t_1;
	double t_4 = t + (x + y);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = a * ((t / t_1) + (fma(z, ((x + y) / (a * t_1)), (y / t_1)) - ((b / t_1) * (y / a))));
	} else if (t_3 <= 1e+259) {
		tmp = ((z * ((x / t_4) + (y / t_4))) + (t_2 / t_4)) - ((y * b) / t_4);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(y + t) * a)
	t_3 = Float64(Float64(Float64(t_2 + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	t_4 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(a * Float64(Float64(t / t_1) + Float64(fma(z, Float64(Float64(x + y) / Float64(a * t_1)), Float64(y / t_1)) - Float64(Float64(b / t_1) * Float64(y / a)))));
	elseif (t_3 <= 1e+259)
		tmp = Float64(Float64(Float64(z * Float64(Float64(x / t_4) + Float64(y / t_4))) + Float64(t_2 / t_4)) - Float64(Float64(y * b) / t_4));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return 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[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(z * N[(N[(x + y), $MachinePrecision] / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(b / t$95$1), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+259], N[(N[(N[(z * N[(N[(x / t$95$4), $MachinePrecision] + N[(y / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 / t$95$4), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $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)) < -inf.0

   1. Initial program 5.9%

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

   3. Taylor expanded in a around inf 40.5%

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

      1. associate--l+ 40.5%

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

      2. +-commutative 40.5%

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

      3. +-commutative 40.5%

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

      4. associate-+l+ 40.5%

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

      5. +-commutative 40.5%

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

   5. Simplified 66.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.999999999999999e258

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 99.1%

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

   if 9.999999999999999e258 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.1%

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

   3. Taylor expanded in y around inf 71.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;a \cdot \left(\frac{t}{y + \left(x + t\right)} + \left(\mathsf{fma}\left(z, \frac{x + y}{a \cdot \left(y + \left(x + t\right)\right)}, \frac{y}{y + \left(x + t\right)}\right) - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{a}\right)\right)\\ \mathbf{elif}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+259}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \frac{\left(y + t\right) \cdot a}{t + \left(x + y\right)}\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \left(y + t\right) \cdot a\\ t_3 := \frac{\left(t\_2 + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+194} \lor \neg \left(t\_3 \leq 10^{+259}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t\_1} + \frac{y}{t\_1}\right) + \frac{t\_2}{t\_1}\right) - \frac{y \cdot b}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (* (+ y t) a))
        (t_3 (/ (- (+ t_2 (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_3 -1e+194) (not (<= t_3 1e+259)))
     (- (+ z a) b)
     (- (+ (* z (+ (/ x t_1) (/ y t_1))) (/ t_2 t_1)) (/ (* y b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = (y + t) * a;
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_3 <= -1e+194) || !(t_3 <= 1e+259)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t + (x + y)
    t_2 = (y + t) * a
    t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t))
    if ((t_3 <= (-1d+194)) .or. (.not. (t_3 <= 1d+259))) then
        tmp = (z + a) - b
    else
        tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = (y + t) * a;
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_3 <= -1e+194) || !(t_3 <= 1e+259)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = (y + t) * a
	t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_3 <= -1e+194) or not (t_3 <= 1e+259):
		tmp = (z + a) - b
	else:
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(Float64(y + t) * a)
	t_3 = Float64(Float64(Float64(t_2 + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_3 <= -1e+194) || !(t_3 <= 1e+259))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))) + Float64(t_2 / t_1)) - Float64(Float64(y * b) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = (y + t) * a;
	t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_3 <= -1e+194) || ~((t_3 <= 1e+259)))
		tmp = (z + a) - b;
	else
		tmp = ((z * ((x / t_1) + (y / t_1))) + (t_2 / t_1)) - ((y * b) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$3, -1e+194], N[Not[LessEqual[t$95$3, 1e+259]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.99999999999999945e193 or 9.999999999999999e258 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 15.1%

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

   3. Taylor expanded in y around inf 71.9%

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

   if -9.99999999999999945e193 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.999999999999999e258

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 99.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+194} \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+259}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \frac{\left(y + t\right) \cdot a}{t + \left(x + y\right)}\right) - \frac{y \cdot b}{t + \left(x + y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+194} \lor \neg \left(t\_1 \leq 10^{+259}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 -1e+194) (not (<= t_1 1e+259))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -1e+194) || !(t_1 <= 1e+259)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t))
    if ((t_1 <= (-1d+194)) .or. (.not. (t_1 <= 1d+259))) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -1e+194) || !(t_1 <= 1e+259)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -1e+194) or not (t_1 <= 1e+259):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= -1e+194) || !(t_1 <= 1e+259))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -1e+194) || ~((t_1 <= 1e+259)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+194], N[Not[LessEqual[t$95$1, 1e+259]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.99999999999999945e193 or 9.999999999999999e258 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 15.1%

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

   3. Taylor expanded in y around inf 71.9%

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

   if -9.99999999999999945e193 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.999999999999999e258

   1. Initial program 99.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+194} \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+259}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := z \cdot \left(x + y\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+76}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{\left(y \cdot a + t\_3\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{1}{\frac{t + \left(x + y\right)}{t\_3 - y \cdot b}}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-60}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(1 + \left(\frac{z}{a} - \frac{b}{t\_1} \cdot \frac{y}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)) (t_3 (* z (+ x y))))
   (if (<= y -1.06e+154)
     t_2
     (if (<= y -1.2e+76)
       (+ z (- (* a (/ y x)) (* b (/ y x))))
       (if (<= y -3.4e+14)
         (/ (- (+ (* y a) t_3) (* y b)) (+ x y))
         (if (<= y -2.65e-36)
           (* a (/ (+ y t) t_1))
           (if (<= y -4.6e-134)
             (/ 1.0 (/ (+ t (+ x y)) (- t_3 (* y b))))
             (if (<= y 1.75e-60)
               (/ (+ (* t a) (* x z)) (+ x t))
               (if (<= y 6e+69)
                 (* a (+ 1.0 (- (/ z a) (* (/ b t_1) (/ y a)))))
                 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double t_3 = z * (x + y);
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_2;
	} else if (y <= -1.2e+76) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -3.4e+14) {
		tmp = (((y * a) + t_3) - (y * b)) / (x + y);
	} else if (y <= -2.65e-36) {
		tmp = a * ((y + t) / t_1);
	} else if (y <= -4.6e-134) {
		tmp = 1.0 / ((t + (x + y)) / (t_3 - (y * b)));
	} else if (y <= 1.75e-60) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 6e+69) {
		tmp = a * (1.0 + ((z / a) - ((b / t_1) * (y / a))));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (z + a) - b
    t_3 = z * (x + y)
    if (y <= (-1.06d+154)) then
        tmp = t_2
    else if (y <= (-1.2d+76)) then
        tmp = z + ((a * (y / x)) - (b * (y / x)))
    else if (y <= (-3.4d+14)) then
        tmp = (((y * a) + t_3) - (y * b)) / (x + y)
    else if (y <= (-2.65d-36)) then
        tmp = a * ((y + t) / t_1)
    else if (y <= (-4.6d-134)) then
        tmp = 1.0d0 / ((t + (x + y)) / (t_3 - (y * b)))
    else if (y <= 1.75d-60) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 6d+69) then
        tmp = a * (1.0d0 + ((z / a) - ((b / t_1) * (y / a))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double t_3 = z * (x + y);
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_2;
	} else if (y <= -1.2e+76) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -3.4e+14) {
		tmp = (((y * a) + t_3) - (y * b)) / (x + y);
	} else if (y <= -2.65e-36) {
		tmp = a * ((y + t) / t_1);
	} else if (y <= -4.6e-134) {
		tmp = 1.0 / ((t + (x + y)) / (t_3 - (y * b)));
	} else if (y <= 1.75e-60) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 6e+69) {
		tmp = a * (1.0 + ((z / a) - ((b / t_1) * (y / a))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	t_3 = z * (x + y)
	tmp = 0
	if y <= -1.06e+154:
		tmp = t_2
	elif y <= -1.2e+76:
		tmp = z + ((a * (y / x)) - (b * (y / x)))
	elif y <= -3.4e+14:
		tmp = (((y * a) + t_3) - (y * b)) / (x + y)
	elif y <= -2.65e-36:
		tmp = a * ((y + t) / t_1)
	elif y <= -4.6e-134:
		tmp = 1.0 / ((t + (x + y)) / (t_3 - (y * b)))
	elif y <= 1.75e-60:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 6e+69:
		tmp = a * (1.0 + ((z / a) - ((b / t_1) * (y / a))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	t_3 = Float64(z * Float64(x + y))
	tmp = 0.0
	if (y <= -1.06e+154)
		tmp = t_2;
	elseif (y <= -1.2e+76)
		tmp = Float64(z + Float64(Float64(a * Float64(y / x)) - Float64(b * Float64(y / x))));
	elseif (y <= -3.4e+14)
		tmp = Float64(Float64(Float64(Float64(y * a) + t_3) - Float64(y * b)) / Float64(x + y));
	elseif (y <= -2.65e-36)
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	elseif (y <= -4.6e-134)
		tmp = Float64(1.0 / Float64(Float64(t + Float64(x + y)) / Float64(t_3 - Float64(y * b))));
	elseif (y <= 1.75e-60)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 6e+69)
		tmp = Float64(a * Float64(1.0 + Float64(Float64(z / a) - Float64(Float64(b / t_1) * Float64(y / a)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	t_3 = z * (x + y);
	tmp = 0.0;
	if (y <= -1.06e+154)
		tmp = t_2;
	elseif (y <= -1.2e+76)
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	elseif (y <= -3.4e+14)
		tmp = (((y * a) + t_3) - (y * b)) / (x + y);
	elseif (y <= -2.65e-36)
		tmp = a * ((y + t) / t_1);
	elseif (y <= -4.6e-134)
		tmp = 1.0 / ((t + (x + y)) / (t_3 - (y * b)));
	elseif (y <= 1.75e-60)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 6e+69)
		tmp = a * (1.0 + ((z / a) - ((b / t_1) * (y / a))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e+154], t$95$2, If[LessEqual[y, -1.2e+76], N[(z + N[(N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.4e+14], N[(N[(N[(N[(y * a), $MachinePrecision] + t$95$3), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.65e-36], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e-134], N[(1.0 / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(t$95$3 - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-60], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+69], N[(a * N[(1.0 + N[(N[(z / a), $MachinePrecision] - N[(N[(b / t$95$1), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.06e154 or 5.99999999999999967e69 < y

   1. Initial program 29.2%

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

   3. Taylor expanded in y around inf 82.3%

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

   if -1.06e154 < y < -1.2e76

   1. Initial program 41.1%

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

   3. Taylor expanded in x around inf 32.9%

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

      1. associate--l+ 40.4%

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

      2. associate-/l* 47.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 58.4%

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

      5. associate-/l* 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in t around 0 48.3%

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

      1. associate-/l* 55.7%

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

      2. associate-*r/ 66.4%

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

   8. Simplified 66.4%

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

   if -1.2e76 < y < -3.4e14

   1. Initial program 76.1%

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

   3. Taylor expanded in t around 0 67.7%

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

   if -3.4e14 < y < -2.6499999999999999e-36

   1. Initial program 65.3%

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

   3. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 73.2%

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

      2. +-commutative 73.2%

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

      3. +-commutative 73.2%

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

      4. associate-+l+ 73.2%

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

      5. +-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -2.6499999999999999e-36 < y < -4.6000000000000001e-134

   1. Initial program 86.3%

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

   3. Taylor expanded in a around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. *-commutative 76.6%

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

   5. Simplified 76.6%

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

      1. clear-num 76.9%

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

      2. inv-pow 76.9%

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

      3. +-commutative 76.9%

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

      4. +-commutative 76.9%

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

      5. +-commutative 76.9%

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

      6. *-commutative 76.9%

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

   7. Applied egg-rr 76.9%

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

      1. unpow-1 76.9%

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

      2. +-commutative 76.9%

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

      3. +-commutative 76.9%

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

      4. associate-+r+ 76.9%

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

      5. +-commutative 76.9%

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

   9. Simplified 76.9%

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

   if -4.6000000000000001e-134 < y < 1.74999999999999988e-60

   1. Initial program 83.7%

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

   3. Taylor expanded in y around 0 70.4%

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

   if 1.74999999999999988e-60 < y < 5.99999999999999967e69

   1. Initial program 74.2%

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

   3. Taylor expanded in a around inf 81.6%

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

      1. associate--l+ 81.6%

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

      2. +-commutative 81.6%

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

      3. +-commutative 81.6%

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

      4. associate-+l+ 81.6%

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

      5. +-commutative 81.6%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in x around inf 76.1%

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

   7. Taylor expanded in t around inf 77.2%

      \[\leadsto a \cdot \left(\color{blue}{1} + \left(\frac{z}{a} - \frac{b}{y + \left(t + x\right)} \cdot \frac{y}{a}\right)\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+76}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{\left(y \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{1}{\frac{t + \left(x + y\right)}{z \cdot \left(x + y\right) - y \cdot b}}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-60}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(1 + \left(\frac{z}{a} - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := z \cdot \left(x + y\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{+76}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+28}:\\ \;\;\;\;\frac{\left(y \cdot a + t\_3\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_1} - b \cdot \frac{\frac{y}{a}}{t\_1}\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-134}:\\ \;\;\;\;\frac{1}{\frac{t + \left(x + y\right)}{t\_3 - y \cdot b}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(1 + \left(\frac{z}{a} - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (- (+ z a) b)) (t_3 (* z (+ x y))))
   (if (<= y -1.06e+154)
     t_2
     (if (<= y -1.28e+76)
       (+ z (- (* a (/ y x)) (* b (/ y x))))
       (if (<= y -3.3e+28)
         (/ (- (+ (* y a) t_3) (* y b)) (+ x y))
         (if (<= y -8.6e-36)
           (* a (- (/ t t_1) (* b (/ (/ y a) t_1))))
           (if (<= y -4.8e-134)
             (/ 1.0 (/ (+ t (+ x y)) (- t_3 (* y b))))
             (if (<= y 1.55e-61)
               (/ (+ (* t a) (* x z)) (+ x t))
               (if (<= y 6.6e+69)
                 (* a (+ 1.0 (- (/ z a) (* (/ b (+ y (+ x t))) (/ y a)))))
                 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = (z + a) - b;
	double t_3 = z * (x + y);
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_2;
	} else if (y <= -1.28e+76) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -3.3e+28) {
		tmp = (((y * a) + t_3) - (y * b)) / (x + y);
	} else if (y <= -8.6e-36) {
		tmp = a * ((t / t_1) - (b * ((y / a) / t_1)));
	} else if (y <= -4.8e-134) {
		tmp = 1.0 / ((t + (x + y)) / (t_3 - (y * b)));
	} else if (y <= 1.55e-61) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 6.6e+69) {
		tmp = a * (1.0 + ((z / a) - ((b / (y + (x + t))) * (y / a))));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x + (y + t)
    t_2 = (z + a) - b
    t_3 = z * (x + y)
    if (y <= (-1.06d+154)) then
        tmp = t_2
    else if (y <= (-1.28d+76)) then
        tmp = z + ((a * (y / x)) - (b * (y / x)))
    else if (y <= (-3.3d+28)) then
        tmp = (((y * a) + t_3) - (y * b)) / (x + y)
    else if (y <= (-8.6d-36)) then
        tmp = a * ((t / t_1) - (b * ((y / a) / t_1)))
    else if (y <= (-4.8d-134)) then
        tmp = 1.0d0 / ((t + (x + y)) / (t_3 - (y * b)))
    else if (y <= 1.55d-61) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 6.6d+69) then
        tmp = a * (1.0d0 + ((z / a) - ((b / (y + (x + t))) * (y / a))))
    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 = x + (y + t);
	double t_2 = (z + a) - b;
	double t_3 = z * (x + y);
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_2;
	} else if (y <= -1.28e+76) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -3.3e+28) {
		tmp = (((y * a) + t_3) - (y * b)) / (x + y);
	} else if (y <= -8.6e-36) {
		tmp = a * ((t / t_1) - (b * ((y / a) / t_1)));
	} else if (y <= -4.8e-134) {
		tmp = 1.0 / ((t + (x + y)) / (t_3 - (y * b)));
	} else if (y <= 1.55e-61) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 6.6e+69) {
		tmp = a * (1.0 + ((z / a) - ((b / (y + (x + t))) * (y / a))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = (z + a) - b
	t_3 = z * (x + y)
	tmp = 0
	if y <= -1.06e+154:
		tmp = t_2
	elif y <= -1.28e+76:
		tmp = z + ((a * (y / x)) - (b * (y / x)))
	elif y <= -3.3e+28:
		tmp = (((y * a) + t_3) - (y * b)) / (x + y)
	elif y <= -8.6e-36:
		tmp = a * ((t / t_1) - (b * ((y / a) / t_1)))
	elif y <= -4.8e-134:
		tmp = 1.0 / ((t + (x + y)) / (t_3 - (y * b)))
	elif y <= 1.55e-61:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 6.6e+69:
		tmp = a * (1.0 + ((z / a) - ((b / (y + (x + t))) * (y / a))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(Float64(z + a) - b)
	t_3 = Float64(z * Float64(x + y))
	tmp = 0.0
	if (y <= -1.06e+154)
		tmp = t_2;
	elseif (y <= -1.28e+76)
		tmp = Float64(z + Float64(Float64(a * Float64(y / x)) - Float64(b * Float64(y / x))));
	elseif (y <= -3.3e+28)
		tmp = Float64(Float64(Float64(Float64(y * a) + t_3) - Float64(y * b)) / Float64(x + y));
	elseif (y <= -8.6e-36)
		tmp = Float64(a * Float64(Float64(t / t_1) - Float64(b * Float64(Float64(y / a) / t_1))));
	elseif (y <= -4.8e-134)
		tmp = Float64(1.0 / Float64(Float64(t + Float64(x + y)) / Float64(t_3 - Float64(y * b))));
	elseif (y <= 1.55e-61)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 6.6e+69)
		tmp = Float64(a * Float64(1.0 + Float64(Float64(z / a) - Float64(Float64(b / Float64(y + Float64(x + t))) * Float64(y / a)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = (z + a) - b;
	t_3 = z * (x + y);
	tmp = 0.0;
	if (y <= -1.06e+154)
		tmp = t_2;
	elseif (y <= -1.28e+76)
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	elseif (y <= -3.3e+28)
		tmp = (((y * a) + t_3) - (y * b)) / (x + y);
	elseif (y <= -8.6e-36)
		tmp = a * ((t / t_1) - (b * ((y / a) / t_1)));
	elseif (y <= -4.8e-134)
		tmp = 1.0 / ((t + (x + y)) / (t_3 - (y * b)));
	elseif (y <= 1.55e-61)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 6.6e+69)
		tmp = a * (1.0 + ((z / a) - ((b / (y + (x + t))) * (y / a))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e+154], t$95$2, If[LessEqual[y, -1.28e+76], N[(z + N[(N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.3e+28], N[(N[(N[(N[(y * a), $MachinePrecision] + t$95$3), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.6e-36], N[(a * N[(N[(t / t$95$1), $MachinePrecision] - N[(b * N[(N[(y / a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-134], N[(1.0 / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(t$95$3 - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-61], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+69], N[(a * N[(1.0 + N[(N[(z / a), $MachinePrecision] - N[(N[(b / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.06e154 or 6.5999999999999997e69 < y

   1. Initial program 29.2%

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

   3. Taylor expanded in y around inf 82.3%

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

   if -1.06e154 < y < -1.27999999999999994e76

   1. Initial program 41.1%

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

   3. Taylor expanded in x around inf 32.9%

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

      1. associate--l+ 40.4%

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

      2. associate-/l* 47.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 58.4%

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

      5. associate-/l* 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in t around 0 48.3%

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

      1. associate-/l* 55.7%

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

      2. associate-*r/ 66.4%

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

   8. Simplified 66.4%

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

   if -1.27999999999999994e76 < y < -3.3e28

   1. Initial program 86.3%

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

   3. Taylor expanded in t around 0 86.3%

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

   if -3.3e28 < y < -8.6000000000000004e-36

   1. Initial program 64.1%

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

   3. Taylor expanded in a around inf 82.3%

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

      1. associate--l+ 82.3%

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

      2. +-commutative 82.3%

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

      3. +-commutative 82.3%

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

      4. associate-+l+ 82.3%

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

      5. +-commutative 82.3%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in x around inf 57.7%

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

   7. Taylor expanded in z around 0 64.1%

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

      1. +-commutative 64.1%

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

      2. associate-+r+ 64.1%

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

      3. +-commutative 64.1%

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

      4. associate-/l* 70.0%

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

      5. associate-/r* 70.0%

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

      6. +-commutative 70.0%

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

      7. associate-+r+ 70.0%

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

      8. +-commutative 70.0%

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

   9. Simplified 70.0%

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

   if -8.6000000000000004e-36 < y < -4.80000000000000019e-134

   1. Initial program 86.3%

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

   3. Taylor expanded in a around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. *-commutative 76.6%

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

   5. Simplified 76.6%

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

      1. clear-num 76.9%

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

      2. inv-pow 76.9%

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

      3. +-commutative 76.9%

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

      4. +-commutative 76.9%

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

      5. +-commutative 76.9%

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

      6. *-commutative 76.9%

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

   7. Applied egg-rr 76.9%

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

      1. unpow-1 76.9%

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

      2. +-commutative 76.9%

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

      3. +-commutative 76.9%

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

      4. associate-+r+ 76.9%

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

      5. +-commutative 76.9%

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

   9. Simplified 76.9%

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

   if -4.80000000000000019e-134 < y < 1.54999999999999997e-61

   1. Initial program 83.7%

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

   3. Taylor expanded in y around 0 70.4%

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

   if 1.54999999999999997e-61 < y < 6.5999999999999997e69

   1. Initial program 74.2%

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

   3. Taylor expanded in a around inf 81.6%

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

      1. associate--l+ 81.6%

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

      2. +-commutative 81.6%

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

      3. +-commutative 81.6%

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

      4. associate-+l+ 81.6%

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

      5. +-commutative 81.6%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in x around inf 76.1%

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

   7. Taylor expanded in t around inf 77.2%

      \[\leadsto a \cdot \left(\color{blue}{1} + \left(\frac{z}{a} - \frac{b}{y + \left(t + x\right)} \cdot \frac{y}{a}\right)\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{+76}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+28}:\\ \;\;\;\;\frac{\left(y \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + \left(y + t\right)} - b \cdot \frac{\frac{y}{a}}{x + \left(y + t\right)}\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-134}:\\ \;\;\;\;\frac{1}{\frac{t + \left(x + y\right)}{z \cdot \left(x + y\right) - y \cdot b}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(1 + \left(\frac{z}{a} - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+76}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{y \cdot t\_1}{t\_2}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_2}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{1}{\frac{t + \left(x + y\right)}{z \cdot \left(x + y\right) - y \cdot b}}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-29}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ y (+ x t))))
   (if (<= y -1.06e+154)
     t_1
     (if (<= y -1.25e+76)
       (+ z (- (* a (/ y x)) (* b (/ y x))))
       (if (<= y -2.7e+14)
         (/ (* y t_1) t_2)
         (if (<= y -2.9e-40)
           (* a (/ (+ y t) t_2))
           (if (<= y -4.6e-134)
             (/ 1.0 (/ (+ t (+ x y)) (- (* z (+ x y)) (* y b))))
             (if (<= y 1.18e-29) (/ (+ (* t a) (* x z)) (+ x t)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -1.25e+76) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -2.7e+14) {
		tmp = (y * t_1) / t_2;
	} else if (y <= -2.9e-40) {
		tmp = a * ((y + t) / t_2);
	} else if (y <= -4.6e-134) {
		tmp = 1.0 / ((t + (x + y)) / ((z * (x + y)) - (y * b)));
	} else if (y <= 1.18e-29) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    if (y <= (-1.06d+154)) then
        tmp = t_1
    else if (y <= (-1.25d+76)) then
        tmp = z + ((a * (y / x)) - (b * (y / x)))
    else if (y <= (-2.7d+14)) then
        tmp = (y * t_1) / t_2
    else if (y <= (-2.9d-40)) then
        tmp = a * ((y + t) / t_2)
    else if (y <= (-4.6d-134)) then
        tmp = 1.0d0 / ((t + (x + y)) / ((z * (x + y)) - (y * b)))
    else if (y <= 1.18d-29) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -1.25e+76) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -2.7e+14) {
		tmp = (y * t_1) / t_2;
	} else if (y <= -2.9e-40) {
		tmp = a * ((y + t) / t_2);
	} else if (y <= -4.6e-134) {
		tmp = 1.0 / ((t + (x + y)) / ((z * (x + y)) - (y * b)));
	} else if (y <= 1.18e-29) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	tmp = 0
	if y <= -1.06e+154:
		tmp = t_1
	elif y <= -1.25e+76:
		tmp = z + ((a * (y / x)) - (b * (y / x)))
	elif y <= -2.7e+14:
		tmp = (y * t_1) / t_2
	elif y <= -2.9e-40:
		tmp = a * ((y + t) / t_2)
	elif y <= -4.6e-134:
		tmp = 1.0 / ((t + (x + y)) / ((z * (x + y)) - (y * b)))
	elif y <= 1.18e-29:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -1.25e+76)
		tmp = Float64(z + Float64(Float64(a * Float64(y / x)) - Float64(b * Float64(y / x))));
	elseif (y <= -2.7e+14)
		tmp = Float64(Float64(y * t_1) / t_2);
	elseif (y <= -2.9e-40)
		tmp = Float64(a * Float64(Float64(y + t) / t_2));
	elseif (y <= -4.6e-134)
		tmp = Float64(1.0 / Float64(Float64(t + Float64(x + y)) / Float64(Float64(z * Float64(x + y)) - Float64(y * b))));
	elseif (y <= 1.18e-29)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	tmp = 0.0;
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -1.25e+76)
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	elseif (y <= -2.7e+14)
		tmp = (y * t_1) / t_2;
	elseif (y <= -2.9e-40)
		tmp = a * ((y + t) / t_2);
	elseif (y <= -4.6e-134)
		tmp = 1.0 / ((t + (x + y)) / ((z * (x + y)) - (y * b)));
	elseif (y <= 1.18e-29)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e+154], t$95$1, If[LessEqual[y, -1.25e+76], N[(z + N[(N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e+14], N[(N[(y * t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, -2.9e-40], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e-134], N[(1.0 / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.18e-29], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.06e154 or 1.17999999999999996e-29 < y

   1. Initial program 37.7%

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

   3. Taylor expanded in y around inf 76.7%

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

   if -1.06e154 < y < -1.24999999999999998e76

   1. Initial program 41.1%

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

   3. Taylor expanded in x around inf 32.9%

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

      1. associate--l+ 40.4%

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

      2. associate-/l* 47.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 58.4%

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

      5. associate-/l* 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in t around 0 48.3%

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

      1. associate-/l* 55.7%

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

      2. associate-*r/ 66.4%

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

   8. Simplified 66.4%

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

   if -1.24999999999999998e76 < y < -2.7e14

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 67.7%

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

   if -2.7e14 < y < -2.8999999999999999e-40

   1. Initial program 65.3%

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

   3. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 73.2%

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

      2. +-commutative 73.2%

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

      3. +-commutative 73.2%

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

      4. associate-+l+ 73.2%

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

      5. +-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -2.8999999999999999e-40 < y < -4.6000000000000001e-134

   1. Initial program 86.3%

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

   3. Taylor expanded in a around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. *-commutative 76.6%

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

   5. Simplified 76.6%

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

      1. clear-num 76.9%

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

      2. inv-pow 76.9%

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

      3. +-commutative 76.9%

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

      4. +-commutative 76.9%

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

      5. +-commutative 76.9%

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

      6. *-commutative 76.9%

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

   7. Applied egg-rr 76.9%

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

      1. unpow-1 76.9%

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

      2. +-commutative 76.9%

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

      3. +-commutative 76.9%

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

      4. associate-+r+ 76.9%

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

      5. +-commutative 76.9%

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

   9. Simplified 76.9%

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

   if -4.6000000000000001e-134 < y < 1.17999999999999996e-29

   1. Initial program 83.5%

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

   3. Taylor expanded in y around 0 69.9%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+76}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{1}{\frac{t + \left(x + y\right)}{z \cdot \left(x + y\right) - y \cdot b}}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-29}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z \cdot \left(x + y\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.1 \cdot 10^{+75}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\left(y \cdot a + t\_2\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{1}{\frac{t + \left(x + y\right)}{t\_2 - y \cdot b}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-29}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* z (+ x y))))
   (if (<= y -1.06e+154)
     t_1
     (if (<= y -6.1e+75)
       (+ z (- (* a (/ y x)) (* b (/ y x))))
       (if (<= y -8.2e+15)
         (/ (- (+ (* y a) t_2) (* y b)) (+ x y))
         (if (<= y -8.2e-40)
           (* a (/ (+ y t) (+ y (+ x t))))
           (if (<= y -4.6e-134)
             (/ 1.0 (/ (+ t (+ x y)) (- t_2 (* y b))))
             (if (<= y 1.15e-29) (/ (+ (* t a) (* x z)) (+ x t)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z * (x + y);
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -6.1e+75) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -8.2e+15) {
		tmp = (((y * a) + t_2) - (y * b)) / (x + y);
	} else if (y <= -8.2e-40) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (y <= -4.6e-134) {
		tmp = 1.0 / ((t + (x + y)) / (t_2 - (y * b)));
	} else if (y <= 1.15e-29) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z * (x + y)
    if (y <= (-1.06d+154)) then
        tmp = t_1
    else if (y <= (-6.1d+75)) then
        tmp = z + ((a * (y / x)) - (b * (y / x)))
    else if (y <= (-8.2d+15)) then
        tmp = (((y * a) + t_2) - (y * b)) / (x + y)
    else if (y <= (-8.2d-40)) then
        tmp = a * ((y + t) / (y + (x + t)))
    else if (y <= (-4.6d-134)) then
        tmp = 1.0d0 / ((t + (x + y)) / (t_2 - (y * b)))
    else if (y <= 1.15d-29) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z * (x + y);
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -6.1e+75) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -8.2e+15) {
		tmp = (((y * a) + t_2) - (y * b)) / (x + y);
	} else if (y <= -8.2e-40) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (y <= -4.6e-134) {
		tmp = 1.0 / ((t + (x + y)) / (t_2 - (y * b)));
	} else if (y <= 1.15e-29) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z * (x + y)
	tmp = 0
	if y <= -1.06e+154:
		tmp = t_1
	elif y <= -6.1e+75:
		tmp = z + ((a * (y / x)) - (b * (y / x)))
	elif y <= -8.2e+15:
		tmp = (((y * a) + t_2) - (y * b)) / (x + y)
	elif y <= -8.2e-40:
		tmp = a * ((y + t) / (y + (x + t)))
	elif y <= -4.6e-134:
		tmp = 1.0 / ((t + (x + y)) / (t_2 - (y * b)))
	elif y <= 1.15e-29:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z * Float64(x + y))
	tmp = 0.0
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -6.1e+75)
		tmp = Float64(z + Float64(Float64(a * Float64(y / x)) - Float64(b * Float64(y / x))));
	elseif (y <= -8.2e+15)
		tmp = Float64(Float64(Float64(Float64(y * a) + t_2) - Float64(y * b)) / Float64(x + y));
	elseif (y <= -8.2e-40)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	elseif (y <= -4.6e-134)
		tmp = Float64(1.0 / Float64(Float64(t + Float64(x + y)) / Float64(t_2 - Float64(y * b))));
	elseif (y <= 1.15e-29)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = z * (x + y);
	tmp = 0.0;
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -6.1e+75)
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	elseif (y <= -8.2e+15)
		tmp = (((y * a) + t_2) - (y * b)) / (x + y);
	elseif (y <= -8.2e-40)
		tmp = a * ((y + t) / (y + (x + t)));
	elseif (y <= -4.6e-134)
		tmp = 1.0 / ((t + (x + y)) / (t_2 - (y * b)));
	elseif (y <= 1.15e-29)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e+154], t$95$1, If[LessEqual[y, -6.1e+75], N[(z + N[(N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e+15], N[(N[(N[(N[(y * a), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e-40], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e-134], N[(1.0 / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(t$95$2 - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-29], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.06e154 or 1.14999999999999996e-29 < y

   1. Initial program 37.7%

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

   3. Taylor expanded in y around inf 76.7%

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

   if -1.06e154 < y < -6.10000000000000009e75

   1. Initial program 41.1%

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

   3. Taylor expanded in x around inf 32.9%

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

      1. associate--l+ 40.4%

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

      2. associate-/l* 47.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 58.4%

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

      5. associate-/l* 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in t around 0 48.3%

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

      1. associate-/l* 55.7%

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

      2. associate-*r/ 66.4%

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

   8. Simplified 66.4%

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

   if -6.10000000000000009e75 < y < -8.2e15

   1. Initial program 76.1%

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

   3. Taylor expanded in t around 0 67.7%

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

   if -8.2e15 < y < -8.19999999999999926e-40

   1. Initial program 65.3%

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

   3. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 73.2%

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

      2. +-commutative 73.2%

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

      3. +-commutative 73.2%

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

      4. associate-+l+ 73.2%

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

      5. +-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -8.19999999999999926e-40 < y < -4.6000000000000001e-134

   1. Initial program 86.3%

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

   3. Taylor expanded in a around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. *-commutative 76.6%

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

   5. Simplified 76.6%

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

      1. clear-num 76.9%

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

      2. inv-pow 76.9%

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

      3. +-commutative 76.9%

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

      4. +-commutative 76.9%

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

      5. +-commutative 76.9%

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

      6. *-commutative 76.9%

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

   7. Applied egg-rr 76.9%

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

      1. unpow-1 76.9%

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

      2. +-commutative 76.9%

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

      3. +-commutative 76.9%

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

      4. associate-+r+ 76.9%

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

      5. +-commutative 76.9%

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

   9. Simplified 76.9%

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

   if -4.6000000000000001e-134 < y < 1.14999999999999996e-29

   1. Initial program 83.5%

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

   3. Taylor expanded in y around 0 69.9%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6.1 \cdot 10^{+75}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\left(y \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{1}{\frac{t + \left(x + y\right)}{z \cdot \left(x + y\right) - y \cdot b}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-29}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{+76}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-119}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)))
   (if (<= y -1.1e+154)
     t_2
     (if (<= y -1.28e+76)
       (+ z (* y (- (/ a x) (/ b x))))
       (if (<= y -1.9e+54)
         t_2
         (if (<= y -1.5e-59)
           (* a (/ (+ y t) t_1))
           (if (<= y -6.2e-119)
             (* z (/ (+ x y) t_1))
             (if (<= y 8.6e-30) (/ (+ (* t a) (* x z)) (+ x t)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.1e+154) {
		tmp = t_2;
	} else if (y <= -1.28e+76) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (y <= -1.9e+54) {
		tmp = t_2;
	} else if (y <= -1.5e-59) {
		tmp = a * ((y + t) / t_1);
	} else if (y <= -6.2e-119) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= 8.6e-30) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (z + a) - b
    if (y <= (-1.1d+154)) then
        tmp = t_2
    else if (y <= (-1.28d+76)) then
        tmp = z + (y * ((a / x) - (b / x)))
    else if (y <= (-1.9d+54)) then
        tmp = t_2
    else if (y <= (-1.5d-59)) then
        tmp = a * ((y + t) / t_1)
    else if (y <= (-6.2d-119)) then
        tmp = z * ((x + y) / t_1)
    else if (y <= 8.6d-30) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.1e+154) {
		tmp = t_2;
	} else if (y <= -1.28e+76) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (y <= -1.9e+54) {
		tmp = t_2;
	} else if (y <= -1.5e-59) {
		tmp = a * ((y + t) / t_1);
	} else if (y <= -6.2e-119) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= 8.6e-30) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -1.1e+154:
		tmp = t_2
	elif y <= -1.28e+76:
		tmp = z + (y * ((a / x) - (b / x)))
	elif y <= -1.9e+54:
		tmp = t_2
	elif y <= -1.5e-59:
		tmp = a * ((y + t) / t_1)
	elif y <= -6.2e-119:
		tmp = z * ((x + y) / t_1)
	elif y <= 8.6e-30:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.1e+154)
		tmp = t_2;
	elseif (y <= -1.28e+76)
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	elseif (y <= -1.9e+54)
		tmp = t_2;
	elseif (y <= -1.5e-59)
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	elseif (y <= -6.2e-119)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	elseif (y <= 8.6e-30)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.1e+154)
		tmp = t_2;
	elseif (y <= -1.28e+76)
		tmp = z + (y * ((a / x) - (b / x)));
	elseif (y <= -1.9e+54)
		tmp = t_2;
	elseif (y <= -1.5e-59)
		tmp = a * ((y + t) / t_1);
	elseif (y <= -6.2e-119)
		tmp = z * ((x + y) / t_1);
	elseif (y <= 8.6e-30)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.1e+154], t$95$2, If[LessEqual[y, -1.28e+76], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e+54], t$95$2, If[LessEqual[y, -1.5e-59], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.2e-119], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e-30], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.1000000000000001e154 or -1.27999999999999994e76 < y < -1.9000000000000001e54 or 8.59999999999999932e-30 < y

   1. Initial program 39.1%

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

   3. Taylor expanded in y around inf 77.5%

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

   if -1.1000000000000001e154 < y < -1.27999999999999994e76

   1. Initial program 41.1%

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

   3. Taylor expanded in x around inf 32.9%

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

      1. associate--l+ 40.4%

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

      2. associate-/l* 47.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 58.4%

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

      5. associate-/l* 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in y around inf 66.2%

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

   if -1.9000000000000001e54 < y < -1.5e-59

   1. Initial program 72.0%

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

   3. Taylor expanded in a around inf 31.3%

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

      1. associate-/l* 51.1%

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

      2. +-commutative 51.1%

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

      3. +-commutative 51.1%

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

      4. associate-+l+ 51.1%

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

      5. +-commutative 51.1%

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

   5. Simplified 51.1%

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

   if -1.5e-59 < y < -6.19999999999999956e-119

   1. Initial program 85.5%

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

   3. Taylor expanded in z around inf 55.2%

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

      1. associate-/l* 62.2%

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

      2. +-commutative 62.2%

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

      3. +-commutative 62.2%

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

      4. +-commutative 62.2%

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

      5. associate-+l+ 62.2%

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

      6. +-commutative 62.2%

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

   5. Simplified 62.2%

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

   if -6.19999999999999956e-119 < y < 8.59999999999999932e-30

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0 68.8%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{+76}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+54}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-119}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{+76}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{y \cdot z - y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.06e+154)
     t_1
     (if (<= y -1.28e+76)
       (+ z (* y (- (/ a x) (/ b x))))
       (if (<= y -1.9e+54)
         t_1
         (if (<= y -2.35e-42)
           (* a (/ (+ y t) (+ y (+ x t))))
           (if (<= y -8.5e-88)
             (/ (- (* y z) (* y b)) (+ y t))
             (if (<= y 1.4e-29) (/ (+ (* t a) (* x z)) (+ x t)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -1.28e+76) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (y <= -1.9e+54) {
		tmp = t_1;
	} else if (y <= -2.35e-42) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (y <= -8.5e-88) {
		tmp = ((y * z) - (y * b)) / (y + t);
	} else if (y <= 1.4e-29) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.06d+154)) then
        tmp = t_1
    else if (y <= (-1.28d+76)) then
        tmp = z + (y * ((a / x) - (b / x)))
    else if (y <= (-1.9d+54)) then
        tmp = t_1
    else if (y <= (-2.35d-42)) then
        tmp = a * ((y + t) / (y + (x + t)))
    else if (y <= (-8.5d-88)) then
        tmp = ((y * z) - (y * b)) / (y + t)
    else if (y <= 1.4d-29) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -1.28e+76) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (y <= -1.9e+54) {
		tmp = t_1;
	} else if (y <= -2.35e-42) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (y <= -8.5e-88) {
		tmp = ((y * z) - (y * b)) / (y + t);
	} else if (y <= 1.4e-29) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.06e+154:
		tmp = t_1
	elif y <= -1.28e+76:
		tmp = z + (y * ((a / x) - (b / x)))
	elif y <= -1.9e+54:
		tmp = t_1
	elif y <= -2.35e-42:
		tmp = a * ((y + t) / (y + (x + t)))
	elif y <= -8.5e-88:
		tmp = ((y * z) - (y * b)) / (y + t)
	elif y <= 1.4e-29:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -1.28e+76)
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	elseif (y <= -1.9e+54)
		tmp = t_1;
	elseif (y <= -2.35e-42)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	elseif (y <= -8.5e-88)
		tmp = Float64(Float64(Float64(y * z) - Float64(y * b)) / Float64(y + t));
	elseif (y <= 1.4e-29)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -1.28e+76)
		tmp = z + (y * ((a / x) - (b / x)));
	elseif (y <= -1.9e+54)
		tmp = t_1;
	elseif (y <= -2.35e-42)
		tmp = a * ((y + t) / (y + (x + t)));
	elseif (y <= -8.5e-88)
		tmp = ((y * z) - (y * b)) / (y + t);
	elseif (y <= 1.4e-29)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.06e+154], t$95$1, If[LessEqual[y, -1.28e+76], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e+54], t$95$1, If[LessEqual[y, -2.35e-42], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e-88], N[(N[(N[(y * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-29], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.06e154 or -1.27999999999999994e76 < y < -1.9000000000000001e54 or 1.4000000000000001e-29 < y

   1. Initial program 39.1%

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

   3. Taylor expanded in y around inf 77.5%

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

   if -1.06e154 < y < -1.27999999999999994e76

   1. Initial program 41.1%

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

   3. Taylor expanded in x around inf 32.9%

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

      1. associate--l+ 40.4%

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

      2. associate-/l* 47.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 58.4%

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

      5. associate-/l* 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in y around inf 66.2%

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

   if -1.9000000000000001e54 < y < -2.35e-42

   1. Initial program 72.5%

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

   3. Taylor expanded in a around inf 35.3%

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

      1. associate-/l* 53.4%

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

      2. +-commutative 53.4%

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

      3. +-commutative 53.4%

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

      4. associate-+l+ 53.4%

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

      5. +-commutative 53.4%

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

   5. Simplified 53.4%

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

   if -2.35e-42 < y < -8.4999999999999996e-88

   1. Initial program 81.0%

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

   3. Taylor expanded in a around 0 70.9%

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

      1. +-commutative 70.9%

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

      2. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in x around 0 51.0%

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

      1. *-commutative 51.0%

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

   8. Simplified 51.0%

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

   if -8.4999999999999996e-88 < y < 1.4000000000000001e-29

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0 68.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{+76}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+54}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{y \cdot z - y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{+75}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-87}:\\ \;\;\;\;\frac{y \cdot z - y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.06e+154)
     t_1
     (if (<= y -2.85e+75)
       (+ z (- (* a (/ y x)) (* b (/ y x))))
       (if (<= y -2.45e+54)
         t_1
         (if (<= y -2.1e-42)
           (* a (/ (+ y t) (+ y (+ x t))))
           (if (<= y -3.25e-87)
             (/ (- (* y z) (* y b)) (+ y t))
             (if (<= y 9.2e-30) (/ (+ (* t a) (* x z)) (+ x t)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -2.85e+75) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -2.45e+54) {
		tmp = t_1;
	} else if (y <= -2.1e-42) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (y <= -3.25e-87) {
		tmp = ((y * z) - (y * b)) / (y + t);
	} else if (y <= 9.2e-30) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.06d+154)) then
        tmp = t_1
    else if (y <= (-2.85d+75)) then
        tmp = z + ((a * (y / x)) - (b * (y / x)))
    else if (y <= (-2.45d+54)) then
        tmp = t_1
    else if (y <= (-2.1d-42)) then
        tmp = a * ((y + t) / (y + (x + t)))
    else if (y <= (-3.25d-87)) then
        tmp = ((y * z) - (y * b)) / (y + t)
    else if (y <= 9.2d-30) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -2.85e+75) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -2.45e+54) {
		tmp = t_1;
	} else if (y <= -2.1e-42) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (y <= -3.25e-87) {
		tmp = ((y * z) - (y * b)) / (y + t);
	} else if (y <= 9.2e-30) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.06e+154:
		tmp = t_1
	elif y <= -2.85e+75:
		tmp = z + ((a * (y / x)) - (b * (y / x)))
	elif y <= -2.45e+54:
		tmp = t_1
	elif y <= -2.1e-42:
		tmp = a * ((y + t) / (y + (x + t)))
	elif y <= -3.25e-87:
		tmp = ((y * z) - (y * b)) / (y + t)
	elif y <= 9.2e-30:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -2.85e+75)
		tmp = Float64(z + Float64(Float64(a * Float64(y / x)) - Float64(b * Float64(y / x))));
	elseif (y <= -2.45e+54)
		tmp = t_1;
	elseif (y <= -2.1e-42)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	elseif (y <= -3.25e-87)
		tmp = Float64(Float64(Float64(y * z) - Float64(y * b)) / Float64(y + t));
	elseif (y <= 9.2e-30)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -2.85e+75)
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	elseif (y <= -2.45e+54)
		tmp = t_1;
	elseif (y <= -2.1e-42)
		tmp = a * ((y + t) / (y + (x + t)));
	elseif (y <= -3.25e-87)
		tmp = ((y * z) - (y * b)) / (y + t);
	elseif (y <= 9.2e-30)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.06e+154], t$95$1, If[LessEqual[y, -2.85e+75], N[(z + N[(N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.45e+54], t$95$1, If[LessEqual[y, -2.1e-42], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.25e-87], N[(N[(N[(y * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-30], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.06e154 or -2.8500000000000002e75 < y < -2.45e54 or 9.19999999999999937e-30 < y

   1. Initial program 39.1%

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

   3. Taylor expanded in y around inf 77.5%

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

   if -1.06e154 < y < -2.8500000000000002e75

   1. Initial program 41.1%

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

   3. Taylor expanded in x around inf 32.9%

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

      1. associate--l+ 40.4%

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

      2. associate-/l* 47.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 58.4%

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

      5. associate-/l* 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in t around 0 48.3%

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

      1. associate-/l* 55.7%

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

      2. associate-*r/ 66.4%

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

   8. Simplified 66.4%

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

   if -2.45e54 < y < -2.10000000000000006e-42

   1. Initial program 72.5%

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

   3. Taylor expanded in a around inf 35.3%

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

      1. associate-/l* 53.4%

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

      2. +-commutative 53.4%

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

      3. +-commutative 53.4%

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

      4. associate-+l+ 53.4%

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

      5. +-commutative 53.4%

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

   5. Simplified 53.4%

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

   if -2.10000000000000006e-42 < y < -3.2500000000000001e-87

   1. Initial program 81.0%

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

   3. Taylor expanded in a around 0 70.9%

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

      1. +-commutative 70.9%

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

      2. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in x around 0 51.0%

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

      1. *-commutative 51.0%

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

   8. Simplified 51.0%

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

   if -3.2500000000000001e-87 < y < 9.19999999999999937e-30

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0 68.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{+75}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+54}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-87}:\\ \;\;\;\;\frac{y \cdot z - y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+76}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+14}:\\ \;\;\;\;\frac{y \cdot t\_1}{t\_2}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_2}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t\_2}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-29}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ y (+ x t))))
   (if (<= y -1.06e+154)
     t_1
     (if (<= y -1.12e+76)
       (+ z (- (* a (/ y x)) (* b (/ y x))))
       (if (<= y -2.45e+14)
         (/ (* y t_1) t_2)
         (if (<= y -8e-36)
           (* a (/ (+ y t) t_2))
           (if (<= y -4.6e-134)
             (/ (- (* z (+ x y)) (* y b)) t_2)
             (if (<= y 1.18e-29) (/ (+ (* t a) (* x z)) (+ x t)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -1.12e+76) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -2.45e+14) {
		tmp = (y * t_1) / t_2;
	} else if (y <= -8e-36) {
		tmp = a * ((y + t) / t_2);
	} else if (y <= -4.6e-134) {
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	} else if (y <= 1.18e-29) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    if (y <= (-1.06d+154)) then
        tmp = t_1
    else if (y <= (-1.12d+76)) then
        tmp = z + ((a * (y / x)) - (b * (y / x)))
    else if (y <= (-2.45d+14)) then
        tmp = (y * t_1) / t_2
    else if (y <= (-8d-36)) then
        tmp = a * ((y + t) / t_2)
    else if (y <= (-4.6d-134)) then
        tmp = ((z * (x + y)) - (y * b)) / t_2
    else if (y <= 1.18d-29) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -1.12e+76) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -2.45e+14) {
		tmp = (y * t_1) / t_2;
	} else if (y <= -8e-36) {
		tmp = a * ((y + t) / t_2);
	} else if (y <= -4.6e-134) {
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	} else if (y <= 1.18e-29) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	tmp = 0
	if y <= -1.06e+154:
		tmp = t_1
	elif y <= -1.12e+76:
		tmp = z + ((a * (y / x)) - (b * (y / x)))
	elif y <= -2.45e+14:
		tmp = (y * t_1) / t_2
	elif y <= -8e-36:
		tmp = a * ((y + t) / t_2)
	elif y <= -4.6e-134:
		tmp = ((z * (x + y)) - (y * b)) / t_2
	elif y <= 1.18e-29:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -1.12e+76)
		tmp = Float64(z + Float64(Float64(a * Float64(y / x)) - Float64(b * Float64(y / x))));
	elseif (y <= -2.45e+14)
		tmp = Float64(Float64(y * t_1) / t_2);
	elseif (y <= -8e-36)
		tmp = Float64(a * Float64(Float64(y + t) / t_2));
	elseif (y <= -4.6e-134)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / t_2);
	elseif (y <= 1.18e-29)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	tmp = 0.0;
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -1.12e+76)
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	elseif (y <= -2.45e+14)
		tmp = (y * t_1) / t_2;
	elseif (y <= -8e-36)
		tmp = a * ((y + t) / t_2);
	elseif (y <= -4.6e-134)
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	elseif (y <= 1.18e-29)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e+154], t$95$1, If[LessEqual[y, -1.12e+76], N[(z + N[(N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.45e+14], N[(N[(y * t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, -8e-36], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e-134], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 1.18e-29], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.06e154 or 1.17999999999999996e-29 < y

   1. Initial program 37.7%

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

   3. Taylor expanded in y around inf 76.7%

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

   if -1.06e154 < y < -1.12000000000000005e76

   1. Initial program 41.1%

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

   3. Taylor expanded in x around inf 32.9%

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

      1. associate--l+ 40.4%

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

      2. associate-/l* 47.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 58.4%

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

      5. associate-/l* 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in t around 0 48.3%

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

      1. associate-/l* 55.7%

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

      2. associate-*r/ 66.4%

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

   8. Simplified 66.4%

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

   if -1.12000000000000005e76 < y < -2.45e14

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 67.7%

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

   if -2.45e14 < y < -7.9999999999999995e-36

   1. Initial program 65.3%

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

   3. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 73.2%

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

      2. +-commutative 73.2%

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

      3. +-commutative 73.2%

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

      4. associate-+l+ 73.2%

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

      5. +-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -7.9999999999999995e-36 < y < -4.6000000000000001e-134

   1. Initial program 86.3%

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

   3. Taylor expanded in a around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   if -4.6000000000000001e-134 < y < 1.17999999999999996e-29

   1. Initial program 83.5%

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

   3. Taylor expanded in y around 0 69.9%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+76}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+14}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-29}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{x + y}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} \cdot t\_1 + \frac{z}{b}\right) - t\_1\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-134}:\\ \;\;\;\;\frac{1}{\frac{t + \left(x + y\right)}{z \cdot \left(x + y\right) - y \cdot b}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-60}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(1 + \left(\frac{z}{a} - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (+ x y))))
   (if (<= y -7.2e-26)
     (* b (- (+ (* (/ a b) t_1) (/ z b)) t_1))
     (if (<= y -4.8e-134)
       (/ 1.0 (/ (+ t (+ x y)) (- (* z (+ x y)) (* y b))))
       (if (<= y 1.1e-60)
         (/ (+ (* t a) (* x z)) (+ x t))
         (if (<= y 2.15e+68)
           (* a (+ 1.0 (- (/ z a) (* (/ b (+ y (+ x t))) (/ y a)))))
           (- (+ z a) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / (x + y);
	double tmp;
	if (y <= -7.2e-26) {
		tmp = b * ((((a / b) * t_1) + (z / b)) - t_1);
	} else if (y <= -4.8e-134) {
		tmp = 1.0 / ((t + (x + y)) / ((z * (x + y)) - (y * b)));
	} else if (y <= 1.1e-60) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 2.15e+68) {
		tmp = a * (1.0 + ((z / a) - ((b / (y + (x + t))) * (y / a))));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (x + y)
    if (y <= (-7.2d-26)) then
        tmp = b * ((((a / b) * t_1) + (z / b)) - t_1)
    else if (y <= (-4.8d-134)) then
        tmp = 1.0d0 / ((t + (x + y)) / ((z * (x + y)) - (y * b)))
    else if (y <= 1.1d-60) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 2.15d+68) then
        tmp = a * (1.0d0 + ((z / a) - ((b / (y + (x + t))) * (y / a))))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / (x + y);
	double tmp;
	if (y <= -7.2e-26) {
		tmp = b * ((((a / b) * t_1) + (z / b)) - t_1);
	} else if (y <= -4.8e-134) {
		tmp = 1.0 / ((t + (x + y)) / ((z * (x + y)) - (y * b)));
	} else if (y <= 1.1e-60) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 2.15e+68) {
		tmp = a * (1.0 + ((z / a) - ((b / (y + (x + t))) * (y / a))));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y / (x + y)
	tmp = 0
	if y <= -7.2e-26:
		tmp = b * ((((a / b) * t_1) + (z / b)) - t_1)
	elif y <= -4.8e-134:
		tmp = 1.0 / ((t + (x + y)) / ((z * (x + y)) - (y * b)))
	elif y <= 1.1e-60:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 2.15e+68:
		tmp = a * (1.0 + ((z / a) - ((b / (y + (x + t))) * (y / a))))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(x + y))
	tmp = 0.0
	if (y <= -7.2e-26)
		tmp = Float64(b * Float64(Float64(Float64(Float64(a / b) * t_1) + Float64(z / b)) - t_1));
	elseif (y <= -4.8e-134)
		tmp = Float64(1.0 / Float64(Float64(t + Float64(x + y)) / Float64(Float64(z * Float64(x + y)) - Float64(y * b))));
	elseif (y <= 1.1e-60)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 2.15e+68)
		tmp = Float64(a * Float64(1.0 + Float64(Float64(z / a) - Float64(Float64(b / Float64(y + Float64(x + t))) * Float64(y / a)))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y / (x + y);
	tmp = 0.0;
	if (y <= -7.2e-26)
		tmp = b * ((((a / b) * t_1) + (z / b)) - t_1);
	elseif (y <= -4.8e-134)
		tmp = 1.0 / ((t + (x + y)) / ((z * (x + y)) - (y * b)));
	elseif (y <= 1.1e-60)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 2.15e+68)
		tmp = a * (1.0 + ((z / a) - ((b / (y + (x + t))) * (y / a))));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e-26], N[(b * N[(N[(N[(N[(a / b), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-134], N[(1.0 / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-60], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+68], N[(a * N[(1.0 + N[(N[(z / a), $MachinePrecision] - N[(N[(b / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.2000000000000003e-26

   1. Initial program 39.7%

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

   3. Taylor expanded in b around inf 51.5%

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

   4. Taylor expanded in t around 0 56.8%

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

      1. +-commutative 56.8%

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

      2. mul-1-neg 56.8%

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

      3. unsub-neg 56.8%

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

      4. +-commutative 56.8%

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

      5. times-frac 69.8%

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

      6. +-commutative 69.8%

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

      7. +-commutative 69.8%

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

   6. Simplified 69.8%

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

   if -7.2000000000000003e-26 < y < -4.80000000000000019e-134

   1. Initial program 84.0%

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

   3. Taylor expanded in a around 0 71.3%

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

      1. +-commutative 71.3%

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

      2. *-commutative 71.3%

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

   5. Simplified 71.3%

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

      1. clear-num 71.4%

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

      2. inv-pow 71.4%

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

      3. +-commutative 71.4%

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

      4. +-commutative 71.4%

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

      5. +-commutative 71.4%

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

      6. *-commutative 71.4%

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

   7. Applied egg-rr 71.4%

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

      1. unpow-1 71.4%

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

      2. +-commutative 71.4%

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

      3. +-commutative 71.4%

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

      4. associate-+r+ 71.4%

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

      5. +-commutative 71.4%

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

   9. Simplified 71.4%

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

   if -4.80000000000000019e-134 < y < 1.0999999999999999e-60

   1. Initial program 83.7%

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

   3. Taylor expanded in y around 0 70.4%

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

   if 1.0999999999999999e-60 < y < 2.1500000000000001e68

   1. Initial program 74.2%

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

   3. Taylor expanded in a around inf 81.6%

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

      1. associate--l+ 81.6%

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

      2. +-commutative 81.6%

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

      3. +-commutative 81.6%

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

      4. associate-+l+ 81.6%

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

      5. +-commutative 81.6%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in x around inf 76.1%

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

   7. Taylor expanded in t around inf 77.2%

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

   if 2.1500000000000001e68 < y

   1. Initial program 35.4%

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

   3. Taylor expanded in y around inf 82.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} \cdot \frac{y}{x + y} + \frac{z}{b}\right) - \frac{y}{x + y}\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-134}:\\ \;\;\;\;\frac{1}{\frac{t + \left(x + y\right)}{z \cdot \left(x + y\right) - y \cdot b}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-60}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(1 + \left(\frac{z}{a} - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+75}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.38 \cdot 10^{-86}:\\ \;\;\;\;\frac{y \cdot t\_1}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.06e+154)
     t_1
     (if (<= y -2.65e+75)
       (+ z (- (* a (/ y x)) (* b (/ y x))))
       (if (<= y -2.2e+69)
         t_1
         (if (<= y -1.38e-86)
           (/ (* y t_1) (+ y (+ x t)))
           (if (<= y 8.6e-30) (/ (+ (* t a) (* x z)) (+ x t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -2.65e+75) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -2.2e+69) {
		tmp = t_1;
	} else if (y <= -1.38e-86) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (y <= 8.6e-30) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.06d+154)) then
        tmp = t_1
    else if (y <= (-2.65d+75)) then
        tmp = z + ((a * (y / x)) - (b * (y / x)))
    else if (y <= (-2.2d+69)) then
        tmp = t_1
    else if (y <= (-1.38d-86)) then
        tmp = (y * t_1) / (y + (x + t))
    else if (y <= 8.6d-30) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -2.65e+75) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -2.2e+69) {
		tmp = t_1;
	} else if (y <= -1.38e-86) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (y <= 8.6e-30) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.06e+154:
		tmp = t_1
	elif y <= -2.65e+75:
		tmp = z + ((a * (y / x)) - (b * (y / x)))
	elif y <= -2.2e+69:
		tmp = t_1
	elif y <= -1.38e-86:
		tmp = (y * t_1) / (y + (x + t))
	elif y <= 8.6e-30:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -2.65e+75)
		tmp = Float64(z + Float64(Float64(a * Float64(y / x)) - Float64(b * Float64(y / x))));
	elseif (y <= -2.2e+69)
		tmp = t_1;
	elseif (y <= -1.38e-86)
		tmp = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)));
	elseif (y <= 8.6e-30)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -2.65e+75)
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	elseif (y <= -2.2e+69)
		tmp = t_1;
	elseif (y <= -1.38e-86)
		tmp = (y * t_1) / (y + (x + t));
	elseif (y <= 8.6e-30)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.06e+154], t$95$1, If[LessEqual[y, -2.65e+75], N[(z + N[(N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.2e+69], t$95$1, If[LessEqual[y, -1.38e-86], N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e-30], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.06e154 or -2.6499999999999999e75 < y < -2.2000000000000002e69 or 8.59999999999999932e-30 < y

   1. Initial program 38.6%

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

   3. Taylor expanded in y around inf 77.3%

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

   if -1.06e154 < y < -2.6499999999999999e75

   1. Initial program 41.1%

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

   3. Taylor expanded in x around inf 32.9%

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

      1. associate--l+ 40.4%

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

      2. associate-/l* 47.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 58.4%

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

      5. associate-/l* 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in t around 0 48.3%

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

      1. associate-/l* 55.7%

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

      2. associate-*r/ 66.4%

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

   8. Simplified 66.4%

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

   if -2.2000000000000002e69 < y < -1.38000000000000008e-86

   1. Initial program 76.0%

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

   3. Taylor expanded in y around inf 55.9%

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

   if -1.38000000000000008e-86 < y < 8.59999999999999932e-30

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0 68.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+75}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+69}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.38 \cdot 10^{-86}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+74}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-87}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.06e+154)
     t_1
     (if (<= y -6.5e+74)
       (+ z (- (* a (/ y x)) (* b (/ y x))))
       (if (<= y -9e+55)
         t_1
         (if (<= y -3.7e-87)
           (/ (- (* (+ y t) a) (* y b)) (+ y (+ x t)))
           (if (<= y 9.2e-30) (/ (+ (* t a) (* x z)) (+ x t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -6.5e+74) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -9e+55) {
		tmp = t_1;
	} else if (y <= -3.7e-87) {
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	} else if (y <= 9.2e-30) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.06d+154)) then
        tmp = t_1
    else if (y <= (-6.5d+74)) then
        tmp = z + ((a * (y / x)) - (b * (y / x)))
    else if (y <= (-9d+55)) then
        tmp = t_1
    else if (y <= (-3.7d-87)) then
        tmp = (((y + t) * a) - (y * b)) / (y + (x + t))
    else if (y <= 9.2d-30) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.06e+154) {
		tmp = t_1;
	} else if (y <= -6.5e+74) {
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	} else if (y <= -9e+55) {
		tmp = t_1;
	} else if (y <= -3.7e-87) {
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	} else if (y <= 9.2e-30) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.06e+154:
		tmp = t_1
	elif y <= -6.5e+74:
		tmp = z + ((a * (y / x)) - (b * (y / x)))
	elif y <= -9e+55:
		tmp = t_1
	elif y <= -3.7e-87:
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t))
	elif y <= 9.2e-30:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -6.5e+74)
		tmp = Float64(z + Float64(Float64(a * Float64(y / x)) - Float64(b * Float64(y / x))));
	elseif (y <= -9e+55)
		tmp = t_1;
	elseif (y <= -3.7e-87)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (y <= 9.2e-30)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.06e+154)
		tmp = t_1;
	elseif (y <= -6.5e+74)
		tmp = z + ((a * (y / x)) - (b * (y / x)));
	elseif (y <= -9e+55)
		tmp = t_1;
	elseif (y <= -3.7e-87)
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	elseif (y <= 9.2e-30)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.06e+154], t$95$1, If[LessEqual[y, -6.5e+74], N[(z + N[(N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e+55], t$95$1, If[LessEqual[y, -3.7e-87], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-30], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.06e154 or -6.49999999999999962e74 < y < -8.99999999999999996e55 or 9.19999999999999937e-30 < y

   1. Initial program 39.1%

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

   3. Taylor expanded in y around inf 77.5%

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

   if -1.06e154 < y < -6.49999999999999962e74

   1. Initial program 41.1%

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

   3. Taylor expanded in x around inf 32.9%

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

      1. associate--l+ 40.4%

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

      2. associate-/l* 47.7%

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

      3. associate-/l* 47.7%

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

      4. associate-/l* 58.4%

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

      5. associate-/l* 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in t around 0 48.3%

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

      1. associate-/l* 55.7%

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

      2. associate-*r/ 66.4%

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

   8. Simplified 66.4%

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

   if -8.99999999999999996e55 < y < -3.7000000000000002e-87

   1. Initial program 75.3%

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

   3. Taylor expanded in z around 0 56.6%

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

      1. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   if -3.7000000000000002e-87 < y < 9.19999999999999937e-30

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0 68.9%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+74}:\\ \;\;\;\;z + \left(a \cdot \frac{y}{x} - b \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+55}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-87}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+73}:\\ \;\;\;\;z - y \cdot \frac{b}{x}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+136}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.35e+73)
   (- z (* y (/ b x)))
   (if (<= x 2.8e+136) (- (+ z a) b) (* z (/ (+ x y) (+ y (+ x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.35e+73) {
		tmp = z - (y * (b / x));
	} else if (x <= 2.8e+136) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.35d+73)) then
        tmp = z - (y * (b / x))
    else if (x <= 2.8d+136) then
        tmp = (z + a) - b
    else
        tmp = z * ((x + y) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.35e+73) {
		tmp = z - (y * (b / x));
	} else if (x <= 2.8e+136) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.35e+73:
		tmp = z - (y * (b / x))
	elif x <= 2.8e+136:
		tmp = (z + a) - b
	else:
		tmp = z * ((x + y) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.35e+73)
		tmp = Float64(z - Float64(y * Float64(b / x)));
	elseif (x <= 2.8e+136)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.35e+73)
		tmp = z - (y * (b / x));
	elseif (x <= 2.8e+136)
		tmp = (z + a) - b;
	else
		tmp = z * ((x + y) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.35e+73], N[(z - N[(y * N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+136], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e73

   1. Initial program 55.8%

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

   3. Taylor expanded in x around inf 58.0%

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

      1. associate--l+ 58.1%

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

      2. associate-/l* 57.9%

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

      3. associate-/l* 58.2%

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

      4. associate-/l* 59.1%

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

      5. associate-/l* 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in y around inf 70.4%

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

   7. Taylor expanded in a around 0 64.9%

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

      1. neg-mul-1 64.9%

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

      2. distribute-neg-frac 64.9%

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

   9. Simplified 64.9%

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

   if -1.35e73 < x < 2.8000000000000002e136

   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. Add Preprocessing

   3. Taylor expanded in y around inf 63.0%

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

   if 2.8000000000000002e136 < x

   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. Add Preprocessing

   3. Taylor expanded in z around inf 33.2%

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

      1. associate-/l* 68.6%

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

      2. +-commutative 68.6%

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

      3. +-commutative 68.6%

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

      4. +-commutative 68.6%

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

      5. associate-+l+ 68.6%

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

      6. +-commutative 68.6%

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

   5. Simplified 68.6%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+73}:\\ \;\;\;\;z - y \cdot \frac{b}{x}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+136}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+72}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+135}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.05e+72)
   (+ z (* y (- (/ a x) (/ b x))))
   (if (<= x 3.5e+135) (- (+ z a) b) (* z (/ (+ x y) (+ y (+ x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.05e+72) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (x <= 3.5e+135) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.05d+72)) then
        tmp = z + (y * ((a / x) - (b / x)))
    else if (x <= 3.5d+135) then
        tmp = (z + a) - b
    else
        tmp = z * ((x + y) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.05e+72) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (x <= 3.5e+135) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.05e+72:
		tmp = z + (y * ((a / x) - (b / x)))
	elif x <= 3.5e+135:
		tmp = (z + a) - b
	else:
		tmp = z * ((x + y) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.05e+72)
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	elseif (x <= 3.5e+135)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.05e+72)
		tmp = z + (y * ((a / x) - (b / x)));
	elseif (x <= 3.5e+135)
		tmp = (z + a) - b;
	else
		tmp = z * ((x + y) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.05e+72], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+135], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0500000000000001e72

   1. Initial program 55.8%

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

   3. Taylor expanded in x around inf 58.0%

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

      1. associate--l+ 58.1%

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

      2. associate-/l* 57.9%

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

      3. associate-/l* 58.2%

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

      4. associate-/l* 59.1%

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

      5. associate-/l* 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in y around inf 70.4%

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

   if -1.0500000000000001e72 < x < 3.5000000000000003e135

   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. Add Preprocessing

   3. Taylor expanded in y around inf 63.0%

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

   if 3.5000000000000003e135 < x

   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. Add Preprocessing

   3. Taylor expanded in z around inf 33.2%

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

      1. associate-/l* 68.6%

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

      2. +-commutative 68.6%

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

      3. +-commutative 68.6%

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

      4. +-commutative 68.6%

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

      5. associate-+l+ 68.6%

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

      6. +-commutative 68.6%

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

   5. Simplified 68.6%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+72}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+135}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+162} \lor \neg \left(x \leq 7.5 \cdot 10^{+139}\right):\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -2.2e+162) (not (<= x 7.5e+139)))
   (+ z (* y (/ a x)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.2e+162) || !(x <= 7.5e+139)) {
		tmp = z + (y * (a / x));
	} 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 ((x <= (-2.2d+162)) .or. (.not. (x <= 7.5d+139))) then
        tmp = z + (y * (a / x))
    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 ((x <= -2.2e+162) || !(x <= 7.5e+139)) {
		tmp = z + (y * (a / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -2.2e+162) or not (x <= 7.5e+139):
		tmp = z + (y * (a / x))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -2.2e+162) || !(x <= 7.5e+139))
		tmp = Float64(z + Float64(y * Float64(a / x)));
	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 ((x <= -2.2e+162) || ~((x <= 7.5e+139)))
		tmp = z + (y * (a / x));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -2.2e+162], N[Not[LessEqual[x, 7.5e+139]], $MachinePrecision]], N[(z + N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2000000000000002e162 or 7.49999999999999992e139 < x

   1. Initial program 56.0%

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

   3. Taylor expanded in x around inf 60.2%

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

      1. associate--l+ 60.2%

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

      2. associate-/l* 62.1%

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

      3. associate-/l* 62.4%

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

      4. associate-/l* 62.6%

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

      5. associate-/l* 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in y around inf 72.7%

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

   7. Taylor expanded in a around inf 59.2%

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

   if -2.2000000000000002e162 < x < 7.49999999999999992e139

   1. Initial program 63.2%

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

   3. Taylor expanded in y around inf 61.8%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+162} \lor \neg \left(x \leq 7.5 \cdot 10^{+139}\right):\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 59.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+71} \lor \neg \left(x \leq 2.4 \cdot 10^{+125}\right):\\ \;\;\;\;z - b \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.5e+71) (not (<= x 2.4e+125)))
   (- z (* b (/ y x)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.5e+71) || !(x <= 2.4e+125)) {
		tmp = z - (b * (y / x));
	} 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 ((x <= (-1.5d+71)) .or. (.not. (x <= 2.4d+125))) then
        tmp = z - (b * (y / x))
    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 ((x <= -1.5e+71) || !(x <= 2.4e+125)) {
		tmp = z - (b * (y / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.5e+71) or not (x <= 2.4e+125):
		tmp = z - (b * (y / x))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.5e+71) || !(x <= 2.4e+125))
		tmp = Float64(z - Float64(b * Float64(y / x)));
	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 ((x <= -1.5e+71) || ~((x <= 2.4e+125)))
		tmp = z - (b * (y / x));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.5e+71], N[Not[LessEqual[x, 2.4e+125]], $MachinePrecision]], N[(z - N[(b * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000006e71 or 2.4e125 < x

   1. Initial program 52.9%

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

   3. Taylor expanded in x around inf 56.1%

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

      1. associate--l+ 56.1%

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

      2. associate-/l* 57.7%

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

      3. associate-/l* 58.0%

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

      4. associate-/l* 58.7%

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

      5. associate-/l* 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in y around inf 69.7%

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

   7. Taylor expanded in a around 0 55.8%

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

      1. mul-1-neg 55.8%

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

      2. unsub-neg 55.8%

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

      3. associate-/l* 62.6%

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

   9. Simplified 62.6%

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

   if -1.50000000000000006e71 < x < 2.4e125

   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. Add Preprocessing

   3. Taylor expanded in y around inf 63.0%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+71} \lor \neg \left(x \leq 2.4 \cdot 10^{+125}\right):\\ \;\;\;\;z - b \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 57.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+162}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+134}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.5e+162)
   z
   (if (<= x 7.5e+134) (- (+ z a) b) (* x (/ z (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.5e+162) {
		tmp = z;
	} else if (x <= 7.5e+134) {
		tmp = (z + a) - b;
	} else {
		tmp = x * (z / (x + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-7.5d+162)) then
        tmp = z
    else if (x <= 7.5d+134) then
        tmp = (z + a) - b
    else
        tmp = x * (z / (x + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.5e+162) {
		tmp = z;
	} else if (x <= 7.5e+134) {
		tmp = (z + a) - b;
	} else {
		tmp = x * (z / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.5e+162:
		tmp = z
	elif x <= 7.5e+134:
		tmp = (z + a) - b
	else:
		tmp = x * (z / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.5e+162)
		tmp = z;
	elseif (x <= 7.5e+134)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(x * Float64(z / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7.5e+162)
		tmp = z;
	elseif (x <= 7.5e+134)
		tmp = (z + a) - b;
	else
		tmp = x * (z / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.5e+162], z, If[LessEqual[x, 7.5e+134], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.50000000000000033e162

   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. Add Preprocessing

   3. Taylor expanded in x around inf 51.0%

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

   if -7.50000000000000033e162 < x < 7.5000000000000001e134

   1. Initial program 63.2%

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

   3. Taylor expanded in y around inf 61.8%

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

   if 7.5000000000000001e134 < x

   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. Add Preprocessing

   3. Taylor expanded in a around 0 36.5%

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

      1. +-commutative 36.5%

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

      2. *-commutative 36.5%

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

   5. Simplified 36.5%

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

   6. Taylor expanded in y around 0 33.2%

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

      1. +-commutative 33.2%

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

   8. Simplified 33.2%

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

      1. associate-/l* 54.9%

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

      2. +-commutative 54.9%

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

   10. Applied egg-rr 54.9%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+162}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+134}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 60.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+73}:\\ \;\;\;\;z - y \cdot \frac{b}{x}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+140}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - b \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.3e+73)
   (- z (* y (/ b x)))
   (if (<= x 1.3e+140) (- (+ z a) b) (- z (* b (/ y x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.3e+73) {
		tmp = z - (y * (b / x));
	} else if (x <= 1.3e+140) {
		tmp = (z + a) - b;
	} else {
		tmp = z - (b * (y / 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 (x <= (-1.3d+73)) then
        tmp = z - (y * (b / x))
    else if (x <= 1.3d+140) then
        tmp = (z + a) - b
    else
        tmp = z - (b * (y / 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 (x <= -1.3e+73) {
		tmp = z - (y * (b / x));
	} else if (x <= 1.3e+140) {
		tmp = (z + a) - b;
	} else {
		tmp = z - (b * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.3e+73:
		tmp = z - (y * (b / x))
	elif x <= 1.3e+140:
		tmp = (z + a) - b
	else:
		tmp = z - (b * (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.3e+73)
		tmp = Float64(z - Float64(y * Float64(b / x)));
	elseif (x <= 1.3e+140)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z - Float64(b * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.3e+73)
		tmp = z - (y * (b / x));
	elseif (x <= 1.3e+140)
		tmp = (z + a) - b;
	else
		tmp = z - (b * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.3e+73], N[(z - N[(y * N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+140], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z - N[(b * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3e73

   1. Initial program 55.8%

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

   3. Taylor expanded in x around inf 58.0%

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

      1. associate--l+ 58.1%

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

      2. associate-/l* 57.9%

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

      3. associate-/l* 58.2%

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

      4. associate-/l* 59.1%

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

      5. associate-/l* 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in y around inf 70.4%

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

   7. Taylor expanded in a around 0 64.9%

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

      1. neg-mul-1 64.9%

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

      2. distribute-neg-frac 64.9%

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

   9. Simplified 64.9%

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

   if -1.3e73 < x < 1.3000000000000001e140

   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. Add Preprocessing

   3. Taylor expanded in y around inf 63.0%

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

   if 1.3000000000000001e140 < x

   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. Add Preprocessing

   3. Taylor expanded in x around inf 52.2%

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

      1. associate--l+ 52.2%

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

      2. associate-/l* 57.2%

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

      3. associate-/l* 57.7%

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

      4. associate-/l* 58.0%

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

      5. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in y around inf 68.3%

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

   7. Taylor expanded in a around 0 53.3%

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

      1. mul-1-neg 53.3%

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

      2. unsub-neg 53.3%

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

      3. associate-/l* 61.5%

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

   9. Simplified 61.5%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+73}:\\ \;\;\;\;z - y \cdot \frac{b}{x}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+140}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - b \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 58.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+162}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+135}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.9e+162) z (if (<= x 5e+135) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.9e+162) {
		tmp = z;
	} else if (x <= 5e+135) {
		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 <= (-5.9d+162)) then
        tmp = z
    else if (x <= 5d+135) 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 <= -5.9e+162) {
		tmp = z;
	} else if (x <= 5e+135) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.9e+162:
		tmp = z
	elif x <= 5e+135:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.9e+162)
		tmp = z;
	elseif (x <= 5e+135)
		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 <= -5.9e+162)
		tmp = z;
	elseif (x <= 5e+135)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.9e+162], z, If[LessEqual[x, 5e+135], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -5.90000000000000027e162 or 5.00000000000000029e135 < x

   1. Initial program 56.0%

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

   3. Taylor expanded in x around inf 52.3%

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

   if -5.90000000000000027e162 < x < 5.00000000000000029e135

   1. Initial program 63.2%

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

   3. Taylor expanded in y around inf 61.8%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+162}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+135}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 47.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-48}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.4e-48) a (if (<= a 1.4e+20) (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.4e-48) {
		tmp = a;
	} else if (a <= 1.4e+20) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5.4d-48)) then
        tmp = a
    else if (a <= 1.4d+20) then
        tmp = z - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.4e-48) {
		tmp = a;
	} else if (a <= 1.4e+20) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.4e-48:
		tmp = a
	elif a <= 1.4e+20:
		tmp = z - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.4e-48)
		tmp = a;
	elseif (a <= 1.4e+20)
		tmp = Float64(z - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.4e-48)
		tmp = a;
	elseif (a <= 1.4e+20)
		tmp = z - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.4e-48], a, If[LessEqual[a, 1.4e+20], N[(z - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if a < -5.40000000000000023e-48 or 1.4e20 < a

   1. Initial program 53.7%

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

   3. Taylor expanded in t around inf 52.3%

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

   if -5.40000000000000023e-48 < a < 1.4e20

   1. Initial program 68.2%

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

   3. Taylor expanded in a around 0 59.2%

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

      1. +-commutative 59.2%

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

      2. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in y around inf 50.1%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-48}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 44.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-48}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 7500000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.55e-48) a (if (<= a 7500000000.0) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.55e-48) {
		tmp = a;
	} else if (a <= 7500000000.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.55d-48)) then
        tmp = a
    else if (a <= 7500000000.0d0) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.55e-48) {
		tmp = a;
	} else if (a <= 7500000000.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.55e-48:
		tmp = a
	elif a <= 7500000000.0:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.55e-48)
		tmp = a;
	elseif (a <= 7500000000.0)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.55e-48)
		tmp = a;
	elseif (a <= 7500000000.0)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.55e-48], a, If[LessEqual[a, 7500000000.0], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.55000000000000006e-48 or 7.5e9 < a

   1. Initial program 53.3%

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

   3. Taylor expanded in t around inf 51.9%

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

   if -2.55000000000000006e-48 < a < 7.5e9

   1. Initial program 68.7%

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

   3. Taylor expanded in x around inf 43.9%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-48}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 7500000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 32.5% 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 61.3%

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

3. Taylor expanded in t around inf 29.9%

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

4. Final simplification 29.9%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.4% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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