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

Percentage Accurate: 61.2% → 88.6%

Time: 11.5s

Alternatives: 13

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: 61.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+236} \lor \neg \left(t\_3 \leq 10^{+306}\right):\\ \;\;\;\;a \cdot \left(\frac{t}{t\_1} + \left(\left(\frac{y}{t\_1} + \frac{z}{a} \cdot \frac{x + y}{t\_1}\right) - b \cdot \frac{y}{a \cdot t\_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_2)))
   (if (or (<= t_3 -5e+236) (not (<= t_3 1e+306)))
     (*
      a
      (+
       (/ t t_1)
       (- (+ (/ y t_1) (* (/ z a) (/ (+ x y) t_1))) (* b (/ y (* a t_1))))))
     (/ (+ (* t a) (+ (* x z) (* y (- (+ z a) b)))) t_2))))

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 + (x + t);
	double t_3 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -5e+236) || !(t_3 <= 1e+306)) {
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * ((x + y) / t_1))) - (b * (y / (a * t_1)))));
	} else {
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / 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 = t + (x + y)
    t_2 = y + (x + t)
    t_3 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_2
    if ((t_3 <= (-5d+236)) .or. (.not. (t_3 <= 1d+306))) then
        tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * ((x + y) / t_1))) - (b * (y / (a * t_1)))))
    else
        tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = y + (x + t);
	double t_3 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -5e+236) || !(t_3 <= 1e+306)) {
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * ((x + y) / t_1))) - (b * (y / (a * t_1)))));
	} else {
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = y + (x + t)
	t_3 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_2
	tmp = 0
	if (t_3 <= -5e+236) or not (t_3 <= 1e+306):
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * ((x + y) / t_1))) - (b * (y / (a * t_1)))))
	else:
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_3 <= -5e+236) || !(t_3 <= 1e+306))
		tmp = Float64(a * Float64(Float64(t / t_1) + Float64(Float64(Float64(y / t_1) + Float64(Float64(z / a) * Float64(Float64(x + y) / t_1))) - Float64(b * Float64(y / Float64(a * t_1))))));
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * Float64(Float64(z + a) - b)))) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = y + (x + t);
	t_3 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_2;
	tmp = 0.0;
	if ((t_3 <= -5e+236) || ~((t_3 <= 1e+306)))
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * ((x + y) / t_1))) - (b * (y / (a * t_1)))));
	else
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2;
	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[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, -5e+236], N[Not[LessEqual[t$95$3, 1e+306]], $MachinePrecision]], N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $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)) < -4.9999999999999997e236 or 1.00000000000000002e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 13.1%

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

   3. Taylor expanded in a around inf 40.0%

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

      1. associate--l+ 40.0%

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

      2. +-commutative 40.0%

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

      3. +-commutative 40.0%

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

      4. times-frac 63.9%

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

      5. +-commutative 63.9%

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

      6. +-commutative 63.9%

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

      7. associate-/l* 80.3%

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

      8. +-commutative 80.3%

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

   5. Simplified 80.3%

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

   if -4.9999999999999997e236 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000002e306

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+236} \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+306}\right):\\ \;\;\;\;a \cdot \left(\frac{t}{t + \left(x + y\right)} + \left(\left(\frac{y}{t + \left(x + y\right)} + \frac{z}{a} \cdot \frac{x + y}{t + \left(x + y\right)}\right) - b \cdot \frac{y}{a \cdot \left(t + \left(x + y\right)\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 10^{+306}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot t\_3\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+306)))
     t_3
     (/ (+ (* t a) (+ (* x z) (* y t_3))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 1e+306)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 1e+306)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	t_3 = (z + a) - b
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 1e+306):
		tmp = t_3
	else:
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 1e+306))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * t_3))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 1e+306)))
		tmp = t_3;
	else
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 1e+306]], $MachinePrecision]], t$95$3, N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.00000000000000002e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.2%

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

   3. Taylor expanded in y around inf 71.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000002e306

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+306}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := t \cdot \frac{a + x \cdot \frac{z}{t}}{x + t}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-292}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* t (/ (+ a (* x (/ z t))) (+ x t)))))
   (if (<= t -1.3e+25)
     t_2
     (if (<= t -5.5e-290)
       t_1
       (if (<= t 2.4e-292)
         (- z (/ (* y b) (+ x y)))
         (if (<= t 1.3e-93)
           t_1
           (if (<= t 9e-14)
             (/ (- (* x z) (* y b)) (+ y (+ x t)))
             (if (<= t 1.15e+15) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = t * ((a + (x * (z / t))) / (x + t));
	double tmp;
	if (t <= -1.3e+25) {
		tmp = t_2;
	} else if (t <= -5.5e-290) {
		tmp = t_1;
	} else if (t <= 2.4e-292) {
		tmp = z - ((y * b) / (x + y));
	} else if (t <= 1.3e-93) {
		tmp = t_1;
	} else if (t <= 9e-14) {
		tmp = ((x * z) - (y * b)) / (y + (x + t));
	} else if (t <= 1.15e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = t * ((a + (x * (z / t))) / (x + t))
    if (t <= (-1.3d+25)) then
        tmp = t_2
    else if (t <= (-5.5d-290)) then
        tmp = t_1
    else if (t <= 2.4d-292) then
        tmp = z - ((y * b) / (x + y))
    else if (t <= 1.3d-93) then
        tmp = t_1
    else if (t <= 9d-14) then
        tmp = ((x * z) - (y * b)) / (y + (x + t))
    else if (t <= 1.15d+15) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = t * ((a + (x * (z / t))) / (x + t));
	double tmp;
	if (t <= -1.3e+25) {
		tmp = t_2;
	} else if (t <= -5.5e-290) {
		tmp = t_1;
	} else if (t <= 2.4e-292) {
		tmp = z - ((y * b) / (x + y));
	} else if (t <= 1.3e-93) {
		tmp = t_1;
	} else if (t <= 9e-14) {
		tmp = ((x * z) - (y * b)) / (y + (x + t));
	} else if (t <= 1.15e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = t * ((a + (x * (z / t))) / (x + t))
	tmp = 0
	if t <= -1.3e+25:
		tmp = t_2
	elif t <= -5.5e-290:
		tmp = t_1
	elif t <= 2.4e-292:
		tmp = z - ((y * b) / (x + y))
	elif t <= 1.3e-93:
		tmp = t_1
	elif t <= 9e-14:
		tmp = ((x * z) - (y * b)) / (y + (x + t))
	elif t <= 1.15e+15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(t * Float64(Float64(a + Float64(x * Float64(z / t))) / Float64(x + t)))
	tmp = 0.0
	if (t <= -1.3e+25)
		tmp = t_2;
	elseif (t <= -5.5e-290)
		tmp = t_1;
	elseif (t <= 2.4e-292)
		tmp = Float64(z - Float64(Float64(y * b) / Float64(x + y)));
	elseif (t <= 1.3e-93)
		tmp = t_1;
	elseif (t <= 9e-14)
		tmp = Float64(Float64(Float64(x * z) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (t <= 1.15e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = t * ((a + (x * (z / t))) / (x + t));
	tmp = 0.0;
	if (t <= -1.3e+25)
		tmp = t_2;
	elseif (t <= -5.5e-290)
		tmp = t_1;
	elseif (t <= 2.4e-292)
		tmp = z - ((y * b) / (x + y));
	elseif (t <= 1.3e-93)
		tmp = t_1;
	elseif (t <= 9e-14)
		tmp = ((x * z) - (y * b)) / (y + (x + t));
	elseif (t <= 1.15e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+25], t$95$2, If[LessEqual[t, -5.5e-290], t$95$1, If[LessEqual[t, 2.4e-292], N[(z - N[(N[(y * b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-93], t$95$1, If[LessEqual[t, 9e-14], N[(N[(N[(x * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+15], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2999999999999999e25 or 1.15e15 < t

   1. Initial program 55.6%

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

   3. Taylor expanded in t around inf 55.4%

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

      1. associate-/l* 55.6%

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

      2. associate-/l* 54.9%

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

      3. +-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in y around 0 42.9%

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

      1. associate-/l* 56.5%

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

      2. associate-/l* 63.7%

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

   8. Simplified 63.7%

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

   if -1.2999999999999999e25 < t < -5.5e-290 or 2.4000000000000001e-292 < t < 1.2999999999999999e-93 or 8.9999999999999995e-14 < t < 1.15e15

   1. Initial program 66.0%

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

   3. Taylor expanded in y around inf 68.0%

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

   if -5.5e-290 < t < 2.4000000000000001e-292

   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 a around inf 35.7%

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

      1. associate--l+ 35.7%

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

      2. +-commutative 35.7%

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

      3. +-commutative 35.7%

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

      4. times-frac 51.8%

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

      5. +-commutative 51.8%

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

      6. +-commutative 51.8%

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

      7. associate-/l* 52.0%

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

      8. +-commutative 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in t around 0 51.8%

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

      1. +-commutative 51.8%

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

      2. associate-/l* 52.0%

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

      3. associate-/r* 52.5%

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

      4. +-commutative 52.5%

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

   8. Simplified 52.5%

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

   9. Taylor expanded in a around 0 92.1%

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

       1. +-commutative 92.1%

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

   11. Simplified 92.1%

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

   if 1.2999999999999999e-93 < t < 8.9999999999999995e-14

   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 inf 72.6%

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

      1. associate-/l* 72.6%

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

      2. associate-/l* 72.3%

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

      3. +-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in x around inf 65.6%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{a + x \cdot \frac{z}{t}}{x + t}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-290}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-292}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-93}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+15}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a + x \cdot \frac{z}{t}}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{\frac{x + \left(y + t\right)}{y}}{a + \left(z - b\right)}}\\ t_2 := a \cdot \left(\left(\frac{z}{a} + \frac{y}{x + y}\right) - b \cdot \frac{\frac{y}{a}}{x + y}\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ (/ (+ x (+ y t)) y) (+ a (- z b)))))
        (t_2 (* a (- (+ (/ z a) (/ y (+ x y))) (* b (/ (/ y a) (+ x y)))))))
   (if (<= y -3.5e+133)
     t_1
     (if (<= y -3.25e-31)
       t_2
       (if (<= y -1.5e-60)
         (/ (- (* t a) (* y b)) (+ y (+ x t)))
         (if (<= y -3.25e-146)
           t_2
           (if (<= y 1.3e+31) (/ (+ (* 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 = 1.0 / (((x + (y + t)) / y) / (a + (z - b)));
	double t_2 = a * (((z / a) + (y / (x + y))) - (b * ((y / a) / (x + y))));
	double tmp;
	if (y <= -3.5e+133) {
		tmp = t_1;
	} else if (y <= -3.25e-31) {
		tmp = t_2;
	} else if (y <= -1.5e-60) {
		tmp = ((t * a) - (y * b)) / (y + (x + t));
	} else if (y <= -3.25e-146) {
		tmp = t_2;
	} else if (y <= 1.3e+31) {
		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 = 1.0d0 / (((x + (y + t)) / y) / (a + (z - b)))
    t_2 = a * (((z / a) + (y / (x + y))) - (b * ((y / a) / (x + y))))
    if (y <= (-3.5d+133)) then
        tmp = t_1
    else if (y <= (-3.25d-31)) then
        tmp = t_2
    else if (y <= (-1.5d-60)) then
        tmp = ((t * a) - (y * b)) / (y + (x + t))
    else if (y <= (-3.25d-146)) then
        tmp = t_2
    else if (y <= 1.3d+31) 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 = 1.0 / (((x + (y + t)) / y) / (a + (z - b)));
	double t_2 = a * (((z / a) + (y / (x + y))) - (b * ((y / a) / (x + y))));
	double tmp;
	if (y <= -3.5e+133) {
		tmp = t_1;
	} else if (y <= -3.25e-31) {
		tmp = t_2;
	} else if (y <= -1.5e-60) {
		tmp = ((t * a) - (y * b)) / (y + (x + t));
	} else if (y <= -3.25e-146) {
		tmp = t_2;
	} else if (y <= 1.3e+31) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 / (((x + (y + t)) / y) / (a + (z - b)))
	t_2 = a * (((z / a) + (y / (x + y))) - (b * ((y / a) / (x + y))))
	tmp = 0
	if y <= -3.5e+133:
		tmp = t_1
	elif y <= -3.25e-31:
		tmp = t_2
	elif y <= -1.5e-60:
		tmp = ((t * a) - (y * b)) / (y + (x + t))
	elif y <= -3.25e-146:
		tmp = t_2
	elif y <= 1.3e+31:
		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(1.0 / Float64(Float64(Float64(x + Float64(y + t)) / y) / Float64(a + Float64(z - b))))
	t_2 = Float64(a * Float64(Float64(Float64(z / a) + Float64(y / Float64(x + y))) - Float64(b * Float64(Float64(y / a) / Float64(x + y)))))
	tmp = 0.0
	if (y <= -3.5e+133)
		tmp = t_1;
	elseif (y <= -3.25e-31)
		tmp = t_2;
	elseif (y <= -1.5e-60)
		tmp = Float64(Float64(Float64(t * a) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (y <= -3.25e-146)
		tmp = t_2;
	elseif (y <= 1.3e+31)
		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 = 1.0 / (((x + (y + t)) / y) / (a + (z - b)));
	t_2 = a * (((z / a) + (y / (x + y))) - (b * ((y / a) / (x + y))));
	tmp = 0.0;
	if (y <= -3.5e+133)
		tmp = t_1;
	elseif (y <= -3.25e-31)
		tmp = t_2;
	elseif (y <= -1.5e-60)
		tmp = ((t * a) - (y * b)) / (y + (x + t));
	elseif (y <= -3.25e-146)
		tmp = t_2;
	elseif (y <= 1.3e+31)
		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[(1.0 / N[(N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(N[(z / a), $MachinePrecision] + N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(y / a), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+133], t$95$1, If[LessEqual[y, -3.25e-31], t$95$2, If[LessEqual[y, -1.5e-60], N[(N[(N[(t * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.25e-146], t$95$2, If[LessEqual[y, 1.3e+31], 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 < -3.4999999999999998e133 or 1.3e31 < y

   1. Initial program 38.8%

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

   3. Taylor expanded in y around inf 34.4%

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

      1. clear-num 34.4%

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

      2. inv-pow 34.4%

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

      3. +-commutative 34.4%

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

      4. +-commutative 34.4%

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

      5. associate--l+ 34.4%

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

   5. Applied egg-rr 34.4%

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

      1. unpow-1 34.4%

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

      2. associate-+r- 34.4%

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

      3. associate-/r* 84.5%

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

      4. associate-+r+ 84.5%

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

      5. +-commutative 84.5%

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

      6. +-commutative 84.5%

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

      7. +-commutative 84.5%

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

      8. associate-+r- 84.5%

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

   7. Simplified 84.5%

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

   if -3.4999999999999998e133 < y < -3.24999999999999983e-31 or -1.50000000000000009e-60 < y < -3.2499999999999999e-146

   1. Initial program 71.5%

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

   3. Taylor expanded in a around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. +-commutative 78.2%

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

      3. +-commutative 78.2%

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

      4. times-frac 95.8%

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

      5. +-commutative 95.8%

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

      6. +-commutative 95.8%

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

      7. associate-/l* 95.8%

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

      8. +-commutative 95.8%

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

   5. Simplified 95.8%

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

   6. Taylor expanded in t around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. associate-/l* 77.8%

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

      3. associate-/r* 77.8%

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

      4. +-commutative 77.8%

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

   8. Simplified 77.8%

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

   if -3.24999999999999983e-31 < y < -1.50000000000000009e-60

   1. Initial program 87.4%

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

   3. Taylor expanded in t around inf 75.1%

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

      1. associate-/l* 75.1%

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

      2. associate-/l* 75.1%

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

      3. +-commutative 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in t around inf 82.1%

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

   if -3.2499999999999999e-146 < y < 1.3e31

   1. Initial program 76.6%

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

   3. Taylor expanded in y around 0 58.1%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{1}{\frac{\frac{x + \left(y + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-31}:\\ \;\;\;\;a \cdot \left(\left(\frac{z}{a} + \frac{y}{x + y}\right) - b \cdot \frac{\frac{y}{a}}{x + y}\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-146}:\\ \;\;\;\;a \cdot \left(\left(\frac{z}{a} + \frac{y}{x + y}\right) - b \cdot \frac{\frac{y}{a}}{x + y}\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{x + \left(y + t\right)}{y}}{a + \left(z - b\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{\frac{x + \left(y + t\right)}{y}}{a + \left(z - b\right)}}\\ t_2 := t \cdot \frac{a + x \cdot \frac{z}{t}}{x + t}\\ \mathbf{if}\;t \leq -1 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-275}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{elif}\;t \leq 1050000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ (/ (+ x (+ y t)) y) (+ a (- z b)))))
        (t_2 (* t (/ (+ a (* x (/ z t))) (+ x t)))))
   (if (<= t -1e+24)
     t_2
     (if (<= t -1.12e-268)
       t_1
       (if (<= t 3.9e-275)
         (- z (/ (* y b) (+ x y)))
         (if (<= t 1050000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 / (((x + (y + t)) / y) / (a + (z - b)));
	double t_2 = t * ((a + (x * (z / t))) / (x + t));
	double tmp;
	if (t <= -1e+24) {
		tmp = t_2;
	} else if (t <= -1.12e-268) {
		tmp = t_1;
	} else if (t <= 3.9e-275) {
		tmp = z - ((y * b) / (x + y));
	} else if (t <= 1050000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 / (((x + (y + t)) / y) / (a + (z - b)))
    t_2 = t * ((a + (x * (z / t))) / (x + t))
    if (t <= (-1d+24)) then
        tmp = t_2
    else if (t <= (-1.12d-268)) then
        tmp = t_1
    else if (t <= 3.9d-275) then
        tmp = z - ((y * b) / (x + y))
    else if (t <= 1050000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 / (((x + (y + t)) / y) / (a + (z - b)));
	double t_2 = t * ((a + (x * (z / t))) / (x + t));
	double tmp;
	if (t <= -1e+24) {
		tmp = t_2;
	} else if (t <= -1.12e-268) {
		tmp = t_1;
	} else if (t <= 3.9e-275) {
		tmp = z - ((y * b) / (x + y));
	} else if (t <= 1050000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 / (((x + (y + t)) / y) / (a + (z - b)))
	t_2 = t * ((a + (x * (z / t))) / (x + t))
	tmp = 0
	if t <= -1e+24:
		tmp = t_2
	elif t <= -1.12e-268:
		tmp = t_1
	elif t <= 3.9e-275:
		tmp = z - ((y * b) / (x + y))
	elif t <= 1050000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 / Float64(Float64(Float64(x + Float64(y + t)) / y) / Float64(a + Float64(z - b))))
	t_2 = Float64(t * Float64(Float64(a + Float64(x * Float64(z / t))) / Float64(x + t)))
	tmp = 0.0
	if (t <= -1e+24)
		tmp = t_2;
	elseif (t <= -1.12e-268)
		tmp = t_1;
	elseif (t <= 3.9e-275)
		tmp = Float64(z - Float64(Float64(y * b) / Float64(x + y)));
	elseif (t <= 1050000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 / (((x + (y + t)) / y) / (a + (z - b)));
	t_2 = t * ((a + (x * (z / t))) / (x + t));
	tmp = 0.0;
	if (t <= -1e+24)
		tmp = t_2;
	elseif (t <= -1.12e-268)
		tmp = t_1;
	elseif (t <= 3.9e-275)
		tmp = z - ((y * b) / (x + y));
	elseif (t <= 1050000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 / N[(N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+24], t$95$2, If[LessEqual[t, -1.12e-268], t$95$1, If[LessEqual[t, 3.9e-275], N[(z - N[(N[(y * b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1050000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.9999999999999998e23 or 1.05e12 < t

   1. Initial program 54.8%

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

   3. Taylor expanded in t around inf 54.6%

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

      1. associate-/l* 54.8%

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

      2. associate-/l* 54.0%

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

      3. +-commutative 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in y around 0 42.3%

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

      1. associate-/l* 56.4%

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

      2. associate-/l* 63.6%

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

   8. Simplified 63.6%

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

   if -9.9999999999999998e23 < t < -1.11999999999999998e-268 or 3.89999999999999973e-275 < t < 1.05e12

   1. Initial program 68.5%

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

   3. Taylor expanded in y around inf 44.4%

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

      1. clear-num 44.3%

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

      2. inv-pow 44.3%

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

      3. +-commutative 44.3%

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

      4. +-commutative 44.3%

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

      5. associate--l+ 44.3%

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

   5. Applied egg-rr 44.3%

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

      1. unpow-1 44.3%

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

      2. associate-+r- 44.3%

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

      3. associate-/r* 69.0%

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

      4. associate-+r+ 69.0%

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

      5. +-commutative 69.0%

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

      6. +-commutative 69.0%

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

      7. +-commutative 69.0%

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

      8. associate-+r- 69.0%

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

   7. Simplified 69.0%

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

   if -1.11999999999999998e-268 < t < 3.89999999999999973e-275

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 46.3%

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

      1. associate--l+ 46.3%

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

      2. +-commutative 46.3%

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

      3. +-commutative 46.3%

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

      4. times-frac 57.0%

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

      5. +-commutative 57.0%

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

      6. +-commutative 57.0%

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

      7. associate-/l* 57.2%

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

      8. +-commutative 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in t around 0 57.0%

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

      1. +-commutative 57.0%

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

      2. associate-/l* 57.2%

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

      3. associate-/r* 52.0%

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

      4. +-commutative 52.0%

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

   8. Simplified 52.0%

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

   9. Taylor expanded in a around 0 89.3%

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

       1. +-commutative 89.3%

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

   11. Simplified 89.3%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \frac{a + x \cdot \frac{z}{t}}{x + t}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-268}:\\ \;\;\;\;\frac{1}{\frac{\frac{x + \left(y + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-275}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{elif}\;t \leq 1050000000000:\\ \;\;\;\;\frac{1}{\frac{\frac{x + \left(y + t\right)}{y}}{a + \left(z - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a + x \cdot \frac{z}{t}}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := t \cdot \frac{a + x \cdot \frac{z}{t}}{x + t}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-291}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* t (/ (+ a (* x (/ z t))) (+ x t)))))
   (if (<= t -2.1e+26)
     t_2
     (if (<= t -6e-287)
       t_1
       (if (<= t 2.15e-291)
         (- z (/ (* y b) (+ x y)))
         (if (<= t 2.25e+14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = t * ((a + (x * (z / t))) / (x + t));
	double tmp;
	if (t <= -2.1e+26) {
		tmp = t_2;
	} else if (t <= -6e-287) {
		tmp = t_1;
	} else if (t <= 2.15e-291) {
		tmp = z - ((y * b) / (x + y));
	} else if (t <= 2.25e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = t * ((a + (x * (z / t))) / (x + t))
    if (t <= (-2.1d+26)) then
        tmp = t_2
    else if (t <= (-6d-287)) then
        tmp = t_1
    else if (t <= 2.15d-291) then
        tmp = z - ((y * b) / (x + y))
    else if (t <= 2.25d+14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = t * ((a + (x * (z / t))) / (x + t));
	double tmp;
	if (t <= -2.1e+26) {
		tmp = t_2;
	} else if (t <= -6e-287) {
		tmp = t_1;
	} else if (t <= 2.15e-291) {
		tmp = z - ((y * b) / (x + y));
	} else if (t <= 2.25e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = t * ((a + (x * (z / t))) / (x + t))
	tmp = 0
	if t <= -2.1e+26:
		tmp = t_2
	elif t <= -6e-287:
		tmp = t_1
	elif t <= 2.15e-291:
		tmp = z - ((y * b) / (x + y))
	elif t <= 2.25e+14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(t * Float64(Float64(a + Float64(x * Float64(z / t))) / Float64(x + t)))
	tmp = 0.0
	if (t <= -2.1e+26)
		tmp = t_2;
	elseif (t <= -6e-287)
		tmp = t_1;
	elseif (t <= 2.15e-291)
		tmp = Float64(z - Float64(Float64(y * b) / Float64(x + y)));
	elseif (t <= 2.25e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = t * ((a + (x * (z / t))) / (x + t));
	tmp = 0.0;
	if (t <= -2.1e+26)
		tmp = t_2;
	elseif (t <= -6e-287)
		tmp = t_1;
	elseif (t <= 2.15e-291)
		tmp = z - ((y * b) / (x + y));
	elseif (t <= 2.25e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+26], t$95$2, If[LessEqual[t, -6e-287], t$95$1, If[LessEqual[t, 2.15e-291], N[(z - N[(N[(y * b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e+14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1000000000000001e26 or 2.25e14 < t

   1. Initial program 55.6%

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

   3. Taylor expanded in t around inf 55.4%

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

      1. associate-/l* 55.6%

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

      2. associate-/l* 54.9%

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

      3. +-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in y around 0 42.9%

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

      1. associate-/l* 56.5%

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

      2. associate-/l* 63.7%

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

   8. Simplified 63.7%

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

   if -2.1000000000000001e26 < t < -5.99999999999999984e-287 or 2.15000000000000018e-291 < t < 2.25e14

   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 y around inf 63.9%

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

   if -5.99999999999999984e-287 < t < 2.15000000000000018e-291

   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 a around inf 35.7%

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

      1. associate--l+ 35.7%

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

      2. +-commutative 35.7%

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

      3. +-commutative 35.7%

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

      4. times-frac 51.8%

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

      5. +-commutative 51.8%

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

      6. +-commutative 51.8%

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

      7. associate-/l* 52.0%

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

      8. +-commutative 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in t around 0 51.8%

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

      1. +-commutative 51.8%

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

      2. associate-/l* 52.0%

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

      3. associate-/r* 52.5%

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

      4. +-commutative 52.5%

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

   8. Simplified 52.5%

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

   9. Taylor expanded in a around 0 92.1%

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

       1. +-commutative 92.1%

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

   11. Simplified 92.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \frac{a + x \cdot \frac{z}{t}}{x + t}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-287}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-291}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+14}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a + x \cdot \frac{z}{t}}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -0.035:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-255}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* a (/ (+ y t) (+ y (+ x t))))))
   (if (<= a -6.2e+162)
     t_2
     (if (<= a -0.035)
       t_1
       (if (<= a 1.8e-255)
         (- z (/ (* y b) (+ x y)))
         (if (<= a 2.5e+83) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (y + (x + t)));
	double tmp;
	if (a <= -6.2e+162) {
		tmp = t_2;
	} else if (a <= -0.035) {
		tmp = t_1;
	} else if (a <= 1.8e-255) {
		tmp = z - ((y * b) / (x + y));
	} else if (a <= 2.5e+83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a * ((y + t) / (y + (x + t)))
    if (a <= (-6.2d+162)) then
        tmp = t_2
    else if (a <= (-0.035d0)) then
        tmp = t_1
    else if (a <= 1.8d-255) then
        tmp = z - ((y * b) / (x + y))
    else if (a <= 2.5d+83) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (y + (x + t)));
	double tmp;
	if (a <= -6.2e+162) {
		tmp = t_2;
	} else if (a <= -0.035) {
		tmp = t_1;
	} else if (a <= 1.8e-255) {
		tmp = z - ((y * b) / (x + y));
	} else if (a <= 2.5e+83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a * ((y + t) / (y + (x + t)))
	tmp = 0
	if a <= -6.2e+162:
		tmp = t_2
	elif a <= -0.035:
		tmp = t_1
	elif a <= 1.8e-255:
		tmp = z - ((y * b) / (x + y))
	elif a <= 2.5e+83:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (a <= -6.2e+162)
		tmp = t_2;
	elseif (a <= -0.035)
		tmp = t_1;
	elseif (a <= 1.8e-255)
		tmp = Float64(z - Float64(Float64(y * b) / Float64(x + y)));
	elseif (a <= 2.5e+83)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a * ((y + t) / (y + (x + t)));
	tmp = 0.0;
	if (a <= -6.2e+162)
		tmp = t_2;
	elseif (a <= -0.035)
		tmp = t_1;
	elseif (a <= 1.8e-255)
		tmp = z - ((y * b) / (x + y));
	elseif (a <= 2.5e+83)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+162], t$95$2, If[LessEqual[a, -0.035], t$95$1, If[LessEqual[a, 1.8e-255], N[(z - N[(N[(y * b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+83], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.1999999999999999e162 or 2.50000000000000014e83 < a

   1. Initial program 46.9%

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

   3. Taylor expanded in a around inf 31.6%

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

      1. associate-/l* 75.7%

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

      2. associate-+r+ 75.7%

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

   5. Simplified 75.7%

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

   if -6.1999999999999999e162 < a < -0.035000000000000003 or 1.8000000000000001e-255 < a < 2.50000000000000014e83

   1. Initial program 64.3%

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

   3. Taylor expanded in y around inf 64.0%

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

   if -0.035000000000000003 < a < 1.8000000000000001e-255

   1. Initial program 77.9%

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

   3. Taylor expanded in a around inf 58.9%

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

      1. associate--l+ 58.9%

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

      2. +-commutative 58.9%

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

      3. +-commutative 58.9%

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

      4. times-frac 60.2%

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

      5. +-commutative 60.2%

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

      6. +-commutative 60.2%

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

      7. associate-/l* 63.1%

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

      8. +-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in t around 0 40.6%

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

      1. +-commutative 40.6%

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

      2. associate-/l* 40.7%

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

      3. associate-/r* 40.1%

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

      4. +-commutative 40.1%

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

   8. Simplified 40.1%

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

   9. Taylor expanded in a around 0 56.8%

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

       1. +-commutative 56.8%

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

   11. Simplified 56.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -0.035:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-255}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+83}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -8 \cdot 10^{+230}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-292}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -8e+230)
     a
     (if (<= t -8.5e-289)
       t_1
       (if (<= t 1.8e-292)
         (- z (/ (* y b) (+ x y)))
         (if (<= t 4.8e+106) t_1 a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -8e+230) {
		tmp = a;
	} else if (t <= -8.5e-289) {
		tmp = t_1;
	} else if (t <= 1.8e-292) {
		tmp = z - ((y * b) / (x + y));
	} else if (t <= 4.8e+106) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-8d+230)) then
        tmp = a
    else if (t <= (-8.5d-289)) then
        tmp = t_1
    else if (t <= 1.8d-292) then
        tmp = z - ((y * b) / (x + y))
    else if (t <= 4.8d+106) then
        tmp = t_1
    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 t_1 = (z + a) - b;
	double tmp;
	if (t <= -8e+230) {
		tmp = a;
	} else if (t <= -8.5e-289) {
		tmp = t_1;
	} else if (t <= 1.8e-292) {
		tmp = z - ((y * b) / (x + y));
	} else if (t <= 4.8e+106) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -8e+230:
		tmp = a
	elif t <= -8.5e-289:
		tmp = t_1
	elif t <= 1.8e-292:
		tmp = z - ((y * b) / (x + y))
	elif t <= 4.8e+106:
		tmp = t_1
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -8e+230)
		tmp = a;
	elseif (t <= -8.5e-289)
		tmp = t_1;
	elseif (t <= 1.8e-292)
		tmp = Float64(z - Float64(Float64(y * b) / Float64(x + y)));
	elseif (t <= 4.8e+106)
		tmp = t_1;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -8e+230)
		tmp = a;
	elseif (t <= -8.5e-289)
		tmp = t_1;
	elseif (t <= 1.8e-292)
		tmp = z - ((y * b) / (x + y));
	elseif (t <= 4.8e+106)
		tmp = t_1;
	else
		tmp = a;
	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[t, -8e+230], a, If[LessEqual[t, -8.5e-289], t$95$1, If[LessEqual[t, 1.8e-292], N[(z - N[(N[(y * b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+106], t$95$1, a]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.0000000000000008e230 or 4.8000000000000001e106 < t

   1. Initial program 52.4%

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

   3. Taylor expanded in t around inf 63.3%

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

   if -8.0000000000000008e230 < t < -8.49999999999999931e-289 or 1.8000000000000001e-292 < t < 4.8000000000000001e106

   1. Initial program 65.1%

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

   3. Taylor expanded in y around inf 59.8%

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

   if -8.49999999999999931e-289 < t < 1.8000000000000001e-292

   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 a around inf 35.7%

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

      1. associate--l+ 35.7%

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

      2. +-commutative 35.7%

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

      3. +-commutative 35.7%

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

      4. times-frac 51.8%

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

      5. +-commutative 51.8%

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

      6. +-commutative 51.8%

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

      7. associate-/l* 52.0%

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

      8. +-commutative 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in t around 0 51.8%

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

      1. +-commutative 51.8%

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

      2. associate-/l* 52.0%

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

      3. associate-/r* 52.5%

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

      4. +-commutative 52.5%

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

   8. Simplified 52.5%

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

   9. Taylor expanded in a around 0 92.1%

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

       1. +-commutative 92.1%

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

   11. Simplified 92.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+230}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-289}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-292}:\\ \;\;\;\;z - \frac{y \cdot b}{x + y}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+106}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-72} \lor \neg \left(y \leq 3.2 \cdot 10^{-24}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.35e-72) (not (<= y 3.2e-24)))
   (- (+ z a) b)
   (/ (+ (* t a) (* x z)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e-72) || !(y <= 3.2e-24)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (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 ((y <= (-1.35d-72)) .or. (.not. (y <= 3.2d-24))) then
        tmp = (z + a) - b
    else
        tmp = ((t * a) + (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 ((y <= -1.35e-72) || !(y <= 3.2e-24)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.35e-72) or not (y <= 3.2e-24):
		tmp = (z + a) - b
	else:
		tmp = ((t * a) + (x * z)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.35e-72) || !(y <= 3.2e-24))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.35e-72) || ~((y <= 3.2e-24)))
		tmp = (z + a) - b;
	else
		tmp = ((t * a) + (x * z)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.35e-72], N[Not[LessEqual[y, 3.2e-24]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e-72 or 3.20000000000000012e-24 < y

   1. Initial program 51.3%

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

   3. Taylor expanded in y around inf 67.2%

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

   if -1.35e-72 < y < 3.20000000000000012e-24

   1. Initial program 77.4%

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

   3. Taylor expanded in y around 0 57.5%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-72} \lor \neg \left(y \leq 3.2 \cdot 10^{-24}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+155} \lor \neg \left(b \leq 6.5 \cdot 10^{+143}\right):\\ \;\;\;\;b \cdot \frac{y}{\left(-y\right) - \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9e+155) (not (<= b 6.5e+143)))
   (* b (/ y (- (- y) (+ x t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9e+155) || !(b <= 6.5e+143)) {
		tmp = b * (y / (-y - (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-9d+155)) .or. (.not. (b <= 6.5d+143))) then
        tmp = b * (y / (-y - (x + t)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9e+155) || !(b <= 6.5e+143)) {
		tmp = b * (y / (-y - (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -9e+155) or not (b <= 6.5e+143):
		tmp = b * (y / (-y - (x + t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9e+155) || !(b <= 6.5e+143))
		tmp = Float64(b * Float64(y / Float64(Float64(-y) - Float64(x + t))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -9e+155) || ~((b <= 6.5e+143)))
		tmp = b * (y / (-y - (x + t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9e+155], N[Not[LessEqual[b, 6.5e+143]], $MachinePrecision]], N[(b * N[(y / N[((-y) - N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.99999999999999947e155 or 6.4999999999999997e143 < b

   1. Initial program 61.4%

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

   3. Taylor expanded in b around inf 34.2%

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

      1. mul-1-neg 34.2%

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

      2. associate-/l* 55.5%

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

      3. distribute-rgt-neg-in 55.5%

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

      4. mul-1-neg 55.5%

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

      5. associate-*r/ 55.5%

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

      6. neg-mul-1 55.5%

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

      7. associate-+r+ 55.5%

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

   5. Simplified 55.5%

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

   if -8.99999999999999947e155 < b < 6.4999999999999997e143

   1. Initial program 63.4%

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

   3. Taylor expanded in y around inf 63.4%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+155} \lor \neg \left(b \leq 6.5 \cdot 10^{+143}\right):\\ \;\;\;\;b \cdot \frac{y}{\left(-y\right) - \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+230}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 10^{+109}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.6e+230) a (if (<= t 1e+109) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.6e+230) {
		tmp = a;
	} else if (t <= 1e+109) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.6d+230)) then
        tmp = a
    else if (t <= 1d+109) then
        tmp = (z + a) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.6e+230) {
		tmp = a;
	} else if (t <= 1e+109) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.6e+230:
		tmp = a
	elif t <= 1e+109:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.6e+230)
		tmp = a;
	elseif (t <= 1e+109)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.6e+230)
		tmp = a;
	elseif (t <= 1e+109)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.6e+230], a, If[LessEqual[t, 1e+109], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -7.6e230 or 9.99999999999999982e108 < t

   1. Initial program 52.4%

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

   3. Taylor expanded in t around inf 63.3%

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

   if -7.6e230 < t < 9.99999999999999982e108

   1. Initial program 65.7%

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

   3. Taylor expanded in y around inf 59.3%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+230}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 10^{+109}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+148}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+40}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8.6e+148) a (if (<= a 5.2e+40) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8.6e+148) {
		tmp = a;
	} else if (a <= 5.2e+40) {
		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 <= (-8.6d+148)) then
        tmp = a
    else if (a <= 5.2d+40) 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 <= -8.6e+148) {
		tmp = a;
	} else if (a <= 5.2e+40) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8.6e+148:
		tmp = a
	elif a <= 5.2e+40:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8.6e+148)
		tmp = a;
	elseif (a <= 5.2e+40)
		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 <= -8.6e+148)
		tmp = a;
	elseif (a <= 5.2e+40)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8.6e+148], a, If[LessEqual[a, 5.2e+40], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -8.6000000000000003e148 or 5.2000000000000001e40 < a

   1. Initial program 46.8%

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

   3. Taylor expanded in t around inf 52.2%

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

   if -8.6000000000000003e148 < a < 5.2000000000000001e40

   1. Initial program 70.6%

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

   3. Taylor expanded in x around inf 42.4%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+148}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+40}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.6% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.8%

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

3. Taylor expanded in t around inf 30.3%

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

4. Final simplification 30.3%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.3% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024072 
(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)))