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

Percentage Accurate: 60.4% → 99.2%

Time: 14.7s

Alternatives: 22

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + t_1\right) - y \cdot b}{y + \left(x + t\right)}\\ t_3 := x + \left(y + t\right)\\ t_4 := \frac{y}{t_3}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 4 \cdot 10^{+287}\right):\\ \;\;\;\;\frac{x + y}{\frac{t_3}{z}} + \left(a \cdot \left(t_4 + \frac{t}{t_3}\right) - \frac{y}{\frac{t_3}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t_4 + \frac{x}{t_3}\right) + \frac{t_1 - y \cdot b}{t_3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (/ (- (+ (* z (+ x y)) t_1) (* y b)) (+ y (+ x t))))
        (t_3 (+ x (+ y t)))
        (t_4 (/ y t_3)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 4e+287)))
     (+ (/ (+ x y) (/ t_3 z)) (- (* a (+ t_4 (/ t t_3))) (/ y (/ t_3 b))))
     (+ (* z (+ t_4 (/ x t_3))) (/ (- t_1 (* y b)) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t));
	double t_3 = x + (y + t);
	double t_4 = y / t_3;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 4e+287)) {
		tmp = ((x + y) / (t_3 / z)) + ((a * (t_4 + (t / t_3))) - (y / (t_3 / b)));
	} else {
		tmp = (z * (t_4 + (x / t_3))) + ((t_1 - (y * b)) / t_3);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t));
	double t_3 = x + (y + t);
	double t_4 = y / t_3;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 4e+287)) {
		tmp = ((x + y) / (t_3 / z)) + ((a * (t_4 + (t / t_3))) - (y / (t_3 / b)));
	} else {
		tmp = (z * (t_4 + (x / t_3))) + ((t_1 - (y * b)) / t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t))
	t_3 = x + (y + t)
	t_4 = y / t_3
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 4e+287):
		tmp = ((x + y) / (t_3 / z)) + ((a * (t_4 + (t / t_3))) - (y / (t_3 / b)))
	else:
		tmp = (z * (t_4 + (x / t_3))) + ((t_1 - (y * b)) / t_3)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + t_1) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_3 = Float64(x + Float64(y + t))
	t_4 = Float64(y / t_3)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 4e+287))
		tmp = Float64(Float64(Float64(x + y) / Float64(t_3 / z)) + Float64(Float64(a * Float64(t_4 + Float64(t / t_3))) - Float64(y / Float64(t_3 / b))));
	else
		tmp = Float64(Float64(z * Float64(t_4 + Float64(x / t_3))) + Float64(Float64(t_1 - Float64(y * b)) / t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t));
	t_3 = x + (y + t);
	t_4 = y / t_3;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 4e+287)))
		tmp = ((x + y) / (t_3 / z)) + ((a * (t_4 + (t / t_3))) - (y / (t_3 / b)));
	else
		tmp = (z * (t_4 + (x / t_3))) + ((t_1 - (y * b)) / t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y / t$95$3), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 4e+287]], $MachinePrecision]], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$3 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(t$95$4 + N[(t / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t$95$3 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(t$95$4 + N[(x / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.0000000000000003e287 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.7%

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

   2. Taylor expanded in a around 0 30.4%

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

      1. associate--l+ 30.4%

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

      2. associate-/l* 69.7%

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

      3. associate-+r+ 69.7%

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

      4. associate-+r+ 69.7%

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

      5. associate-+r+ 69.7%

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

      6. associate-/l* 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000003e287

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-+r+ 99.7%

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

      4. associate-+r+ 99.7%

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

      5. div-sub 99.6%

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

      6. associate-+r+ 99.6%

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

   4. Simplified 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+287}\right):\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}} + \left(a \cdot \left(\frac{y}{x + \left(y + t\right)} + \frac{t}{x + \left(y + t\right)}\right) - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{y}{x + \left(y + t\right)} + \frac{x}{x + \left(y + t\right)}\right) + \frac{a \cdot \left(y + t\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \]

Alternative 2: 95.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + t_1\right) - y \cdot b}{y + \left(x + t\right)}\\ t_3 := x + \left(y + t\right)\\ t_4 := \frac{y}{t_3}\\ t_5 := \frac{y}{\frac{t_3}{b}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{x + y}{\frac{t_3}{z}} + \left(a - t_5\right)\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+287}:\\ \;\;\;\;z \cdot \left(t_4 + \frac{x}{t_3}\right) + \frac{t_1 - y \cdot b}{t_3}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a \cdot \left(t_4 + \frac{t}{t_3}\right) - t_5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (/ (- (+ (* z (+ x y)) t_1) (* y b)) (+ y (+ x t))))
        (t_3 (+ x (+ y t)))
        (t_4 (/ y t_3))
        (t_5 (/ y (/ t_3 b))))
   (if (<= t_2 (- INFINITY))
     (+ (/ (+ x y) (/ t_3 z)) (- a t_5))
     (if (<= t_2 4e+287)
       (+ (* z (+ t_4 (/ x t_3))) (/ (- t_1 (* y b)) t_3))
       (+ z (- (* a (+ t_4 (/ t t_3))) t_5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t));
	double t_3 = x + (y + t);
	double t_4 = y / t_3;
	double t_5 = y / (t_3 / b);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((x + y) / (t_3 / z)) + (a - t_5);
	} else if (t_2 <= 4e+287) {
		tmp = (z * (t_4 + (x / t_3))) + ((t_1 - (y * b)) / t_3);
	} else {
		tmp = z + ((a * (t_4 + (t / t_3))) - t_5);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t));
	double t_3 = x + (y + t);
	double t_4 = y / t_3;
	double t_5 = y / (t_3 / b);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = ((x + y) / (t_3 / z)) + (a - t_5);
	} else if (t_2 <= 4e+287) {
		tmp = (z * (t_4 + (x / t_3))) + ((t_1 - (y * b)) / t_3);
	} else {
		tmp = z + ((a * (t_4 + (t / t_3))) - t_5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t))
	t_3 = x + (y + t)
	t_4 = y / t_3
	t_5 = y / (t_3 / b)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = ((x + y) / (t_3 / z)) + (a - t_5)
	elif t_2 <= 4e+287:
		tmp = (z * (t_4 + (x / t_3))) + ((t_1 - (y * b)) / t_3)
	else:
		tmp = z + ((a * (t_4 + (t / t_3))) - t_5)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + t_1) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_3 = Float64(x + Float64(y + t))
	t_4 = Float64(y / t_3)
	t_5 = Float64(y / Float64(t_3 / b))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(x + y) / Float64(t_3 / z)) + Float64(a - t_5));
	elseif (t_2 <= 4e+287)
		tmp = Float64(Float64(z * Float64(t_4 + Float64(x / t_3))) + Float64(Float64(t_1 - Float64(y * b)) / t_3));
	else
		tmp = Float64(z + Float64(Float64(a * Float64(t_4 + Float64(t / t_3))) - t_5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t));
	t_3 = x + (y + t);
	t_4 = y / t_3;
	t_5 = y / (t_3 / b);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = ((x + y) / (t_3 / z)) + (a - t_5);
	elseif (t_2 <= 4e+287)
		tmp = (z * (t_4 + (x / t_3))) + ((t_1 - (y * b)) / t_3);
	else
		tmp = z + ((a * (t_4 + (t / t_3))) - t_5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(y / N[(t$95$3 / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$3 / z), $MachinePrecision]), $MachinePrecision] + N[(a - t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+287], N[(N[(z * N[(t$95$4 + N[(x / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision], N[(z + N[(N[(a * N[(t$95$4 + N[(t / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.5%

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

   2. Taylor expanded in a around 0 27.4%

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

      1. associate--l+ 27.4%

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

      2. associate-/l* 74.9%

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

      3. associate-+r+ 74.9%

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

      4. associate-+r+ 74.9%

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

      5. associate-+r+ 74.9%

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

      6. associate-/l* 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 97.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000003e287

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-+r+ 99.7%

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

      4. associate-+r+ 99.7%

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

      5. div-sub 99.6%

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

      6. associate-+r+ 99.6%

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

   4. Simplified 99.6%

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

   if 4.0000000000000003e287 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.0%

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

   2. Taylor expanded in a around 0 32.8%

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

      1. associate--l+ 32.8%

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

      2. associate-/l* 65.5%

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

      3. associate-+r+ 65.5%

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

      4. associate-+r+ 65.5%

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

      5. associate-+r+ 65.5%

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

      6. associate-/l* 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 92.5%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}} + \left(a - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+287}:\\ \;\;\;\;z \cdot \left(\frac{y}{x + \left(y + t\right)} + \frac{x}{x + \left(y + t\right)}\right) + \frac{a \cdot \left(y + t\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a \cdot \left(\frac{y}{x + \left(y + t\right)} + \frac{t}{x + \left(y + t\right)}\right) - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \end{array} \]

Alternative 3: 95.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := x + \left(y + t\right)\\ t_3 := \frac{y}{\frac{t_2}{b}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{x + y}{\frac{t_2}{z}} + \left(a - t_3\right)\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+287}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + \left(a \cdot \left(\frac{y}{t_2} + \frac{t}{t_2}\right) - t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t))))
        (t_2 (+ x (+ y t)))
        (t_3 (/ y (/ t_2 b))))
   (if (<= t_1 (- INFINITY))
     (+ (/ (+ x y) (/ t_2 z)) (- a t_3))
     (if (<= t_1 4e+287) t_1 (+ z (- (* a (+ (/ y t_2) (/ t t_2))) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = x + (y + t);
	double t_3 = y / (t_2 / b);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((x + y) / (t_2 / z)) + (a - t_3);
	} else if (t_1 <= 4e+287) {
		tmp = t_1;
	} else {
		tmp = z + ((a * ((y / t_2) + (t / t_2))) - t_3);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = x + (y + t);
	double t_3 = y / (t_2 / b);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((x + y) / (t_2 / z)) + (a - t_3);
	} else if (t_1 <= 4e+287) {
		tmp = t_1;
	} else {
		tmp = z + ((a * ((y / t_2) + (t / t_2))) - t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	t_2 = x + (y + t)
	t_3 = y / (t_2 / b)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((x + y) / (t_2 / z)) + (a - t_3)
	elif t_1 <= 4e+287:
		tmp = t_1
	else:
		tmp = z + ((a * ((y / t_2) + (t / t_2))) - t_3)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(y / Float64(t_2 / b))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(x + y) / Float64(t_2 / z)) + Float64(a - t_3));
	elseif (t_1 <= 4e+287)
		tmp = t_1;
	else
		tmp = Float64(z + Float64(Float64(a * Float64(Float64(y / t_2) + Float64(t / t_2))) - t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	t_2 = x + (y + t);
	t_3 = y / (t_2 / b);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((x + y) / (t_2 / z)) + (a - t_3);
	elseif (t_1 <= 4e+287)
		tmp = t_1;
	else
		tmp = z + ((a * ((y / t_2) + (t / t_2))) - t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(t$95$2 / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision] + N[(a - t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+287], t$95$1, N[(z + N[(N[(a * N[(N[(y / t$95$2), $MachinePrecision] + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.5%

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

   2. Taylor expanded in a around 0 27.4%

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

      1. associate--l+ 27.4%

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

      2. associate-/l* 74.9%

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

      3. associate-+r+ 74.9%

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

      4. associate-+r+ 74.9%

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

      5. associate-+r+ 74.9%

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

      6. associate-/l* 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 97.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000003e287

   1. Initial program 99.6%

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

   if 4.0000000000000003e287 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.0%

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

   2. Taylor expanded in a around 0 32.8%

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

      1. associate--l+ 32.8%

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

      2. associate-/l* 65.5%

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

      3. associate-+r+ 65.5%

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

      4. associate-+r+ 65.5%

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

      5. associate-+r+ 65.5%

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

      6. associate-/l* 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 92.5%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}} + \left(a - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+287}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a \cdot \left(\frac{y}{x + \left(y + t\right)} + \frac{t}{x + \left(y + t\right)}\right) - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \end{array} \]

Alternative 4: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 10^{+276}\right):\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(a - \frac{y}{\frac{t_1}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+276)))
     (+ (/ (+ x y) (/ t_1 z)) (- a (/ y (/ t_1 b))))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 1e+276)) {
		tmp = ((x + y) / (t_1 / z)) + (a - (y / (t_1 / b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 1e+276)) {
		tmp = ((x + y) / (t_1 / z)) + (a - (y / (t_1 / b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 1e+276):
		tmp = ((x + y) / (t_1 / z)) + (a - (y / (t_1 / b)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 1e+276))
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(a - Float64(y / Float64(t_1 / b))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 1e+276)))
		tmp = ((x + y) / (t_1 / z)) + (a - (y / (t_1 / b)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 1e+276]], $MachinePrecision]], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(a - N[(y / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

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 1.0000000000000001e276 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.4%

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

   2. Taylor expanded in a around 0 32.4%

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

      1. associate--l+ 32.4%

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

      2. associate-/l* 70.6%

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

      3. associate-+r+ 70.6%

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

      4. associate-+r+ 70.6%

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

      5. associate-+r+ 70.6%

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

      6. associate-/l* 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 94.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e276

   1. Initial program 99.6%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+276}\right):\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}} + \left(a - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 5: 91.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.5%

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

   2. Taylor expanded in a around 0 27.4%

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

      1. associate--l+ 27.4%

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

      2. associate-/l* 74.9%

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

      3. associate-+r+ 74.9%

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

      4. associate-+r+ 74.9%

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

      5. associate-+r+ 74.9%

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

      6. associate-/l* 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 88.1%

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

   6. Taylor expanded in y around inf 85.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000029e278

   1. Initial program 99.6%

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

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

   1. Initial program 8.3%

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

   2. Taylor expanded in a around 0 35.2%

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

      1. associate--l+ 35.2%

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

      2. associate-/l* 66.7%

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

      3. associate-+r+ 66.7%

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

      4. associate-+r+ 66.7%

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

      5. associate-+r+ 66.7%

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

      6. associate-/l* 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 92.1%

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

   6. Taylor expanded in y around inf 87.2%

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

4. Final simplification 94.4%

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

Alternative 6: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{y}{\frac{t_1}{b}}\\ t_3 := z + \left(a \cdot \frac{y + t}{x} - t_2\right)\\ t_4 := z + \left(a - t_2\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+169}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-113}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-141}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(a - b\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+33}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t)))
        (t_2 (/ y (/ t_1 b)))
        (t_3 (+ z (- (* a (/ (+ y t) x)) t_2)))
        (t_4 (+ z (- a t_2))))
   (if (<= x -4.5e+169)
     t_3
     (if (<= x -1.15e-113)
       t_4
       (if (<= x 1.1e-141)
         (+ (/ (+ x y) (/ t_1 z)) (- a b))
         (if (<= x 1.1e+33) t_4 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = y / (t_1 / b);
	double t_3 = z + ((a * ((y + t) / x)) - t_2);
	double t_4 = z + (a - t_2);
	double tmp;
	if (x <= -4.5e+169) {
		tmp = t_3;
	} else if (x <= -1.15e-113) {
		tmp = t_4;
	} else if (x <= 1.1e-141) {
		tmp = ((x + y) / (t_1 / z)) + (a - b);
	} else if (x <= 1.1e+33) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x + (y + t)
    t_2 = y / (t_1 / b)
    t_3 = z + ((a * ((y + t) / x)) - t_2)
    t_4 = z + (a - t_2)
    if (x <= (-4.5d+169)) then
        tmp = t_3
    else if (x <= (-1.15d-113)) then
        tmp = t_4
    else if (x <= 1.1d-141) then
        tmp = ((x + y) / (t_1 / z)) + (a - b)
    else if (x <= 1.1d+33) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = y / (t_1 / b);
	double t_3 = z + ((a * ((y + t) / x)) - t_2);
	double t_4 = z + (a - t_2);
	double tmp;
	if (x <= -4.5e+169) {
		tmp = t_3;
	} else if (x <= -1.15e-113) {
		tmp = t_4;
	} else if (x <= 1.1e-141) {
		tmp = ((x + y) / (t_1 / z)) + (a - b);
	} else if (x <= 1.1e+33) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = y / (t_1 / b)
	t_3 = z + ((a * ((y + t) / x)) - t_2)
	t_4 = z + (a - t_2)
	tmp = 0
	if x <= -4.5e+169:
		tmp = t_3
	elif x <= -1.15e-113:
		tmp = t_4
	elif x <= 1.1e-141:
		tmp = ((x + y) / (t_1 / z)) + (a - b)
	elif x <= 1.1e+33:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(y / Float64(t_1 / b))
	t_3 = Float64(z + Float64(Float64(a * Float64(Float64(y + t) / x)) - t_2))
	t_4 = Float64(z + Float64(a - t_2))
	tmp = 0.0
	if (x <= -4.5e+169)
		tmp = t_3;
	elseif (x <= -1.15e-113)
		tmp = t_4;
	elseif (x <= 1.1e-141)
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(a - b));
	elseif (x <= 1.1e+33)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = y / (t_1 / b);
	t_3 = z + ((a * ((y + t) / x)) - t_2);
	t_4 = z + (a - t_2);
	tmp = 0.0;
	if (x <= -4.5e+169)
		tmp = t_3;
	elseif (x <= -1.15e-113)
		tmp = t_4;
	elseif (x <= 1.1e-141)
		tmp = ((x + y) / (t_1 / z)) + (a - b);
	elseif (x <= 1.1e+33)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z + N[(N[(a * N[(N[(y + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z + N[(a - t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+169], t$95$3, If[LessEqual[x, -1.15e-113], t$95$4, If[LessEqual[x, 1.1e-141], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(a - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+33], t$95$4, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5e169 or 1.09999999999999997e33 < x

   1. Initial program 57.3%

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

   2. Taylor expanded in a around 0 62.3%

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

      1. associate--l+ 62.3%

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

      2. associate-/l* 82.1%

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

      3. associate-+r+ 82.1%

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

      4. associate-+r+ 82.1%

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

      5. associate-+r+ 82.1%

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

      6. associate-/l* 91.7%

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

      7. associate-+r+ 91.7%

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

      8. +-commutative 91.7%

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

      9. +-commutative 91.7%

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

   4. Simplified 91.7%

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

   5. Taylor expanded in y around inf 88.8%

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

   6. Taylor expanded in x around inf 80.2%

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

   if -4.5e169 < x < -1.15000000000000004e-113 or 1.10000000000000005e-141 < x < 1.09999999999999997e33

   1. Initial program 62.1%

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

   2. Taylor expanded in a around 0 73.9%

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

      1. associate--l+ 73.9%

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

      2. associate-/l* 81.9%

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

      3. associate-+r+ 81.9%

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

      4. associate-+r+ 81.9%

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

      5. associate-+r+ 81.9%

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

      6. associate-/l* 92.6%

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

      7. associate-+r+ 92.6%

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

      8. +-commutative 92.6%

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

      9. +-commutative 92.6%

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

   4. Simplified 92.6%

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

   5. Taylor expanded in y around inf 81.0%

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

   6. Taylor expanded in y around inf 74.4%

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

   if -1.15000000000000004e-113 < x < 1.10000000000000005e-141

   1. Initial program 70.4%

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

   2. Taylor expanded in a around 0 81.2%

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

      1. associate--l+ 81.2%

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

      2. associate-/l* 79.9%

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

      3. associate-+r+ 79.9%

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

      4. associate-+r+ 79.9%

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

      5. associate-+r+ 79.9%

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

      6. associate-/l* 91.8%

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

      7. associate-+r+ 91.8%

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

      8. +-commutative 91.8%

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

      9. +-commutative 91.8%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in y around inf 90.6%

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

   6. Taylor expanded in y around inf 81.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+169}:\\ \;\;\;\;z + \left(a \cdot \frac{y + t}{x} - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-113}:\\ \;\;\;\;z + \left(a - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-141}:\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}} + \left(a - b\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+33}:\\ \;\;\;\;z + \left(a - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(a \cdot \frac{y + t}{x} - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \end{array} \]

Alternative 7: 71.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := z + \left(\frac{a}{\frac{x + t}{t}} - \frac{y}{\frac{t_1}{b}}\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(a - b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t)))
        (t_2 (+ z (- (/ a (/ (+ x t) t)) (/ y (/ t_1 b))))))
   (if (<= z -2.55e-292)
     t_2
     (if (<= z 2.05e-209)
       (/ (* y (- (+ z a) b)) (+ y (+ x t)))
       (if (<= z 2.05e+152) t_2 (+ (/ (+ x y) (/ t_1 z)) (- a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = z + ((a / ((x + t) / t)) - (y / (t_1 / b)));
	double tmp;
	if (z <= -2.55e-292) {
		tmp = t_2;
	} else if (z <= 2.05e-209) {
		tmp = (y * ((z + a) - b)) / (y + (x + t));
	} else if (z <= 2.05e+152) {
		tmp = t_2;
	} else {
		tmp = ((x + y) / (t_1 / z)) + (a - b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y + t)
    t_2 = z + ((a / ((x + t) / t)) - (y / (t_1 / b)))
    if (z <= (-2.55d-292)) then
        tmp = t_2
    else if (z <= 2.05d-209) then
        tmp = (y * ((z + a) - b)) / (y + (x + t))
    else if (z <= 2.05d+152) then
        tmp = t_2
    else
        tmp = ((x + y) / (t_1 / z)) + (a - b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = z + ((a / ((x + t) / t)) - (y / (t_1 / b)));
	double tmp;
	if (z <= -2.55e-292) {
		tmp = t_2;
	} else if (z <= 2.05e-209) {
		tmp = (y * ((z + a) - b)) / (y + (x + t));
	} else if (z <= 2.05e+152) {
		tmp = t_2;
	} else {
		tmp = ((x + y) / (t_1 / z)) + (a - b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = z + ((a / ((x + t) / t)) - (y / (t_1 / b)))
	tmp = 0
	if z <= -2.55e-292:
		tmp = t_2
	elif z <= 2.05e-209:
		tmp = (y * ((z + a) - b)) / (y + (x + t))
	elif z <= 2.05e+152:
		tmp = t_2
	else:
		tmp = ((x + y) / (t_1 / z)) + (a - b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(z + Float64(Float64(a / Float64(Float64(x + t) / t)) - Float64(y / Float64(t_1 / b))))
	tmp = 0.0
	if (z <= -2.55e-292)
		tmp = t_2;
	elseif (z <= 2.05e-209)
		tmp = Float64(Float64(y * Float64(Float64(z + a) - b)) / Float64(y + Float64(x + t)));
	elseif (z <= 2.05e+152)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(a - b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = z + ((a / ((x + t) / t)) - (y / (t_1 / b)));
	tmp = 0.0;
	if (z <= -2.55e-292)
		tmp = t_2;
	elseif (z <= 2.05e-209)
		tmp = (y * ((z + a) - b)) / (y + (x + t));
	elseif (z <= 2.05e+152)
		tmp = t_2;
	else
		tmp = ((x + y) / (t_1 / z)) + (a - b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e-292], t$95$2, If[LessEqual[z, 2.05e-209], N[(N[(y * N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+152], t$95$2, N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(a - b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.55e-292 or 2.04999999999999989e-209 < z < 2.0499999999999999e152

   1. Initial program 63.7%

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

   2. Taylor expanded in a around 0 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-/l* 81.1%

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

      3. associate-+r+ 81.1%

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

      4. associate-+r+ 81.1%

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

      5. associate-+r+ 81.1%

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

      6. associate-/l* 92.5%

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

      7. associate-+r+ 92.5%

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

      8. +-commutative 92.5%

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

      9. +-commutative 92.5%

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

   4. Simplified 92.5%

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

   5. Taylor expanded in y around inf 86.5%

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

   6. Taylor expanded in y around 0 70.1%

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

      1. associate-/l* 78.7%

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

      2. +-commutative 78.7%

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

   8. Simplified 78.7%

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

   if -2.55e-292 < z < 2.04999999999999989e-209

   1. Initial program 81.9%

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

   2. Taylor expanded in y around inf 78.5%

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

   if 2.0499999999999999e152 < z

   1. Initial program 49.6%

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

   2. Taylor expanded in a around 0 52.1%

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

      1. associate--l+ 52.1%

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

      2. associate-/l* 75.7%

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

      3. associate-+r+ 75.7%

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

      4. associate-+r+ 75.7%

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

      5. associate-+r+ 75.7%

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

      6. associate-/l* 86.7%

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

      7. associate-+r+ 86.7%

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

      8. +-commutative 86.7%

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

      9. +-commutative 86.7%

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

   4. Simplified 86.7%

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

   5. Taylor expanded in y around inf 86.7%

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

   6. Taylor expanded in y around inf 79.7%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-292}:\\ \;\;\;\;z + \left(\frac{a}{\frac{x + t}{t}} - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+152}:\\ \;\;\;\;z + \left(\frac{a}{\frac{x + t}{t}} - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}} + \left(a - b\right)\\ \end{array} \]

Alternative 8: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := z + \left(a - \frac{y}{\frac{t_1}{b}}\right)\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-207}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(a - b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (+ z (- a (/ y (/ t_1 b))))))
   (if (<= z -7.6e-302)
     t_2
     (if (<= z 5.4e-207)
       (/ (* y (- (+ z a) b)) (+ y (+ x t)))
       (if (<= z 1.7e+29) t_2 (+ (/ (+ x y) (/ t_1 z)) (- a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = z + (a - (y / (t_1 / b)));
	double tmp;
	if (z <= -7.6e-302) {
		tmp = t_2;
	} else if (z <= 5.4e-207) {
		tmp = (y * ((z + a) - b)) / (y + (x + t));
	} else if (z <= 1.7e+29) {
		tmp = t_2;
	} else {
		tmp = ((x + y) / (t_1 / z)) + (a - b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y + t)
    t_2 = z + (a - (y / (t_1 / b)))
    if (z <= (-7.6d-302)) then
        tmp = t_2
    else if (z <= 5.4d-207) then
        tmp = (y * ((z + a) - b)) / (y + (x + t))
    else if (z <= 1.7d+29) then
        tmp = t_2
    else
        tmp = ((x + y) / (t_1 / z)) + (a - b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = z + (a - (y / (t_1 / b)));
	double tmp;
	if (z <= -7.6e-302) {
		tmp = t_2;
	} else if (z <= 5.4e-207) {
		tmp = (y * ((z + a) - b)) / (y + (x + t));
	} else if (z <= 1.7e+29) {
		tmp = t_2;
	} else {
		tmp = ((x + y) / (t_1 / z)) + (a - b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = z + (a - (y / (t_1 / b)))
	tmp = 0
	if z <= -7.6e-302:
		tmp = t_2
	elif z <= 5.4e-207:
		tmp = (y * ((z + a) - b)) / (y + (x + t))
	elif z <= 1.7e+29:
		tmp = t_2
	else:
		tmp = ((x + y) / (t_1 / z)) + (a - b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(z + Float64(a - Float64(y / Float64(t_1 / b))))
	tmp = 0.0
	if (z <= -7.6e-302)
		tmp = t_2;
	elseif (z <= 5.4e-207)
		tmp = Float64(Float64(y * Float64(Float64(z + a) - b)) / Float64(y + Float64(x + t)));
	elseif (z <= 1.7e+29)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(a - b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = z + (a - (y / (t_1 / b)));
	tmp = 0.0;
	if (z <= -7.6e-302)
		tmp = t_2;
	elseif (z <= 5.4e-207)
		tmp = (y * ((z + a) - b)) / (y + (x + t));
	elseif (z <= 1.7e+29)
		tmp = t_2;
	else
		tmp = ((x + y) / (t_1 / z)) + (a - b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(a - N[(y / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.6e-302], t$95$2, If[LessEqual[z, 5.4e-207], N[(N[(y * N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+29], t$95$2, N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(a - b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5999999999999999e-302 or 5.4e-207 < z < 1.69999999999999991e29

   1. Initial program 65.0%

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

   2. Taylor expanded in a around 0 74.6%

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

      1. associate--l+ 74.6%

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

      2. associate-/l* 80.8%

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

      3. associate-+r+ 80.8%

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

      4. associate-+r+ 80.8%

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

      5. associate-+r+ 80.8%

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

      6. associate-/l* 92.1%

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

      7. associate-+r+ 92.1%

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

      8. +-commutative 92.1%

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

      9. +-commutative 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in y around inf 86.2%

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

   6. Taylor expanded in y around inf 75.2%

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

   if -7.5999999999999999e-302 < z < 5.4e-207

   1. Initial program 78.0%

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

   2. Taylor expanded in y around inf 74.5%

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

   if 1.69999999999999991e29 < z

   1. Initial program 52.6%

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

   2. Taylor expanded in a around 0 58.6%

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

      1. associate--l+ 58.6%

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

      2. associate-/l* 78.3%

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

      3. associate-+r+ 78.3%

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

      4. associate-+r+ 78.3%

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

      5. associate-+r+ 78.3%

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

      6. associate-/l* 89.8%

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

      7. associate-+r+ 89.8%

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

      8. +-commutative 89.8%

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

      9. +-commutative 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in y around inf 83.2%

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

   6. Taylor expanded in y around inf 78.7%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-302}:\\ \;\;\;\;z + \left(a - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-207}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+29}:\\ \;\;\;\;z + \left(a - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}} + \left(a - b\right)\\ \end{array} \]

Alternative 9: 70.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := z + \left(a - \frac{y}{\frac{t_1}{b}}\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{-218}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (+ z (- a (/ y (/ t_1 b))))))
   (if (<= y -1.06e-218)
     t_2
     (if (<= y 1.5e-119)
       (/ (+ (* x z) (* t a)) (+ x t))
       (if (<= y 6.5e-40) (/ a (/ t_1 (+ y t))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = z + (a - (y / (t_1 / b)));
	double tmp;
	if (y <= -1.06e-218) {
		tmp = t_2;
	} else if (y <= 1.5e-119) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 6.5e-40) {
		tmp = a / (t_1 / (y + t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y + t)
    t_2 = z + (a - (y / (t_1 / b)))
    if (y <= (-1.06d-218)) then
        tmp = t_2
    else if (y <= 1.5d-119) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 6.5d-40) then
        tmp = a / (t_1 / (y + t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = z + (a - (y / (t_1 / b)));
	double tmp;
	if (y <= -1.06e-218) {
		tmp = t_2;
	} else if (y <= 1.5e-119) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 6.5e-40) {
		tmp = a / (t_1 / (y + t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = z + (a - (y / (t_1 / b)))
	tmp = 0
	if y <= -1.06e-218:
		tmp = t_2
	elif y <= 1.5e-119:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 6.5e-40:
		tmp = a / (t_1 / (y + t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(z + Float64(a - Float64(y / Float64(t_1 / b))))
	tmp = 0.0
	if (y <= -1.06e-218)
		tmp = t_2;
	elseif (y <= 1.5e-119)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 6.5e-40)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = z + (a - (y / (t_1 / b)));
	tmp = 0.0;
	if (y <= -1.06e-218)
		tmp = t_2;
	elseif (y <= 1.5e-119)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 6.5e-40)
		tmp = a / (t_1 / (y + t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(a - N[(y / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e-218], t$95$2, If[LessEqual[y, 1.5e-119], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-40], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0600000000000001e-218 or 6.4999999999999999e-40 < y

   1. Initial program 57.1%

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

   2. Taylor expanded in a around 0 67.2%

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

      1. associate--l+ 67.2%

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

      2. associate-/l* 78.4%

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

      3. associate-+r+ 78.4%

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

      4. associate-+r+ 78.4%

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

      5. associate-+r+ 78.4%

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

      6. associate-/l* 94.0%

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

      7. associate-+r+ 94.0%

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

      8. +-commutative 94.0%

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

      9. +-commutative 94.0%

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

   4. Simplified 94.0%

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

   5. Taylor expanded in y around inf 89.6%

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

   6. Taylor expanded in y around inf 79.4%

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

   if -1.0600000000000001e-218 < y < 1.5000000000000001e-119

   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. Taylor expanded in y around 0 63.6%

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

   if 1.5000000000000001e-119 < y < 6.4999999999999999e-40

   1. Initial program 80.2%

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

   2. Taylor expanded in a around inf 72.4%

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

      1. associate-/l* 85.7%

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

      2. associate-+r+ 85.7%

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

   4. Simplified 85.7%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-218}:\\ \;\;\;\;z + \left(a - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a - \frac{y}{\frac{x + \left(y + t\right)}{b}}\right)\\ \end{array} \]

Alternative 10: 54.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-126}:\\ \;\;\;\;\frac{x \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.5e-240)
     t_1
     (if (<= y 2.2e-126)
       (/ (* x z) (+ y (+ x t)))
       (if (<= y 1.4e-19) (/ a (/ (+ x (+ y t)) (+ y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.5e-240) {
		tmp = t_1;
	} else if (y <= 2.2e-126) {
		tmp = (x * z) / (y + (x + t));
	} else if (y <= 1.4e-19) {
		tmp = a / ((x + (y + t)) / (y + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.5d-240)) then
        tmp = t_1
    else if (y <= 2.2d-126) then
        tmp = (x * z) / (y + (x + t))
    else if (y <= 1.4d-19) then
        tmp = a / ((x + (y + t)) / (y + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.5e-240) {
		tmp = t_1;
	} else if (y <= 2.2e-126) {
		tmp = (x * z) / (y + (x + t));
	} else if (y <= 1.4e-19) {
		tmp = a / ((x + (y + t)) / (y + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.5e-240:
		tmp = t_1
	elif y <= 2.2e-126:
		tmp = (x * z) / (y + (x + t))
	elif y <= 1.4e-19:
		tmp = a / ((x + (y + t)) / (y + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.5e-240)
		tmp = t_1;
	elseif (y <= 2.2e-126)
		tmp = Float64(Float64(x * z) / Float64(y + Float64(x + t)));
	elseif (y <= 1.4e-19)
		tmp = Float64(a / Float64(Float64(x + Float64(y + t)) / Float64(y + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.5e-240)
		tmp = t_1;
	elseif (y <= 2.2e-126)
		tmp = (x * z) / (y + (x + t));
	elseif (y <= 1.4e-19)
		tmp = a / ((x + (y + t)) / (y + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.5e-240], t$95$1, If[LessEqual[y, 2.2e-126], N[(N[(x * z), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-19], N[(a / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.49999999999999995e-240 or 1.40000000000000001e-19 < y

   1. Initial program 56.5%

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

   2. Taylor expanded in y around inf 67.3%

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

   if -1.49999999999999995e-240 < y < 2.20000000000000014e-126

   1. Initial program 77.5%

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

   2. Taylor expanded in x around inf 52.6%

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

   3. Taylor expanded in z around inf 43.6%

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

   if 2.20000000000000014e-126 < y < 1.40000000000000001e-19

   1. Initial program 82.0%

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

   2. Taylor expanded in a around inf 54.6%

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

      1. associate-/l* 68.0%

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

      2. associate-+r+ 68.0%

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

   4. Simplified 68.0%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-240}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-126}:\\ \;\;\;\;\frac{x \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 55.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-124}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.3e-242)
     t_1
     (if (<= y 3.1e-124)
       (/ (* z (+ x y)) (+ y (+ x t)))
       (if (<= y 5.4e-20) (/ a (/ (+ x (+ y t)) (+ y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.3e-242) {
		tmp = t_1;
	} else if (y <= 3.1e-124) {
		tmp = (z * (x + y)) / (y + (x + t));
	} else if (y <= 5.4e-20) {
		tmp = a / ((x + (y + t)) / (y + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.3d-242)) then
        tmp = t_1
    else if (y <= 3.1d-124) then
        tmp = (z * (x + y)) / (y + (x + t))
    else if (y <= 5.4d-20) then
        tmp = a / ((x + (y + t)) / (y + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.3e-242) {
		tmp = t_1;
	} else if (y <= 3.1e-124) {
		tmp = (z * (x + y)) / (y + (x + t));
	} else if (y <= 5.4e-20) {
		tmp = a / ((x + (y + t)) / (y + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.3e-242:
		tmp = t_1
	elif y <= 3.1e-124:
		tmp = (z * (x + y)) / (y + (x + t))
	elif y <= 5.4e-20:
		tmp = a / ((x + (y + t)) / (y + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.3e-242)
		tmp = t_1;
	elseif (y <= 3.1e-124)
		tmp = Float64(Float64(z * Float64(x + y)) / Float64(y + Float64(x + t)));
	elseif (y <= 5.4e-20)
		tmp = Float64(a / Float64(Float64(x + Float64(y + t)) / Float64(y + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.3e-242)
		tmp = t_1;
	elseif (y <= 3.1e-124)
		tmp = (z * (x + y)) / (y + (x + t));
	elseif (y <= 5.4e-20)
		tmp = a / ((x + (y + t)) / (y + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.3e-242], t$95$1, If[LessEqual[y, 3.1e-124], N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-20], N[(a / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.30000000000000009e-242 or 5.3999999999999999e-20 < y

   1. Initial program 56.5%

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

   2. Taylor expanded in y around inf 67.3%

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

   if -1.30000000000000009e-242 < y < 3.0999999999999998e-124

   1. Initial program 77.5%

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

   2. Taylor expanded in z around inf 45.4%

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

   if 3.0999999999999998e-124 < y < 5.3999999999999999e-20

   1. Initial program 82.0%

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

   2. Taylor expanded in a around inf 54.6%

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

      1. associate-/l* 68.0%

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

      2. associate-+r+ 68.0%

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

   4. Simplified 68.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-242}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-124}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 12: 56.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-126}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-18}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (- (+ z a) b)))
   (if (<= y -1.05e-227)
     t_2
     (if (<= y 1.95e-126)
       (/ (+ x y) (/ t_1 z))
       (if (<= y 5.9e-18) (/ a (/ t_1 (+ y t))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.05e-227) {
		tmp = t_2;
	} else if (y <= 1.95e-126) {
		tmp = (x + y) / (t_1 / z);
	} else if (y <= 5.9e-18) {
		tmp = a / (t_1 / (y + t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y + t)
    t_2 = (z + a) - b
    if (y <= (-1.05d-227)) then
        tmp = t_2
    else if (y <= 1.95d-126) then
        tmp = (x + y) / (t_1 / z)
    else if (y <= 5.9d-18) then
        tmp = a / (t_1 / (y + t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.05e-227) {
		tmp = t_2;
	} else if (y <= 1.95e-126) {
		tmp = (x + y) / (t_1 / z);
	} else if (y <= 5.9e-18) {
		tmp = a / (t_1 / (y + t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -1.05e-227:
		tmp = t_2
	elif y <= 1.95e-126:
		tmp = (x + y) / (t_1 / z)
	elif y <= 5.9e-18:
		tmp = a / (t_1 / (y + t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.05e-227)
		tmp = t_2;
	elseif (y <= 1.95e-126)
		tmp = Float64(Float64(x + y) / Float64(t_1 / z));
	elseif (y <= 5.9e-18)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.05e-227)
		tmp = t_2;
	elseif (y <= 1.95e-126)
		tmp = (x + y) / (t_1 / z);
	elseif (y <= 5.9e-18)
		tmp = a / (t_1 / (y + t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.05e-227], t$95$2, If[LessEqual[y, 1.95e-126], N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.9e-18], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e-227 or 5.90000000000000019e-18 < y

   1. Initial program 56.9%

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

   2. Taylor expanded in y around inf 67.9%

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

   if -1.05e-227 < y < 1.9499999999999999e-126

   1. Initial program 75.2%

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

   2. Taylor expanded in z around inf 44.4%

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

      1. associate-/l* 53.2%

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

      2. associate-+r+ 53.2%

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

   4. Simplified 53.2%

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

   if 1.9499999999999999e-126 < y < 5.90000000000000019e-18

   1. Initial program 82.0%

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

   2. Taylor expanded in a around inf 54.6%

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

      1. associate-/l* 68.0%

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

      2. associate-+r+ 68.0%

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

   4. Simplified 68.0%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-227}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-126}:\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-18}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 13: 63.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.45e-113)
     t_1
     (if (<= y 9.8e-105)
       (/ (+ (* x z) (* t a)) (+ x t))
       (if (<= y 3.3e-18) (/ a (/ (+ x (+ y t)) (+ y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.45e-113) {
		tmp = t_1;
	} else if (y <= 9.8e-105) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 3.3e-18) {
		tmp = a / ((x + (y + t)) / (y + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.45d-113)) then
        tmp = t_1
    else if (y <= 9.8d-105) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 3.3d-18) then
        tmp = a / ((x + (y + t)) / (y + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.45e-113) {
		tmp = t_1;
	} else if (y <= 9.8e-105) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 3.3e-18) {
		tmp = a / ((x + (y + t)) / (y + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.45e-113:
		tmp = t_1
	elif y <= 9.8e-105:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 3.3e-18:
		tmp = a / ((x + (y + t)) / (y + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.45e-113)
		tmp = t_1;
	elseif (y <= 9.8e-105)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 3.3e-18)
		tmp = Float64(a / Float64(Float64(x + Float64(y + t)) / Float64(y + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.45e-113)
		tmp = t_1;
	elseif (y <= 9.8e-105)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 3.3e-18)
		tmp = a / ((x + (y + t)) / (y + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.45e-113], t$95$1, If[LessEqual[y, 9.8e-105], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-18], N[(a / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4500000000000001e-113 or 3.3000000000000002e-18 < y

   1. Initial program 53.2%

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

   2. Taylor expanded in y around inf 70.2%

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

   if -2.4500000000000001e-113 < y < 9.7999999999999999e-105

   1. Initial program 77.8%

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

   2. Taylor expanded in y around 0 60.2%

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

   if 9.7999999999999999e-105 < y < 3.3000000000000002e-18

   1. Initial program 82.4%

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

   2. Taylor expanded in a around inf 63.9%

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

      1. associate-/l* 75.7%

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

      2. associate-+r+ 75.7%

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

   4. Simplified 75.7%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-113}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 14: 58.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-113}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2e-38)
     t_1
     (if (<= y 5.2e-113)
       (+ z a)
       (if (<= y 4.6e-20) (/ a (/ (+ x t) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2e-38) {
		tmp = t_1;
	} else if (y <= 5.2e-113) {
		tmp = z + a;
	} else if (y <= 4.6e-20) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2d-38)) then
        tmp = t_1
    else if (y <= 5.2d-113) then
        tmp = z + a
    else if (y <= 4.6d-20) then
        tmp = a / ((x + t) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2e-38) {
		tmp = t_1;
	} else if (y <= 5.2e-113) {
		tmp = z + a;
	} else if (y <= 4.6e-20) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2e-38:
		tmp = t_1
	elif y <= 5.2e-113:
		tmp = z + a
	elif y <= 4.6e-20:
		tmp = a / ((x + t) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2e-38)
		tmp = t_1;
	elseif (y <= 5.2e-113)
		tmp = Float64(z + a);
	elseif (y <= 4.6e-20)
		tmp = Float64(a / Float64(Float64(x + t) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2e-38)
		tmp = t_1;
	elseif (y <= 5.2e-113)
		tmp = z + a;
	elseif (y <= 4.6e-20)
		tmp = a / ((x + t) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2e-38], t$95$1, If[LessEqual[y, 5.2e-113], N[(z + a), $MachinePrecision], If[LessEqual[y, 4.6e-20], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e-38 or 4.5999999999999998e-20 < y

   1. Initial program 50.5%

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

   2. Taylor expanded in y around inf 74.9%

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

   if -1.9999999999999999e-38 < y < 5.1999999999999998e-113

   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. Taylor expanded in y around inf 35.1%

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

   3. Taylor expanded in b around 0 42.6%

      \[\leadsto \color{blue}{a + z} \]
   4. Step-by-step derivation

      1. +-commutative 42.6%

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

   5. Simplified 42.6%

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

   if 5.1999999999999998e-113 < y < 4.5999999999999998e-20

   1. Initial program 84.2%

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

   2. Taylor expanded in t around inf 51.4%

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

   3. Taylor expanded in y around 0 39.7%

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

      1. associate-/l* 49.4%

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

   5. Simplified 49.4%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-38}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-113}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 15: 54.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-125}:\\ \;\;\;\;\frac{x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.45e-245)
     t_1
     (if (<= y 2.9e-125)
       (/ (* x z) (+ x t))
       (if (<= y 4.6e-20) (/ a (/ (+ x t) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.45e-245) {
		tmp = t_1;
	} else if (y <= 2.9e-125) {
		tmp = (x * z) / (x + t);
	} else if (y <= 4.6e-20) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.45d-245)) then
        tmp = t_1
    else if (y <= 2.9d-125) then
        tmp = (x * z) / (x + t)
    else if (y <= 4.6d-20) then
        tmp = a / ((x + t) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.45e-245) {
		tmp = t_1;
	} else if (y <= 2.9e-125) {
		tmp = (x * z) / (x + t);
	} else if (y <= 4.6e-20) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.45e-245:
		tmp = t_1
	elif y <= 2.9e-125:
		tmp = (x * z) / (x + t)
	elif y <= 4.6e-20:
		tmp = a / ((x + t) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.45e-245)
		tmp = t_1;
	elseif (y <= 2.9e-125)
		tmp = Float64(Float64(x * z) / Float64(x + t));
	elseif (y <= 4.6e-20)
		tmp = Float64(a / Float64(Float64(x + t) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.45e-245)
		tmp = t_1;
	elseif (y <= 2.9e-125)
		tmp = (x * z) / (x + t);
	elseif (y <= 4.6e-20)
		tmp = a / ((x + t) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.45e-245], t$95$1, If[LessEqual[y, 2.9e-125], N[(N[(x * z), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-20], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e-245 or 4.5999999999999998e-20 < y

   1. Initial program 56.5%

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

   2. Taylor expanded in y around inf 67.3%

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

   if -1.45e-245 < y < 2.9000000000000002e-125

   1. Initial program 77.5%

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

   2. Taylor expanded in z around inf 45.4%

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

      1. associate-/l* 52.8%

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

      2. associate-+r+ 52.8%

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

   4. Simplified 52.8%

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

   5. Taylor expanded in y around 0 43.6%

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

      1. +-commutative 43.6%

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

   7. Simplified 43.6%

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

   if 2.9000000000000002e-125 < y < 4.5999999999999998e-20

   1. Initial program 82.0%

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

   2. Taylor expanded in t around inf 49.4%

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

   3. Taylor expanded in y around 0 34.7%

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

      1. associate-/l* 47.4%

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

   5. Simplified 47.4%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-245}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-125}:\\ \;\;\;\;\frac{x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 16: 54.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-125}:\\ \;\;\;\;\frac{x \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-20}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.1e-240)
     t_1
     (if (<= y 1.15e-125)
       (/ (* x z) (+ y (+ x t)))
       (if (<= y 9e-20) (/ a (/ (+ x t) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.1e-240) {
		tmp = t_1;
	} else if (y <= 1.15e-125) {
		tmp = (x * z) / (y + (x + t));
	} else if (y <= 9e-20) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.1d-240)) then
        tmp = t_1
    else if (y <= 1.15d-125) then
        tmp = (x * z) / (y + (x + t))
    else if (y <= 9d-20) then
        tmp = a / ((x + t) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.1e-240) {
		tmp = t_1;
	} else if (y <= 1.15e-125) {
		tmp = (x * z) / (y + (x + t));
	} else if (y <= 9e-20) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.1e-240:
		tmp = t_1
	elif y <= 1.15e-125:
		tmp = (x * z) / (y + (x + t))
	elif y <= 9e-20:
		tmp = a / ((x + t) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.1e-240)
		tmp = t_1;
	elseif (y <= 1.15e-125)
		tmp = Float64(Float64(x * z) / Float64(y + Float64(x + t)));
	elseif (y <= 9e-20)
		tmp = Float64(a / Float64(Float64(x + t) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.1e-240)
		tmp = t_1;
	elseif (y <= 1.15e-125)
		tmp = (x * z) / (y + (x + t));
	elseif (y <= 9e-20)
		tmp = a / ((x + t) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.1e-240], t$95$1, If[LessEqual[y, 1.15e-125], N[(N[(x * z), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-20], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999994e-240 or 9.0000000000000003e-20 < y

   1. Initial program 56.5%

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

   2. Taylor expanded in y around inf 67.3%

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

   if -2.09999999999999994e-240 < y < 1.15e-125

   1. Initial program 77.5%

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

   2. Taylor expanded in x around inf 52.6%

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

   3. Taylor expanded in z around inf 43.6%

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

   if 1.15e-125 < y < 9.0000000000000003e-20

   1. Initial program 82.0%

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

   2. Taylor expanded in t around inf 49.4%

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

   3. Taylor expanded in y around 0 34.7%

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

      1. associate-/l* 47.4%

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

   5. Simplified 47.4%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-240}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-125}:\\ \;\;\;\;\frac{x \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-20}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 17: 59.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-113}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-60}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -5e-40)
     t_1
     (if (<= y 1.7e-113) (+ z a) (if (<= y 1.6e-60) a t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5e-40) {
		tmp = t_1;
	} else if (y <= 1.7e-113) {
		tmp = z + a;
	} else if (y <= 1.6e-60) {
		tmp = a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-5d-40)) then
        tmp = t_1
    else if (y <= 1.7d-113) then
        tmp = z + a
    else if (y <= 1.6d-60) then
        tmp = a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5e-40) {
		tmp = t_1;
	} else if (y <= 1.7e-113) {
		tmp = z + a;
	} else if (y <= 1.6e-60) {
		tmp = a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -5e-40:
		tmp = t_1
	elif y <= 1.7e-113:
		tmp = z + a
	elif y <= 1.6e-60:
		tmp = a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -5e-40)
		tmp = t_1;
	elseif (y <= 1.7e-113)
		tmp = Float64(z + a);
	elseif (y <= 1.6e-60)
		tmp = a;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -5e-40)
		tmp = t_1;
	elseif (y <= 1.7e-113)
		tmp = z + a;
	elseif (y <= 1.6e-60)
		tmp = a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5e-40], t$95$1, If[LessEqual[y, 1.7e-113], N[(z + a), $MachinePrecision], If[LessEqual[y, 1.6e-60], a, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.99999999999999965e-40 or 1.6000000000000001e-60 < y

   1. Initial program 52.1%

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

   2. Taylor expanded in y around inf 71.2%

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

   if -4.99999999999999965e-40 < y < 1.7000000000000001e-113

   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. Taylor expanded in y around inf 35.1%

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

   3. Taylor expanded in b around 0 42.6%

      \[\leadsto \color{blue}{a + z} \]
   4. Step-by-step derivation

      1. +-commutative 42.6%

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

   5. Simplified 42.6%

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

   if 1.7000000000000001e-113 < y < 1.6000000000000001e-60

   1. Initial program 89.9%

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

   2. Taylor expanded in t around inf 80.9%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-40}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-113}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-60}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 18: 52.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+25} \lor \neg \left(a \leq 3.1 \cdot 10^{-24}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.5e+25) (not (<= a 3.1e-24))) (+ z a) (- z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.5e+25) || !(a <= 3.1e-24)) {
		tmp = z + a;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.5d+25)) .or. (.not. (a <= 3.1d-24))) then
        tmp = z + a
    else
        tmp = z - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.5e+25) || !(a <= 3.1e-24)) {
		tmp = z + a;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.5e+25) or not (a <= 3.1e-24):
		tmp = z + a
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.5e+25) || !(a <= 3.1e-24))
		tmp = Float64(z + a);
	else
		tmp = Float64(z - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.5e+25) || ~((a <= 3.1e-24)))
		tmp = z + a;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.5e+25], N[Not[LessEqual[a, 3.1e-24]], $MachinePrecision]], N[(z + a), $MachinePrecision], N[(z - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.50000000000000003e25 or 3.1e-24 < a

   1. Initial program 53.6%

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

   2. Taylor expanded in y around inf 59.5%

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

   3. Taylor expanded in b around 0 60.0%

      \[\leadsto \color{blue}{a + z} \]
   4. Step-by-step derivation

      1. +-commutative 60.0%

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

   5. Simplified 60.0%

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

   if -1.50000000000000003e25 < a < 3.1e-24

   1. Initial program 71.2%

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

   2. Taylor expanded in y around inf 52.3%

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

   3. Taylor expanded in a around 0 50.3%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+25} \lor \neg \left(a \leq 3.1 \cdot 10^{-24}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \]

Alternative 19: 53.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-100}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-166}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.8e-100) (+ z a) (if (<= z 2.9e-166) (- a b) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.8e-100) {
		tmp = z + a;
	} else if (z <= 2.9e-166) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5.8d-100)) then
        tmp = z + a
    else if (z <= 2.9d-166) then
        tmp = a - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.8e-100) {
		tmp = z + a;
	} else if (z <= 2.9e-166) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.8e-100:
		tmp = z + a
	elif z <= 2.9e-166:
		tmp = a - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.8e-100)
		tmp = Float64(z + a);
	elseif (z <= 2.9e-166)
		tmp = Float64(a - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.8e-100)
		tmp = z + a;
	elseif (z <= 2.9e-166)
		tmp = a - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.8e-100], N[(z + a), $MachinePrecision], If[LessEqual[z, 2.9e-166], N[(a - b), $MachinePrecision], N[(z + a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999951e-100 or 2.9e-166 < z

   1. Initial program 56.4%

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

   2. Taylor expanded in y around inf 59.1%

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

   3. Taylor expanded in b around 0 54.8%

      \[\leadsto \color{blue}{a + z} \]
   4. Step-by-step derivation

      1. +-commutative 54.8%

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

   5. Simplified 54.8%

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

   if -5.79999999999999951e-100 < z < 2.9e-166

   1. Initial program 78.3%

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

   2. Taylor expanded in y around inf 47.7%

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

   3. Taylor expanded in z around 0 50.2%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-100}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-166}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 20: 44.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -108000000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-26}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -108000000.0) z (if (<= z 1.22e-26) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -108000000.0) {
		tmp = z;
	} else if (z <= 1.22e-26) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-108000000.0d0)) then
        tmp = z
    else if (z <= 1.22d-26) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -108000000.0) {
		tmp = z;
	} else if (z <= 1.22e-26) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -108000000.0:
		tmp = z
	elif z <= 1.22e-26:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -108000000.0)
		tmp = z;
	elseif (z <= 1.22e-26)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -108000000.0)
		tmp = z;
	elseif (z <= 1.22e-26)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -108000000.0], z, If[LessEqual[z, 1.22e-26], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.08e8 or 1.22e-26 < z

   1. Initial program 49.1%

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

   2. Taylor expanded in x around inf 50.4%

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

   if -1.08e8 < z < 1.22e-26

   1. Initial program 77.1%

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

   2. Taylor expanded in t around inf 42.0%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -108000000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-26}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 21: 52.1% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{+216}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 2.3e+216) (+ z a) (- b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.3e+216) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.3d+216) then
        tmp = z + a
    else
        tmp = -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.3e+216) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.3e+216:
		tmp = z + a
	else:
		tmp = -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.3e+216)
		tmp = Float64(z + a);
	else
		tmp = Float64(-b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.3e+216)
		tmp = z + a;
	else
		tmp = -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.3e+216], N[(z + a), $MachinePrecision], (-b)]

Derivation

1. Split input into 2 regimes

2. if b < 2.29999999999999996e216

   1. Initial program 63.7%

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

   2. Taylor expanded in y around inf 55.4%

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

   3. Taylor expanded in b around 0 51.2%

      \[\leadsto \color{blue}{a + z} \]
   4. Step-by-step derivation

      1. +-commutative 51.2%

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

   5. Simplified 51.2%

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

   if 2.29999999999999996e216 < b

   1. Initial program 50.3%

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

   2. Taylor expanded in y around inf 61.0%

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

   3. Taylor expanded in b around inf 48.7%

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

      1. neg-mul-1 48.7%

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

   5. Simplified 48.7%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{+216}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \]

Alternative 22: 32.8% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.9%

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

2. Taylor expanded in t around inf 27.5%

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

3. Final simplification 27.5%

   \[\leadsto a \]

Developer target: 82.1% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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