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

Percentage Accurate: 60.4% → 87.9%

Time: 13.8s

Alternatives: 15

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+246}\right):\\ \;\;\;\;a + z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t)))
        (t_2 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+246)))
     (+ a (* z (+ (/ x t_1) (/ y t_1))))
     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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+246)) {
		tmp = a + (z * ((x / t_1) + (y / t_1)));
	} 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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+246)) {
		tmp = a + (z * ((x / t_1) + (y / t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+246):
		tmp = a + (z * ((x / t_1) + (y / t_1)))
	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(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+246))
		tmp = Float64(a + Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))));
	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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+246)))
		tmp = a + (z * ((x / t_1) + (y / t_1)));
	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[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+246]], $MachinePrecision]], N[(a + N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $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 4.99999999999999976e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   2. Taylor expanded in z around 0 39.9%

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

      1. associate--l+ 39.9%

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

      2. *-commutative 39.9%

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

      3. associate-+r+ 39.9%

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

      4. associate-+r+ 39.9%

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

      5. div-sub 39.9%

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

      6. associate-+r+ 39.9%

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

   4. Simplified 39.9%

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

   5. Taylor expanded in t around inf 76.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999976e246

   1. Initial program 99.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+246}\right):\\ \;\;\;\;a + z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{y}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 2: 58.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := x + \left(y + t\right)\\ t_4 := z \cdot \frac{x + y}{t_3}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+112}:\\ \;\;\;\;\frac{x + y}{\frac{t_3}{z}}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+49}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -24:\\ \;\;\;\;\frac{y \cdot t_1}{t_2}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-290}:\\ \;\;\;\;\left(a \cdot \left(y + t\right) - y \cdot b\right) \cdot \frac{1}{t_2}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{\left(y \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ x t)))
        (t_3 (+ x (+ y t)))
        (t_4 (* z (/ (+ x y) t_3))))
   (if (<= z -9e+112)
     (/ (+ x y) (/ t_3 z))
     (if (<= z -2.4e+76)
       a
       (if (<= z -5.8e+49)
         t_4
         (if (<= z -24.0)
           (/ (* y t_1) t_2)
           (if (<= z -1.2e-160)
             t_1
             (if (<= z 4.2e-290)
               (* (- (* a (+ y t)) (* y b)) (/ 1.0 t_2))
               (if (<= z 1.2e-28)
                 (/ (- (+ (* y a) (* z (+ x y))) (* y b)) (+ x y))
                 (if (<= z 3.4e+97) t_1 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = x + (y + t);
	double t_4 = z * ((x + y) / t_3);
	double tmp;
	if (z <= -9e+112) {
		tmp = (x + y) / (t_3 / z);
	} else if (z <= -2.4e+76) {
		tmp = a;
	} else if (z <= -5.8e+49) {
		tmp = t_4;
	} else if (z <= -24.0) {
		tmp = (y * t_1) / t_2;
	} else if (z <= -1.2e-160) {
		tmp = t_1;
	} else if (z <= 4.2e-290) {
		tmp = ((a * (y + t)) - (y * b)) * (1.0 / t_2);
	} else if (z <= 1.2e-28) {
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	} else if (z <= 3.4e+97) {
		tmp = t_1;
	} 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 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = x + (y + t)
    t_4 = z * ((x + y) / t_3)
    if (z <= (-9d+112)) then
        tmp = (x + y) / (t_3 / z)
    else if (z <= (-2.4d+76)) then
        tmp = a
    else if (z <= (-5.8d+49)) then
        tmp = t_4
    else if (z <= (-24.0d0)) then
        tmp = (y * t_1) / t_2
    else if (z <= (-1.2d-160)) then
        tmp = t_1
    else if (z <= 4.2d-290) then
        tmp = ((a * (y + t)) - (y * b)) * (1.0d0 / t_2)
    else if (z <= 1.2d-28) then
        tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y)
    else if (z <= 3.4d+97) then
        tmp = t_1
    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 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = x + (y + t);
	double t_4 = z * ((x + y) / t_3);
	double tmp;
	if (z <= -9e+112) {
		tmp = (x + y) / (t_3 / z);
	} else if (z <= -2.4e+76) {
		tmp = a;
	} else if (z <= -5.8e+49) {
		tmp = t_4;
	} else if (z <= -24.0) {
		tmp = (y * t_1) / t_2;
	} else if (z <= -1.2e-160) {
		tmp = t_1;
	} else if (z <= 4.2e-290) {
		tmp = ((a * (y + t)) - (y * b)) * (1.0 / t_2);
	} else if (z <= 1.2e-28) {
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	} else if (z <= 3.4e+97) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = x + (y + t)
	t_4 = z * ((x + y) / t_3)
	tmp = 0
	if z <= -9e+112:
		tmp = (x + y) / (t_3 / z)
	elif z <= -2.4e+76:
		tmp = a
	elif z <= -5.8e+49:
		tmp = t_4
	elif z <= -24.0:
		tmp = (y * t_1) / t_2
	elif z <= -1.2e-160:
		tmp = t_1
	elif z <= 4.2e-290:
		tmp = ((a * (y + t)) - (y * b)) * (1.0 / t_2)
	elif z <= 1.2e-28:
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y)
	elif z <= 3.4e+97:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(x + Float64(y + t))
	t_4 = Float64(z * Float64(Float64(x + y) / t_3))
	tmp = 0.0
	if (z <= -9e+112)
		tmp = Float64(Float64(x + y) / Float64(t_3 / z));
	elseif (z <= -2.4e+76)
		tmp = a;
	elseif (z <= -5.8e+49)
		tmp = t_4;
	elseif (z <= -24.0)
		tmp = Float64(Float64(y * t_1) / t_2);
	elseif (z <= -1.2e-160)
		tmp = t_1;
	elseif (z <= 4.2e-290)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) * Float64(1.0 / t_2));
	elseif (z <= 1.2e-28)
		tmp = Float64(Float64(Float64(Float64(y * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(x + y));
	elseif (z <= 3.4e+97)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = x + (y + t);
	t_4 = z * ((x + y) / t_3);
	tmp = 0.0;
	if (z <= -9e+112)
		tmp = (x + y) / (t_3 / z);
	elseif (z <= -2.4e+76)
		tmp = a;
	elseif (z <= -5.8e+49)
		tmp = t_4;
	elseif (z <= -24.0)
		tmp = (y * t_1) / t_2;
	elseif (z <= -1.2e-160)
		tmp = t_1;
	elseif (z <= 4.2e-290)
		tmp = ((a * (y + t)) - (y * b)) * (1.0 / t_2);
	elseif (z <= 1.2e-28)
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	elseif (z <= 3.4e+97)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+112], N[(N[(x + y), $MachinePrecision] / N[(t$95$3 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e+76], a, If[LessEqual[z, -5.8e+49], t$95$4, If[LessEqual[z, -24.0], N[(N[(y * t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, -1.2e-160], t$95$1, If[LessEqual[z, 4.2e-290], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-28], N[(N[(N[(N[(y * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+97], t$95$1, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -8.9999999999999998e112

   1. Initial program 45.7%

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

   2. Taylor expanded in z around inf 32.0%

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

      1. associate-/l* 68.5%

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

      2. associate-+r+ 68.5%

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

   4. Simplified 68.5%

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

   if -8.9999999999999998e112 < z < -2.4e76

   1. Initial program 52.8%

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

   2. Taylor expanded in t around inf 83.6%

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

   if -2.4e76 < z < -5.8e49 or 3.4000000000000001e97 < z

   1. Initial program 36.2%

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

   2. Taylor expanded in z around inf 25.3%

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

      1. associate-/l* 75.7%

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

      2. associate-+r+ 75.7%

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

   4. Simplified 75.7%

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

      1. associate-/r/ 75.8%

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

      2. +-commutative 75.8%

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

      3. +-commutative 75.8%

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

   6. Applied egg-rr 75.8%

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

   if -5.8e49 < z < -24

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 99.7%

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

   if -24 < z < -1.19999999999999995e-160 or 1.2000000000000001e-28 < z < 3.4000000000000001e97

   1. Initial program 62.7%

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

   2. Taylor expanded in y around inf 75.1%

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

   if -1.19999999999999995e-160 < z < 4.2000000000000002e-290

   1. Initial program 75.9%

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

   2. Taylor expanded in z around 0 73.4%

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

      1. associate-+r+ 73.4%

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

   4. Simplified 73.4%

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

      1. div-inv 73.7%

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

      2. associate-+l+ 73.7%

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

   6. Applied egg-rr 73.7%

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

   if 4.2000000000000002e-290 < z < 1.2000000000000001e-28

   1. Initial program 84.6%

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

   2. Taylor expanded in t around 0 71.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+112}:\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq -24:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-160}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-290}:\\ \;\;\;\;\left(a \cdot \left(y + t\right) - y \cdot b\right) \cdot \frac{1}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{\left(y \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{x + y}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+97}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \end{array} \]

Alternative 3: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := x + \left(y + t\right)\\ t_4 := z \cdot \frac{x + y}{t_3}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+112}:\\ \;\;\;\;\frac{x + y}{\frac{t_3}{z}}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+78}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+49}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -24:\\ \;\;\;\;\frac{y \cdot t_1}{t_2}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-67}:\\ \;\;\;\;\left(a \cdot \left(y + t\right) - y \cdot b\right) \cdot \frac{1}{t_2}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ x t)))
        (t_3 (+ x (+ y t)))
        (t_4 (* z (/ (+ x y) t_3))))
   (if (<= z -9e+112)
     (/ (+ x y) (/ t_3 z))
     (if (<= z -6.5e+78)
       a
       (if (<= z -3e+49)
         t_4
         (if (<= z -24.0)
           (/ (* y t_1) t_2)
           (if (<= z -6e-161)
             t_1
             (if (<= z 1.8e-67)
               (* (- (* a (+ y t)) (* y b)) (/ 1.0 t_2))
               (if (<= z 4e+97) t_1 t_4)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = x + (y + t);
	double t_4 = z * ((x + y) / t_3);
	double tmp;
	if (z <= -9e+112) {
		tmp = (x + y) / (t_3 / z);
	} else if (z <= -6.5e+78) {
		tmp = a;
	} else if (z <= -3e+49) {
		tmp = t_4;
	} else if (z <= -24.0) {
		tmp = (y * t_1) / t_2;
	} else if (z <= -6e-161) {
		tmp = t_1;
	} else if (z <= 1.8e-67) {
		tmp = ((a * (y + t)) - (y * b)) * (1.0 / t_2);
	} else if (z <= 4e+97) {
		tmp = t_1;
	} 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 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = x + (y + t)
    t_4 = z * ((x + y) / t_3)
    if (z <= (-9d+112)) then
        tmp = (x + y) / (t_3 / z)
    else if (z <= (-6.5d+78)) then
        tmp = a
    else if (z <= (-3d+49)) then
        tmp = t_4
    else if (z <= (-24.0d0)) then
        tmp = (y * t_1) / t_2
    else if (z <= (-6d-161)) then
        tmp = t_1
    else if (z <= 1.8d-67) then
        tmp = ((a * (y + t)) - (y * b)) * (1.0d0 / t_2)
    else if (z <= 4d+97) then
        tmp = t_1
    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 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = x + (y + t);
	double t_4 = z * ((x + y) / t_3);
	double tmp;
	if (z <= -9e+112) {
		tmp = (x + y) / (t_3 / z);
	} else if (z <= -6.5e+78) {
		tmp = a;
	} else if (z <= -3e+49) {
		tmp = t_4;
	} else if (z <= -24.0) {
		tmp = (y * t_1) / t_2;
	} else if (z <= -6e-161) {
		tmp = t_1;
	} else if (z <= 1.8e-67) {
		tmp = ((a * (y + t)) - (y * b)) * (1.0 / t_2);
	} else if (z <= 4e+97) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = x + (y + t)
	t_4 = z * ((x + y) / t_3)
	tmp = 0
	if z <= -9e+112:
		tmp = (x + y) / (t_3 / z)
	elif z <= -6.5e+78:
		tmp = a
	elif z <= -3e+49:
		tmp = t_4
	elif z <= -24.0:
		tmp = (y * t_1) / t_2
	elif z <= -6e-161:
		tmp = t_1
	elif z <= 1.8e-67:
		tmp = ((a * (y + t)) - (y * b)) * (1.0 / t_2)
	elif z <= 4e+97:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(x + Float64(y + t))
	t_4 = Float64(z * Float64(Float64(x + y) / t_3))
	tmp = 0.0
	if (z <= -9e+112)
		tmp = Float64(Float64(x + y) / Float64(t_3 / z));
	elseif (z <= -6.5e+78)
		tmp = a;
	elseif (z <= -3e+49)
		tmp = t_4;
	elseif (z <= -24.0)
		tmp = Float64(Float64(y * t_1) / t_2);
	elseif (z <= -6e-161)
		tmp = t_1;
	elseif (z <= 1.8e-67)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) * Float64(1.0 / t_2));
	elseif (z <= 4e+97)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = x + (y + t);
	t_4 = z * ((x + y) / t_3);
	tmp = 0.0;
	if (z <= -9e+112)
		tmp = (x + y) / (t_3 / z);
	elseif (z <= -6.5e+78)
		tmp = a;
	elseif (z <= -3e+49)
		tmp = t_4;
	elseif (z <= -24.0)
		tmp = (y * t_1) / t_2;
	elseif (z <= -6e-161)
		tmp = t_1;
	elseif (z <= 1.8e-67)
		tmp = ((a * (y + t)) - (y * b)) * (1.0 / t_2);
	elseif (z <= 4e+97)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+112], N[(N[(x + y), $MachinePrecision] / N[(t$95$3 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e+78], a, If[LessEqual[z, -3e+49], t$95$4, If[LessEqual[z, -24.0], N[(N[(y * t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, -6e-161], t$95$1, If[LessEqual[z, 1.8e-67], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+97], t$95$1, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -8.9999999999999998e112

   1. Initial program 45.7%

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

   2. Taylor expanded in z around inf 32.0%

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

      1. associate-/l* 68.5%

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

      2. associate-+r+ 68.5%

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

   4. Simplified 68.5%

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

   if -8.9999999999999998e112 < z < -6.50000000000000036e78

   1. Initial program 52.8%

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

   2. Taylor expanded in t around inf 83.6%

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

   if -6.50000000000000036e78 < z < -3.0000000000000002e49 or 4.0000000000000003e97 < z

   1. Initial program 36.2%

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

   2. Taylor expanded in z around inf 25.3%

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

      1. associate-/l* 75.7%

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

      2. associate-+r+ 75.7%

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

   4. Simplified 75.7%

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

      1. associate-/r/ 75.8%

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

      2. +-commutative 75.8%

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

      3. +-commutative 75.8%

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

   6. Applied egg-rr 75.8%

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

   if -3.0000000000000002e49 < z < -24

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 99.7%

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

   if -24 < z < -5.99999999999999977e-161 or 1.8e-67 < z < 4.0000000000000003e97

   1. Initial program 67.7%

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

   2. Taylor expanded in y around inf 74.2%

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

   if -5.99999999999999977e-161 < z < 1.8e-67

   1. Initial program 78.8%

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

   2. Taylor expanded in z around 0 67.0%

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

      1. associate-+r+ 67.0%

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

   4. Simplified 67.0%

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

      1. div-inv 67.1%

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

      2. associate-+l+ 67.1%

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

   6. Applied egg-rr 67.1%

      \[\leadsto \color{blue}{\left(a \cdot \left(y + t\right) - y \cdot b\right) \cdot \frac{1}{y + \left(t + x\right)}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+112}:\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+78}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq -24:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-161}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-67}:\\ \;\;\;\;\left(a \cdot \left(y + t\right) - y \cdot b\right) \cdot \frac{1}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+97}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \end{array} \]

Alternative 4: 64.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := a \cdot \left(y + t\right) - y \cdot b\\ t_3 := a + z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{t_2}{t_1}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-160}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-290}:\\ \;\;\;\;t_2 \cdot \frac{1}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{\left(y \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t)))
        (t_2 (- (* a (+ y t)) (* y b)))
        (t_3 (+ a (* z (+ (/ x t_1) (/ y t_1))))))
   (if (<= z -2.5e+49)
     t_3
     (if (<= z -3.5e-89)
       (/ t_2 t_1)
       (if (<= z -4.2e-160)
         (- a b)
         (if (<= z 3.7e-290)
           (* t_2 (/ 1.0 (+ y (+ x t))))
           (if (<= z 8.5e-16)
             (/ (- (+ (* y a) (* z (+ x y))) (* y b)) (+ x y))
             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 = (a * (y + t)) - (y * b);
	double t_3 = a + (z * ((x / t_1) + (y / t_1)));
	double tmp;
	if (z <= -2.5e+49) {
		tmp = t_3;
	} else if (z <= -3.5e-89) {
		tmp = t_2 / t_1;
	} else if (z <= -4.2e-160) {
		tmp = a - b;
	} else if (z <= 3.7e-290) {
		tmp = t_2 * (1.0 / (y + (x + t)));
	} else if (z <= 8.5e-16) {
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (y + t)
    t_2 = (a * (y + t)) - (y * b)
    t_3 = a + (z * ((x / t_1) + (y / t_1)))
    if (z <= (-2.5d+49)) then
        tmp = t_3
    else if (z <= (-3.5d-89)) then
        tmp = t_2 / t_1
    else if (z <= (-4.2d-160)) then
        tmp = a - b
    else if (z <= 3.7d-290) then
        tmp = t_2 * (1.0d0 / (y + (x + t)))
    else if (z <= 8.5d-16) then
        tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y)
    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 = (a * (y + t)) - (y * b);
	double t_3 = a + (z * ((x / t_1) + (y / t_1)));
	double tmp;
	if (z <= -2.5e+49) {
		tmp = t_3;
	} else if (z <= -3.5e-89) {
		tmp = t_2 / t_1;
	} else if (z <= -4.2e-160) {
		tmp = a - b;
	} else if (z <= 3.7e-290) {
		tmp = t_2 * (1.0 / (y + (x + t)));
	} else if (z <= 8.5e-16) {
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = (a * (y + t)) - (y * b)
	t_3 = a + (z * ((x / t_1) + (y / t_1)))
	tmp = 0
	if z <= -2.5e+49:
		tmp = t_3
	elif z <= -3.5e-89:
		tmp = t_2 / t_1
	elif z <= -4.2e-160:
		tmp = a - b
	elif z <= 3.7e-290:
		tmp = t_2 * (1.0 / (y + (x + t)))
	elif z <= 8.5e-16:
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y)
	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(Float64(a * Float64(y + t)) - Float64(y * b))
	t_3 = Float64(a + Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))))
	tmp = 0.0
	if (z <= -2.5e+49)
		tmp = t_3;
	elseif (z <= -3.5e-89)
		tmp = Float64(t_2 / t_1);
	elseif (z <= -4.2e-160)
		tmp = Float64(a - b);
	elseif (z <= 3.7e-290)
		tmp = Float64(t_2 * Float64(1.0 / Float64(y + Float64(x + t))));
	elseif (z <= 8.5e-16)
		tmp = Float64(Float64(Float64(Float64(y * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(x + y));
	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 = (a * (y + t)) - (y * b);
	t_3 = a + (z * ((x / t_1) + (y / t_1)));
	tmp = 0.0;
	if (z <= -2.5e+49)
		tmp = t_3;
	elseif (z <= -3.5e-89)
		tmp = t_2 / t_1;
	elseif (z <= -4.2e-160)
		tmp = a - b;
	elseif (z <= 3.7e-290)
		tmp = t_2 * (1.0 / (y + (x + t)));
	elseif (z <= 8.5e-16)
		tmp = (((y * a) + (z * (x + y))) - (y * b)) / (x + y);
	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[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+49], t$95$3, If[LessEqual[z, -3.5e-89], N[(t$95$2 / t$95$1), $MachinePrecision], If[LessEqual[z, -4.2e-160], N[(a - b), $MachinePrecision], If[LessEqual[z, 3.7e-290], N[(t$95$2 * N[(1.0 / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-16], N[(N[(N[(N[(y * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.5000000000000002e49 or 8.5000000000000001e-16 < z

   1. Initial program 44.4%

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

   2. Taylor expanded in z around 0 70.7%

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

      1. associate--l+ 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-+r+ 70.7%

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

      4. associate-+r+ 70.7%

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

      5. div-sub 70.7%

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

      6. associate-+r+ 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in t around inf 83.1%

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

   if -2.5000000000000002e49 < z < -3.4999999999999997e-89

   1. Initial program 84.1%

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

   2. Taylor expanded in z around 0 68.0%

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

      1. associate-+r+ 68.0%

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

   4. Simplified 68.0%

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

   if -3.4999999999999997e-89 < z < -4.2000000000000001e-160

   1. Initial program 59.7%

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

   2. Taylor expanded in z around 0 42.0%

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

      1. associate-+r+ 42.0%

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

   4. Simplified 42.0%

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

   5. Taylor expanded in y around inf 69.9%

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

   if -4.2000000000000001e-160 < z < 3.69999999999999977e-290

   1. Initial program 75.9%

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

   2. Taylor expanded in z around 0 73.4%

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

      1. associate-+r+ 73.4%

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

   4. Simplified 73.4%

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

      1. div-inv 73.7%

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

      2. associate-+l+ 73.7%

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

   6. Applied egg-rr 73.7%

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

   if 3.69999999999999977e-290 < z < 8.5000000000000001e-16

   1. Initial program 83.7%

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

   2. Taylor expanded in t around 0 71.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+49}:\\ \;\;\;\;a + z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{y}{x + \left(y + t\right)}\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-160}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-290}:\\ \;\;\;\;\left(a \cdot \left(y + t\right) - y \cdot b\right) \cdot \frac{1}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{\left(y \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;a + z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{y}{x + \left(y + t\right)}\right)\\ \end{array} \]

Alternative 5: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := x + \left(y + t\right)\\ t_3 := z \cdot \frac{x + y}{t_2}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{x + y}{\frac{t_2}{z}}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+77}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -24:\\ \;\;\;\;\frac{y \cdot t_1}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-68}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t_2}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ x (+ y t))) (t_3 (* z (/ (+ x y) t_2))))
   (if (<= z -1.2e+113)
     (/ (+ x y) (/ t_2 z))
     (if (<= z -5.5e+77)
       a
       (if (<= z -3.4e+49)
         t_3
         (if (<= z -24.0)
           (/ (* y t_1) (+ y (+ x t)))
           (if (<= z -2.2e-162)
             t_1
             (if (<= z 2.6e-68)
               (/ (- (* a (+ y t)) (* y b)) t_2)
               (if (<= z 3.4e+97) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = x + (y + t);
	double t_3 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -1.2e+113) {
		tmp = (x + y) / (t_2 / z);
	} else if (z <= -5.5e+77) {
		tmp = a;
	} else if (z <= -3.4e+49) {
		tmp = t_3;
	} else if (z <= -24.0) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (z <= -2.2e-162) {
		tmp = t_1;
	} else if (z <= 2.6e-68) {
		tmp = ((a * (y + t)) - (y * b)) / t_2;
	} else if (z <= 3.4e+97) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = x + (y + t)
    t_3 = z * ((x + y) / t_2)
    if (z <= (-1.2d+113)) then
        tmp = (x + y) / (t_2 / z)
    else if (z <= (-5.5d+77)) then
        tmp = a
    else if (z <= (-3.4d+49)) then
        tmp = t_3
    else if (z <= (-24.0d0)) then
        tmp = (y * t_1) / (y + (x + t))
    else if (z <= (-2.2d-162)) then
        tmp = t_1
    else if (z <= 2.6d-68) then
        tmp = ((a * (y + t)) - (y * b)) / t_2
    else if (z <= 3.4d+97) then
        tmp = t_1
    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 = (z + a) - b;
	double t_2 = x + (y + t);
	double t_3 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -1.2e+113) {
		tmp = (x + y) / (t_2 / z);
	} else if (z <= -5.5e+77) {
		tmp = a;
	} else if (z <= -3.4e+49) {
		tmp = t_3;
	} else if (z <= -24.0) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (z <= -2.2e-162) {
		tmp = t_1;
	} else if (z <= 2.6e-68) {
		tmp = ((a * (y + t)) - (y * b)) / t_2;
	} else if (z <= 3.4e+97) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = x + (y + t)
	t_3 = z * ((x + y) / t_2)
	tmp = 0
	if z <= -1.2e+113:
		tmp = (x + y) / (t_2 / z)
	elif z <= -5.5e+77:
		tmp = a
	elif z <= -3.4e+49:
		tmp = t_3
	elif z <= -24.0:
		tmp = (y * t_1) / (y + (x + t))
	elif z <= -2.2e-162:
		tmp = t_1
	elif z <= 2.6e-68:
		tmp = ((a * (y + t)) - (y * b)) / t_2
	elif z <= 3.4e+97:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(z * Float64(Float64(x + y) / t_2))
	tmp = 0.0
	if (z <= -1.2e+113)
		tmp = Float64(Float64(x + y) / Float64(t_2 / z));
	elseif (z <= -5.5e+77)
		tmp = a;
	elseif (z <= -3.4e+49)
		tmp = t_3;
	elseif (z <= -24.0)
		tmp = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)));
	elseif (z <= -2.2e-162)
		tmp = t_1;
	elseif (z <= 2.6e-68)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_2);
	elseif (z <= 3.4e+97)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = x + (y + t);
	t_3 = z * ((x + y) / t_2);
	tmp = 0.0;
	if (z <= -1.2e+113)
		tmp = (x + y) / (t_2 / z);
	elseif (z <= -5.5e+77)
		tmp = a;
	elseif (z <= -3.4e+49)
		tmp = t_3;
	elseif (z <= -24.0)
		tmp = (y * t_1) / (y + (x + t));
	elseif (z <= -2.2e-162)
		tmp = t_1;
	elseif (z <= 2.6e-68)
		tmp = ((a * (y + t)) - (y * b)) / t_2;
	elseif (z <= 3.4e+97)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+113], N[(N[(x + y), $MachinePrecision] / N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e+77], a, If[LessEqual[z, -3.4e+49], t$95$3, If[LessEqual[z, -24.0], N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e-162], t$95$1, If[LessEqual[z, 2.6e-68], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 3.4e+97], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.19999999999999992e113

   1. Initial program 45.7%

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

   2. Taylor expanded in z around inf 32.0%

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

      1. associate-/l* 68.5%

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

      2. associate-+r+ 68.5%

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

   4. Simplified 68.5%

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

   if -1.19999999999999992e113 < z < -5.50000000000000036e77

   1. Initial program 52.8%

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

   2. Taylor expanded in t around inf 83.6%

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

   if -5.50000000000000036e77 < z < -3.4000000000000001e49 or 3.4000000000000001e97 < z

   1. Initial program 36.2%

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

   2. Taylor expanded in z around inf 25.3%

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

      1. associate-/l* 75.7%

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

      2. associate-+r+ 75.7%

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

   4. Simplified 75.7%

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

      1. associate-/r/ 75.8%

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

      2. +-commutative 75.8%

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

      3. +-commutative 75.8%

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

   6. Applied egg-rr 75.8%

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

   if -3.4000000000000001e49 < z < -24

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 99.7%

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

   if -24 < z < -2.1999999999999999e-162 or 2.5999999999999998e-68 < z < 3.4000000000000001e97

   1. Initial program 67.7%

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

   2. Taylor expanded in y around inf 74.2%

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

   if -2.1999999999999999e-162 < z < 2.5999999999999998e-68

   1. Initial program 78.8%

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

   2. Taylor expanded in z around 0 67.0%

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

      1. associate-+r+ 67.0%

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

   4. Simplified 67.0%

      \[\leadsto \color{blue}{\frac{a \cdot \left(y + t\right) - y \cdot b}{\left(y + t\right) + x}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+77}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq -24:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-162}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-68}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+97}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \end{array} \]

Alternative 6: 59.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{if}\;x \leq -1.82 \cdot 10^{+176}:\\ \;\;\;\;z + \left(a - b\right) \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.06 \cdot 10^{-44}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{+77}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ (+ x y) (+ x (+ y t))))))
   (if (<= x -1.82e+176)
     (+ z (* (- a b) (/ y x)))
     (if (<= x -2.35e+22)
       t_1
       (if (<= x -2.06e-44) a (if (<= x 1.04e+77) (- (+ z a) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((x + y) / (x + (y + t)));
	double tmp;
	if (x <= -1.82e+176) {
		tmp = z + ((a - b) * (y / x));
	} else if (x <= -2.35e+22) {
		tmp = t_1;
	} else if (x <= -2.06e-44) {
		tmp = a;
	} else if (x <= 1.04e+77) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x + y) / (x + (y + t)))
    if (x <= (-1.82d+176)) then
        tmp = z + ((a - b) * (y / x))
    else if (x <= (-2.35d+22)) then
        tmp = t_1
    else if (x <= (-2.06d-44)) then
        tmp = a
    else if (x <= 1.04d+77) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((x + y) / (x + (y + t)));
	double tmp;
	if (x <= -1.82e+176) {
		tmp = z + ((a - b) * (y / x));
	} else if (x <= -2.35e+22) {
		tmp = t_1;
	} else if (x <= -2.06e-44) {
		tmp = a;
	} else if (x <= 1.04e+77) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * ((x + y) / (x + (y + t)))
	tmp = 0
	if x <= -1.82e+176:
		tmp = z + ((a - b) * (y / x))
	elif x <= -2.35e+22:
		tmp = t_1
	elif x <= -2.06e-44:
		tmp = a
	elif x <= 1.04e+77:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(Float64(x + y) / Float64(x + Float64(y + t))))
	tmp = 0.0
	if (x <= -1.82e+176)
		tmp = Float64(z + Float64(Float64(a - b) * Float64(y / x)));
	elseif (x <= -2.35e+22)
		tmp = t_1;
	elseif (x <= -2.06e-44)
		tmp = a;
	elseif (x <= 1.04e+77)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * ((x + y) / (x + (y + t)));
	tmp = 0.0;
	if (x <= -1.82e+176)
		tmp = z + ((a - b) * (y / x));
	elseif (x <= -2.35e+22)
		tmp = t_1;
	elseif (x <= -2.06e-44)
		tmp = a;
	elseif (x <= 1.04e+77)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(N[(x + y), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.82e+176], N[(z + N[(N[(a - b), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.35e+22], t$95$1, If[LessEqual[x, -2.06e-44], a, If[LessEqual[x, 1.04e+77], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.8200000000000001e176

   1. Initial program 45.4%

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

   2. Taylor expanded in x around inf 58.7%

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

      1. associate--l+ 58.7%

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

      2. associate-/l* 66.3%

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

      3. associate-/l* 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in t around 0 69.5%

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

      1. associate--l+ 69.5%

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

      2. *-commutative 69.5%

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

      3. associate-/l* 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in y around 0 73.4%

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

      1. +-commutative 73.4%

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

      2. distribute-lft-out-- 73.4%

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

      3. associate-*r/ 66.4%

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

      4. associate-/l* 73.4%

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

      5. associate-*r/ 76.5%

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

      6. associate-*l/ 72.7%

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

      7. associate-/r/ 72.8%

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

      8. distribute-lft-out-- 72.8%

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

   10. Simplified 72.8%

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

   if -1.8200000000000001e176 < x < -2.3500000000000001e22 or 1.04e77 < x

   1. Initial program 56.1%

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

   2. Taylor expanded in z around inf 32.9%

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

      1. associate-/l* 50.1%

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

      2. associate-+r+ 50.1%

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

   4. Simplified 50.1%

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

      1. associate-/r/ 59.9%

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

      2. +-commutative 59.9%

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

      3. +-commutative 59.9%

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

   6. Applied egg-rr 59.9%

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

   if -2.3500000000000001e22 < x < -2.06e-44

   1. Initial program 87.2%

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

   2. Taylor expanded in t around inf 61.3%

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

   if -2.06e-44 < x < 1.04e77

   1. Initial program 63.9%

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

   2. Taylor expanded in y around inf 69.3%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.82 \cdot 10^{+176}:\\ \;\;\;\;z + \left(a - b\right) \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+22}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;x \leq -2.06 \cdot 10^{-44}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{+77}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \end{array} \]

Alternative 7: 60.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ \mathbf{if}\;x \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;z + \left(a - b\right) \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+119}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+77}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+80}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))))
   (if (<= x -1.06e+154)
     (+ z (* (- a b) (/ y x)))
     (if (<= x -1.3e+119)
       (/ a (/ t_1 (+ y t)))
       (if (<= x -1.5e+77)
         z
         (if (<= x 8.8e+80) (- (+ z a) b) (* z (/ (+ x y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if (x <= -1.06e+154) {
		tmp = z + ((a - b) * (y / x));
	} else if (x <= -1.3e+119) {
		tmp = a / (t_1 / (y + t));
	} else if (x <= -1.5e+77) {
		tmp = z;
	} else if (x <= 8.8e+80) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y + t)
    if (x <= (-1.06d+154)) then
        tmp = z + ((a - b) * (y / x))
    else if (x <= (-1.3d+119)) then
        tmp = a / (t_1 / (y + t))
    else if (x <= (-1.5d+77)) then
        tmp = z
    else if (x <= 8.8d+80) then
        tmp = (z + a) - b
    else
        tmp = z * ((x + y) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if (x <= -1.06e+154) {
		tmp = z + ((a - b) * (y / x));
	} else if (x <= -1.3e+119) {
		tmp = a / (t_1 / (y + t));
	} else if (x <= -1.5e+77) {
		tmp = z;
	} else if (x <= 8.8e+80) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	tmp = 0
	if x <= -1.06e+154:
		tmp = z + ((a - b) * (y / x))
	elif x <= -1.3e+119:
		tmp = a / (t_1 / (y + t))
	elif x <= -1.5e+77:
		tmp = z
	elif x <= 8.8e+80:
		tmp = (z + a) - b
	else:
		tmp = z * ((x + y) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	tmp = 0.0
	if (x <= -1.06e+154)
		tmp = Float64(z + Float64(Float64(a - b) * Float64(y / x)));
	elseif (x <= -1.3e+119)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (x <= -1.5e+77)
		tmp = z;
	elseif (x <= 8.8e+80)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	tmp = 0.0;
	if (x <= -1.06e+154)
		tmp = z + ((a - b) * (y / x));
	elseif (x <= -1.3e+119)
		tmp = a / (t_1 / (y + t));
	elseif (x <= -1.5e+77)
		tmp = z;
	elseif (x <= 8.8e+80)
		tmp = (z + a) - b;
	else
		tmp = z * ((x + y) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.06e+154], N[(z + N[(N[(a - b), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e+119], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e+77], z, If[LessEqual[x, 8.8e+80], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.06e154

   1. Initial program 42.6%

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

   2. Taylor expanded in x around inf 52.6%

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

      1. associate--l+ 52.6%

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

      2. associate-/l* 61.4%

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

      3. associate-/l* 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in t around 0 64.3%

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

      1. associate--l+ 64.3%

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

      2. *-commutative 64.3%

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

      3. associate-/l* 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in y around 0 67.4%

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

      1. +-commutative 67.4%

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

      2. distribute-lft-out-- 67.4%

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

      3. associate-*r/ 61.8%

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

      4. associate-/l* 67.3%

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

      5. associate-*r/ 69.8%

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

      6. associate-*l/ 66.8%

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

      7. associate-/r/ 66.8%

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

      8. distribute-lft-out-- 66.8%

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

   10. Simplified 66.8%

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

   if -1.06e154 < x < -1.3e119

   1. Initial program 44.4%

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

   2. Taylor expanded in a around inf 27.8%

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

      1. associate-/l* 59.4%

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

      2. associate-+r+ 59.4%

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

   4. Simplified 59.4%

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

   if -1.3e119 < x < -1.4999999999999999e77

   1. Initial program 81.1%

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

   2. Taylor expanded in x around inf 62.9%

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

   if -1.4999999999999999e77 < x < 8.80000000000000011e80

   1. Initial program 66.0%

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

   2. Taylor expanded in y around inf 66.1%

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

   if 8.80000000000000011e80 < x

   1. Initial program 58.9%

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

   2. Taylor expanded in z around inf 35.1%

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

      1. associate-/l* 51.8%

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

      2. associate-+r+ 51.8%

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

   4. Simplified 51.8%

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

      1. associate-/r/ 65.3%

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

      2. +-commutative 65.3%

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

      3. +-commutative 65.3%

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

   6. Applied egg-rr 65.3%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;z + \left(a - b\right) \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+119}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+77}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+80}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \end{array} \]

Alternative 8: 58.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{if}\;x \leq -6 \cdot 10^{+175}:\\ \;\;\;\;z + \left(a - b\right) \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-58}:\\ \;\;\;\;\frac{y \cdot t_1}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* z (/ (+ x y) (+ x (+ y t))))))
   (if (<= x -6e+175)
     (+ z (* (- a b) (/ y x)))
     (if (<= x -1.15e+20)
       t_2
       (if (<= x -1.12e-58)
         (/ (* y t_1) (+ y (+ x t)))
         (if (<= x 4.5e+76) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z * ((x + y) / (x + (y + t)));
	double tmp;
	if (x <= -6e+175) {
		tmp = z + ((a - b) * (y / x));
	} else if (x <= -1.15e+20) {
		tmp = t_2;
	} else if (x <= -1.12e-58) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (x <= 4.5e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z * ((x + y) / (x + (y + t)))
    if (x <= (-6d+175)) then
        tmp = z + ((a - b) * (y / x))
    else if (x <= (-1.15d+20)) then
        tmp = t_2
    else if (x <= (-1.12d-58)) then
        tmp = (y * t_1) / (y + (x + t))
    else if (x <= 4.5d+76) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z * ((x + y) / (x + (y + t)));
	double tmp;
	if (x <= -6e+175) {
		tmp = z + ((a - b) * (y / x));
	} else if (x <= -1.15e+20) {
		tmp = t_2;
	} else if (x <= -1.12e-58) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (x <= 4.5e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z * ((x + y) / (x + (y + t)))
	tmp = 0
	if x <= -6e+175:
		tmp = z + ((a - b) * (y / x))
	elif x <= -1.15e+20:
		tmp = t_2
	elif x <= -1.12e-58:
		tmp = (y * t_1) / (y + (x + t))
	elif x <= 4.5e+76:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z * Float64(Float64(x + y) / Float64(x + Float64(y + t))))
	tmp = 0.0
	if (x <= -6e+175)
		tmp = Float64(z + Float64(Float64(a - b) * Float64(y / x)));
	elseif (x <= -1.15e+20)
		tmp = t_2;
	elseif (x <= -1.12e-58)
		tmp = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)));
	elseif (x <= 4.5e+76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = z * ((x + y) / (x + (y + t)));
	tmp = 0.0;
	if (x <= -6e+175)
		tmp = z + ((a - b) * (y / x));
	elseif (x <= -1.15e+20)
		tmp = t_2;
	elseif (x <= -1.12e-58)
		tmp = (y * t_1) / (y + (x + t));
	elseif (x <= 4.5e+76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+175], N[(z + N[(N[(a - b), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.15e+20], t$95$2, If[LessEqual[x, -1.12e-58], N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+76], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.0000000000000003e175

   1. Initial program 45.4%

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

   2. Taylor expanded in x around inf 58.7%

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

      1. associate--l+ 58.7%

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

      2. associate-/l* 66.3%

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

      3. associate-/l* 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in t around 0 69.5%

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

      1. associate--l+ 69.5%

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

      2. *-commutative 69.5%

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

      3. associate-/l* 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in y around 0 73.4%

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

      1. +-commutative 73.4%

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

      2. distribute-lft-out-- 73.4%

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

      3. associate-*r/ 66.4%

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

      4. associate-/l* 73.4%

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

      5. associate-*r/ 76.5%

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

      6. associate-*l/ 72.7%

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

      7. associate-/r/ 72.8%

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

      8. distribute-lft-out-- 72.8%

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

   10. Simplified 72.8%

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

   if -6.0000000000000003e175 < x < -1.15e20 or 4.4999999999999997e76 < x

   1. Initial program 56.6%

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

   2. Taylor expanded in z around inf 32.6%

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

      1. associate-/l* 49.6%

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

      2. associate-+r+ 49.6%

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

   4. Simplified 49.6%

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

      1. associate-/r/ 59.3%

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

      2. +-commutative 59.3%

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

      3. +-commutative 59.3%

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

   6. Applied egg-rr 59.3%

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

   if -1.15e20 < x < -1.11999999999999992e-58

   1. Initial program 87.9%

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

   2. Taylor expanded in y around inf 69.7%

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

   if -1.11999999999999992e-58 < x < 4.4999999999999997e76

   1. Initial program 63.3%

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

   2. Taylor expanded in y around inf 69.6%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+175}:\\ \;\;\;\;z + \left(a - b\right) \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-58}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+76}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \end{array} \]

Alternative 9: 62.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+67} \lor \neg \left(x \leq 9.4 \cdot 10^{+141}\right):\\ \;\;\;\;z + \left(a - b\right) \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -4.9e+67) (not (<= x 9.4e+141)))
   (+ z (* (- a b) (/ y x)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -4.9e+67) || !(x <= 9.4e+141)) {
		tmp = z + ((a - b) * (y / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-4.9d+67)) .or. (.not. (x <= 9.4d+141))) then
        tmp = z + ((a - b) * (y / x))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -4.9e+67) || !(x <= 9.4e+141)) {
		tmp = z + ((a - b) * (y / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -4.9e+67) or not (x <= 9.4e+141):
		tmp = z + ((a - b) * (y / x))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -4.9e+67) || !(x <= 9.4e+141))
		tmp = Float64(z + Float64(Float64(a - b) * Float64(y / x)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -4.9e+67) || ~((x <= 9.4e+141)))
		tmp = z + ((a - b) * (y / x));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -4.9e+67], N[Not[LessEqual[x, 9.4e+141]], $MachinePrecision]], N[(z + N[(N[(a - b), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8999999999999999e67 or 9.39999999999999958e141 < x

   1. Initial program 50.9%

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

   2. Taylor expanded in x around inf 53.7%

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

      1. associate--l+ 53.8%

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

      2. associate-/l* 58.3%

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

      3. associate-/l* 57.5%

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

   4. Simplified 57.5%

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

   5. Taylor expanded in t around 0 58.5%

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

      1. associate--l+ 58.5%

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

      2. *-commutative 58.5%

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

      3. associate-/l* 59.9%

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

   7. Simplified 59.9%

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

   8. Taylor expanded in y around 0 64.1%

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

      1. +-commutative 64.1%

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

      2. distribute-lft-out-- 64.1%

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

      3. associate-*r/ 59.8%

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

      4. associate-/l* 64.1%

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

      5. associate-*r/ 62.8%

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

      6. associate-*l/ 63.9%

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

      7. associate-/r/ 63.9%

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

      8. distribute-lft-out-- 63.9%

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

   10. Simplified 63.9%

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

   if -4.8999999999999999e67 < x < 9.39999999999999958e141

   1. Initial program 65.8%

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

   2. Taylor expanded in y around inf 62.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+67} \lor \neg \left(x \leq 9.4 \cdot 10^{+141}\right):\\ \;\;\;\;z + \left(a - b\right) \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 61.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+142} \lor \neg \left(x \leq 7.2 \cdot 10^{+142}\right):\\ \;\;\;\;z - y \cdot \frac{b}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -4.1e+142) (not (<= x 7.2e+142)))
   (- z (* y (/ b x)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -4.1e+142) || !(x <= 7.2e+142)) {
		tmp = z - (y * (b / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-4.1d+142)) .or. (.not. (x <= 7.2d+142))) then
        tmp = z - (y * (b / x))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -4.1e+142) || !(x <= 7.2e+142)) {
		tmp = z - (y * (b / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -4.1e+142) or not (x <= 7.2e+142):
		tmp = z - (y * (b / x))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -4.1e+142) || !(x <= 7.2e+142))
		tmp = Float64(z - Float64(y * Float64(b / x)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -4.1e+142) || ~((x <= 7.2e+142)))
		tmp = z - (y * (b / x));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -4.1e+142], N[Not[LessEqual[x, 7.2e+142]], $MachinePrecision]], N[(z - N[(y * N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.09999999999999982e142 or 7.2000000000000003e142 < x

   1. Initial program 49.2%

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

   2. Taylor expanded in x around inf 56.9%

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

      1. associate--l+ 57.0%

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

      2. associate-/l* 61.0%

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

      3. associate-/l* 60.0%

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

   4. Simplified 60.0%

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

   5. Taylor expanded in t around 0 63.6%

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

      1. associate--l+ 63.7%

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

      2. *-commutative 63.7%

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

      3. associate-/l* 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in a around 0 60.9%

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

      1. associate-*r/ 62.5%

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

   10. Simplified 62.5%

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

   if -4.09999999999999982e142 < x < 7.2000000000000003e142

   1. Initial program 65.3%

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

   2. Taylor expanded in y around inf 61.3%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+142} \lor \neg \left(x \leq 7.2 \cdot 10^{+142}\right):\\ \;\;\;\;z - y \cdot \frac{b}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 60.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+142}:\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+142}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \frac{b}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.2e+142)
   (- z (/ (* y b) x))
   (if (<= x 1.85e+142) (- (+ z a) b) (- z (* y (/ b x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.2e+142) {
		tmp = z - ((y * b) / x);
	} else if (x <= 1.85e+142) {
		tmp = (z + a) - b;
	} else {
		tmp = z - (y * (b / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-7.2d+142)) then
        tmp = z - ((y * b) / x)
    else if (x <= 1.85d+142) then
        tmp = (z + a) - b
    else
        tmp = z - (y * (b / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.2e+142) {
		tmp = z - ((y * b) / x);
	} else if (x <= 1.85e+142) {
		tmp = (z + a) - b;
	} else {
		tmp = z - (y * (b / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.2e+142:
		tmp = z - ((y * b) / x)
	elif x <= 1.85e+142:
		tmp = (z + a) - b
	else:
		tmp = z - (y * (b / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.2e+142)
		tmp = Float64(z - Float64(Float64(y * b) / x));
	elseif (x <= 1.85e+142)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z - Float64(y * Float64(b / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7.2e+142)
		tmp = z - ((y * b) / x);
	elseif (x <= 1.85e+142)
		tmp = (z + a) - b;
	else
		tmp = z - (y * (b / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.2e+142], N[(z - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e+142], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z - N[(y * N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.2000000000000003e142

   1. Initial program 42.6%

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

   2. Taylor expanded in x around inf 48.5%

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

      1. associate--l+ 48.5%

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

      2. associate-/l* 56.3%

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

      3. associate-/l* 54.3%

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

   4. Simplified 54.3%

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

   5. Taylor expanded in t around 0 58.3%

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

      1. associate--l+ 58.3%

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

      2. *-commutative 58.3%

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

      3. associate-/l* 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in a around 0 54.1%

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

   if -7.2000000000000003e142 < x < 1.8499999999999999e142

   1. Initial program 65.3%

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

   2. Taylor expanded in y around inf 61.3%

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

   if 1.8499999999999999e142 < x

   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 x around inf 65.9%

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

      1. associate--l+ 66.1%

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

      2. associate-/l* 66.2%

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

      3. associate-/l* 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in t around 0 69.4%

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

      1. associate--l+ 69.4%

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

      2. *-commutative 69.4%

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

      3. associate-/l* 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in a around 0 68.3%

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

      1. associate-*r/ 73.9%

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

   10. Simplified 73.9%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+142}:\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+142}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \frac{b}{x}\\ \end{array} \]

Alternative 12: 48.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+76}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+79}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.5e+76) z (if (<= x 4.8e+79) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.5e+76) {
		tmp = z;
	} else if (x <= 4.8e+79) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.5d+76)) then
        tmp = z
    else if (x <= 4.8d+79) then
        tmp = a - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.5e+76) {
		tmp = z;
	} else if (x <= 4.8e+79) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.5e+76:
		tmp = z
	elif x <= 4.8e+79:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.5e+76)
		tmp = z;
	elseif (x <= 4.8e+79)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.5e+76)
		tmp = z;
	elseif (x <= 4.8e+79)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.5e+76], z, If[LessEqual[x, 4.8e+79], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e76 or 4.79999999999999971e79 < x

   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 x around inf 46.7%

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

   if -3.5e76 < x < 4.79999999999999971e79

   1. Initial program 66.0%

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

   2. Taylor expanded in z around 0 50.0%

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

      1. associate-+r+ 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in y around inf 53.2%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+76}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+79}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 13: 58.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+150}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= t -9e+150) a (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9e+150) {
		tmp = a;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9d+150)) then
        tmp = a
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9e+150) {
		tmp = a;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9e+150:
		tmp = a
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9e+150)
		tmp = a;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9e+150)
		tmp = a;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9e+150], a, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.00000000000000001e150

   1. Initial program 46.8%

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

   2. Taylor expanded in t around inf 66.3%

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

   if -9.00000000000000001e150 < t

   1. Initial program 62.8%

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

   2. Taylor expanded in y around inf 59.4%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+150}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 14: 45.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+45}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -9.2e+45) a (if (<= a 1.15e+66) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9.2e+45) {
		tmp = a;
	} else if (a <= 1.15e+66) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-9.2d+45)) then
        tmp = a
    else if (a <= 1.15d+66) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9.2e+45) {
		tmp = a;
	} else if (a <= 1.15e+66) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -9.2e+45:
		tmp = a
	elif a <= 1.15e+66:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -9.2e+45)
		tmp = a;
	elseif (a <= 1.15e+66)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -9.2e+45)
		tmp = a;
	elseif (a <= 1.15e+66)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -9.2e+45], a, If[LessEqual[a, 1.15e+66], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -9.20000000000000049e45 or 1.15e66 < a

   1. Initial program 44.9%

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

   2. Taylor expanded in t around inf 55.3%

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

   if -9.20000000000000049e45 < a < 1.15e66

   1. Initial program 70.5%

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

   2. Taylor expanded in x around inf 39.9%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+45}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 15: 33.0% 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 60.7%

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

2. Taylor expanded in t around inf 31.0%

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

3. Final simplification 31.0%

   \[\leadsto a \]

Developer target: 82.6% 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 2023263 
(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)))