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

Percentage Accurate: 60.7% → 88.1%

Time: 18.4s

Alternatives: 15

Speedup: 0.7×

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: 60.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+273}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* (+ x y) z)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+273))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+273)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+273)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+273):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(Float64(x + y) * z)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+273))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+273)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+273]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.99999999999999961e273 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.2%

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

   3. Taylor expanded in y around inf 76.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999961e273

   1. Initial program 99.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+273}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) \cdot a\\ t_2 := \frac{y}{y + t}\\ t_3 := y + \left(x + t\right)\\ t_4 := z \cdot \frac{x + y}{t\_3}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+103}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{t\_1 + \left(x + y\right) \cdot z}{t\_3}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-238}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t\_3}\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-107}:\\ \;\;\;\;\frac{t\_1 - y \cdot b}{t\_3}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(a \cdot \frac{t}{b \cdot \left(x + t\right)} + x \cdot \frac{\frac{z}{b}}{x + t}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+259}:\\ \;\;\;\;z \cdot \left(\frac{a}{z} + \left(t\_2 - t\_2 \cdot \frac{b}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y t) a))
        (t_2 (/ y (+ y t)))
        (t_3 (+ y (+ x t)))
        (t_4 (* z (/ (+ x y) t_3))))
   (if (<= z -4.2e+103)
     t_4
     (if (<= z -3.1e-148)
       (/ (+ t_1 (* (+ x y) z)) t_3)
       (if (<= z -2.2e-238)
         (* b (- (/ a b) (/ y t_3)))
         (if (<= z 3.6e-107)
           (/ (- t_1 (* y b)) t_3)
           (if (<= z 9.5e-44)
             (* b (+ (* a (/ t (* b (+ x t)))) (* x (/ (/ z b) (+ x t)))))
             (if (<= z 1.1e+259)
               (* z (+ (/ a z) (- t_2 (* t_2 (/ b z)))))
               t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * a;
	double t_2 = y / (y + t);
	double t_3 = y + (x + t);
	double t_4 = z * ((x + y) / t_3);
	double tmp;
	if (z <= -4.2e+103) {
		tmp = t_4;
	} else if (z <= -3.1e-148) {
		tmp = (t_1 + ((x + y) * z)) / t_3;
	} else if (z <= -2.2e-238) {
		tmp = b * ((a / b) - (y / t_3));
	} else if (z <= 3.6e-107) {
		tmp = (t_1 - (y * b)) / t_3;
	} else if (z <= 9.5e-44) {
		tmp = b * ((a * (t / (b * (x + t)))) + (x * ((z / b) / (x + t))));
	} else if (z <= 1.1e+259) {
		tmp = z * ((a / z) + (t_2 - (t_2 * (b / z))));
	} 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 = (y + t) * a
    t_2 = y / (y + t)
    t_3 = y + (x + t)
    t_4 = z * ((x + y) / t_3)
    if (z <= (-4.2d+103)) then
        tmp = t_4
    else if (z <= (-3.1d-148)) then
        tmp = (t_1 + ((x + y) * z)) / t_3
    else if (z <= (-2.2d-238)) then
        tmp = b * ((a / b) - (y / t_3))
    else if (z <= 3.6d-107) then
        tmp = (t_1 - (y * b)) / t_3
    else if (z <= 9.5d-44) then
        tmp = b * ((a * (t / (b * (x + t)))) + (x * ((z / b) / (x + t))))
    else if (z <= 1.1d+259) then
        tmp = z * ((a / z) + (t_2 - (t_2 * (b / z))))
    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 = (y + t) * a;
	double t_2 = y / (y + t);
	double t_3 = y + (x + t);
	double t_4 = z * ((x + y) / t_3);
	double tmp;
	if (z <= -4.2e+103) {
		tmp = t_4;
	} else if (z <= -3.1e-148) {
		tmp = (t_1 + ((x + y) * z)) / t_3;
	} else if (z <= -2.2e-238) {
		tmp = b * ((a / b) - (y / t_3));
	} else if (z <= 3.6e-107) {
		tmp = (t_1 - (y * b)) / t_3;
	} else if (z <= 9.5e-44) {
		tmp = b * ((a * (t / (b * (x + t)))) + (x * ((z / b) / (x + t))));
	} else if (z <= 1.1e+259) {
		tmp = z * ((a / z) + (t_2 - (t_2 * (b / z))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + t) * a
	t_2 = y / (y + t)
	t_3 = y + (x + t)
	t_4 = z * ((x + y) / t_3)
	tmp = 0
	if z <= -4.2e+103:
		tmp = t_4
	elif z <= -3.1e-148:
		tmp = (t_1 + ((x + y) * z)) / t_3
	elif z <= -2.2e-238:
		tmp = b * ((a / b) - (y / t_3))
	elif z <= 3.6e-107:
		tmp = (t_1 - (y * b)) / t_3
	elif z <= 9.5e-44:
		tmp = b * ((a * (t / (b * (x + t)))) + (x * ((z / b) / (x + t))))
	elif z <= 1.1e+259:
		tmp = z * ((a / z) + (t_2 - (t_2 * (b / z))))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) * a)
	t_2 = Float64(y / Float64(y + t))
	t_3 = Float64(y + Float64(x + t))
	t_4 = Float64(z * Float64(Float64(x + y) / t_3))
	tmp = 0.0
	if (z <= -4.2e+103)
		tmp = t_4;
	elseif (z <= -3.1e-148)
		tmp = Float64(Float64(t_1 + Float64(Float64(x + y) * z)) / t_3);
	elseif (z <= -2.2e-238)
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / t_3)));
	elseif (z <= 3.6e-107)
		tmp = Float64(Float64(t_1 - Float64(y * b)) / t_3);
	elseif (z <= 9.5e-44)
		tmp = Float64(b * Float64(Float64(a * Float64(t / Float64(b * Float64(x + t)))) + Float64(x * Float64(Float64(z / b) / Float64(x + t)))));
	elseif (z <= 1.1e+259)
		tmp = Float64(z * Float64(Float64(a / z) + Float64(t_2 - Float64(t_2 * Float64(b / z)))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + t) * a;
	t_2 = y / (y + t);
	t_3 = y + (x + t);
	t_4 = z * ((x + y) / t_3);
	tmp = 0.0;
	if (z <= -4.2e+103)
		tmp = t_4;
	elseif (z <= -3.1e-148)
		tmp = (t_1 + ((x + y) * z)) / t_3;
	elseif (z <= -2.2e-238)
		tmp = b * ((a / b) - (y / t_3));
	elseif (z <= 3.6e-107)
		tmp = (t_1 - (y * b)) / t_3;
	elseif (z <= 9.5e-44)
		tmp = b * ((a * (t / (b * (x + t)))) + (x * ((z / b) / (x + t))));
	elseif (z <= 1.1e+259)
		tmp = z * ((a / z) + (t_2 - (t_2 * (b / z))));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+103], t$95$4, If[LessEqual[z, -3.1e-148], N[(N[(t$95$1 + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[z, -2.2e-238], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-107], N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[z, 9.5e-44], N[(b * N[(N[(a * N[(t / N[(b * N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(z / b), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+259], N[(z * N[(N[(a / z), $MachinePrecision] + N[(t$95$2 - N[(t$95$2 * N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.2000000000000003e103 or 1.09999999999999996e259 < z

   1. Initial program 33.0%

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

   3. Taylor expanded in z around inf 30.2%

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

      1. associate-/l* 93.0%

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

      2. +-commutative 93.0%

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

      3. +-commutative 93.0%

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

      4. associate-+r+ 93.0%

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

      5. +-commutative 93.0%

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

      6. associate-+l+ 93.0%

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

   5. Simplified 93.0%

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

   if -4.2000000000000003e103 < z < -3.1000000000000001e-148

   1. Initial program 76.7%

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

   3. Taylor expanded in b around 0 70.2%

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

   if -3.1000000000000001e-148 < z < -2.19999999999999991e-238

   1. Initial program 56.4%

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

   3. Taylor expanded in b around -inf 77.8%

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

      1. mul-1-neg 77.8%

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

      2. *-commutative 77.8%

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

      3. distribute-rgt-neg-in 77.8%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in t around inf 74.4%

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

   if -2.19999999999999991e-238 < z < 3.59999999999999976e-107

   1. Initial program 83.2%

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

   3. Taylor expanded in z around 0 77.6%

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

      1. *-commutative 77.6%

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

   5. Simplified 77.6%

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

   if 3.59999999999999976e-107 < z < 9.49999999999999924e-44

   1. Initial program 71.1%

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

   3. Taylor expanded in b around -inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. *-commutative 75.5%

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

      3. distribute-rgt-neg-in 75.5%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in y around 0 61.1%

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

      1. associate-/l* 79.8%

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

      2. associate-/l* 80.0%

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

      3. associate-/r* 80.2%

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

   8. Simplified 80.2%

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

   if 9.49999999999999924e-44 < z < 1.09999999999999996e259

   1. Initial program 52.6%

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

   3. Taylor expanded in x around 0 44.1%

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

   4. Taylor expanded in z around inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. times-frac 78.5%

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

   6. Simplified 78.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + \left(x + y\right) \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-238}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-107}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(a \cdot \frac{t}{b \cdot \left(x + t\right)} + x \cdot \frac{\frac{z}{b}}{x + t}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+259}:\\ \;\;\;\;z \cdot \left(\frac{a}{z} + \left(\frac{y}{y + t} - \frac{y}{y + t} \cdot \frac{b}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) \cdot a\\ t_2 := y + \left(x + t\right)\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -9 \cdot 10^{+14}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{t\_1 - y \cdot b}{t\_2}\\ \mathbf{elif}\;y \leq 33000000000000:\\ \;\;\;\;\frac{t\_1 + \left(x + y\right) \cdot z}{t\_2}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z - b}{\left(x + y\right) + t}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y t) a)) (t_2 (+ y (+ x t))) (t_3 (- (+ z a) b)))
   (if (<= y -9e+14)
     t_3
     (if (<= y -3.1e-148)
       (/ (- t_1 (* y b)) t_2)
       (if (<= y 33000000000000.0)
         (/ (+ t_1 (* (+ x y) z)) t_2)
         (if (<= y 5.2e+86) (* y (/ (- z b) (+ (+ x y) t))) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * a;
	double t_2 = y + (x + t);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -9e+14) {
		tmp = t_3;
	} else if (y <= -3.1e-148) {
		tmp = (t_1 - (y * b)) / t_2;
	} else if (y <= 33000000000000.0) {
		tmp = (t_1 + ((x + y) * z)) / t_2;
	} else if (y <= 5.2e+86) {
		tmp = y * ((z - b) / ((x + y) + t));
	} 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 = (y + t) * a
    t_2 = y + (x + t)
    t_3 = (z + a) - b
    if (y <= (-9d+14)) then
        tmp = t_3
    else if (y <= (-3.1d-148)) then
        tmp = (t_1 - (y * b)) / t_2
    else if (y <= 33000000000000.0d0) then
        tmp = (t_1 + ((x + y) * z)) / t_2
    else if (y <= 5.2d+86) then
        tmp = y * ((z - b) / ((x + y) + t))
    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 = (y + t) * a;
	double t_2 = y + (x + t);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -9e+14) {
		tmp = t_3;
	} else if (y <= -3.1e-148) {
		tmp = (t_1 - (y * b)) / t_2;
	} else if (y <= 33000000000000.0) {
		tmp = (t_1 + ((x + y) * z)) / t_2;
	} else if (y <= 5.2e+86) {
		tmp = y * ((z - b) / ((x + y) + t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + t) * a
	t_2 = y + (x + t)
	t_3 = (z + a) - b
	tmp = 0
	if y <= -9e+14:
		tmp = t_3
	elif y <= -3.1e-148:
		tmp = (t_1 - (y * b)) / t_2
	elif y <= 33000000000000.0:
		tmp = (t_1 + ((x + y) * z)) / t_2
	elif y <= 5.2e+86:
		tmp = y * ((z - b) / ((x + y) + t))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) * a)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -9e+14)
		tmp = t_3;
	elseif (y <= -3.1e-148)
		tmp = Float64(Float64(t_1 - Float64(y * b)) / t_2);
	elseif (y <= 33000000000000.0)
		tmp = Float64(Float64(t_1 + Float64(Float64(x + y) * z)) / t_2);
	elseif (y <= 5.2e+86)
		tmp = Float64(y * Float64(Float64(z - b) / Float64(Float64(x + y) + t)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + t) * a;
	t_2 = y + (x + t);
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -9e+14)
		tmp = t_3;
	elseif (y <= -3.1e-148)
		tmp = (t_1 - (y * b)) / t_2;
	elseif (y <= 33000000000000.0)
		tmp = (t_1 + ((x + y) * z)) / t_2;
	elseif (y <= 5.2e+86)
		tmp = y * ((z - b) / ((x + y) + t));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -9e+14], t$95$3, If[LessEqual[y, -3.1e-148], N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 33000000000000.0], N[(N[(t$95$1 + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 5.2e+86], N[(y * N[(N[(z - b), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9e14 or 5.1999999999999995e86 < y

   1. Initial program 29.9%

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

   3. Taylor expanded in y around inf 75.0%

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

   if -9e14 < y < -3.1000000000000001e-148

   1. Initial program 86.3%

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

   3. Taylor expanded in z around 0 69.4%

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

      1. *-commutative 69.4%

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

   5. Simplified 69.4%

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

   if -3.1000000000000001e-148 < y < 3.3e13

   1. Initial program 79.1%

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

   3. Taylor expanded in b around 0 71.1%

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

   if 3.3e13 < y < 5.1999999999999995e86

   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. Add Preprocessing

   3. Taylor expanded in a around inf 68.1%

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

      1. sub-neg 68.1%

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

      2. associate-+r+ 68.1%

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

      3. associate-+l+ 68.1%

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

      4. sub-neg 68.1%

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

      5. div-sub 68.1%

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

      6. cancel-sign-sub-inv 68.1%

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

      7. distribute-rgt-in 68.1%

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

      8. *-commutative 68.1%

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

      9. associate-+l+ 68.1%

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

      10. *-commutative 68.1%

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

      11. distribute-rgt-neg-out 68.1%

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

      12. distribute-lft-neg-in 68.1%

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

      13. cancel-sign-sub-inv 68.1%

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

      14. distribute-lft-out-- 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in y around inf 59.6%

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

      1. associate-*r* 67.2%

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

      2. associate--l+ 67.2%

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

      3. div-sub 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in a around 0 75.8%

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

       1. associate-/l* 83.5%

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

       2. +-commutative 83.5%

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

   11. Simplified 83.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+14}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 33000000000000:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + \left(x + y\right) \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z - b}{\left(x + y\right) + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -1.86 \cdot 10^{+208}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{-199}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{a}{y} + \frac{z - b}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -1.86e+208)
     (- a (* y (/ b t)))
     (if (<= t -4.1e-100)
       t_1
       (if (<= t -7.3e-199)
         z
         (if (<= t 4.8e+203) t_1 (* y (+ (/ a y) (/ (- z b) t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -1.86e+208) {
		tmp = a - (y * (b / t));
	} else if (t <= -4.1e-100) {
		tmp = t_1;
	} else if (t <= -7.3e-199) {
		tmp = z;
	} else if (t <= 4.8e+203) {
		tmp = t_1;
	} else {
		tmp = y * ((a / y) + ((z - b) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-1.86d+208)) then
        tmp = a - (y * (b / t))
    else if (t <= (-4.1d-100)) then
        tmp = t_1
    else if (t <= (-7.3d-199)) then
        tmp = z
    else if (t <= 4.8d+203) then
        tmp = t_1
    else
        tmp = y * ((a / y) + ((z - b) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -1.86e+208) {
		tmp = a - (y * (b / t));
	} else if (t <= -4.1e-100) {
		tmp = t_1;
	} else if (t <= -7.3e-199) {
		tmp = z;
	} else if (t <= 4.8e+203) {
		tmp = t_1;
	} else {
		tmp = y * ((a / y) + ((z - b) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -1.86e+208:
		tmp = a - (y * (b / t))
	elif t <= -4.1e-100:
		tmp = t_1
	elif t <= -7.3e-199:
		tmp = z
	elif t <= 4.8e+203:
		tmp = t_1
	else:
		tmp = y * ((a / y) + ((z - b) / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -1.86e+208)
		tmp = Float64(a - Float64(y * Float64(b / t)));
	elseif (t <= -4.1e-100)
		tmp = t_1;
	elseif (t <= -7.3e-199)
		tmp = z;
	elseif (t <= 4.8e+203)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(a / y) + Float64(Float64(z - b) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -1.86e+208)
		tmp = a - (y * (b / t));
	elseif (t <= -4.1e-100)
		tmp = t_1;
	elseif (t <= -7.3e-199)
		tmp = z;
	elseif (t <= 4.8e+203)
		tmp = t_1;
	else
		tmp = y * ((a / y) + ((z - b) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t, -1.86e+208], N[(a - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.1e-100], t$95$1, If[LessEqual[t, -7.3e-199], z, If[LessEqual[t, 4.8e+203], t$95$1, N[(y * N[(N[(a / y), $MachinePrecision] + N[(N[(z - b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.85999999999999993e208

   1. Initial program 48.7%

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

   3. Taylor expanded in x around 0 47.6%

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

   4. Taylor expanded in y around 0 86.1%

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

   5. Taylor expanded in z around 0 81.7%

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

      1. neg-mul-1 81.7%

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

      2. distribute-neg-frac2 81.7%

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

   7. Simplified 81.7%

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

   if -1.85999999999999993e208 < t < -4.0999999999999999e-100 or -7.3e-199 < t < 4.8000000000000002e203

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 61.7%

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

   if -4.0999999999999999e-100 < t < -7.3e-199

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 81.4%

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

   if 4.8000000000000002e203 < t

   1. Initial program 40.3%

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

   3. Taylor expanded in x around 0 40.0%

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

   4. Taylor expanded in y around 0 81.9%

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

   5. Taylor expanded in y around inf 75.5%

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

      1. associate--l+ 75.5%

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

      2. div-sub 75.5%

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

   7. Simplified 75.5%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.86 \cdot 10^{+208}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-100}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{-199}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+203}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{a}{y} + \frac{z - b}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \frac{x + y}{t\_2}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_2}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+252}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ y (+ x t))) (t_3 (* z (/ (+ x y) t_2))))
   (if (<= z -3.8e-5)
     t_3
     (if (<= z -1.65e-199)
       t_1
       (if (<= z 1.45e-12)
         (* a (/ (+ y t) t_2))
         (if (<= z 1.15e+252) 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 = y + (x + t);
	double t_3 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -3.8e-5) {
		tmp = t_3;
	} else if (z <= -1.65e-199) {
		tmp = t_1;
	} else if (z <= 1.45e-12) {
		tmp = a * ((y + t) / t_2);
	} else if (z <= 1.15e+252) {
		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 = y + (x + t)
    t_3 = z * ((x + y) / t_2)
    if (z <= (-3.8d-5)) then
        tmp = t_3
    else if (z <= (-1.65d-199)) then
        tmp = t_1
    else if (z <= 1.45d-12) then
        tmp = a * ((y + t) / t_2)
    else if (z <= 1.15d+252) 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 = y + (x + t);
	double t_3 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -3.8e-5) {
		tmp = t_3;
	} else if (z <= -1.65e-199) {
		tmp = t_1;
	} else if (z <= 1.45e-12) {
		tmp = a * ((y + t) / t_2);
	} else if (z <= 1.15e+252) {
		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 = y + (x + t)
	t_3 = z * ((x + y) / t_2)
	tmp = 0
	if z <= -3.8e-5:
		tmp = t_3
	elif z <= -1.65e-199:
		tmp = t_1
	elif z <= 1.45e-12:
		tmp = a * ((y + t) / t_2)
	elif z <= 1.15e+252:
		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(y + Float64(x + t))
	t_3 = Float64(z * Float64(Float64(x + y) / t_2))
	tmp = 0.0
	if (z <= -3.8e-5)
		tmp = t_3;
	elseif (z <= -1.65e-199)
		tmp = t_1;
	elseif (z <= 1.45e-12)
		tmp = Float64(a * Float64(Float64(y + t) / t_2));
	elseif (z <= 1.15e+252)
		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 = y + (x + t);
	t_3 = z * ((x + y) / t_2);
	tmp = 0.0;
	if (z <= -3.8e-5)
		tmp = t_3;
	elseif (z <= -1.65e-199)
		tmp = t_1;
	elseif (z <= 1.45e-12)
		tmp = a * ((y + t) / t_2);
	elseif (z <= 1.15e+252)
		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[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e-5], t$95$3, If[LessEqual[z, -1.65e-199], t$95$1, If[LessEqual[z, 1.45e-12], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+252], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e-5 or 1.15e252 < z

   1. Initial program 49.9%

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

   3. Taylor expanded in z around inf 39.4%

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

      1. associate-/l* 82.8%

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

      2. +-commutative 82.8%

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

      3. +-commutative 82.8%

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

      4. associate-+r+ 82.8%

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

      5. +-commutative 82.8%

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

      6. associate-+l+ 82.8%

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

   5. Simplified 82.8%

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

   if -3.8000000000000002e-5 < z < -1.6500000000000001e-199 or 1.4500000000000001e-12 < z < 1.15e252

   1. Initial program 58.1%

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

   3. Taylor expanded in y around inf 64.9%

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

   if -1.6500000000000001e-199 < z < 1.4500000000000001e-12

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 44.6%

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

      1. associate-/l* 58.7%

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

      2. +-commutative 58.7%

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

      3. associate-+r+ 58.7%

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

      4. +-commutative 58.7%

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

      5. associate-+l+ 58.7%

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

   5. Simplified 58.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-199}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+252}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + t}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+251}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -7.8e-72)
     t_2
     (if (<= z -1.8e-162)
       (* a (/ (+ y t) t_1))
       (if (<= z 2.6e-44)
         (* b (- (/ a b) (/ y (+ y t))))
         (if (<= z 3.4e+251) (- (+ z a) b) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -7.8e-72) {
		tmp = t_2;
	} else if (z <= -1.8e-162) {
		tmp = a * ((y + t) / t_1);
	} else if (z <= 2.6e-44) {
		tmp = b * ((a / b) - (y / (y + t)));
	} else if (z <= 3.4e+251) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * ((x + y) / t_1)
    if (z <= (-7.8d-72)) then
        tmp = t_2
    else if (z <= (-1.8d-162)) then
        tmp = a * ((y + t) / t_1)
    else if (z <= 2.6d-44) then
        tmp = b * ((a / b) - (y / (y + t)))
    else if (z <= 3.4d+251) then
        tmp = (z + a) - b
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -7.8e-72) {
		tmp = t_2;
	} else if (z <= -1.8e-162) {
		tmp = a * ((y + t) / t_1);
	} else if (z <= 2.6e-44) {
		tmp = b * ((a / b) - (y / (y + t)));
	} else if (z <= 3.4e+251) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -7.8e-72:
		tmp = t_2
	elif z <= -1.8e-162:
		tmp = a * ((y + t) / t_1)
	elif z <= 2.6e-44:
		tmp = b * ((a / b) - (y / (y + t)))
	elif z <= 3.4e+251:
		tmp = (z + a) - b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -7.8e-72)
		tmp = t_2;
	elseif (z <= -1.8e-162)
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	elseif (z <= 2.6e-44)
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / Float64(y + t))));
	elseif (z <= 3.4e+251)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -7.8e-72)
		tmp = t_2;
	elseif (z <= -1.8e-162)
		tmp = a * ((y + t) / t_1);
	elseif (z <= 2.6e-44)
		tmp = b * ((a / b) - (y / (y + t)));
	elseif (z <= 3.4e+251)
		tmp = (z + a) - b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e-72], t$95$2, If[LessEqual[z, -1.8e-162], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-44], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+251], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.8e-72 or 3.40000000000000011e251 < z

   1. Initial program 52.9%

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

   3. Taylor expanded in z around inf 42.5%

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

      1. associate-/l* 80.5%

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

      2. +-commutative 80.5%

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

      3. +-commutative 80.5%

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

      4. associate-+r+ 80.5%

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

      5. +-commutative 80.5%

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

      6. associate-+l+ 80.5%

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

   5. Simplified 80.5%

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

   if -7.8e-72 < z < -1.7999999999999999e-162

   1. Initial program 65.2%

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

   3. Taylor expanded in a around inf 29.9%

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

      1. associate-/l* 54.9%

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

      2. +-commutative 54.9%

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

      3. associate-+r+ 54.9%

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

      4. +-commutative 54.9%

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

      5. associate-+l+ 54.9%

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

   5. Simplified 54.9%

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

   if -1.7999999999999999e-162 < z < 2.5999999999999998e-44

   1. Initial program 76.9%

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

   3. Taylor expanded in x around 0 46.9%

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

   4. Taylor expanded in z around 0 44.6%

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

   5. Taylor expanded in b around inf 62.2%

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

   if 2.5999999999999998e-44 < z < 3.40000000000000011e251

   1. Initial program 52.6%

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

   3. Taylor expanded in y around inf 70.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + t}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+251}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -8 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t\_1}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+251}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -8e-68)
     t_2
     (if (<= z -8.2e-163)
       (* a (/ (+ y t) t_1))
       (if (<= z 2.05e-43)
         (* b (- (/ a b) (/ y t_1)))
         (if (<= z 3.4e+251) (- (+ z a) b) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -8e-68) {
		tmp = t_2;
	} else if (z <= -8.2e-163) {
		tmp = a * ((y + t) / t_1);
	} else if (z <= 2.05e-43) {
		tmp = b * ((a / b) - (y / t_1));
	} else if (z <= 3.4e+251) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * ((x + y) / t_1)
    if (z <= (-8d-68)) then
        tmp = t_2
    else if (z <= (-8.2d-163)) then
        tmp = a * ((y + t) / t_1)
    else if (z <= 2.05d-43) then
        tmp = b * ((a / b) - (y / t_1))
    else if (z <= 3.4d+251) then
        tmp = (z + a) - b
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -8e-68) {
		tmp = t_2;
	} else if (z <= -8.2e-163) {
		tmp = a * ((y + t) / t_1);
	} else if (z <= 2.05e-43) {
		tmp = b * ((a / b) - (y / t_1));
	} else if (z <= 3.4e+251) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -8e-68:
		tmp = t_2
	elif z <= -8.2e-163:
		tmp = a * ((y + t) / t_1)
	elif z <= 2.05e-43:
		tmp = b * ((a / b) - (y / t_1))
	elif z <= 3.4e+251:
		tmp = (z + a) - b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -8e-68)
		tmp = t_2;
	elseif (z <= -8.2e-163)
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	elseif (z <= 2.05e-43)
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / t_1)));
	elseif (z <= 3.4e+251)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -8e-68)
		tmp = t_2;
	elseif (z <= -8.2e-163)
		tmp = a * ((y + t) / t_1);
	elseif (z <= 2.05e-43)
		tmp = b * ((a / b) - (y / t_1));
	elseif (z <= 3.4e+251)
		tmp = (z + a) - b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e-68], t$95$2, If[LessEqual[z, -8.2e-163], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-43], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+251], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.00000000000000053e-68 or 3.40000000000000011e251 < z

   1. Initial program 52.9%

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

   3. Taylor expanded in z around inf 42.5%

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

      1. associate-/l* 80.5%

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

      2. +-commutative 80.5%

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

      3. +-commutative 80.5%

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

      4. associate-+r+ 80.5%

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

      5. +-commutative 80.5%

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

      6. associate-+l+ 80.5%

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

   5. Simplified 80.5%

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

   if -8.00000000000000053e-68 < z < -8.19999999999999965e-163

   1. Initial program 65.2%

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

   3. Taylor expanded in a around inf 29.9%

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

      1. associate-/l* 54.9%

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

      2. +-commutative 54.9%

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

      3. associate-+r+ 54.9%

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

      4. +-commutative 54.9%

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

      5. associate-+l+ 54.9%

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

   5. Simplified 54.9%

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

   if -8.19999999999999965e-163 < z < 2.0499999999999999e-43

   1. Initial program 76.9%

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

   3. Taylor expanded in b around -inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. *-commutative 78.6%

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

      3. distribute-rgt-neg-in 78.6%

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

   5. Simplified 94.3%

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

   6. Taylor expanded in t around inf 69.4%

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

   if 2.0499999999999999e-43 < z < 3.40000000000000011e251

   1. Initial program 52.6%

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

   3. Taylor expanded in y around inf 70.4%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-68}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+251}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{y}{t\_1}\\ t_3 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+71}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-147}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - t\_2\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - t\_2\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+254}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ y t_1)) (t_3 (* z (/ (+ x y) t_1))))
   (if (<= z -1.3e+71)
     t_3
     (if (<= z -2.3e-147)
       (* b (- (/ z b) t_2))
       (if (<= z 1.85e-44)
         (* b (- (/ a b) t_2))
         (if (<= z 2.2e+254) (- (+ z a) b) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = y / t_1;
	double t_3 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -1.3e+71) {
		tmp = t_3;
	} else if (z <= -2.3e-147) {
		tmp = b * ((z / b) - t_2);
	} else if (z <= 1.85e-44) {
		tmp = b * ((a / b) - t_2);
	} else if (z <= 2.2e+254) {
		tmp = (z + a) - b;
	} 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 = y + (x + t)
    t_2 = y / t_1
    t_3 = z * ((x + y) / t_1)
    if (z <= (-1.3d+71)) then
        tmp = t_3
    else if (z <= (-2.3d-147)) then
        tmp = b * ((z / b) - t_2)
    else if (z <= 1.85d-44) then
        tmp = b * ((a / b) - t_2)
    else if (z <= 2.2d+254) then
        tmp = (z + a) - b
    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 = y + (x + t);
	double t_2 = y / t_1;
	double t_3 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -1.3e+71) {
		tmp = t_3;
	} else if (z <= -2.3e-147) {
		tmp = b * ((z / b) - t_2);
	} else if (z <= 1.85e-44) {
		tmp = b * ((a / b) - t_2);
	} else if (z <= 2.2e+254) {
		tmp = (z + a) - b;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = y / t_1
	t_3 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -1.3e+71:
		tmp = t_3
	elif z <= -2.3e-147:
		tmp = b * ((z / b) - t_2)
	elif z <= 1.85e-44:
		tmp = b * ((a / b) - t_2)
	elif z <= 2.2e+254:
		tmp = (z + a) - b
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(y / t_1)
	t_3 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -1.3e+71)
		tmp = t_3;
	elseif (z <= -2.3e-147)
		tmp = Float64(b * Float64(Float64(z / b) - t_2));
	elseif (z <= 1.85e-44)
		tmp = Float64(b * Float64(Float64(a / b) - t_2));
	elseif (z <= 2.2e+254)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = y / t_1;
	t_3 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -1.3e+71)
		tmp = t_3;
	elseif (z <= -2.3e-147)
		tmp = b * ((z / b) - t_2);
	elseif (z <= 1.85e-44)
		tmp = b * ((a / b) - t_2);
	elseif (z <= 2.2e+254)
		tmp = (z + a) - b;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+71], t$95$3, If[LessEqual[z, -2.3e-147], N[(b * N[(N[(z / b), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-44], N[(b * N[(N[(a / b), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+254], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.29999999999999996e71 or 2.2000000000000001e254 < z

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 37.5%

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

      1. associate-/l* 90.9%

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

      2. +-commutative 90.9%

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

      3. +-commutative 90.9%

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

      4. associate-+r+ 90.9%

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

      5. +-commutative 90.9%

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

      6. associate-+l+ 90.9%

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

   5. Simplified 90.9%

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

   if -1.29999999999999996e71 < z < -2.2999999999999999e-147

   1. Initial program 72.7%

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

   3. Taylor expanded in b around -inf 76.1%

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

      1. mul-1-neg 76.1%

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

      2. *-commutative 76.1%

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

      3. distribute-rgt-neg-in 76.1%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in x around inf 57.8%

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

   if -2.2999999999999999e-147 < z < 1.85e-44

   1. Initial program 74.6%

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

   3. Taylor expanded in b around -inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. *-commutative 77.4%

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

      3. distribute-rgt-neg-in 77.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in t around inf 68.7%

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

   if 1.85e-44 < z < 2.2000000000000001e254

   1. Initial program 52.6%

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

   3. Taylor expanded in y around inf 70.4%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-147}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+254}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-211}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{t\_1}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-98}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{t\_1}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+251}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -3.5e+71)
     t_2
     (if (<= z -1.56e-211)
       (* b (- (/ z b) (/ y t_1)))
       (if (<= z 2.1e-98)
         (/ (- (* (+ y t) a) (* y b)) t_1)
         (if (<= z 3.5e+251) (- (+ z a) b) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -3.5e+71) {
		tmp = t_2;
	} else if (z <= -1.56e-211) {
		tmp = b * ((z / b) - (y / t_1));
	} else if (z <= 2.1e-98) {
		tmp = (((y + t) * a) - (y * b)) / t_1;
	} else if (z <= 3.5e+251) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * ((x + y) / t_1)
    if (z <= (-3.5d+71)) then
        tmp = t_2
    else if (z <= (-1.56d-211)) then
        tmp = b * ((z / b) - (y / t_1))
    else if (z <= 2.1d-98) then
        tmp = (((y + t) * a) - (y * b)) / t_1
    else if (z <= 3.5d+251) then
        tmp = (z + a) - b
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -3.5e+71) {
		tmp = t_2;
	} else if (z <= -1.56e-211) {
		tmp = b * ((z / b) - (y / t_1));
	} else if (z <= 2.1e-98) {
		tmp = (((y + t) * a) - (y * b)) / t_1;
	} else if (z <= 3.5e+251) {
		tmp = (z + a) - b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -3.5e+71:
		tmp = t_2
	elif z <= -1.56e-211:
		tmp = b * ((z / b) - (y / t_1))
	elif z <= 2.1e-98:
		tmp = (((y + t) * a) - (y * b)) / t_1
	elif z <= 3.5e+251:
		tmp = (z + a) - b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -3.5e+71)
		tmp = t_2;
	elseif (z <= -1.56e-211)
		tmp = Float64(b * Float64(Float64(z / b) - Float64(y / t_1)));
	elseif (z <= 2.1e-98)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / t_1);
	elseif (z <= 3.5e+251)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -3.5e+71)
		tmp = t_2;
	elseif (z <= -1.56e-211)
		tmp = b * ((z / b) - (y / t_1));
	elseif (z <= 2.1e-98)
		tmp = (((y + t) * a) - (y * b)) / t_1;
	elseif (z <= 3.5e+251)
		tmp = (z + a) - b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+71], t$95$2, If[LessEqual[z, -1.56e-211], N[(b * N[(N[(z / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-98], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 3.5e+251], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4999999999999999e71 or 3.50000000000000004e251 < z

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 37.5%

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

      1. associate-/l* 90.9%

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

      2. +-commutative 90.9%

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

      3. +-commutative 90.9%

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

      4. associate-+r+ 90.9%

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

      5. +-commutative 90.9%

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

      6. associate-+l+ 90.9%

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

   5. Simplified 90.9%

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

   if -3.4999999999999999e71 < z < -1.56e-211

   1. Initial program 67.5%

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

   3. Taylor expanded in b around -inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. distribute-rgt-neg-in 76.7%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in x around inf 59.1%

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

   if -1.56e-211 < z < 2.09999999999999992e-98

   1. Initial program 81.8%

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

   3. Taylor expanded in z around 0 74.3%

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

      1. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   if 2.09999999999999992e-98 < z < 3.50000000000000004e251

   1. Initial program 54.7%

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

   3. Taylor expanded in y around inf 67.8%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-211}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-98}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+251}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z \cdot \frac{x}{x + t}\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+177}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-302}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* z (/ x (+ x t)))))
   (if (<= x -2.7e+177)
     t_2
     (if (<= x -1.46e-211)
       t_1
       (if (<= x -2.6e-302) a (if (<= x 1.75e+118) 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 / (x + t));
	double tmp;
	if (x <= -2.7e+177) {
		tmp = t_2;
	} else if (x <= -1.46e-211) {
		tmp = t_1;
	} else if (x <= -2.6e-302) {
		tmp = a;
	} else if (x <= 1.75e+118) {
		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 / (x + t))
    if (x <= (-2.7d+177)) then
        tmp = t_2
    else if (x <= (-1.46d-211)) then
        tmp = t_1
    else if (x <= (-2.6d-302)) then
        tmp = a
    else if (x <= 1.75d+118) 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 / (x + t));
	double tmp;
	if (x <= -2.7e+177) {
		tmp = t_2;
	} else if (x <= -1.46e-211) {
		tmp = t_1;
	} else if (x <= -2.6e-302) {
		tmp = a;
	} else if (x <= 1.75e+118) {
		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 / (x + t))
	tmp = 0
	if x <= -2.7e+177:
		tmp = t_2
	elif x <= -1.46e-211:
		tmp = t_1
	elif x <= -2.6e-302:
		tmp = a
	elif x <= 1.75e+118:
		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(x / Float64(x + t)))
	tmp = 0.0
	if (x <= -2.7e+177)
		tmp = t_2;
	elseif (x <= -1.46e-211)
		tmp = t_1;
	elseif (x <= -2.6e-302)
		tmp = a;
	elseif (x <= 1.75e+118)
		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 / (x + t));
	tmp = 0.0;
	if (x <= -2.7e+177)
		tmp = t_2;
	elseif (x <= -1.46e-211)
		tmp = t_1;
	elseif (x <= -2.6e-302)
		tmp = a;
	elseif (x <= 1.75e+118)
		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[(x / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+177], t$95$2, If[LessEqual[x, -1.46e-211], t$95$1, If[LessEqual[x, -2.6e-302], a, If[LessEqual[x, 1.75e+118], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.69999999999999991e177 or 1.75000000000000008e118 < x

   1. Initial program 56.2%

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

   3. Taylor expanded in z around inf 41.0%

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

      1. associate-/l* 69.3%

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

      2. +-commutative 69.3%

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

      3. +-commutative 69.3%

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

      4. associate-+r+ 69.3%

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

      5. +-commutative 69.3%

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

      6. associate-+l+ 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in y around 0 69.2%

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

   if -2.69999999999999991e177 < x < -1.4600000000000001e-211 or -2.60000000000000011e-302 < x < 1.75000000000000008e118

   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. Add Preprocessing

   3. Taylor expanded in y around inf 61.5%

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

   if -1.4600000000000001e-211 < x < -2.60000000000000011e-302

   1. Initial program 68.3%

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

   3. Taylor expanded in t around inf 68.9%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+177}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-211}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-302}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+118}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a + y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-196}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ a (* y (/ z t)))))
   (if (<= t -8.5e+196)
     t_2
     (if (<= t -3.8e-100)
       t_1
       (if (<= t -1.56e-196) z (if (<= t 1.9e+200) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (y * (z / t));
	double tmp;
	if (t <= -8.5e+196) {
		tmp = t_2;
	} else if (t <= -3.8e-100) {
		tmp = t_1;
	} else if (t <= -1.56e-196) {
		tmp = z;
	} else if (t <= 1.9e+200) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a + (y * (z / t))
    if (t <= (-8.5d+196)) then
        tmp = t_2
    else if (t <= (-3.8d-100)) then
        tmp = t_1
    else if (t <= (-1.56d-196)) then
        tmp = z
    else if (t <= 1.9d+200) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (y * (z / t));
	double tmp;
	if (t <= -8.5e+196) {
		tmp = t_2;
	} else if (t <= -3.8e-100) {
		tmp = t_1;
	} else if (t <= -1.56e-196) {
		tmp = z;
	} else if (t <= 1.9e+200) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a + (y * (z / t))
	tmp = 0
	if t <= -8.5e+196:
		tmp = t_2
	elif t <= -3.8e-100:
		tmp = t_1
	elif t <= -1.56e-196:
		tmp = z
	elif t <= 1.9e+200:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -8.5e+196)
		tmp = t_2;
	elseif (t <= -3.8e-100)
		tmp = t_1;
	elseif (t <= -1.56e-196)
		tmp = z;
	elseif (t <= 1.9e+200)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a + (y * (z / t));
	tmp = 0.0;
	if (t <= -8.5e+196)
		tmp = t_2;
	elseif (t <= -3.8e-100)
		tmp = t_1;
	elseif (t <= -1.56e-196)
		tmp = z;
	elseif (t <= 1.9e+200)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+196], t$95$2, If[LessEqual[t, -3.8e-100], t$95$1, If[LessEqual[t, -1.56e-196], z, If[LessEqual[t, 1.9e+200], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.50000000000000041e196 or 1.89999999999999991e200 < t

   1. Initial program 44.3%

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

   3. Taylor expanded in x around 0 43.6%

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

   4. Taylor expanded in y around 0 84.3%

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

   5. Taylor expanded in z around inf 65.0%

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

      1. associate-/l* 73.6%

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

   7. Simplified 73.6%

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

   if -8.50000000000000041e196 < t < -3.79999999999999997e-100 or -1.56e-196 < t < 1.89999999999999991e200

   1. Initial program 64.7%

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

   3. Taylor expanded in y around inf 61.8%

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

   if -3.79999999999999997e-100 < t < -1.56e-196

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 81.4%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+196}:\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-100}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-196}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+200}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -3.25 \cdot 10^{+211}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-194}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -3.25e+211)
     (- a (* y (/ b t)))
     (if (<= t -1.4e-98)
       t_1
       (if (<= t -1.45e-194)
         z
         (if (<= t 3.2e+200) t_1 (+ a (* y (/ z t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -3.25e+211) {
		tmp = a - (y * (b / t));
	} else if (t <= -1.4e-98) {
		tmp = t_1;
	} else if (t <= -1.45e-194) {
		tmp = z;
	} else if (t <= 3.2e+200) {
		tmp = t_1;
	} else {
		tmp = a + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-3.25d+211)) then
        tmp = a - (y * (b / t))
    else if (t <= (-1.4d-98)) then
        tmp = t_1
    else if (t <= (-1.45d-194)) then
        tmp = z
    else if (t <= 3.2d+200) then
        tmp = t_1
    else
        tmp = a + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -3.25e+211) {
		tmp = a - (y * (b / t));
	} else if (t <= -1.4e-98) {
		tmp = t_1;
	} else if (t <= -1.45e-194) {
		tmp = z;
	} else if (t <= 3.2e+200) {
		tmp = t_1;
	} else {
		tmp = a + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -3.25e+211:
		tmp = a - (y * (b / t))
	elif t <= -1.4e-98:
		tmp = t_1
	elif t <= -1.45e-194:
		tmp = z
	elif t <= 3.2e+200:
		tmp = t_1
	else:
		tmp = a + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -3.25e+211)
		tmp = Float64(a - Float64(y * Float64(b / t)));
	elseif (t <= -1.4e-98)
		tmp = t_1;
	elseif (t <= -1.45e-194)
		tmp = z;
	elseif (t <= 3.2e+200)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -3.25e+211)
		tmp = a - (y * (b / t));
	elseif (t <= -1.4e-98)
		tmp = t_1;
	elseif (t <= -1.45e-194)
		tmp = z;
	elseif (t <= 3.2e+200)
		tmp = t_1;
	else
		tmp = a + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t, -3.25e+211], N[(a - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.4e-98], t$95$1, If[LessEqual[t, -1.45e-194], z, If[LessEqual[t, 3.2e+200], t$95$1, N[(a + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.2499999999999998e211

   1. Initial program 48.7%

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

   3. Taylor expanded in x around 0 47.6%

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

   4. Taylor expanded in y around 0 86.1%

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

   5. Taylor expanded in z around 0 81.7%

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

      1. neg-mul-1 81.7%

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

      2. distribute-neg-frac2 81.7%

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

   7. Simplified 81.7%

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

   if -3.2499999999999998e211 < t < -1.3999999999999999e-98 or -1.44999999999999985e-194 < t < 3.20000000000000031e200

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 61.7%

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

   if -1.3999999999999999e-98 < t < -1.44999999999999985e-194

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 81.4%

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

   if 3.20000000000000031e200 < t

   1. Initial program 40.3%

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

   3. Taylor expanded in x around 0 40.0%

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

   4. Taylor expanded in y around 0 81.9%

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

   5. Taylor expanded in z around inf 57.0%

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

      1. associate-/l* 72.5%

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

   7. Simplified 72.5%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.25 \cdot 10^{+211}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-98}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-194}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+200}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+213}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-196}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -1.8e+213)
     a
     (if (<= t -6.8e-100)
       t_1
       (if (<= t -3.4e-196) z (if (<= t 5.7e+200) t_1 a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -1.8e+213) {
		tmp = a;
	} else if (t <= -6.8e-100) {
		tmp = t_1;
	} else if (t <= -3.4e-196) {
		tmp = z;
	} else if (t <= 5.7e+200) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-1.8d+213)) then
        tmp = a
    else if (t <= (-6.8d-100)) then
        tmp = t_1
    else if (t <= (-3.4d-196)) then
        tmp = z
    else if (t <= 5.7d+200) then
        tmp = t_1
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -1.8e+213) {
		tmp = a;
	} else if (t <= -6.8e-100) {
		tmp = t_1;
	} else if (t <= -3.4e-196) {
		tmp = z;
	} else if (t <= 5.7e+200) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -1.8e+213:
		tmp = a
	elif t <= -6.8e-100:
		tmp = t_1
	elif t <= -3.4e-196:
		tmp = z
	elif t <= 5.7e+200:
		tmp = t_1
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -1.8e+213)
		tmp = a;
	elseif (t <= -6.8e-100)
		tmp = t_1;
	elseif (t <= -3.4e-196)
		tmp = z;
	elseif (t <= 5.7e+200)
		tmp = t_1;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -1.8e+213)
		tmp = a;
	elseif (t <= -6.8e-100)
		tmp = t_1;
	elseif (t <= -3.4e-196)
		tmp = z;
	elseif (t <= 5.7e+200)
		tmp = t_1;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t, -1.8e+213], a, If[LessEqual[t, -6.8e-100], t$95$1, If[LessEqual[t, -3.4e-196], z, If[LessEqual[t, 5.7e+200], t$95$1, a]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8000000000000001e213 or 5.70000000000000007e200 < t

   1. Initial program 44.0%

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

   3. Taylor expanded in t around inf 61.3%

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

   if -1.8000000000000001e213 < t < -6.79999999999999953e-100 or -3.4e-196 < t < 5.70000000000000007e200

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 61.7%

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

   if -6.79999999999999953e-100 < t < -3.4e-196

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 81.4%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+213}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-100}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-196}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+200}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+170}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.5e+131) a (if (<= t 1.2e+170) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e+131) {
		tmp = a;
	} else if (t <= 1.2e+170) {
		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 (t <= (-7.5d+131)) then
        tmp = a
    else if (t <= 1.2d+170) 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 (t <= -7.5e+131) {
		tmp = a;
	} else if (t <= 1.2e+170) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.5e+131:
		tmp = a
	elif t <= 1.2e+170:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.5e+131)
		tmp = a;
	elseif (t <= 1.2e+170)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.5e+131)
		tmp = a;
	elseif (t <= 1.2e+170)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.5e+131], a, If[LessEqual[t, 1.2e+170], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -7.4999999999999995e131 or 1.2e170 < t

   1. Initial program 44.6%

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

   3. Taylor expanded in t around inf 61.8%

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

   if -7.4999999999999995e131 < t < 1.2e170

   1. Initial program 68.4%

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

   3. Taylor expanded in x around inf 45.3%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+170}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.7% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.7%

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

3. Taylor expanded in t around inf 30.4%

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

4. Final simplification 30.4%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.4% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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