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

Percentage Accurate: 60.8% → 87.8%

Time: 11.5s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+286}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+286))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+286)) {
		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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+286)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+286):
		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(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+286))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+286)))
		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[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+286]], $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 1.00000000000000003e286 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.7%

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

   3. Taylor expanded in y around inf 74.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000003e286

   1. Initial program 99.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+286}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.95 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-170}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* a (/ (+ y t) (+ x (+ y t))))))
   (if (<= a -8.2e+133)
     t_2
     (if (<= a -3.95e-22)
       t_1
       (if (<= a 1.7e-170)
         (/ (- (* z (+ x y)) (* y b)) (+ y (+ x t)))
         (if (<= a 7.6e+76) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (x + (y + t)));
	double tmp;
	if (a <= -8.2e+133) {
		tmp = t_2;
	} else if (a <= -3.95e-22) {
		tmp = t_1;
	} else if (a <= 1.7e-170) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else if (a <= 7.6e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a * ((y + t) / (x + (y + t)))
    if (a <= (-8.2d+133)) then
        tmp = t_2
    else if (a <= (-3.95d-22)) then
        tmp = t_1
    else if (a <= 1.7d-170) then
        tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
    else if (a <= 7.6d+76) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (x + (y + t)));
	double tmp;
	if (a <= -8.2e+133) {
		tmp = t_2;
	} else if (a <= -3.95e-22) {
		tmp = t_1;
	} else if (a <= 1.7e-170) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else if (a <= 7.6e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a * ((y + t) / (x + (y + t)))
	tmp = 0
	if a <= -8.2e+133:
		tmp = t_2
	elif a <= -3.95e-22:
		tmp = t_1
	elif a <= 1.7e-170:
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
	elif a <= 7.6e+76:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a * Float64(Float64(y + t) / Float64(x + Float64(y + t))))
	tmp = 0.0
	if (a <= -8.2e+133)
		tmp = t_2;
	elseif (a <= -3.95e-22)
		tmp = t_1;
	elseif (a <= 1.7e-170)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (a <= 7.6e+76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a * ((y + t) / (x + (y + t)));
	tmp = 0.0;
	if (a <= -8.2e+133)
		tmp = t_2;
	elseif (a <= -3.95e-22)
		tmp = t_1;
	elseif (a <= 1.7e-170)
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	elseif (a <= 7.6e+76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+133], t$95$2, If[LessEqual[a, -3.95e-22], t$95$1, If[LessEqual[a, 1.7e-170], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+76], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.20000000000000008e133 or 7.60000000000000049e76 < a

   1. Initial program 50.3%

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

   3. Taylor expanded in a around inf 40.8%

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

      1. associate-/l* 79.2%

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

      2. +-commutative 79.2%

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

      3. +-commutative 79.2%

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

      4. associate-+r+ 79.2%

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

   5. Simplified 79.2%

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

   if -8.20000000000000008e133 < a < -3.9499999999999999e-22 or 1.70000000000000006e-170 < a < 7.60000000000000049e76

   1. Initial program 51.5%

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

   3. Taylor expanded in y around inf 65.1%

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

   if -3.9499999999999999e-22 < a < 1.70000000000000006e-170

   1. Initial program 76.1%

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

   3. Taylor expanded in a around 0 65.7%

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

      1. +-commutative 65.7%

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

      2. *-commutative 65.7%

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

   5. Simplified 65.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{elif}\;a \leq -3.95 \cdot 10^{-22}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-170}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+76}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-202}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 190000:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.3e-149)
     t_1
     (if (<= y 1.46e-202)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 190000.0) (/ (- (* a (+ y t)) (* y b)) (+ y (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.3e-149) {
		tmp = t_1;
	} else if (y <= 1.46e-202) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 190000.0) {
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.3d-149)) then
        tmp = t_1
    else if (y <= 1.46d-202) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 190000.0d0) then
        tmp = ((a * (y + t)) - (y * b)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.3e-149) {
		tmp = t_1;
	} else if (y <= 1.46e-202) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 190000.0) {
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.3e-149:
		tmp = t_1
	elif y <= 1.46e-202:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 190000.0:
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.3e-149)
		tmp = t_1;
	elseif (y <= 1.46e-202)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 190000.0)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.3e-149)
		tmp = t_1;
	elseif (y <= 1.46e-202)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 190000.0)
		tmp = ((a * (y + t)) - (y * b)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.3e-149], t$95$1, If[LessEqual[y, 1.46e-202], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 190000.0], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.29999999999999999e-149 or 1.9e5 < y

   1. Initial program 48.5%

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

   3. Taylor expanded in y around inf 67.8%

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

   if -1.29999999999999999e-149 < y < 1.45999999999999996e-202

   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 y around 0 70.9%

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

   if 1.45999999999999996e-202 < y < 1.9e5

   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 57.7%

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

      1. +-commutative 57.7%

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

      2. *-commutative 57.7%

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

   5. Simplified 57.7%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-149}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-202}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 190000:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := a \cdot \frac{y + t}{t\_1}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-289}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (* a (/ (+ y t) t_1))))
   (if (<= a -8.2e+133)
     t_2
     (if (<= a -7.5e-289)
       (- (+ z a) b)
       (if (<= a 1.8e+61) (* z (/ (+ x y) t_1)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (a <= -8.2e+133) {
		tmp = t_2;
	} else if (a <= -7.5e-289) {
		tmp = (z + a) - b;
	} else if (a <= 1.8e+61) {
		tmp = z * ((x + y) / 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 = x + (y + t)
    t_2 = a * ((y + t) / t_1)
    if (a <= (-8.2d+133)) then
        tmp = t_2
    else if (a <= (-7.5d-289)) then
        tmp = (z + a) - b
    else if (a <= 1.8d+61) then
        tmp = z * ((x + y) / 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 = x + (y + t);
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (a <= -8.2e+133) {
		tmp = t_2;
	} else if (a <= -7.5e-289) {
		tmp = (z + a) - b;
	} else if (a <= 1.8e+61) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = a * ((y + t) / t_1)
	tmp = 0
	if a <= -8.2e+133:
		tmp = t_2
	elif a <= -7.5e-289:
		tmp = (z + a) - b
	elif a <= 1.8e+61:
		tmp = z * ((x + y) / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(a * Float64(Float64(y + t) / t_1))
	tmp = 0.0
	if (a <= -8.2e+133)
		tmp = t_2;
	elseif (a <= -7.5e-289)
		tmp = Float64(Float64(z + a) - b);
	elseif (a <= 1.8e+61)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = a * ((y + t) / t_1);
	tmp = 0.0;
	if (a <= -8.2e+133)
		tmp = t_2;
	elseif (a <= -7.5e-289)
		tmp = (z + a) - b;
	elseif (a <= 1.8e+61)
		tmp = z * ((x + y) / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+133], t$95$2, If[LessEqual[a, -7.5e-289], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[a, 1.8e+61], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.20000000000000008e133 or 1.80000000000000005e61 < a

   1. Initial program 50.9%

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

   3. Taylor expanded in a around inf 39.4%

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

      1. associate-/l* 77.6%

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

      2. +-commutative 77.6%

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

      3. +-commutative 77.6%

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

      4. associate-+r+ 77.6%

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

   5. Simplified 77.6%

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

   if -8.20000000000000008e133 < a < -7.49999999999999998e-289

   1. Initial program 61.0%

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

   3. Taylor expanded in y around inf 54.8%

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

   if -7.49999999999999998e-289 < a < 1.80000000000000005e61

   1. Initial program 70.3%

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

   3. Taylor expanded in z around inf 44.2%

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

      1. associate-/l* 65.7%

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

      2. +-commutative 65.7%

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

      3. +-commutative 65.7%

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

      4. associate-+r+ 65.7%

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

   5. Simplified 65.7%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-289}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-146} \lor \neg \left(y \leq 1.02 \cdot 10^{-24}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5e-146) (not (<= y 1.02e-24)))
   (- (+ z a) b)
   (/ (+ (* t a) (* x z)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5e-146) || !(y <= 1.02e-24)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5d-146)) .or. (.not. (y <= 1.02d-24))) then
        tmp = (z + a) - b
    else
        tmp = ((t * a) + (x * z)) / (x + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5e-146) || !(y <= 1.02e-24)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5e-146) or not (y <= 1.02e-24):
		tmp = (z + a) - b
	else:
		tmp = ((t * a) + (x * z)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5e-146) || !(y <= 1.02e-24))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5e-146) || ~((y <= 1.02e-24)))
		tmp = (z + a) - b;
	else
		tmp = ((t * a) + (x * z)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5e-146], N[Not[LessEqual[y, 1.02e-24]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999957e-146 or 1.0200000000000001e-24 < y

   1. Initial program 48.8%

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

   3. Taylor expanded in y around inf 67.4%

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

   if -4.99999999999999957e-146 < y < 1.0200000000000001e-24

   1. Initial program 80.4%

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

   3. Taylor expanded in y around 0 59.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-146} \lor \neg \left(y \leq 1.02 \cdot 10^{-24}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+134} \lor \neg \left(a \leq 5.5 \cdot 10^{+75}\right):\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.2e+134) (not (<= a 5.5e+75)))
   (* a (/ (+ y t) (+ x (+ y t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.2e+134) || !(a <= 5.5e+75)) {
		tmp = a * ((y + t) / (x + (y + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.2d+134)) .or. (.not. (a <= 5.5d+75))) then
        tmp = a * ((y + t) / (x + (y + t)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.2e+134) || !(a <= 5.5e+75)) {
		tmp = a * ((y + t) / (x + (y + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.2e+134) or not (a <= 5.5e+75):
		tmp = a * ((y + t) / (x + (y + t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.2e+134) || !(a <= 5.5e+75))
		tmp = Float64(a * Float64(Float64(y + t) / Float64(x + Float64(y + t))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.2e+134) || ~((a <= 5.5e+75)))
		tmp = a * ((y + t) / (x + (y + t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.2e+134], N[Not[LessEqual[a, 5.5e+75]], $MachinePrecision]], N[(a * N[(N[(y + t), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.20000000000000003e134 or 5.5000000000000001e75 < a

   1. Initial program 50.3%

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

   3. Taylor expanded in a around inf 40.8%

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

      1. associate-/l* 79.2%

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

      2. +-commutative 79.2%

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

      3. +-commutative 79.2%

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

      4. associate-+r+ 79.2%

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

   5. Simplified 79.2%

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

   if -1.20000000000000003e134 < a < 5.5000000000000001e75

   1. Initial program 65.4%

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

   3. Taylor expanded in y around inf 54.0%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+134} \lor \neg \left(a \leq 5.5 \cdot 10^{+75}\right):\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-266}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+71}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.85e-142)
     t_1
     (if (<= y -2.05e-266)
       (* x (/ z (+ x t)))
       (if (<= y 5.7e+71) (+ z a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.85e-142) {
		tmp = t_1;
	} else if (y <= -2.05e-266) {
		tmp = x * (z / (x + t));
	} else if (y <= 5.7e+71) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.85d-142)) then
        tmp = t_1
    else if (y <= (-2.05d-266)) then
        tmp = x * (z / (x + t))
    else if (y <= 5.7d+71) then
        tmp = z + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.85e-142) {
		tmp = t_1;
	} else if (y <= -2.05e-266) {
		tmp = x * (z / (x + t));
	} else if (y <= 5.7e+71) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.85e-142:
		tmp = t_1
	elif y <= -2.05e-266:
		tmp = x * (z / (x + t))
	elif y <= 5.7e+71:
		tmp = z + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.85e-142)
		tmp = t_1;
	elseif (y <= -2.05e-266)
		tmp = Float64(x * Float64(z / Float64(x + t)));
	elseif (y <= 5.7e+71)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.85e-142)
		tmp = t_1;
	elseif (y <= -2.05e-266)
		tmp = x * (z / (x + t));
	elseif (y <= 5.7e+71)
		tmp = z + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.85e-142], t$95$1, If[LessEqual[y, -2.05e-266], N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.7e+71], N[(z + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.84999999999999993e-142 or 5.7000000000000001e71 < y

   1. Initial program 46.0%

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

   3. Taylor expanded in y around inf 68.3%

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

   if -1.84999999999999993e-142 < y < -2.0500000000000001e-266

   1. Initial program 80.5%

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

   3. Taylor expanded in z around inf 53.7%

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

      1. +-commutative 53.7%

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

      2. +-commutative 53.7%

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

      3. associate-+r+ 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in y around 0 50.8%

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

      1. associate-/l* 56.1%

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

   8. Simplified 56.1%

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

   if -2.0500000000000001e-266 < y < 5.7000000000000001e71

   1. Initial program 78.6%

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

   3. Taylor expanded in y around inf 41.1%

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

   4. Taylor expanded in b around 0 52.3%

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

      1. +-commutative 52.3%

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

   6. Simplified 52.3%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-142}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-266}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+71}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-261}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+71}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.9e-133)
     t_1
     (if (<= y -2.2e-261) z (if (<= y 5.5e+71) (+ z a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.9e-133) {
		tmp = t_1;
	} else if (y <= -2.2e-261) {
		tmp = z;
	} else if (y <= 5.5e+71) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.9d-133)) then
        tmp = t_1
    else if (y <= (-2.2d-261)) then
        tmp = z
    else if (y <= 5.5d+71) then
        tmp = z + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.9e-133) {
		tmp = t_1;
	} else if (y <= -2.2e-261) {
		tmp = z;
	} else if (y <= 5.5e+71) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.9e-133:
		tmp = t_1
	elif y <= -2.2e-261:
		tmp = z
	elif y <= 5.5e+71:
		tmp = z + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.9e-133)
		tmp = t_1;
	elseif (y <= -2.2e-261)
		tmp = z;
	elseif (y <= 5.5e+71)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.9e-133)
		tmp = t_1;
	elseif (y <= -2.2e-261)
		tmp = z;
	elseif (y <= 5.5e+71)
		tmp = z + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.9e-133], t$95$1, If[LessEqual[y, -2.2e-261], z, If[LessEqual[y, 5.5e+71], N[(z + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000002e-133 or 5.5e71 < y

   1. Initial program 46.0%

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

   3. Taylor expanded in y around inf 68.3%

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

   if -1.9000000000000002e-133 < y < -2.2000000000000002e-261

   1. Initial program 82.4%

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

   3. Taylor expanded in x around inf 51.7%

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

   if -2.2000000000000002e-261 < y < 5.5e71

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 41.3%

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

   4. Taylor expanded in b around 0 52.4%

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

      1. +-commutative 52.4%

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

   6. Simplified 52.4%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-133}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-261}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+71}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+136} \lor \neg \left(b \leq 8.5 \cdot 10^{+192}\right):\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.1e+136) (not (<= b 8.5e+192))) (- a b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.1e+136) || !(b <= 8.5e+192)) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.1d+136)) .or. (.not. (b <= 8.5d+192))) then
        tmp = a - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.1e+136) || !(b <= 8.5e+192)) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.1e+136) or not (b <= 8.5e+192):
		tmp = a - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.1e+136) || !(b <= 8.5e+192))
		tmp = Float64(a - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.1e+136) || ~((b <= 8.5e+192)))
		tmp = a - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.1e+136], N[Not[LessEqual[b, 8.5e+192]], $MachinePrecision]], N[(a - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.09999999999999983e136 or 8.49999999999999965e192 < b

   1. Initial program 46.3%

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

   3. Taylor expanded in y around inf 46.3%

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

   4. Taylor expanded in z around 0 42.0%

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

   if -3.09999999999999983e136 < b < 8.49999999999999965e192

   1. Initial program 65.1%

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

   3. Taylor expanded in y around inf 56.6%

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

   4. Taylor expanded in b around 0 58.1%

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

      1. +-commutative 58.1%

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

   6. Simplified 58.1%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+136} \lor \neg \left(b \leq 8.5 \cdot 10^{+192}\right):\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+136}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+202}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.9e+136) (- a b) (if (<= b 9.5e+202) (+ z a) (- z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.9e+136) {
		tmp = a - b;
	} else if (b <= 9.5e+202) {
		tmp = z + a;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.9d+136)) then
        tmp = a - b
    else if (b <= 9.5d+202) then
        tmp = z + a
    else
        tmp = z - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.9e+136) {
		tmp = a - b;
	} else if (b <= 9.5e+202) {
		tmp = z + a;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.9e+136:
		tmp = a - b
	elif b <= 9.5e+202:
		tmp = z + a
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.9e+136)
		tmp = Float64(a - b);
	elseif (b <= 9.5e+202)
		tmp = Float64(z + a);
	else
		tmp = Float64(z - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.9e+136)
		tmp = a - b;
	elseif (b <= 9.5e+202)
		tmp = z + a;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.9e+136], N[(a - b), $MachinePrecision], If[LessEqual[b, 9.5e+202], N[(z + a), $MachinePrecision], N[(z - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.90000000000000007e136

   1. Initial program 48.9%

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

   3. Taylor expanded in y around inf 47.8%

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

   4. Taylor expanded in z around 0 44.8%

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

   if -1.90000000000000007e136 < b < 9.50000000000000059e202

   1. Initial program 64.8%

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

   3. Taylor expanded in y around inf 56.8%

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

   4. Taylor expanded in b around 0 58.1%

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

      1. +-commutative 58.1%

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

   6. Simplified 58.1%

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

   if 9.50000000000000059e202 < b

   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 y around inf 41.9%

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

   4. Taylor expanded in a around 0 42.0%

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

Alternative 11: 44.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+64}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+42}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.6e+64) a (if (<= a 8.2e+42) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.6e+64) {
		tmp = a;
	} else if (a <= 8.2e+42) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5.6d+64)) then
        tmp = a
    else if (a <= 8.2d+42) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.6e+64) {
		tmp = a;
	} else if (a <= 8.2e+42) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.6e+64:
		tmp = a
	elif a <= 8.2e+42:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.6e+64)
		tmp = a;
	elseif (a <= 8.2e+42)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.6e+64)
		tmp = a;
	elseif (a <= 8.2e+42)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.6e+64], a, If[LessEqual[a, 8.2e+42], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -5.60000000000000047e64 or 8.2000000000000001e42 < a

   1. Initial program 44.7%

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

   3. Taylor expanded in t around inf 51.3%

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

   if -5.60000000000000047e64 < a < 8.2000000000000001e42

   1. Initial program 71.8%

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

   3. Taylor expanded in x around inf 44.1%

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

Alternative 12: 51.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.1 \cdot 10^{+210}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 1.1e+210) (+ z a) (- b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.1e+210) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.1d+210) then
        tmp = z + a
    else
        tmp = -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.1e+210) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.1e+210:
		tmp = z + a
	else:
		tmp = -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.1e+210)
		tmp = Float64(z + a);
	else
		tmp = Float64(-b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.1e+210)
		tmp = z + a;
	else
		tmp = -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.1e+210], N[(z + a), $MachinePrecision], (-b)]

Derivation

1. Split input into 2 regimes

2. if b < 1.09999999999999993e210

   1. Initial program 62.4%

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

   3. Taylor expanded in y around inf 55.5%

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

   4. Taylor expanded in b around 0 53.7%

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

      1. +-commutative 53.7%

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

   6. Simplified 53.7%

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

   if 1.09999999999999993e210 < b

   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 y around inf 41.9%

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

   4. Taylor expanded in b around inf 35.6%

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

      1. mul-1-neg 35.6%

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

   6. Simplified 35.6%

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

Alternative 13: 32.5% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 60.8%

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

3. Taylor expanded in t around inf 29.3%

   \[\leadsto \color{blue}{a} \]
4. Add Preprocessing

Developer Target 1: 81.7% 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 2024163 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ 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)))