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

Percentage Accurate: 60.7% → 87.8%

Time: 10.5s

Alternatives: 11

Speedup: 0.3×

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: 87.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) \cdot a\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+255} \lor \neg \left(t\_2 \leq 10^{+262}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_1\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y t) a))
        (t_2 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_2 -1e+255) (not (<= t_2 1e+262)))
     (- (+ z a) b)
     (/ (- (fma (+ x y) z t_1) (* y b)) (+ x (+ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * a;
	double t_2 = ((((x + y) * z) + t_1) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -1e+255) || !(t_2 <= 1e+262)) {
		tmp = (z + a) - b;
	} else {
		tmp = (fma((x + y), z, t_1) - (y * b)) / (x + (y + t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) * a)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_2 <= -1e+255) || !(t_2 <= 1e+262))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(fma(Float64(x + y), z, t_1) - Float64(y * b)) / Float64(x + Float64(y + t)));
	end
	return 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[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -1e+255], N[Not[LessEqual[t$95$2, 1e+262]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.99999999999999988e254 or 1e262 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.7%

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

   3. Taylor expanded in y around inf 82.7%

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

   if -9.99999999999999988e254 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e262

   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. Step-by-step derivation

      1. fma-define 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+255} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+262}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, \left(y + t\right) \cdot a\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+255} \lor \neg \left(t\_1 \leq 10^{+262}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 -1e+255) (not (<= t_1 1e+262))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -1e+255) || !(t_1 <= 1e+262)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t))
    if ((t_1 <= (-1d+255)) .or. (.not. (t_1 <= 1d+262))) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -1e+255) || !(t_1 <= 1e+262)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -1e+255) or not (t_1 <= 1e+262):
		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(x + y) * z) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= -1e+255) || !(t_1 <= 1e+262))
		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 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -1e+255) || ~((t_1 <= 1e+262)))
		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[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+255], N[Not[LessEqual[t$95$1, 1e+262]], $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)) < -9.99999999999999988e254 or 1e262 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.7%

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

   3. Taylor expanded in y around inf 82.7%

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

   if -9.99999999999999988e254 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e262

   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 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+255} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+262}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(y + t\right) \cdot a - y \cdot b}{t\_2}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+15}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-18}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-61}:\\ \;\;\;\;\frac{z}{\frac{t\_1}{x + y}}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-132}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-224}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-177}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-96}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+41}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{t\_1}{y}}{\left(b - z\right) - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (* (+ y t) a) (* y b)) t_2))
        (t_4 (- (+ z a) b)))
   (if (<= y -3.3e+15)
     t_4
     (if (<= y -1.15e-18)
       t_3
       (if (<= y -8e-61)
         (/ z (/ t_1 (+ x y)))
         (if (<= y -3e-132)
           t_3
           (if (<= y -8.2e-224)
             t_4
             (if (<= y 8.5e-177)
               (/ (+ (* t a) (* x z)) (+ x t))
               (if (<= y 1.46e-96)
                 t_4
                 (if (<= y 2.8e+41)
                   t_3
                   (if (<= y 8.5e+97)
                     (* z (/ (+ x y) t_2))
                     (/ -1.0 (/ (/ t_1 y) (- (- b z) a))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = y + (x + t);
	double t_3 = (((y + t) * a) - (y * b)) / t_2;
	double t_4 = (z + a) - b;
	double tmp;
	if (y <= -3.3e+15) {
		tmp = t_4;
	} else if (y <= -1.15e-18) {
		tmp = t_3;
	} else if (y <= -8e-61) {
		tmp = z / (t_1 / (x + y));
	} else if (y <= -3e-132) {
		tmp = t_3;
	} else if (y <= -8.2e-224) {
		tmp = t_4;
	} else if (y <= 8.5e-177) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.46e-96) {
		tmp = t_4;
	} else if (y <= 2.8e+41) {
		tmp = t_3;
	} else if (y <= 8.5e+97) {
		tmp = z * ((x + y) / t_2);
	} else {
		tmp = -1.0 / ((t_1 / y) / ((b - 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + y) + t
    t_2 = y + (x + t)
    t_3 = (((y + t) * a) - (y * b)) / t_2
    t_4 = (z + a) - b
    if (y <= (-3.3d+15)) then
        tmp = t_4
    else if (y <= (-1.15d-18)) then
        tmp = t_3
    else if (y <= (-8d-61)) then
        tmp = z / (t_1 / (x + y))
    else if (y <= (-3d-132)) then
        tmp = t_3
    else if (y <= (-8.2d-224)) then
        tmp = t_4
    else if (y <= 8.5d-177) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 1.46d-96) then
        tmp = t_4
    else if (y <= 2.8d+41) then
        tmp = t_3
    else if (y <= 8.5d+97) then
        tmp = z * ((x + y) / t_2)
    else
        tmp = (-1.0d0) / ((t_1 / y) / ((b - 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 t_1 = (x + y) + t;
	double t_2 = y + (x + t);
	double t_3 = (((y + t) * a) - (y * b)) / t_2;
	double t_4 = (z + a) - b;
	double tmp;
	if (y <= -3.3e+15) {
		tmp = t_4;
	} else if (y <= -1.15e-18) {
		tmp = t_3;
	} else if (y <= -8e-61) {
		tmp = z / (t_1 / (x + y));
	} else if (y <= -3e-132) {
		tmp = t_3;
	} else if (y <= -8.2e-224) {
		tmp = t_4;
	} else if (y <= 8.5e-177) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.46e-96) {
		tmp = t_4;
	} else if (y <= 2.8e+41) {
		tmp = t_3;
	} else if (y <= 8.5e+97) {
		tmp = z * ((x + y) / t_2);
	} else {
		tmp = -1.0 / ((t_1 / y) / ((b - z) - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + t
	t_2 = y + (x + t)
	t_3 = (((y + t) * a) - (y * b)) / t_2
	t_4 = (z + a) - b
	tmp = 0
	if y <= -3.3e+15:
		tmp = t_4
	elif y <= -1.15e-18:
		tmp = t_3
	elif y <= -8e-61:
		tmp = z / (t_1 / (x + y))
	elif y <= -3e-132:
		tmp = t_3
	elif y <= -8.2e-224:
		tmp = t_4
	elif y <= 8.5e-177:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 1.46e-96:
		tmp = t_4
	elif y <= 2.8e+41:
		tmp = t_3
	elif y <= 8.5e+97:
		tmp = z * ((x + y) / t_2)
	else:
		tmp = -1.0 / ((t_1 / y) / ((b - z) - a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / t_2)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.3e+15)
		tmp = t_4;
	elseif (y <= -1.15e-18)
		tmp = t_3;
	elseif (y <= -8e-61)
		tmp = Float64(z / Float64(t_1 / Float64(x + y)));
	elseif (y <= -3e-132)
		tmp = t_3;
	elseif (y <= -8.2e-224)
		tmp = t_4;
	elseif (y <= 8.5e-177)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 1.46e-96)
		tmp = t_4;
	elseif (y <= 2.8e+41)
		tmp = t_3;
	elseif (y <= 8.5e+97)
		tmp = Float64(z * Float64(Float64(x + y) / t_2));
	else
		tmp = Float64(-1.0 / Float64(Float64(t_1 / y) / Float64(Float64(b - z) - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + t;
	t_2 = y + (x + t);
	t_3 = (((y + t) * a) - (y * b)) / t_2;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.3e+15)
		tmp = t_4;
	elseif (y <= -1.15e-18)
		tmp = t_3;
	elseif (y <= -8e-61)
		tmp = z / (t_1 / (x + y));
	elseif (y <= -3e-132)
		tmp = t_3;
	elseif (y <= -8.2e-224)
		tmp = t_4;
	elseif (y <= 8.5e-177)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 1.46e-96)
		tmp = t_4;
	elseif (y <= 2.8e+41)
		tmp = t_3;
	elseif (y <= 8.5e+97)
		tmp = z * ((x + y) / t_2);
	else
		tmp = -1.0 / ((t_1 / y) / ((b - z) - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.3e+15], t$95$4, If[LessEqual[y, -1.15e-18], t$95$3, If[LessEqual[y, -8e-61], N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-132], t$95$3, If[LessEqual[y, -8.2e-224], t$95$4, If[LessEqual[y, 8.5e-177], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.46e-96], t$95$4, If[LessEqual[y, 2.8e+41], t$95$3, If[LessEqual[y, 8.5e+97], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(N[(t$95$1 / y), $MachinePrecision] / N[(N[(b - z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.3e15 or -3e-132 < y < -8.19999999999999972e-224 or 8.4999999999999993e-177 < y < 1.45999999999999995e-96

   1. Initial program 40.0%

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

   3. Taylor expanded in y around inf 81.3%

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

   if -3.3e15 < y < -1.15e-18 or -8.0000000000000003e-61 < y < -3e-132 or 1.45999999999999995e-96 < y < 2.7999999999999999e41

   1. Initial program 81.7%

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

   3. Taylor expanded in z around 0 64.3%

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

      1. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -1.15e-18 < y < -8.0000000000000003e-61

   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 z around inf 57.2%

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

      1. associate-/l* 78.2%

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

      2. +-commutative 78.2%

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

      3. +-commutative 78.2%

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

      4. associate-+r+ 78.2%

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

      5. +-commutative 78.2%

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

      6. associate-+l+ 78.2%

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

   5. Simplified 78.2%

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

      1. clear-num 78.2%

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

      2. un-div-inv 78.4%

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

      3. +-commutative 78.4%

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

      4. associate-+r+ 78.4%

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

      5. +-commutative 78.4%

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

   7. Applied egg-rr 78.4%

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

   if -8.19999999999999972e-224 < y < 8.4999999999999993e-177

   1. Initial program 85.1%

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

   3. Taylor expanded in y around 0 70.7%

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

   if 2.7999999999999999e41 < y < 8.4999999999999993e97

   1. Initial program 39.1%

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

   3. Taylor expanded in z around inf 23.2%

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

      1. associate-/l* 84.0%

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

      2. +-commutative 84.0%

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

      3. +-commutative 84.0%

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

      4. associate-+r+ 84.0%

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

      5. +-commutative 84.0%

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

      6. associate-+l+ 84.0%

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

   5. Simplified 84.0%

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

   if 8.4999999999999993e97 < y

   1. Initial program 37.1%

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

   3. Taylor expanded in y around inf 34.6%

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

      1. clear-num 34.6%

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

      2. inv-pow 34.6%

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

      3. associate-/r* 93.5%

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

      4. +-commutative 93.5%

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

      5. associate-+l+ 93.5%

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

      6. associate--l+ 93.5%

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

   5. Applied egg-rr 93.5%

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

      1. unpow-1 93.5%

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

   7. Simplified 93.5%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+15}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-18}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-61}:\\ \;\;\;\;\frac{z}{\frac{\left(x + y\right) + t}{x + y}}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-132}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-224}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-177}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-96}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{\left(x + y\right) + t}{y}}{\left(b - z\right) - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ \mathbf{if}\;b \leq -1.85 \cdot 10^{+138}:\\ \;\;\;\;\frac{-1}{\frac{\frac{t\_1}{y}}{\left(b - z\right) - a}}\\ \mathbf{elif}\;b \leq -1.42 \cdot 10^{+60}:\\ \;\;\;\;\frac{z}{\frac{t\_1}{x + y}}\\ \mathbf{elif}\;b \leq -4200000 \lor \neg \left(b \leq 2.25 \cdot 10^{+153}\right):\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t)))
   (if (<= b -1.85e+138)
     (/ -1.0 (/ (/ t_1 y) (- (- b z) a)))
     (if (<= b -1.42e+60)
       (/ z (/ t_1 (+ x y)))
       (if (or (<= b -4200000.0) (not (<= b 2.25e+153)))
         (* b (- (/ a b) (/ y (+ y (+ x t)))))
         (- (+ z a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double tmp;
	if (b <= -1.85e+138) {
		tmp = -1.0 / ((t_1 / y) / ((b - z) - a));
	} else if (b <= -1.42e+60) {
		tmp = z / (t_1 / (x + y));
	} else if ((b <= -4200000.0) || !(b <= 2.25e+153)) {
		tmp = b * ((a / b) - (y / (y + (x + t))));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) + t
    if (b <= (-1.85d+138)) then
        tmp = (-1.0d0) / ((t_1 / y) / ((b - z) - a))
    else if (b <= (-1.42d+60)) then
        tmp = z / (t_1 / (x + y))
    else if ((b <= (-4200000.0d0)) .or. (.not. (b <= 2.25d+153))) then
        tmp = b * ((a / b) - (y / (y + (x + t))))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double tmp;
	if (b <= -1.85e+138) {
		tmp = -1.0 / ((t_1 / y) / ((b - z) - a));
	} else if (b <= -1.42e+60) {
		tmp = z / (t_1 / (x + y));
	} else if ((b <= -4200000.0) || !(b <= 2.25e+153)) {
		tmp = b * ((a / b) - (y / (y + (x + t))));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + t
	tmp = 0
	if b <= -1.85e+138:
		tmp = -1.0 / ((t_1 / y) / ((b - z) - a))
	elif b <= -1.42e+60:
		tmp = z / (t_1 / (x + y))
	elif (b <= -4200000.0) or not (b <= 2.25e+153):
		tmp = b * ((a / b) - (y / (y + (x + t))))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	tmp = 0.0
	if (b <= -1.85e+138)
		tmp = Float64(-1.0 / Float64(Float64(t_1 / y) / Float64(Float64(b - z) - a)));
	elseif (b <= -1.42e+60)
		tmp = Float64(z / Float64(t_1 / Float64(x + y)));
	elseif ((b <= -4200000.0) || !(b <= 2.25e+153))
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / Float64(y + Float64(x + t)))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + t;
	tmp = 0.0;
	if (b <= -1.85e+138)
		tmp = -1.0 / ((t_1 / y) / ((b - z) - a));
	elseif (b <= -1.42e+60)
		tmp = z / (t_1 / (x + y));
	elseif ((b <= -4200000.0) || ~((b <= 2.25e+153)))
		tmp = b * ((a / b) - (y / (y + (x + t))));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[b, -1.85e+138], N[(-1.0 / N[(N[(t$95$1 / y), $MachinePrecision] / N[(N[(b - z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.42e+60], N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -4200000.0], N[Not[LessEqual[b, 2.25e+153]], $MachinePrecision]], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.8499999999999999e138

   1. Initial program 63.6%

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

   3. Taylor expanded in y around inf 45.0%

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

      1. clear-num 44.9%

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

      2. inv-pow 44.9%

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

      3. associate-/r* 72.2%

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

      4. +-commutative 72.2%

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

      5. associate-+l+ 72.2%

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

      6. associate--l+ 72.2%

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

   5. Applied egg-rr 72.2%

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

      1. unpow-1 72.2%

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

   7. Simplified 72.2%

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

   if -1.8499999999999999e138 < b < -1.42000000000000001e60

   1. Initial program 46.1%

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

   3. Taylor expanded in z around inf 36.9%

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

      1. associate-/l* 76.5%

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

      2. +-commutative 76.5%

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

      3. +-commutative 76.5%

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

      4. associate-+r+ 76.5%

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

      5. +-commutative 76.5%

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

      6. associate-+l+ 76.5%

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

   5. Simplified 76.5%

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

      1. clear-num 76.6%

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

      2. un-div-inv 76.7%

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

      3. +-commutative 76.7%

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

      4. associate-+r+ 76.7%

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

      5. +-commutative 76.7%

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

   7. Applied egg-rr 76.7%

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

   if -1.42000000000000001e60 < b < -4.2e6 or 2.25e153 < b

   1. Initial program 47.9%

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

   3. Taylor expanded in b around -inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. *-commutative 53.0%

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

      3. distribute-rgt-neg-in 53.0%

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

   5. Simplified 97.0%

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

   6. Taylor expanded in t around inf 78.9%

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

   if -4.2e6 < b < 2.25e153

   1. Initial program 58.6%

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

   3. Taylor expanded in y around inf 67.2%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+138}:\\ \;\;\;\;\frac{-1}{\frac{\frac{\left(x + y\right) + t}{y}}{\left(b - z\right) - a}}\\ \mathbf{elif}\;b \leq -1.42 \cdot 10^{+60}:\\ \;\;\;\;\frac{z}{\frac{\left(x + y\right) + t}{x + y}}\\ \mathbf{elif}\;b \leq -4200000 \lor \neg \left(b \leq 2.25 \cdot 10^{+153}\right):\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{b}{\left(\left(-t\right) - x\right) - y}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+155}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.5e+194)
   (* y (/ b (- (- (- t) x) y)))
   (if (<= b 1.75e+155) (- (+ z a) b) (* b (- (/ a b) (/ y (+ y (+ x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.5e+194) {
		tmp = y * (b / ((-t - x) - y));
	} else if (b <= 1.75e+155) {
		tmp = (z + a) - b;
	} else {
		tmp = b * ((a / b) - (y / (y + (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 (b <= (-4.5d+194)) then
        tmp = y * (b / ((-t - x) - y))
    else if (b <= 1.75d+155) then
        tmp = (z + a) - b
    else
        tmp = b * ((a / b) - (y / (y + (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 (b <= -4.5e+194) {
		tmp = y * (b / ((-t - x) - y));
	} else if (b <= 1.75e+155) {
		tmp = (z + a) - b;
	} else {
		tmp = b * ((a / b) - (y / (y + (x + t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.5e+194:
		tmp = y * (b / ((-t - x) - y))
	elif b <= 1.75e+155:
		tmp = (z + a) - b
	else:
		tmp = b * ((a / b) - (y / (y + (x + t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.5e+194)
		tmp = Float64(y * Float64(b / Float64(Float64(Float64(-t) - x) - y)));
	elseif (b <= 1.75e+155)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / Float64(y + Float64(x + t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.5e+194)
		tmp = y * (b / ((-t - x) - y));
	elseif (b <= 1.75e+155)
		tmp = (z + a) - b;
	else
		tmp = b * ((a / b) - (y / (y + (x + t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.5e+194], N[(y * N[(b / N[(N[((-t) - x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e+155], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.4999999999999998e194

   1. Initial program 59.5%

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

   3. Taylor expanded in b around inf 38.4%

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

      1. *-commutative 38.4%

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

      2. +-commutative 38.4%

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

      3. associate-+r+ 38.4%

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

      4. associate-*r/ 68.1%

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

      5. neg-mul-1 68.1%

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

      6. distribute-rgt-neg-in 68.1%

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

      7. associate-+r+ 68.1%

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

      8. +-commutative 68.1%

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

      9. distribute-neg-frac 68.1%

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

      10. +-commutative 68.1%

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

      11. associate-+r+ 68.1%

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

      12. +-commutative 68.1%

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

      13. associate-+l+ 68.1%

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

   5. Simplified 68.1%

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

   if -4.4999999999999998e194 < b < 1.74999999999999992e155

   1. Initial program 58.4%

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

   3. Taylor expanded in y around inf 66.2%

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

   if 1.74999999999999992e155 < b

   1. Initial program 42.1%

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

   3. Taylor expanded in b around -inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. *-commutative 48.6%

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

      3. distribute-rgt-neg-in 48.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in t around inf 77.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{b}{\left(\left(-t\right) - x\right) - y}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+155}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+124} \lor \neg \left(x \leq 8.5 \cdot 10^{+88}\right):\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.6e+124) (not (<= x 8.5e+88)))
   (+ z (* t (- (/ a x) (/ z x))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.6e+124) || !(x <= 8.5e+88)) {
		tmp = z + (t * ((a / x) - (z / x)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.6d+124)) .or. (.not. (x <= 8.5d+88))) then
        tmp = z + (t * ((a / x) - (z / x)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.6e+124) || !(x <= 8.5e+88)) {
		tmp = z + (t * ((a / x) - (z / x)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.6e+124) or not (x <= 8.5e+88):
		tmp = z + (t * ((a / x) - (z / x)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.6e+124) || !(x <= 8.5e+88))
		tmp = Float64(z + Float64(t * Float64(Float64(a / x) - Float64(z / x))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.6e+124) || ~((x <= 8.5e+88)))
		tmp = z + (t * ((a / x) - (z / x)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.6e+124], N[Not[LessEqual[x, 8.5e+88]], $MachinePrecision]], N[(z + N[(t * N[(N[(a / x), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999996e124 or 8.5000000000000005e88 < x

   1. Initial program 42.4%

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

   3. Taylor expanded in y around 0 32.3%

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

   4. Taylor expanded in t around 0 71.1%

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

   if -1.59999999999999996e124 < x < 8.5000000000000005e88

   1. Initial program 63.3%

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

   3. Taylor expanded in y around inf 67.4%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+124} \lor \neg \left(x \leq 8.5 \cdot 10^{+88}\right):\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+194} \lor \neg \left(b \leq 3.5 \cdot 10^{+195}\right):\\ \;\;\;\;y \cdot \frac{b}{\left(\left(-t\right) - x\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.5e+194) (not (<= b 3.5e+195)))
   (* y (/ b (- (- (- t) x) y)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.5e+194) || !(b <= 3.5e+195)) {
		tmp = y * (b / ((-t - x) - y));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.5d+194)) .or. (.not. (b <= 3.5d+195))) then
        tmp = y * (b / ((-t - x) - y))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.5e+194) || !(b <= 3.5e+195)) {
		tmp = y * (b / ((-t - x) - y));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.5e+194) or not (b <= 3.5e+195):
		tmp = y * (b / ((-t - x) - y))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.5e+194) || !(b <= 3.5e+195))
		tmp = Float64(y * Float64(b / Float64(Float64(Float64(-t) - x) - y)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.5e+194) || ~((b <= 3.5e+195)))
		tmp = y * (b / ((-t - x) - y));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.5e+194], N[Not[LessEqual[b, 3.5e+195]], $MachinePrecision]], N[(y * N[(b / N[(N[((-t) - x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.49999999999999994e194 or 3.5000000000000002e195 < b

   1. Initial program 46.6%

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

   3. Taylor expanded in b around inf 31.2%

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

      1. *-commutative 31.2%

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

      2. +-commutative 31.2%

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

      3. associate-+r+ 31.2%

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

      4. associate-*r/ 65.7%

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

      5. neg-mul-1 65.7%

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

      6. distribute-rgt-neg-in 65.7%

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

      7. associate-+r+ 65.7%

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

      8. +-commutative 65.7%

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

      9. distribute-neg-frac 65.7%

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

      10. +-commutative 65.7%

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

      11. associate-+r+ 65.7%

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

      12. +-commutative 65.7%

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

      13. associate-+l+ 65.7%

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

   5. Simplified 65.7%

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

   if -2.49999999999999994e194 < b < 3.5000000000000002e195

   1. Initial program 58.3%

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

   3. Taylor expanded in y around inf 66.5%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+194} \lor \neg \left(b \leq 3.5 \cdot 10^{+195}\right):\\ \;\;\;\;y \cdot \frac{b}{\left(\left(-t\right) - x\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+170} \lor \neg \left(x \leq 8.5 \cdot 10^{+138}\right):\\ \;\;\;\;z \cdot \left(1 - \frac{t}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.12e+170) (not (<= x 8.5e+138)))
   (* z (- 1.0 (/ t x)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.12e+170) || !(x <= 8.5e+138)) {
		tmp = z * (1.0 - (t / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.12d+170)) .or. (.not. (x <= 8.5d+138))) then
        tmp = z * (1.0d0 - (t / x))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.12e+170) || !(x <= 8.5e+138)) {
		tmp = z * (1.0 - (t / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.12e+170) or not (x <= 8.5e+138):
		tmp = z * (1.0 - (t / x))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.12e+170) || !(x <= 8.5e+138))
		tmp = Float64(z * Float64(1.0 - Float64(t / x)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.12e+170) || ~((x <= 8.5e+138)))
		tmp = z * (1.0 - (t / x));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.12e+170], N[Not[LessEqual[x, 8.5e+138]], $MachinePrecision]], N[(z * N[(1.0 - N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1200000000000001e170 or 8.5000000000000006e138 < x

   1. Initial program 38.6%

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

   3. Taylor expanded in z around inf 18.2%

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

      1. associate-/l* 66.5%

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

      2. +-commutative 66.5%

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

      3. +-commutative 66.5%

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

      4. associate-+r+ 66.5%

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

      5. +-commutative 66.5%

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

      6. associate-+l+ 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in x around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. unsub-neg 66.6%

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

   8. Simplified 66.6%

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

   if -1.1200000000000001e170 < x < 8.5000000000000006e138

   1. Initial program 62.1%

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

   3. Taylor expanded in y around inf 65.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+170} \lor \neg \left(x \leq 8.5 \cdot 10^{+138}\right):\\ \;\;\;\;z \cdot \left(1 - \frac{t}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+169}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+136}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.8e+169) z (if (<= x 1.7e+136) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+169) {
		tmp = z;
	} else if (x <= 1.7e+136) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.8d+169)) then
        tmp = z
    else if (x <= 1.7d+136) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+169) {
		tmp = z;
	} else if (x <= 1.7e+136) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.8e+169:
		tmp = z
	elif x <= 1.7e+136:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.8e+169)
		tmp = z;
	elseif (x <= 1.7e+136)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.8e+169)
		tmp = z;
	elseif (x <= 1.7e+136)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.8e+169], z, If[LessEqual[x, 1.7e+136], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -8.8000000000000001e169 or 1.69999999999999998e136 < x

   1. Initial program 38.6%

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

   3. Taylor expanded in x around inf 66.0%

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

   if -8.8000000000000001e169 < x < 1.69999999999999998e136

   1. Initial program 62.1%

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

   3. Taylor expanded in y around inf 65.5%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+169}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+136}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+83}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+28}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -9.5e+83) z (if (<= z 1.7e+28) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.5e+83) {
		tmp = z;
	} else if (z <= 1.7e+28) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-9.5d+83)) then
        tmp = z
    else if (z <= 1.7d+28) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.5e+83) {
		tmp = z;
	} else if (z <= 1.7e+28) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -9.5e+83:
		tmp = z
	elif z <= 1.7e+28:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -9.5e+83)
		tmp = z;
	elseif (z <= 1.7e+28)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -9.5e+83)
		tmp = z;
	elseif (z <= 1.7e+28)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -9.5e+83], z, If[LessEqual[z, 1.7e+28], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000002e83 or 1.7e28 < z

   1. Initial program 37.8%

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

   3. Taylor expanded in x around inf 64.2%

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

   if -9.5000000000000002e83 < z < 1.7e28

   1. Initial program 71.0%

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

   3. Taylor expanded in t around inf 47.4%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+83}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+28}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 31.8% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.6%

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

3. Taylor expanded in t around inf 33.0%

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

4. Final simplification 33.0%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.2% 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 2024130 
(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)))