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

Percentage Accurate: 59.9% → 88.6%

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: 59.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{y + t}{t\_2}\\ t_4 := z \cdot \left(\frac{x}{t\_2} + \left(\mathsf{fma}\left(\frac{a}{z}, t\_3, \frac{y}{t\_2}\right) - \frac{b}{t\_2} \cdot \frac{y}{z}\right)\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{-72}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-191}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, a \cdot \left(y + t\right)\right)}{t\_1} - y \cdot \frac{b}{t\_1}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(t\_3 + \frac{\frac{y \cdot \left(z - b\right) + z \cdot x}{t\_2}}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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) t_2))
        (t_4
         (*
          z
          (+
           (/ x t_2)
           (- (fma (/ a z) t_3 (/ y t_2)) (* (/ b t_2) (/ y z)))))))
   (if (<= z -8.8e-72)
     t_4
     (if (<= z 1.02e-191)
       (- (/ (fma (+ x y) z (* a (+ y t))) t_1) (* y (/ b t_1)))
       (if (<= z 1.9e-32)
         (* a (+ t_3 (/ (/ (+ (* y (- z b)) (* z x)) t_2) a)))
         t_4)))))

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) / t_2;
	double t_4 = z * ((x / t_2) + (fma((a / z), t_3, (y / t_2)) - ((b / t_2) * (y / z))));
	double tmp;
	if (z <= -8.8e-72) {
		tmp = t_4;
	} else if (z <= 1.02e-191) {
		tmp = (fma((x + y), z, (a * (y + t))) / t_1) - (y * (b / t_1));
	} else if (z <= 1.9e-32) {
		tmp = a * (t_3 + ((((y * (z - b)) + (z * x)) / t_2) / a));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(y + t) / t_2)
	t_4 = Float64(z * Float64(Float64(x / t_2) + Float64(fma(Float64(a / z), t_3, Float64(y / t_2)) - Float64(Float64(b / t_2) * Float64(y / z)))))
	tmp = 0.0
	if (z <= -8.8e-72)
		tmp = t_4;
	elseif (z <= 1.02e-191)
		tmp = Float64(Float64(fma(Float64(x + y), z, Float64(a * Float64(y + t))) / t_1) - Float64(y * Float64(b / t_1)));
	elseif (z <= 1.9e-32)
		tmp = Float64(a * Float64(t_3 + Float64(Float64(Float64(Float64(y * Float64(z - b)) + Float64(z * x)) / t_2) / a)));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(N[(N[(a / z), $MachinePrecision] * t$95$3 + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(b / t$95$2), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e-72], t$95$4, If[LessEqual[z, 1.02e-191], N[(N[(N[(N[(x + y), $MachinePrecision] * z + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(y * N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-32], N[(a * N[(t$95$3 + N[(N[(N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.8000000000000001e-72 or 1.90000000000000004e-32 < z

   1. Initial program 49.1%

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

   3. Taylor expanded in z around inf 66.8%

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

      1. associate--l+ 66.8%

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

      2. +-commutative 66.8%

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

      3. associate-+r+ 66.8%

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

      4. +-commutative 66.8%

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

      5. associate-+l+ 66.8%

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

   5. Simplified 95.6%

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

   if -8.8000000000000001e-72 < z < 1.02e-191

   1. Initial program 84.1%

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

      1. div-sub 84.1%

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

      2. fma-define 84.1%

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

      3. +-commutative 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-+l+ 84.1%

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

      6. +-commutative 84.1%

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

      7. associate-+l+ 84.1%

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

      8. +-commutative 84.1%

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

      9. associate-/l* 91.4%

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

   4. Applied egg-rr 91.4%

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

   if 1.02e-191 < z < 1.90000000000000004e-32

   1. Initial program 70.8%

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

   3. Taylor expanded in a around -inf 90.9%

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

   5. Simplified 90.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(\frac{x}{y + \left(x + t\right)} + \left(\mathsf{fma}\left(\frac{a}{z}, \frac{y + t}{y + \left(x + t\right)}, \frac{y}{y + \left(x + t\right)}\right) - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{z}\right)\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-191}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, a \cdot \left(y + t\right)\right)}{x + \left(y + t\right)} - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(\frac{y + t}{y + \left(x + t\right)} + \frac{\frac{y \cdot \left(z - b\right) + z \cdot x}{y + \left(x + t\right)}}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{y + \left(x + t\right)} + \left(\mathsf{fma}\left(\frac{a}{z}, \frac{y + t}{y + \left(x + t\right)}, \frac{y}{y + \left(x + t\right)}\right) - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+213} \lor \neg \left(t\_2 \leq 5 \cdot 10^{+295}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(z \cdot x + y \cdot t\_3\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (or (<= t_2 -2e+213) (not (<= t_2 5e+295)))
     t_3
     (/ (+ (* t a) (+ (* z x) (* y t_3))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -2e+213) || !(t_2 <= 5e+295)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((z * x) + (y * t_3))) / 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
    t_3 = (z + a) - b
    if ((t_2 <= (-2d+213)) .or. (.not. (t_2 <= 5d+295))) then
        tmp = t_3
    else
        tmp = ((t * a) + ((z * x) + (y * t_3))) / 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 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -2e+213) || !(t_2 <= 5e+295)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((z * x) + (y * t_3))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	t_3 = (z + a) - b
	tmp = 0
	if (t_2 <= -2e+213) or not (t_2 <= 5e+295):
		tmp = t_3
	else:
		tmp = ((t * a) + ((z * x) + (y * t_3))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if ((t_2 <= -2e+213) || !(t_2 <= 5e+295))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(z * x) + Float64(y * t_3))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	tmp = 0.0;
	if ((t_2 <= -2e+213) || ~((t_2 <= 5e+295)))
		tmp = t_3;
	else
		tmp = ((t * a) + ((z * x) + (y * t_3))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e+213], N[Not[LessEqual[t$95$2, 5e+295]], $MachinePrecision]], t$95$3, N[(N[(N[(t * a), $MachinePrecision] + N[(N[(z * x), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $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)) < -1.99999999999999997e213 or 4.99999999999999991e295 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 11.7%

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

   3. Taylor expanded in y around inf 71.8%

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

   if -1.99999999999999997e213 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999991e295

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -2 \cdot 10^{+213} \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+295}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(z \cdot x + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a \cdot \left(y + t\right)\\ t_3 := y + \left(x + t\right)\\ t_4 := \frac{z \cdot \left(x + y\right) + t\_2}{t\_3}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+191}:\\ \;\;\;\;\frac{z}{\frac{t\_3}{x + y}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+51}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-79}:\\ \;\;\;\;\frac{t\_2 - y \cdot b}{t\_3}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+146}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (* a (+ y t)))
        (t_3 (+ y (+ x t)))
        (t_4 (/ (+ (* z (+ x y)) t_2) t_3)))
   (if (<= z -7e+191)
     (/ z (/ t_3 (+ x y)))
     (if (<= z -7.5e+92)
       t_1
       (if (<= z -1.25e+51)
         t_4
         (if (<= z -1.6e-70)
           t_1
           (if (<= z 1.95e-79)
             (/ (- t_2 (* y b)) t_3)
             (if (<= z 7e+146) t_4 (* z (/ (+ x y) t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * (y + t);
	double t_3 = y + (x + t);
	double t_4 = ((z * (x + y)) + t_2) / t_3;
	double tmp;
	if (z <= -7e+191) {
		tmp = z / (t_3 / (x + y));
	} else if (z <= -7.5e+92) {
		tmp = t_1;
	} else if (z <= -1.25e+51) {
		tmp = t_4;
	} else if (z <= -1.6e-70) {
		tmp = t_1;
	} else if (z <= 1.95e-79) {
		tmp = (t_2 - (y * b)) / t_3;
	} else if (z <= 7e+146) {
		tmp = t_4;
	} else {
		tmp = z * ((x + y) / t_3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a * (y + t)
    t_3 = y + (x + t)
    t_4 = ((z * (x + y)) + t_2) / t_3
    if (z <= (-7d+191)) then
        tmp = z / (t_3 / (x + y))
    else if (z <= (-7.5d+92)) then
        tmp = t_1
    else if (z <= (-1.25d+51)) then
        tmp = t_4
    else if (z <= (-1.6d-70)) then
        tmp = t_1
    else if (z <= 1.95d-79) then
        tmp = (t_2 - (y * b)) / t_3
    else if (z <= 7d+146) then
        tmp = t_4
    else
        tmp = z * ((x + y) / t_3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * (y + t);
	double t_3 = y + (x + t);
	double t_4 = ((z * (x + y)) + t_2) / t_3;
	double tmp;
	if (z <= -7e+191) {
		tmp = z / (t_3 / (x + y));
	} else if (z <= -7.5e+92) {
		tmp = t_1;
	} else if (z <= -1.25e+51) {
		tmp = t_4;
	} else if (z <= -1.6e-70) {
		tmp = t_1;
	} else if (z <= 1.95e-79) {
		tmp = (t_2 - (y * b)) / t_3;
	} else if (z <= 7e+146) {
		tmp = t_4;
	} else {
		tmp = z * ((x + y) / t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a * (y + t)
	t_3 = y + (x + t)
	t_4 = ((z * (x + y)) + t_2) / t_3
	tmp = 0
	if z <= -7e+191:
		tmp = z / (t_3 / (x + y))
	elif z <= -7.5e+92:
		tmp = t_1
	elif z <= -1.25e+51:
		tmp = t_4
	elif z <= -1.6e-70:
		tmp = t_1
	elif z <= 1.95e-79:
		tmp = (t_2 - (y * b)) / t_3
	elif z <= 7e+146:
		tmp = t_4
	else:
		tmp = z * ((x + y) / t_3)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a * Float64(y + t))
	t_3 = Float64(y + Float64(x + t))
	t_4 = Float64(Float64(Float64(z * Float64(x + y)) + t_2) / t_3)
	tmp = 0.0
	if (z <= -7e+191)
		tmp = Float64(z / Float64(t_3 / Float64(x + y)));
	elseif (z <= -7.5e+92)
		tmp = t_1;
	elseif (z <= -1.25e+51)
		tmp = t_4;
	elseif (z <= -1.6e-70)
		tmp = t_1;
	elseif (z <= 1.95e-79)
		tmp = Float64(Float64(t_2 - Float64(y * b)) / t_3);
	elseif (z <= 7e+146)
		tmp = t_4;
	else
		tmp = Float64(z * Float64(Float64(x + y) / t_3));
	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);
	t_3 = y + (x + t);
	t_4 = ((z * (x + y)) + t_2) / t_3;
	tmp = 0.0;
	if (z <= -7e+191)
		tmp = z / (t_3 / (x + y));
	elseif (z <= -7.5e+92)
		tmp = t_1;
	elseif (z <= -1.25e+51)
		tmp = t_4;
	elseif (z <= -1.6e-70)
		tmp = t_1;
	elseif (z <= 1.95e-79)
		tmp = (t_2 - (y * b)) / t_3;
	elseif (z <= 7e+146)
		tmp = t_4;
	else
		tmp = z * ((x + y) / t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[z, -7e+191], N[(z / N[(t$95$3 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e+92], t$95$1, If[LessEqual[z, -1.25e+51], t$95$4, If[LessEqual[z, -1.6e-70], t$95$1, If[LessEqual[z, 1.95e-79], N[(N[(t$95$2 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[z, 7e+146], t$95$4, N[(z * N[(N[(x + y), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.9999999999999994e191

   1. Initial program 41.0%

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

   3. Taylor expanded in z around inf 36.0%

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

      1. associate-/l* 72.9%

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

      2. +-commutative 72.9%

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

      3. +-commutative 72.9%

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

      4. associate-+r+ 72.9%

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

      5. +-commutative 72.9%

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

      6. associate-+l+ 72.9%

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

   5. Simplified 72.9%

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

      1. clear-num 72.9%

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

      2. un-div-inv 73.1%

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

      3. +-commutative 73.1%

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

   7. Applied egg-rr 73.1%

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

   if -6.9999999999999994e191 < z < -7.49999999999999946e92 or -1.25e51 < z < -1.5999999999999999e-70

   1. Initial program 51.3%

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

   3. Taylor expanded in y around inf 77.3%

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

   if -7.49999999999999946e92 < z < -1.25e51 or 1.95000000000000003e-79 < z < 7.0000000000000002e146

   1. Initial program 74.8%

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

   3. Taylor expanded in b around 0 71.0%

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

   if -1.5999999999999999e-70 < z < 1.95000000000000003e-79

   1. Initial program 81.6%

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

   3. Taylor expanded in z around 0 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   if 7.0000000000000002e146 < z

   1. Initial program 16.0%

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

   3. Taylor expanded in z around inf 16.0%

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

      1. associate-/l* 87.1%

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

      2. +-commutative 87.1%

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

      3. +-commutative 87.1%

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

      4. associate-+r+ 87.1%

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

      5. +-commutative 87.1%

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

      6. associate-+l+ 87.1%

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

   5. Simplified 87.1%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+191}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+92}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+51}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + a \cdot \left(y + t\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-70}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-79}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+146}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + a \cdot \left(y + t\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{z}{\frac{t\_2}{x + y}}\\ t_4 := \frac{t \cdot a + y \cdot \left(a - b\right)}{t\_2}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+189}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-191}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_2}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-72}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ x t)))
        (t_3 (/ z (/ t_2 (+ x y))))
        (t_4 (/ (+ (* t a) (* y (- a b))) t_2)))
   (if (<= z -1.55e+189)
     t_3
     (if (<= z -1.3e-74)
       t_1
       (if (<= z 1.2e-191)
         t_4
         (if (<= z 1.35e-162)
           (* a (/ (+ y t) t_2))
           (if (<= z 1.06e-72) t_4 (if (<= z 3.5e+207) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = z / (t_2 / (x + y));
	double t_4 = ((t * a) + (y * (a - b))) / t_2;
	double tmp;
	if (z <= -1.55e+189) {
		tmp = t_3;
	} else if (z <= -1.3e-74) {
		tmp = t_1;
	} else if (z <= 1.2e-191) {
		tmp = t_4;
	} else if (z <= 1.35e-162) {
		tmp = a * ((y + t) / t_2);
	} else if (z <= 1.06e-72) {
		tmp = t_4;
	} else if (z <= 3.5e+207) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = z / (t_2 / (x + y))
    t_4 = ((t * a) + (y * (a - b))) / t_2
    if (z <= (-1.55d+189)) then
        tmp = t_3
    else if (z <= (-1.3d-74)) then
        tmp = t_1
    else if (z <= 1.2d-191) then
        tmp = t_4
    else if (z <= 1.35d-162) then
        tmp = a * ((y + t) / t_2)
    else if (z <= 1.06d-72) then
        tmp = t_4
    else if (z <= 3.5d+207) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = z / (t_2 / (x + y));
	double t_4 = ((t * a) + (y * (a - b))) / t_2;
	double tmp;
	if (z <= -1.55e+189) {
		tmp = t_3;
	} else if (z <= -1.3e-74) {
		tmp = t_1;
	} else if (z <= 1.2e-191) {
		tmp = t_4;
	} else if (z <= 1.35e-162) {
		tmp = a * ((y + t) / t_2);
	} else if (z <= 1.06e-72) {
		tmp = t_4;
	} else if (z <= 3.5e+207) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = z / (t_2 / (x + y))
	t_4 = ((t * a) + (y * (a - b))) / t_2
	tmp = 0
	if z <= -1.55e+189:
		tmp = t_3
	elif z <= -1.3e-74:
		tmp = t_1
	elif z <= 1.2e-191:
		tmp = t_4
	elif z <= 1.35e-162:
		tmp = a * ((y + t) / t_2)
	elif z <= 1.06e-72:
		tmp = t_4
	elif z <= 3.5e+207:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z / Float64(t_2 / Float64(x + y)))
	t_4 = Float64(Float64(Float64(t * a) + Float64(y * Float64(a - b))) / t_2)
	tmp = 0.0
	if (z <= -1.55e+189)
		tmp = t_3;
	elseif (z <= -1.3e-74)
		tmp = t_1;
	elseif (z <= 1.2e-191)
		tmp = t_4;
	elseif (z <= 1.35e-162)
		tmp = Float64(a * Float64(Float64(y + t) / t_2));
	elseif (z <= 1.06e-72)
		tmp = t_4;
	elseif (z <= 3.5e+207)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = z / (t_2 / (x + y));
	t_4 = ((t * a) + (y * (a - b))) / t_2;
	tmp = 0.0;
	if (z <= -1.55e+189)
		tmp = t_3;
	elseif (z <= -1.3e-74)
		tmp = t_1;
	elseif (z <= 1.2e-191)
		tmp = t_4;
	elseif (z <= 1.35e-162)
		tmp = a * ((y + t) / t_2);
	elseif (z <= 1.06e-72)
		tmp = t_4;
	elseif (z <= 3.5e+207)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / N[(t$95$2 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t * a), $MachinePrecision] + N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[z, -1.55e+189], t$95$3, If[LessEqual[z, -1.3e-74], t$95$1, If[LessEqual[z, 1.2e-191], t$95$4, If[LessEqual[z, 1.35e-162], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-72], t$95$4, If[LessEqual[z, 3.5e+207], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.55e189 or 3.50000000000000028e207 < z

   1. Initial program 30.5%

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

   3. Taylor expanded in z around inf 27.8%

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

      1. associate-/l* 82.4%

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

      2. +-commutative 82.4%

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

      3. +-commutative 82.4%

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

      4. associate-+r+ 82.4%

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

      5. +-commutative 82.4%

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

      6. associate-+l+ 82.4%

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

   5. Simplified 82.4%

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

      1. clear-num 82.4%

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

      2. un-div-inv 82.5%

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

      3. +-commutative 82.5%

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

   7. Applied egg-rr 82.5%

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

   if -1.55e189 < z < -1.3e-74 or 1.05999999999999994e-72 < z < 3.50000000000000028e207

   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 68.0%

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

   if -1.3e-74 < z < 1.2e-191 or 1.34999999999999992e-162 < z < 1.05999999999999994e-72

   1. Initial program 84.3%

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

   3. Taylor expanded in z around 0 74.3%

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

      1. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in y around 0 74.4%

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

   if 1.2e-191 < z < 1.34999999999999992e-162

   1. Initial program 46.8%

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

   3. Taylor expanded in z around inf 36.4%

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

      1. associate--l+ 36.4%

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

      2. +-commutative 36.4%

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

      3. associate-+r+ 36.4%

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

      4. +-commutative 36.4%

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

      5. associate-+l+ 36.4%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in a around -inf 47.6%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+189}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-74}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-191}:\\ \;\;\;\;\frac{t \cdot a + y \cdot \left(a - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-72}:\\ \;\;\;\;\frac{t \cdot a + y \cdot \left(a - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+207}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-60}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* a (/ (+ y t) (+ y (+ x t))))))
   (if (<= a -2.7e+95)
     t_2
     (if (<= a 1.95e-274)
       t_1
       (if (<= a 1.18e-60)
         (/ (+ (* t a) (* z x)) (+ x t))
         (if (<= a 3.7e+152) 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) / (y + (x + t)));
	double tmp;
	if (a <= -2.7e+95) {
		tmp = t_2;
	} else if (a <= 1.95e-274) {
		tmp = t_1;
	} else if (a <= 1.18e-60) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (a <= 3.7e+152) {
		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) / (y + (x + t)))
    if (a <= (-2.7d+95)) then
        tmp = t_2
    else if (a <= 1.95d-274) then
        tmp = t_1
    else if (a <= 1.18d-60) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else if (a <= 3.7d+152) 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) / (y + (x + t)));
	double tmp;
	if (a <= -2.7e+95) {
		tmp = t_2;
	} else if (a <= 1.95e-274) {
		tmp = t_1;
	} else if (a <= 1.18e-60) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (a <= 3.7e+152) {
		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) / (y + (x + t)))
	tmp = 0
	if a <= -2.7e+95:
		tmp = t_2
	elif a <= 1.95e-274:
		tmp = t_1
	elif a <= 1.18e-60:
		tmp = ((t * a) + (z * x)) / (x + t)
	elif a <= 3.7e+152:
		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(y + Float64(x + t))))
	tmp = 0.0
	if (a <= -2.7e+95)
		tmp = t_2;
	elseif (a <= 1.95e-274)
		tmp = t_1;
	elseif (a <= 1.18e-60)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	elseif (a <= 3.7e+152)
		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) / (y + (x + t)));
	tmp = 0.0;
	if (a <= -2.7e+95)
		tmp = t_2;
	elseif (a <= 1.95e-274)
		tmp = t_1;
	elseif (a <= 1.18e-60)
		tmp = ((t * a) + (z * x)) / (x + t);
	elseif (a <= 3.7e+152)
		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[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e+95], t$95$2, If[LessEqual[a, 1.95e-274], t$95$1, If[LessEqual[a, 1.18e-60], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e+152], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.7e95

   1. Initial program 33.0%

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

   3. Taylor expanded in a around inf 31.1%

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

      1. associate-/l* 81.3%

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

      2. +-commutative 81.3%

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

      3. associate-+r+ 81.3%

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

      4. +-commutative 81.3%

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

      5. associate-+l+ 81.3%

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

   5. Simplified 81.3%

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

   if -2.7e95 < a < 1.94999999999999993e-274 or 1.17999999999999994e-60 < a < 3.69999999999999996e152

   1. Initial program 70.8%

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

   3. Taylor expanded in y around inf 65.6%

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

   if 1.94999999999999993e-274 < a < 1.17999999999999994e-60

   1. Initial program 74.1%

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

   3. Taylor expanded in y around 0 59.0%

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

   if 3.69999999999999996e152 < a

   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 41.4%

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

      1. associate--l+ 41.4%

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

      2. +-commutative 41.4%

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

      3. associate-+r+ 41.4%

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

      4. +-commutative 41.4%

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

      5. associate-+l+ 41.4%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in a around -inf 43.4%

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

      1. associate-/l* 79.6%

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

      2. +-commutative 79.6%

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

      3. associate-+r+ 79.6%

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

      4. +-commutative 79.6%

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

   8. Simplified 79.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-274}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-60}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+152}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{a - b}{x + y}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-155}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ (- a b) (+ x y)))) (t_2 (- (+ z a) b)))
   (if (<= z -8.2e-64)
     t_2
     (if (<= z 2.2e-196)
       t_1
       (if (<= z 1.22e-155) a (if (<= z 6.6e-78) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * ((a - b) / (x + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (z <= -8.2e-64) {
		tmp = t_2;
	} else if (z <= 2.2e-196) {
		tmp = t_1;
	} else if (z <= 1.22e-155) {
		tmp = a;
	} else if (z <= 6.6e-78) {
		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 = y * ((a - b) / (x + y))
    t_2 = (z + a) - b
    if (z <= (-8.2d-64)) then
        tmp = t_2
    else if (z <= 2.2d-196) then
        tmp = t_1
    else if (z <= 1.22d-155) then
        tmp = a
    else if (z <= 6.6d-78) 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 = y * ((a - b) / (x + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (z <= -8.2e-64) {
		tmp = t_2;
	} else if (z <= 2.2e-196) {
		tmp = t_1;
	} else if (z <= 1.22e-155) {
		tmp = a;
	} else if (z <= 6.6e-78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * ((a - b) / (x + y))
	t_2 = (z + a) - b
	tmp = 0
	if z <= -8.2e-64:
		tmp = t_2
	elif z <= 2.2e-196:
		tmp = t_1
	elif z <= 1.22e-155:
		tmp = a
	elif z <= 6.6e-78:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(Float64(a - b) / Float64(x + y)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (z <= -8.2e-64)
		tmp = t_2;
	elseif (z <= 2.2e-196)
		tmp = t_1;
	elseif (z <= 1.22e-155)
		tmp = a;
	elseif (z <= 6.6e-78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * ((a - b) / (x + y));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (z <= -8.2e-64)
		tmp = t_2;
	elseif (z <= 2.2e-196)
		tmp = t_1;
	elseif (z <= 1.22e-155)
		tmp = a;
	elseif (z <= 6.6e-78)
		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[(y * N[(N[(a - b), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[z, -8.2e-64], t$95$2, If[LessEqual[z, 2.2e-196], t$95$1, If[LessEqual[z, 1.22e-155], a, If[LessEqual[z, 6.6e-78], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2000000000000001e-64 or 6.59999999999999963e-78 < z

   1. Initial program 50.1%

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

   3. Taylor expanded in y around inf 66.1%

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

   if -8.2000000000000001e-64 < z < 2.20000000000000015e-196 or 1.22000000000000001e-155 < z < 6.59999999999999963e-78

   1. Initial program 82.2%

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

   3. Taylor expanded in z around 0 72.5%

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

      1. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in t around 0 49.4%

      \[\leadsto \color{blue}{\frac{a \cdot y - b \cdot y}{x + y}} \]
   7. Step-by-step derivation

      1. distribute-rgt-out-- 49.6%

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

      2. +-commutative 49.6%

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

   8. Simplified 49.6%

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

      1. associate-/l* 63.0%

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

   10. Applied egg-rr 63.0%

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

   if 2.20000000000000015e-196 < z < 1.22000000000000001e-155

   1. Initial program 56.5%

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

   3. Taylor expanded in t around inf 82.0%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-64}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-155}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{a - b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+61} \lor \neg \left(t \leq 3.8 \cdot 10^{+105}\right):\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5e+61) (not (<= t 3.8e+105)))
   (* a (/ (+ y t) (+ y (+ x t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5e+61) || !(t <= 3.8e+105)) {
		tmp = a * ((y + t) / (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) :: tmp
    if ((t <= (-5d+61)) .or. (.not. (t <= 3.8d+105))) then
        tmp = a * ((y + t) / (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 tmp;
	if ((t <= -5e+61) || !(t <= 3.8e+105)) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5e+61) or not (t <= 3.8e+105):
		tmp = a * ((y + t) / (y + (x + t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5e+61) || !(t <= 3.8e+105))
		tmp = Float64(a * Float64(Float64(y + t) / 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)
	tmp = 0.0;
	if ((t <= -5e+61) || ~((t <= 3.8e+105)))
		tmp = a * ((y + t) / (y + (x + t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5e+61], N[Not[LessEqual[t, 3.8e+105]], $MachinePrecision]], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if t < -5.00000000000000018e61

   1. Initial program 49.9%

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

   3. Taylor expanded in a around inf 31.5%

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

      1. associate-/l* 56.3%

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

      2. +-commutative 56.3%

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

      3. associate-+r+ 56.3%

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

      4. +-commutative 56.3%

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

      5. associate-+l+ 56.3%

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

   5. Simplified 56.3%

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

   if -5.00000000000000018e61 < t < 3.8e105

   1. Initial program 69.1%

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

   3. Taylor expanded in y around inf 70.8%

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

   if 3.8e105 < t

   1. Initial program 52.3%

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

   3. Taylor expanded in z around inf 55.8%

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

      1. associate--l+ 55.8%

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

      2. +-commutative 55.8%

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

      3. associate-+r+ 55.8%

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

      4. +-commutative 55.8%

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

      5. associate-+l+ 55.8%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in a around -inf 30.6%

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

      1. associate-/l* 61.2%

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

      2. +-commutative 61.2%

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

      3. associate-+r+ 61.2%

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

      4. +-commutative 61.2%

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

   8. Simplified 61.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+61} \lor \neg \left(t \leq 3.8 \cdot 10^{+105}\right):\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+61} \lor \neg \left(t \leq 2 \cdot 10^{+104}\right):\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.2e+61) (not (<= t 2e+104)))
   (* a (/ (+ y t) (+ y (+ x t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.2e+61) || !(t <= 2e+104)) {
		tmp = a * ((y + t) / (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) :: tmp
    if ((t <= (-5.2d+61)) .or. (.not. (t <= 2d+104))) then
        tmp = a * ((y + t) / (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 tmp;
	if ((t <= -5.2e+61) || !(t <= 2e+104)) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.2e+61) or not (t <= 2e+104):
		tmp = a * ((y + t) / (y + (x + t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.2e+61) || !(t <= 2e+104))
		tmp = Float64(a * Float64(Float64(y + t) / 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)
	tmp = 0.0;
	if ((t <= -5.2e+61) || ~((t <= 2e+104)))
		tmp = a * ((y + t) / (y + (x + t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.2e+61], N[Not[LessEqual[t, 2e+104]], $MachinePrecision]], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.19999999999999945e61 or 2e104 < t

   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 31.1%

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

      1. associate-/l* 58.4%

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

      2. +-commutative 58.4%

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

      3. associate-+r+ 58.4%

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

      4. +-commutative 58.4%

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

      5. associate-+l+ 58.4%

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

   5. Simplified 58.4%

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

   if -5.19999999999999945e61 < t < 2e104

   1. Initial program 69.1%

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

   3. Taylor expanded in y around inf 70.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+61} \lor \neg \left(t \leq 2 \cdot 10^{+104}\right):\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+241}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+181}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.2e+241)
   z
   (if (<= x 1.1e+181) (- (+ z a) b) (* x (/ z (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.2e+241) {
		tmp = z;
	} else if (x <= 1.1e+181) {
		tmp = (z + a) - b;
	} else {
		tmp = 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 (x <= (-7.2d+241)) then
        tmp = z
    else if (x <= 1.1d+181) then
        tmp = (z + a) - b
    else
        tmp = 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 (x <= -7.2e+241) {
		tmp = z;
	} else if (x <= 1.1e+181) {
		tmp = (z + a) - b;
	} else {
		tmp = x * (z / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.2e+241:
		tmp = z
	elif x <= 1.1e+181:
		tmp = (z + a) - b
	else:
		tmp = x * (z / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.2e+241)
		tmp = z;
	elseif (x <= 1.1e+181)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(x * Float64(z / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7.2e+241)
		tmp = z;
	elseif (x <= 1.1e+181)
		tmp = (z + a) - b;
	else
		tmp = x * (z / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.2e+241], z, If[LessEqual[x, 1.1e+181], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.19999999999999966e241

   1. Initial program 68.3%

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

   3. Taylor expanded in x around inf 57.6%

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

   if -7.19999999999999966e241 < x < 1.1000000000000001e181

   1. Initial program 67.2%

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

   3. Taylor expanded in y around inf 63.4%

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

   if 1.1000000000000001e181 < x

   1. Initial program 32.7%

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

   3. Taylor expanded in z around inf 18.9%

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

      1. associate-/l* 64.1%

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

      2. +-commutative 64.1%

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

      3. +-commutative 64.1%

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

      4. associate-+r+ 64.1%

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

      5. +-commutative 64.1%

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

      6. associate-+l+ 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in y around 0 18.9%

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

      1. associate-/l* 58.8%

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

      2. +-commutative 58.8%

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

   8. Simplified 58.8%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+241}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+181}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+75}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-281}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+172}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8e+75) z (if (<= x -7.2e-281) (- a b) (if (<= x 1.2e+172) a z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8e+75) {
		tmp = z;
	} else if (x <= -7.2e-281) {
		tmp = a - b;
	} else if (x <= 1.2e+172) {
		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 (x <= (-8d+75)) then
        tmp = z
    else if (x <= (-7.2d-281)) then
        tmp = a - b
    else if (x <= 1.2d+172) 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 (x <= -8e+75) {
		tmp = z;
	} else if (x <= -7.2e-281) {
		tmp = a - b;
	} else if (x <= 1.2e+172) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8e+75:
		tmp = z
	elif x <= -7.2e-281:
		tmp = a - b
	elif x <= 1.2e+172:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8e+75)
		tmp = z;
	elseif (x <= -7.2e-281)
		tmp = Float64(a - b);
	elseif (x <= 1.2e+172)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8e+75)
		tmp = z;
	elseif (x <= -7.2e-281)
		tmp = a - b;
	elseif (x <= 1.2e+172)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8e+75], z, If[LessEqual[x, -7.2e-281], N[(a - b), $MachinePrecision], If[LessEqual[x, 1.2e+172], a, z]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.99999999999999941e75 or 1.2e172 < x

   1. Initial program 47.2%

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

   3. Taylor expanded in x around inf 48.9%

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

   if -7.99999999999999941e75 < x < -7.20000000000000013e-281

   1. Initial program 69.2%

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

   3. Taylor expanded in z around 0 50.4%

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

      1. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in y around inf 65.1%

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

   if -7.20000000000000013e-281 < x < 1.2e172

   1. Initial program 71.3%

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

   3. Taylor expanded in t around inf 46.2%

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

Alternative 11: 58.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+242}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+190}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.3e+242) z (if (<= x 1.3e+190) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.3e+242) {
		tmp = z;
	} else if (x <= 1.3e+190) {
		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 <= (-3.3d+242)) then
        tmp = z
    else if (x <= 1.3d+190) 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 <= -3.3e+242) {
		tmp = z;
	} else if (x <= 1.3e+190) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.3e+242:
		tmp = z
	elif x <= 1.3e+190:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.3e+242)
		tmp = z;
	elseif (x <= 1.3e+190)
		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 <= -3.3e+242)
		tmp = z;
	elseif (x <= 1.3e+190)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.3e+242], z, If[LessEqual[x, 1.3e+190], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -3.30000000000000023e242 or 1.30000000000000005e190 < x

   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 x around inf 60.2%

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

   if -3.30000000000000023e242 < x < 1.30000000000000005e190

   1. Initial program 66.8%

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

   3. Taylor expanded in y around inf 62.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+242}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+190}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+75}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-52}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.1e+75) z (if (<= z 1.1e-52) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.1e+75) {
		tmp = z;
	} else if (z <= 1.1e-52) {
		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 <= (-4.1d+75)) then
        tmp = z
    else if (z <= 1.1d-52) 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 <= -4.1e+75) {
		tmp = z;
	} else if (z <= 1.1e-52) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.1e+75:
		tmp = z
	elif z <= 1.1e-52:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.1e+75)
		tmp = z;
	elseif (z <= 1.1e-52)
		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 <= -4.1e+75)
		tmp = z;
	elseif (z <= 1.1e-52)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.1e+75], z, If[LessEqual[z, 1.1e-52], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0999999999999998e75 or 1.10000000000000005e-52 < z

   1. Initial program 45.0%

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

   3. Taylor expanded in x around inf 53.6%

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

   if -4.0999999999999998e75 < z < 1.10000000000000005e-52

   1. Initial program 76.9%

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

   3. Taylor expanded in t around inf 43.3%

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

Alternative 13: 32.9% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.5%

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

3. Taylor expanded in t around inf 33.7%

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

Developer target: 82.4% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024103 
(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)))