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

Percentage Accurate: 61.1% → 86.0%

Time: 15.1s

Alternatives: 15

Speedup: 0.6×

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: 61.1% 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: 86.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(y + x\right) + t\\ t_3 := \frac{y}{t\_2}\\ t_4 := \frac{y + x}{t\_2}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+187}:\\ \;\;\;\;z \cdot t\_4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_2} + \left(\left(t\_3 + t\_4 \cdot \frac{z}{a}\right) - b \cdot \frac{y}{t\_2 \cdot a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\left(t\_3 + a \cdot \frac{y + t}{z \cdot t\_2}\right) - \frac{b}{t\_1} \cdot \frac{y}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ (+ y x) t))
        (t_3 (/ y t_2))
        (t_4 (/ (+ y x) t_2)))
   (if (<= z -5.2e+187)
     (* z t_4)
     (if (<= z 2.2e+67)
       (* a (+ (/ t t_2) (- (+ t_3 (* t_4 (/ z a))) (* b (/ y (* t_2 a))))))
       (*
        z
        (+
         (/ x t_1)
         (- (+ t_3 (* a (/ (+ y t) (* z t_2)))) (* (/ b t_1) (/ y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (y + x) + t;
	double t_3 = y / t_2;
	double t_4 = (y + x) / t_2;
	double tmp;
	if (z <= -5.2e+187) {
		tmp = z * t_4;
	} else if (z <= 2.2e+67) {
		tmp = a * ((t / t_2) + ((t_3 + (t_4 * (z / a))) - (b * (y / (t_2 * a)))));
	} else {
		tmp = z * ((x / t_1) + ((t_3 + (a * ((y + t) / (z * t_2)))) - ((b / t_1) * (y / 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (y + x) + t
    t_3 = y / t_2
    t_4 = (y + x) / t_2
    if (z <= (-5.2d+187)) then
        tmp = z * t_4
    else if (z <= 2.2d+67) then
        tmp = a * ((t / t_2) + ((t_3 + (t_4 * (z / a))) - (b * (y / (t_2 * a)))))
    else
        tmp = z * ((x / t_1) + ((t_3 + (a * ((y + t) / (z * t_2)))) - ((b / t_1) * (y / 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 t_1 = y + (x + t);
	double t_2 = (y + x) + t;
	double t_3 = y / t_2;
	double t_4 = (y + x) / t_2;
	double tmp;
	if (z <= -5.2e+187) {
		tmp = z * t_4;
	} else if (z <= 2.2e+67) {
		tmp = a * ((t / t_2) + ((t_3 + (t_4 * (z / a))) - (b * (y / (t_2 * a)))));
	} else {
		tmp = z * ((x / t_1) + ((t_3 + (a * ((y + t) / (z * t_2)))) - ((b / t_1) * (y / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (y + x) + t
	t_3 = y / t_2
	t_4 = (y + x) / t_2
	tmp = 0
	if z <= -5.2e+187:
		tmp = z * t_4
	elif z <= 2.2e+67:
		tmp = a * ((t / t_2) + ((t_3 + (t_4 * (z / a))) - (b * (y / (t_2 * a)))))
	else:
		tmp = z * ((x / t_1) + ((t_3 + (a * ((y + t) / (z * t_2)))) - ((b / t_1) * (y / z))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(y + x) + t)
	t_3 = Float64(y / t_2)
	t_4 = Float64(Float64(y + x) / t_2)
	tmp = 0.0
	if (z <= -5.2e+187)
		tmp = Float64(z * t_4);
	elseif (z <= 2.2e+67)
		tmp = Float64(a * Float64(Float64(t / t_2) + Float64(Float64(t_3 + Float64(t_4 * Float64(z / a))) - Float64(b * Float64(y / Float64(t_2 * a))))));
	else
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(Float64(t_3 + Float64(a * Float64(Float64(y + t) / Float64(z * t_2)))) - Float64(Float64(b / t_1) * Float64(y / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (y + x) + t;
	t_3 = y / t_2;
	t_4 = (y + x) / t_2;
	tmp = 0.0;
	if (z <= -5.2e+187)
		tmp = z * t_4;
	elseif (z <= 2.2e+67)
		tmp = a * ((t / t_2) + ((t_3 + (t_4 * (z / a))) - (b * (y / (t_2 * a)))));
	else
		tmp = z * ((x / t_1) + ((t_3 + (a * ((y + t) / (z * t_2)))) - ((b / t_1) * (y / z))));
	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[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y + x), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[z, -5.2e+187], N[(z * t$95$4), $MachinePrecision], If[LessEqual[z, 2.2e+67], N[(a * N[(N[(t / t$95$2), $MachinePrecision] + N[(N[(t$95$3 + N[(t$95$4 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(t$95$2 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(t$95$3 + N[(a * N[(N[(y + t), $MachinePrecision] / N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b / t$95$1), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999997e187

   1. Initial program 32.1%

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

   3. Taylor expanded in z around inf 28.8%

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

      1. associate-/l* 92.6%

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

      2. +-commutative 92.6%

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

      3. +-commutative 92.6%

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

   5. Simplified 92.6%

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

   if -5.1999999999999997e187 < z < 2.2e67

   1. Initial program 65.5%

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

   3. Taylor expanded in a around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. +-commutative 77.1%

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

      3. +-commutative 77.1%

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

      4. times-frac 82.5%

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

      5. +-commutative 82.5%

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

      6. +-commutative 82.5%

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

      7. associate-/l* 90.3%

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

      8. +-commutative 90.3%

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

   5. Simplified 90.3%

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

   if 2.2e67 < z

   1. Initial program 38.8%

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

   3. Taylor expanded in z around inf 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. associate-+r+ 66.8%

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

      3. +-commutative 66.8%

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

      4. associate-/l* 77.3%

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

      5. fma-define 77.3%

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

      6. associate-+r+ 77.3%

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

      7. associate-+r+ 77.3%

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

   5. Simplified 92.4%

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

      1. fma-undefine 92.4%

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

      2. associate-+r+ 92.4%

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

      3. +-commutative 92.4%

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

      4. associate-+r+ 92.4%

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

      5. +-commutative 92.4%

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

   7. Applied egg-rr 92.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+187}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(\frac{t}{\left(y + x\right) + t} + \left(\left(\frac{y}{\left(y + x\right) + t} + \frac{y + x}{\left(y + x\right) + t} \cdot \frac{z}{a}\right) - b \cdot \frac{y}{\left(\left(y + x\right) + t\right) \cdot a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{y + \left(x + t\right)} + \left(\left(\frac{y}{\left(y + x\right) + t} + a \cdot \frac{y + t}{z \cdot \left(\left(y + x\right) + t\right)}\right) - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+290}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ y t)) (* z (+ y x))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+290))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (y + x))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+290)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (y + x))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+290)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (y + t)) + (z * (y + x))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+290):
		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(a * Float64(y + t)) + Float64(z * Float64(y + x))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+290))
		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 = (((a * (y + t)) + (z * (y + x))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+290)))
		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[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+290]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.00000000000000006e290 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.6%

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

   3. Taylor expanded in y around inf 69.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000006e290

   1. Initial program 99.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+290}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{y + x}{t\_1}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+190} \lor \neg \left(z \leq 4.2 \cdot 10^{+214}\right):\\ \;\;\;\;z \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_1} + \left(\left(\frac{y}{t\_1} + t\_2 \cdot \frac{z}{a}\right) - b \cdot \frac{y}{t\_1 \cdot a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t)) (t_2 (/ (+ y x) t_1)))
   (if (or (<= z -2.3e+190) (not (<= z 4.2e+214)))
     (* z t_2)
     (*
      a
      (+ (/ t t_1) (- (+ (/ y t_1) (* t_2 (/ z a))) (* b (/ y (* t_1 a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = (y + x) / t_1;
	double tmp;
	if ((z <= -2.3e+190) || !(z <= 4.2e+214)) {
		tmp = z * t_2;
	} else {
		tmp = a * ((t / t_1) + (((y / t_1) + (t_2 * (z / a))) - (b * (y / (t_1 * 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) :: tmp
    t_1 = (y + x) + t
    t_2 = (y + x) / t_1
    if ((z <= (-2.3d+190)) .or. (.not. (z <= 4.2d+214))) then
        tmp = z * t_2
    else
        tmp = a * ((t / t_1) + (((y / t_1) + (t_2 * (z / a))) - (b * (y / (t_1 * 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 = (y + x) + t;
	double t_2 = (y + x) / t_1;
	double tmp;
	if ((z <= -2.3e+190) || !(z <= 4.2e+214)) {
		tmp = z * t_2;
	} else {
		tmp = a * ((t / t_1) + (((y / t_1) + (t_2 * (z / a))) - (b * (y / (t_1 * a)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + x) + t
	t_2 = (y + x) / t_1
	tmp = 0
	if (z <= -2.3e+190) or not (z <= 4.2e+214):
		tmp = z * t_2
	else:
		tmp = a * ((t / t_1) + (((y / t_1) + (t_2 * (z / a))) - (b * (y / (t_1 * a)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(Float64(y + x) / t_1)
	tmp = 0.0
	if ((z <= -2.3e+190) || !(z <= 4.2e+214))
		tmp = Float64(z * t_2);
	else
		tmp = Float64(a * Float64(Float64(t / t_1) + Float64(Float64(Float64(y / t_1) + Float64(t_2 * Float64(z / a))) - Float64(b * Float64(y / Float64(t_1 * a))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + x) + t;
	t_2 = (y + x) / t_1;
	tmp = 0.0;
	if ((z <= -2.3e+190) || ~((z <= 4.2e+214)))
		tmp = z * t_2;
	else
		tmp = a * ((t / t_1) + (((y / t_1) + (t_2 * (z / a))) - (b * (y / (t_1 * a)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[z, -2.3e+190], N[Not[LessEqual[z, 4.2e+214]], $MachinePrecision]], N[(z * t$95$2), $MachinePrecision], N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$2 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(t$95$1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e190 or 4.2000000000000001e214 < z

   1. Initial program 27.3%

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

   3. Taylor expanded in z around inf 25.7%

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

      1. associate-/l* 95.3%

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

      2. +-commutative 95.3%

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

      3. +-commutative 95.3%

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

   5. Simplified 95.3%

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

   if -2.3e190 < z < 4.2000000000000001e214

   1. Initial program 63.2%

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

   3. Taylor expanded in a around inf 74.4%

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

      1. associate--l+ 74.4%

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

      2. +-commutative 74.4%

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

      3. +-commutative 74.4%

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

      4. times-frac 82.3%

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

      5. +-commutative 82.3%

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

      6. +-commutative 82.3%

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

      7. associate-/l* 89.5%

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

      8. +-commutative 89.5%

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

   5. Simplified 89.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+190} \lor \neg \left(z \leq 4.2 \cdot 10^{+214}\right):\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{\left(y + x\right) + t} + \left(\left(\frac{y}{\left(y + x\right) + t} + \frac{y + x}{\left(y + x\right) + t} \cdot \frac{z}{a}\right) - b \cdot \frac{y}{\left(\left(y + x\right) + t\right) \cdot a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{y + t}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-99}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-250}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-100}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ (+ y t) (+ y (+ x t))))) (t_2 (- (+ z a) b)))
   (if (<= y -1.2e-26)
     t_2
     (if (<= y -1.3e-43)
       t_1
       (if (<= y -9e-99)
         (+ z a)
         (if (<= y 3.1e-250)
           (/ (+ (* z x) (* t a)) (+ x t))
           (if (<= y 3.9e-100)
             (+ z a)
             (if (<= y 1.25e-17)
               (* z (/ (+ y x) (+ (+ y x) t)))
               (if (<= y 1.2e+69) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * ((y + t) / (y + (x + t)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.2e-26) {
		tmp = t_2;
	} else if (y <= -1.3e-43) {
		tmp = t_1;
	} else if (y <= -9e-99) {
		tmp = z + a;
	} else if (y <= 3.1e-250) {
		tmp = ((z * x) + (t * a)) / (x + t);
	} else if (y <= 3.9e-100) {
		tmp = z + a;
	} else if (y <= 1.25e-17) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 1.2e+69) {
		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 = a * ((y + t) / (y + (x + t)))
    t_2 = (z + a) - b
    if (y <= (-1.2d-26)) then
        tmp = t_2
    else if (y <= (-1.3d-43)) then
        tmp = t_1
    else if (y <= (-9d-99)) then
        tmp = z + a
    else if (y <= 3.1d-250) then
        tmp = ((z * x) + (t * a)) / (x + t)
    else if (y <= 3.9d-100) then
        tmp = z + a
    else if (y <= 1.25d-17) then
        tmp = z * ((y + x) / ((y + x) + t))
    else if (y <= 1.2d+69) 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 = a * ((y + t) / (y + (x + t)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.2e-26) {
		tmp = t_2;
	} else if (y <= -1.3e-43) {
		tmp = t_1;
	} else if (y <= -9e-99) {
		tmp = z + a;
	} else if (y <= 3.1e-250) {
		tmp = ((z * x) + (t * a)) / (x + t);
	} else if (y <= 3.9e-100) {
		tmp = z + a;
	} else if (y <= 1.25e-17) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 1.2e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * ((y + t) / (y + (x + t)))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -1.2e-26:
		tmp = t_2
	elif y <= -1.3e-43:
		tmp = t_1
	elif y <= -9e-99:
		tmp = z + a
	elif y <= 3.1e-250:
		tmp = ((z * x) + (t * a)) / (x + t)
	elif y <= 3.9e-100:
		tmp = z + a
	elif y <= 1.25e-17:
		tmp = z * ((y + x) / ((y + x) + t))
	elif y <= 1.2e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.2e-26)
		tmp = t_2;
	elseif (y <= -1.3e-43)
		tmp = t_1;
	elseif (y <= -9e-99)
		tmp = Float64(z + a);
	elseif (y <= 3.1e-250)
		tmp = Float64(Float64(Float64(z * x) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 3.9e-100)
		tmp = Float64(z + a);
	elseif (y <= 1.25e-17)
		tmp = Float64(z * Float64(Float64(y + x) / Float64(Float64(y + x) + t)));
	elseif (y <= 1.2e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * ((y + t) / (y + (x + t)));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.2e-26)
		tmp = t_2;
	elseif (y <= -1.3e-43)
		tmp = t_1;
	elseif (y <= -9e-99)
		tmp = z + a;
	elseif (y <= 3.1e-250)
		tmp = ((z * x) + (t * a)) / (x + t);
	elseif (y <= 3.9e-100)
		tmp = z + a;
	elseif (y <= 1.25e-17)
		tmp = z * ((y + x) / ((y + x) + t));
	elseif (y <= 1.2e+69)
		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[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.2e-26], t$95$2, If[LessEqual[y, -1.3e-43], t$95$1, If[LessEqual[y, -9e-99], N[(z + a), $MachinePrecision], If[LessEqual[y, 3.1e-250], N[(N[(N[(z * x), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-100], N[(z + a), $MachinePrecision], If[LessEqual[y, 1.25e-17], N[(z * N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+69], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.2e-26 or 1.2000000000000001e69 < y

   1. Initial program 45.1%

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

   3. Taylor expanded in y around inf 70.4%

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

   if -1.2e-26 < y < -1.3e-43 or 1.25e-17 < y < 1.2000000000000001e69

   1. Initial program 64.0%

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

   3. Taylor expanded in a around inf 44.3%

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

      1. associate-/l* 75.9%

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

      2. associate-+r+ 75.9%

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

   5. Simplified 75.9%

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

   if -1.3e-43 < y < -9.0000000000000006e-99 or 3.1000000000000001e-250 < y < 3.89999999999999977e-100

   1. Initial program 62.7%

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

   3. Taylor expanded in b around 0 58.4%

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

   4. Taylor expanded in y around inf 74.8%

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

   if -9.0000000000000006e-99 < y < 3.1000000000000001e-250

   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 y around 0 61.0%

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

   if 3.89999999999999977e-100 < y < 1.25e-17

   1. Initial program 72.1%

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

   3. Taylor expanded in z around inf 55.1%

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

      1. associate-/l* 77.3%

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

      2. +-commutative 77.3%

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

      3. +-commutative 77.3%

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

   5. Simplified 77.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-26}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-99}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-250}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-100}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+17}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-249}:\\ \;\;\;\;\frac{t\_1 + z \cdot x}{t\_2}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-100}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+63}:\\ \;\;\;\;\frac{t\_1 - y \cdot b}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t))) (t_2 (+ y (+ x t))) (t_3 (- (+ z a) b)))
   (if (<= y -1.55e+17)
     t_3
     (if (<= y 1.6e-249)
       (/ (+ t_1 (* z x)) t_2)
       (if (<= y 1.6e-100)
         (+ z a)
         (if (<= y 9.5e-17)
           (* z (/ (+ y x) (+ (+ y x) t)))
           (if (<= y 3e+63) (/ (- t_1 (* y b)) t_2) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -1.55e+17) {
		tmp = t_3;
	} else if (y <= 1.6e-249) {
		tmp = (t_1 + (z * x)) / t_2;
	} else if (y <= 1.6e-100) {
		tmp = z + a;
	} else if (y <= 9.5e-17) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 3e+63) {
		tmp = (t_1 - (y * b)) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (y + t)
    t_2 = y + (x + t)
    t_3 = (z + a) - b
    if (y <= (-1.55d+17)) then
        tmp = t_3
    else if (y <= 1.6d-249) then
        tmp = (t_1 + (z * x)) / t_2
    else if (y <= 1.6d-100) then
        tmp = z + a
    else if (y <= 9.5d-17) then
        tmp = z * ((y + x) / ((y + x) + t))
    else if (y <= 3d+63) then
        tmp = (t_1 - (y * b)) / t_2
    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 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -1.55e+17) {
		tmp = t_3;
	} else if (y <= 1.6e-249) {
		tmp = (t_1 + (z * x)) / t_2;
	} else if (y <= 1.6e-100) {
		tmp = z + a;
	} else if (y <= 9.5e-17) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 3e+63) {
		tmp = (t_1 - (y * b)) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = y + (x + t)
	t_3 = (z + a) - b
	tmp = 0
	if y <= -1.55e+17:
		tmp = t_3
	elif y <= 1.6e-249:
		tmp = (t_1 + (z * x)) / t_2
	elif y <= 1.6e-100:
		tmp = z + a
	elif y <= 9.5e-17:
		tmp = z * ((y + x) / ((y + x) + t))
	elif y <= 3e+63:
		tmp = (t_1 - (y * b)) / t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.55e+17)
		tmp = t_3;
	elseif (y <= 1.6e-249)
		tmp = Float64(Float64(t_1 + Float64(z * x)) / t_2);
	elseif (y <= 1.6e-100)
		tmp = Float64(z + a);
	elseif (y <= 9.5e-17)
		tmp = Float64(z * Float64(Float64(y + x) / Float64(Float64(y + x) + t)));
	elseif (y <= 3e+63)
		tmp = Float64(Float64(t_1 - Float64(y * b)) / t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = y + (x + t);
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.55e+17)
		tmp = t_3;
	elseif (y <= 1.6e-249)
		tmp = (t_1 + (z * x)) / t_2;
	elseif (y <= 1.6e-100)
		tmp = z + a;
	elseif (y <= 9.5e-17)
		tmp = z * ((y + x) / ((y + x) + t));
	elseif (y <= 3e+63)
		tmp = (t_1 - (y * b)) / t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.55e+17], t$95$3, If[LessEqual[y, 1.6e-249], N[(N[(t$95$1 + N[(z * x), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 1.6e-100], N[(z + a), $MachinePrecision], If[LessEqual[y, 9.5e-17], N[(z * N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+63], N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.55e17 or 2.99999999999999999e63 < y

   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 y around inf 71.5%

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

   if -1.55e17 < y < 1.6000000000000001e-249

   1. Initial program 74.4%

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

   3. Taylor expanded in b around 0 65.8%

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

   4. Taylor expanded in x around inf 64.5%

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

   if 1.6000000000000001e-249 < y < 1.60000000000000008e-100

   1. Initial program 59.0%

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

   3. Taylor expanded in b around 0 56.3%

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

   4. Taylor expanded in y around inf 78.0%

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

   if 1.60000000000000008e-100 < y < 9.50000000000000029e-17

   1. Initial program 72.1%

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

   3. Taylor expanded in z around inf 55.1%

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

      1. associate-/l* 77.3%

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

      2. +-commutative 77.3%

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

      3. +-commutative 77.3%

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

   5. Simplified 77.3%

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

   if 9.50000000000000029e-17 < y < 2.99999999999999999e63

   1. Initial program 76.1%

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

   3. Taylor expanded in z around 0 69.9%

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

      1. *-commutative 69.9%

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

   5. Simplified 69.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+17}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-249}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) + z \cdot x}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-100}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+63}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-250}:\\ \;\;\;\;\frac{t\_1 + z \cdot \left(y + x\right)}{t\_3}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-100}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{t\_1 - y \cdot b}{t\_3}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t))) (t_2 (- (+ z a) b)) (t_3 (+ y (+ x t))))
   (if (<= y -7.2e+58)
     t_2
     (if (<= y 6.2e-250)
       (/ (+ t_1 (* z (+ y x))) t_3)
       (if (<= y 3.9e-100)
         (+ z a)
         (if (<= y 9e-18)
           (* z (/ (+ y x) (+ (+ y x) t)))
           (if (<= y 3.1e+63) (/ (- t_1 (* y b)) t_3) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = (z + a) - b;
	double t_3 = y + (x + t);
	double tmp;
	if (y <= -7.2e+58) {
		tmp = t_2;
	} else if (y <= 6.2e-250) {
		tmp = (t_1 + (z * (y + x))) / t_3;
	} else if (y <= 3.9e-100) {
		tmp = z + a;
	} else if (y <= 9e-18) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 3.1e+63) {
		tmp = (t_1 - (y * b)) / t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = a * (y + t)
    t_2 = (z + a) - b
    t_3 = y + (x + t)
    if (y <= (-7.2d+58)) then
        tmp = t_2
    else if (y <= 6.2d-250) then
        tmp = (t_1 + (z * (y + x))) / t_3
    else if (y <= 3.9d-100) then
        tmp = z + a
    else if (y <= 9d-18) then
        tmp = z * ((y + x) / ((y + x) + t))
    else if (y <= 3.1d+63) then
        tmp = (t_1 - (y * b)) / t_3
    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 = a * (y + t);
	double t_2 = (z + a) - b;
	double t_3 = y + (x + t);
	double tmp;
	if (y <= -7.2e+58) {
		tmp = t_2;
	} else if (y <= 6.2e-250) {
		tmp = (t_1 + (z * (y + x))) / t_3;
	} else if (y <= 3.9e-100) {
		tmp = z + a;
	} else if (y <= 9e-18) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 3.1e+63) {
		tmp = (t_1 - (y * b)) / t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = (z + a) - b
	t_3 = y + (x + t)
	tmp = 0
	if y <= -7.2e+58:
		tmp = t_2
	elif y <= 6.2e-250:
		tmp = (t_1 + (z * (y + x))) / t_3
	elif y <= 3.9e-100:
		tmp = z + a
	elif y <= 9e-18:
		tmp = z * ((y + x) / ((y + x) + t))
	elif y <= 3.1e+63:
		tmp = (t_1 - (y * b)) / t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(Float64(z + a) - b)
	t_3 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -7.2e+58)
		tmp = t_2;
	elseif (y <= 6.2e-250)
		tmp = Float64(Float64(t_1 + Float64(z * Float64(y + x))) / t_3);
	elseif (y <= 3.9e-100)
		tmp = Float64(z + a);
	elseif (y <= 9e-18)
		tmp = Float64(z * Float64(Float64(y + x) / Float64(Float64(y + x) + t)));
	elseif (y <= 3.1e+63)
		tmp = Float64(Float64(t_1 - Float64(y * b)) / t_3);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = (z + a) - b;
	t_3 = y + (x + t);
	tmp = 0.0;
	if (y <= -7.2e+58)
		tmp = t_2;
	elseif (y <= 6.2e-250)
		tmp = (t_1 + (z * (y + x))) / t_3;
	elseif (y <= 3.9e-100)
		tmp = z + a;
	elseif (y <= 9e-18)
		tmp = z * ((y + x) / ((y + x) + t));
	elseif (y <= 3.1e+63)
		tmp = (t_1 - (y * b)) / t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+58], t$95$2, If[LessEqual[y, 6.2e-250], N[(N[(t$95$1 + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[y, 3.9e-100], N[(z + a), $MachinePrecision], If[LessEqual[y, 9e-18], N[(z * N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+63], N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.19999999999999993e58 or 3.1000000000000001e63 < y

   1. Initial program 39.6%

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

   3. Taylor expanded in y around inf 73.7%

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

   if -7.19999999999999993e58 < y < 6.2000000000000002e-250

   1. Initial program 74.7%

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

   3. Taylor expanded in b around 0 63.8%

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

   if 6.2000000000000002e-250 < y < 3.89999999999999977e-100

   1. Initial program 59.0%

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

   3. Taylor expanded in b around 0 56.3%

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

   4. Taylor expanded in y around inf 78.0%

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

   if 3.89999999999999977e-100 < y < 8.99999999999999987e-18

   1. Initial program 72.1%

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

   3. Taylor expanded in z around inf 55.1%

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

      1. associate-/l* 77.3%

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

      2. +-commutative 77.3%

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

      3. +-commutative 77.3%

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

   5. Simplified 77.3%

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

   if 8.99999999999999987e-18 < y < 3.1000000000000001e63

   1. Initial program 76.1%

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

   3. Taylor expanded in z around 0 69.9%

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

      1. *-commutative 69.9%

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

   5. Simplified 69.9%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+58}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-250}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) + z \cdot \left(y + x\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-100}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-250}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) + z \cdot x}{t\_1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-100}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)))
   (if (<= y -6.2e+17)
     t_2
     (if (<= y 7e-250)
       (/ (+ (* a (+ y t)) (* z x)) t_1)
       (if (<= y 4e-100)
         (+ z a)
         (if (<= y 7.4e-16)
           (* z (/ (+ y x) (+ (+ y x) t)))
           (if (<= y 8.6e+68) (* a (/ (+ y t) t_1)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.2e+17) {
		tmp = t_2;
	} else if (y <= 7e-250) {
		tmp = ((a * (y + t)) + (z * x)) / t_1;
	} else if (y <= 4e-100) {
		tmp = z + a;
	} else if (y <= 7.4e-16) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 8.6e+68) {
		tmp = a * ((y + t) / 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 + (x + t)
    t_2 = (z + a) - b
    if (y <= (-6.2d+17)) then
        tmp = t_2
    else if (y <= 7d-250) then
        tmp = ((a * (y + t)) + (z * x)) / t_1
    else if (y <= 4d-100) then
        tmp = z + a
    else if (y <= 7.4d-16) then
        tmp = z * ((y + x) / ((y + x) + t))
    else if (y <= 8.6d+68) then
        tmp = a * ((y + t) / 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 + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.2e+17) {
		tmp = t_2;
	} else if (y <= 7e-250) {
		tmp = ((a * (y + t)) + (z * x)) / t_1;
	} else if (y <= 4e-100) {
		tmp = z + a;
	} else if (y <= 7.4e-16) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 8.6e+68) {
		tmp = a * ((y + t) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -6.2e+17:
		tmp = t_2
	elif y <= 7e-250:
		tmp = ((a * (y + t)) + (z * x)) / t_1
	elif y <= 4e-100:
		tmp = z + a
	elif y <= 7.4e-16:
		tmp = z * ((y + x) / ((y + x) + t))
	elif y <= 8.6e+68:
		tmp = a * ((y + t) / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6.2e+17)
		tmp = t_2;
	elseif (y <= 7e-250)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * x)) / t_1);
	elseif (y <= 4e-100)
		tmp = Float64(z + a);
	elseif (y <= 7.4e-16)
		tmp = Float64(z * Float64(Float64(y + x) / Float64(Float64(y + x) + t)));
	elseif (y <= 8.6e+68)
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6.2e+17)
		tmp = t_2;
	elseif (y <= 7e-250)
		tmp = ((a * (y + t)) + (z * x)) / t_1;
	elseif (y <= 4e-100)
		tmp = z + a;
	elseif (y <= 7.4e-16)
		tmp = z * ((y + x) / ((y + x) + t));
	elseif (y <= 8.6e+68)
		tmp = a * ((y + t) / 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[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.2e+17], t$95$2, If[LessEqual[y, 7e-250], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 4e-100], N[(z + a), $MachinePrecision], If[LessEqual[y, 7.4e-16], N[(z * N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e+68], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.2e17 or 8.6000000000000002e68 < y

   1. Initial program 42.8%

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

   3. Taylor expanded in y around inf 71.8%

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

   if -6.2e17 < y < 6.9999999999999998e-250

   1. Initial program 74.4%

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

   3. Taylor expanded in b around 0 65.8%

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

   4. Taylor expanded in x around inf 64.5%

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

   if 6.9999999999999998e-250 < y < 4.0000000000000001e-100

   1. Initial program 59.0%

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

   3. Taylor expanded in b around 0 56.3%

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

   4. Taylor expanded in y around inf 78.0%

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

   if 4.0000000000000001e-100 < y < 7.3999999999999999e-16

   1. Initial program 72.1%

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

   3. Taylor expanded in z around inf 55.1%

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

      1. associate-/l* 77.3%

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

      2. +-commutative 77.3%

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

      3. +-commutative 77.3%

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

   5. Simplified 77.3%

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

   if 7.3999999999999999e-16 < y < 8.6000000000000002e68

   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 a around inf 41.7%

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

      1. associate-/l* 67.9%

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

      2. associate-+r+ 67.9%

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

   5. Simplified 67.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-250}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) + z \cdot x}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-100}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 44.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+81}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-60}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+25}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+84}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.7e+81)
   a
   (if (<= t 7.5e-60) z (if (<= t 1.35e+25) a (if (<= t 2.2e+84) z a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.7e+81) {
		tmp = a;
	} else if (t <= 7.5e-60) {
		tmp = z;
	} else if (t <= 1.35e+25) {
		tmp = a;
	} else if (t <= 2.2e+84) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.7d+81)) then
        tmp = a
    else if (t <= 7.5d-60) then
        tmp = z
    else if (t <= 1.35d+25) then
        tmp = a
    else if (t <= 2.2d+84) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.7e+81) {
		tmp = a;
	} else if (t <= 7.5e-60) {
		tmp = z;
	} else if (t <= 1.35e+25) {
		tmp = a;
	} else if (t <= 2.2e+84) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.7e+81:
		tmp = a
	elif t <= 7.5e-60:
		tmp = z
	elif t <= 1.35e+25:
		tmp = a
	elif t <= 2.2e+84:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.7e+81)
		tmp = a;
	elseif (t <= 7.5e-60)
		tmp = z;
	elseif (t <= 1.35e+25)
		tmp = a;
	elseif (t <= 2.2e+84)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.7e+81)
		tmp = a;
	elseif (t <= 7.5e-60)
		tmp = z;
	elseif (t <= 1.35e+25)
		tmp = a;
	elseif (t <= 2.2e+84)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.7e+81], a, If[LessEqual[t, 7.5e-60], z, If[LessEqual[t, 1.35e+25], a, If[LessEqual[t, 2.2e+84], z, a]]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7000000000000001e81 or 7.5000000000000002e-60 < t < 1.35e25 or 2.1999999999999998e84 < t

   1. Initial program 51.4%

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

   3. Taylor expanded in t around inf 51.7%

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

   if -3.7000000000000001e81 < t < 7.5000000000000002e-60 or 1.35e25 < t < 2.1999999999999998e84

   1. Initial program 62.0%

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

   3. Taylor expanded in x around inf 53.1%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+81}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-60}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+25}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+84}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+75}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-66}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 7000000:\\ \;\;\;\;-b\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+85}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.5e+75)
   a
   (if (<= t 8.5e-66) z (if (<= t 7000000.0) (- b) (if (<= t 2.65e+85) z a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.5e+75) {
		tmp = a;
	} else if (t <= 8.5e-66) {
		tmp = z;
	} else if (t <= 7000000.0) {
		tmp = -b;
	} else if (t <= 2.65e+85) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.5d+75)) then
        tmp = a
    else if (t <= 8.5d-66) then
        tmp = z
    else if (t <= 7000000.0d0) then
        tmp = -b
    else if (t <= 2.65d+85) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.5e+75) {
		tmp = a;
	} else if (t <= 8.5e-66) {
		tmp = z;
	} else if (t <= 7000000.0) {
		tmp = -b;
	} else if (t <= 2.65e+85) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.5e+75:
		tmp = a
	elif t <= 8.5e-66:
		tmp = z
	elif t <= 7000000.0:
		tmp = -b
	elif t <= 2.65e+85:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.5e+75)
		tmp = a;
	elseif (t <= 8.5e-66)
		tmp = z;
	elseif (t <= 7000000.0)
		tmp = Float64(-b);
	elseif (t <= 2.65e+85)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.5e+75)
		tmp = a;
	elseif (t <= 8.5e-66)
		tmp = z;
	elseif (t <= 7000000.0)
		tmp = -b;
	elseif (t <= 2.65e+85)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.5e+75], a, If[LessEqual[t, 8.5e-66], z, If[LessEqual[t, 7000000.0], (-b), If[LessEqual[t, 2.65e+85], z, a]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4999999999999998e75 or 2.65e85 < t

   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 t around inf 55.5%

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

   if -3.4999999999999998e75 < t < 8.49999999999999966e-66 or 7e6 < t < 2.65e85

   1. Initial program 62.8%

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

   3. Taylor expanded in x around inf 51.9%

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

   if 8.49999999999999966e-66 < t < 7e6

   1. Initial program 72.8%

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

   3. Taylor expanded in b around inf 33.8%

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

      1. mul-1-neg 33.8%

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

      2. associate-/l* 54.1%

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

      3. distribute-rgt-neg-in 54.1%

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

      4. mul-1-neg 54.1%

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

      5. associate-*r/ 54.1%

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

      6. neg-mul-1 54.1%

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

      7. associate-+r+ 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in y around inf 40.0%

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

      1. mul-1-neg 40.0%

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

   8. Simplified 40.0%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+75}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-66}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 7000000:\\ \;\;\;\;-b\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+85}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+138}:\\ \;\;\;\;a \cdot \frac{t}{\left(y + x\right) + t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+79}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.2e+138)
   (* a (/ t (+ (+ y x) t)))
   (if (<= t 7.8e+79) (- (+ z a) b) (* a (/ (+ y t) (+ y (+ x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+138) {
		tmp = a * (t / ((y + x) + t));
	} else if (t <= 7.8e+79) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((y + t) / (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 (t <= (-7.2d+138)) then
        tmp = a * (t / ((y + x) + t))
    else if (t <= 7.8d+79) then
        tmp = (z + a) - b
    else
        tmp = a * ((y + t) / (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 (t <= -7.2e+138) {
		tmp = a * (t / ((y + x) + t));
	} else if (t <= 7.8e+79) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.2e+138:
		tmp = a * (t / ((y + x) + t))
	elif t <= 7.8e+79:
		tmp = (z + a) - b
	else:
		tmp = a * ((y + t) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.2e+138)
		tmp = Float64(a * Float64(t / Float64(Float64(y + x) + t)));
	elseif (t <= 7.8e+79)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.2e+138)
		tmp = a * (t / ((y + x) + t));
	elseif (t <= 7.8e+79)
		tmp = (z + a) - b;
	else
		tmp = a * ((y + t) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.2e+138], N[(a * N[(t / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+79], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2000000000000002e138

   1. Initial program 45.9%

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

   3. Taylor expanded in t around inf 21.8%

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

      1. associate-/l* 64.6%

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

      2. +-commutative 64.6%

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

      3. associate-+r+ 64.6%

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

      4. +-commutative 64.6%

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

   5. Applied egg-rr 64.6%

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

   if -7.2000000000000002e138 < t < 7.7999999999999994e79

   1. Initial program 62.4%

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

   3. Taylor expanded in y around inf 66.1%

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

   if 7.7999999999999994e79 < t

   1. Initial program 49.3%

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

   3. Taylor expanded in a around inf 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* 55.9%

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

      2. associate-+r+ 55.9%

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

   5. Simplified 55.9%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+138}:\\ \;\;\;\;a \cdot \frac{t}{\left(y + x\right) + t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+79}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+160} \lor \neg \left(t \leq 3.5 \cdot 10^{+83}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.12e+160) (not (<= t 3.5e+83)))
   (* a (/ t (+ x t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.12e+160) || !(t <= 3.5e+83)) {
		tmp = a * (t / (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 <= (-1.12d+160)) .or. (.not. (t <= 3.5d+83))) then
        tmp = a * (t / (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 <= -1.12e+160) || !(t <= 3.5e+83)) {
		tmp = a * (t / (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.12e+160) or not (t <= 3.5e+83):
		tmp = a * (t / (x + t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.12e+160) || !(t <= 3.5e+83))
		tmp = Float64(a * Float64(t / 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 <= -1.12e+160) || ~((t <= 3.5e+83)))
		tmp = a * (t / (x + t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.12e+160], N[Not[LessEqual[t, 3.5e+83]], $MachinePrecision]], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.12e160 or 3.49999999999999977e83 < t

   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 t around inf 25.0%

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

      1. associate-/l* 53.4%

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

      2. +-commutative 53.4%

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

      3. associate-+r+ 53.4%

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

      4. +-commutative 53.4%

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

   5. Applied egg-rr 53.4%

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

   6. Taylor expanded in y around 0 26.2%

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

      1. associate-/l* 57.5%

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

      2. +-commutative 57.5%

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

   8. Simplified 57.5%

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

   if -1.12e160 < t < 3.49999999999999977e83

   1. Initial program 62.7%

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

   3. Taylor expanded in y around inf 66.3%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+160} \lor \neg \left(t \leq 3.5 \cdot 10^{+83}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \frac{t}{\left(y + x\right) + t}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+82}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.05e+139)
   (* a (/ t (+ (+ y x) t)))
   (if (<= t 7.5e+82) (- (+ z a) b) (* a (/ t (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.05e+139) {
		tmp = a * (t / ((y + x) + t));
	} else if (t <= 7.5e+82) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (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 (t <= (-2.05d+139)) then
        tmp = a * (t / ((y + x) + t))
    else if (t <= 7.5d+82) then
        tmp = (z + a) - b
    else
        tmp = a * (t / (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 (t <= -2.05e+139) {
		tmp = a * (t / ((y + x) + t));
	} else if (t <= 7.5e+82) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.05e+139:
		tmp = a * (t / ((y + x) + t))
	elif t <= 7.5e+82:
		tmp = (z + a) - b
	else:
		tmp = a * (t / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.05e+139)
		tmp = Float64(a * Float64(t / Float64(Float64(y + x) + t)));
	elseif (t <= 7.5e+82)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(t / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.05e+139)
		tmp = a * (t / ((y + x) + t));
	elseif (t <= 7.5e+82)
		tmp = (z + a) - b;
	else
		tmp = a * (t / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.05e+139], N[(a * N[(t / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+82], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0500000000000001e139

   1. Initial program 45.9%

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

   3. Taylor expanded in t around inf 21.8%

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

      1. associate-/l* 64.6%

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

      2. +-commutative 64.6%

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

      3. associate-+r+ 64.6%

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

      4. +-commutative 64.6%

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

   5. Applied egg-rr 64.6%

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

   if -2.0500000000000001e139 < t < 7.4999999999999999e82

   1. Initial program 62.4%

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

   3. Taylor expanded in y around inf 66.1%

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

   if 7.4999999999999999e82 < t

   1. Initial program 49.3%

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

   3. Taylor expanded in t around inf 29.2%

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

      1. associate-/l* 47.6%

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

      2. +-commutative 47.6%

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

      3. associate-+r+ 47.6%

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

      4. +-commutative 47.6%

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

   5. Applied egg-rr 47.6%

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

   6. Taylor expanded in y around 0 31.1%

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

      1. associate-/l* 54.2%

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

      2. +-commutative 54.2%

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

   8. Simplified 54.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \frac{t}{\left(y + x\right) + t}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+82}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+159}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= t -9e+159) a (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9e+159) {
		tmp = a;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9d+159)) then
        tmp = a
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9e+159) {
		tmp = a;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9e+159:
		tmp = a
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9e+159)
		tmp = a;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9e+159)
		tmp = a;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9e+159], a, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.00000000000000053e159

   1. Initial program 42.0%

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

   3. Taylor expanded in t around inf 59.7%

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

   if -9.00000000000000053e159 < t

   1. Initial program 59.6%

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

   3. Taylor expanded in y around inf 61.1%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+159}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8 \cdot 10^{+235}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 8e+235) (+ z a) (- b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8e+235) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 8d+235) then
        tmp = z + a
    else
        tmp = -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8e+235) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 8e+235:
		tmp = z + a
	else:
		tmp = -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8e+235)
		tmp = Float64(z + a);
	else
		tmp = Float64(-b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 8e+235)
		tmp = z + a;
	else
		tmp = -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8e+235], N[(z + a), $MachinePrecision], (-b)]

Derivation

1. Split input into 2 regimes

2. if b < 8.0000000000000004e235

   1. Initial program 58.9%

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

   3. Taylor expanded in b around 0 48.4%

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

   4. Taylor expanded in y around inf 58.8%

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

   if 8.0000000000000004e235 < b

   1. Initial program 28.9%

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

   3. Taylor expanded in b around inf 23.3%

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

      1. mul-1-neg 23.3%

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

      2. associate-/l* 76.7%

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

      3. distribute-rgt-neg-in 76.7%

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

      4. mul-1-neg 76.7%

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

      5. associate-*r/ 76.7%

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

      6. neg-mul-1 76.7%

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

      7. associate-+r+ 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in y around inf 48.9%

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

      1. mul-1-neg 48.9%

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

   8. Simplified 48.9%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 8 \cdot 10^{+235}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.5% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.4%

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

3. Taylor expanded in t around inf 33.6%

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

4. Final simplification 33.6%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.7% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024067 
(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)))