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

Percentage Accurate: 59.6% → 90.9%

Time: 13.9s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.6% 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: 90.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-17} \lor \neg \left(z \leq 4.9 \cdot 10^{-20}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\left(\frac{y}{t\_1} + \frac{a}{z} \cdot \frac{t + y}{t\_1}\right) - \frac{b \cdot \frac{y}{z}}{t\_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_2} + \frac{z \cdot x + y \cdot \left(z - b\right)}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (+ y (+ x t))))
   (if (or (<= z -2.35e-17) (not (<= z 4.9e-20)))
     (*
      z
      (+
       (/ x t_1)
       (- (+ (/ y t_1) (* (/ a z) (/ (+ t y) t_1))) (/ (* b (/ y z)) t_1))))
     (+ (* a (/ (+ t y) t_2)) (/ (+ (* z x) (* y (- z b))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = y + (x + t);
	double tmp;
	if ((z <= -2.35e-17) || !(z <= 4.9e-20)) {
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)));
	} else {
		tmp = (a * ((t + y) / t_2)) + (((z * x) + (y * (z - b))) / 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 = t + (x + y)
    t_2 = y + (x + t)
    if ((z <= (-2.35d-17)) .or. (.not. (z <= 4.9d-20))) then
        tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)))
    else
        tmp = (a * ((t + y) / t_2)) + (((z * x) + (y * (z - b))) / 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 = t + (x + y);
	double t_2 = y + (x + t);
	double tmp;
	if ((z <= -2.35e-17) || !(z <= 4.9e-20)) {
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)));
	} else {
		tmp = (a * ((t + y) / t_2)) + (((z * x) + (y * (z - b))) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = y + (x + t)
	tmp = 0
	if (z <= -2.35e-17) or not (z <= 4.9e-20):
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)))
	else:
		tmp = (a * ((t + y) / t_2)) + (((z * x) + (y * (z - b))) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	tmp = 0.0
	if ((z <= -2.35e-17) || !(z <= 4.9e-20))
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(Float64(Float64(y / t_1) + Float64(Float64(a / z) * Float64(Float64(t + y) / t_1))) - Float64(Float64(b * Float64(y / z)) / t_1))));
	else
		tmp = Float64(Float64(a * Float64(Float64(t + y) / t_2)) + Float64(Float64(Float64(z * x) + Float64(y * Float64(z - b))) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = y + (x + t);
	tmp = 0.0;
	if ((z <= -2.35e-17) || ~((z <= 4.9e-20)))
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)));
	else
		tmp = (a * ((t + y) / t_2)) + (((z * x) + (y * (z - b))) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -2.35e-17], N[Not[LessEqual[z, 4.9e-20]], $MachinePrecision]], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(a / z), $MachinePrecision] * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(y / z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * x), $MachinePrecision] + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.35e-17 or 4.9000000000000002e-20 < z

   1. Initial program 47.6%

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

   3. Taylor expanded in z around inf 72.7%

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

      1. associate--l+ 72.7%

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

      2. +-commutative 72.7%

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

      3. +-commutative 72.7%

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

      4. times-frac 86.9%

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

      5. +-commutative 86.9%

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

      6. associate-/r* 87.5%

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

      7. associate-/l* 95.7%

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

      8. +-commutative 95.7%

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

   5. Simplified 95.7%

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

   if -2.35e-17 < z < 4.9000000000000002e-20

   1. Initial program 81.0%

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

   3. Taylor expanded in b around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. +-commutative 81.1%

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

      3. associate-+l+ 81.1%

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

      4. associate-/l* 93.3%

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

      5. +-commutative 93.3%

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

      6. associate-+r+ 93.3%

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

      7. +-commutative 93.3%

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

      8. associate-+l+ 93.3%

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

      9. sub-neg 93.3%

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

      10. div-sub 93.3%

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

   5. Simplified 93.3%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-17} \lor \neg \left(z \leq 4.9 \cdot 10^{-20}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t + \left(x + y\right)} + \left(\left(\frac{y}{t + \left(x + y\right)} + \frac{a}{z} \cdot \frac{t + y}{t + \left(x + y\right)}\right) - \frac{b \cdot \frac{y}{z}}{t + \left(x + y\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+301} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+217}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ t y)) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 -5e+301) (not (<= t_1 2e+217))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -5e+301) || !(t_1 <= 2e+217)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / (y + (x + t))
    if ((t_1 <= (-5d+301)) .or. (.not. (t_1 <= 2d+217))) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -5e+301) || !(t_1 <= 2e+217)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -5e+301) or not (t_1 <= 2e+217):
		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(t + y)) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= -5e+301) || !(t_1 <= 2e+217))
		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 * (t + y)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -5e+301) || ~((t_1 <= 2e+217)))
		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[(t + y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+301], N[Not[LessEqual[t$95$1, 2e+217]], $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)) < -5.0000000000000004e301 or 1.99999999999999992e217 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 14.7%

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

   3. Taylor expanded in y around inf 66.0%

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

   if -5.0000000000000004e301 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999992e217

   1. Initial program 99.4%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+301} \lor \neg \left(\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+217}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-45}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t + y}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-145}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_1}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-149}:\\ \;\;\;\;-b\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-101}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) - y \cdot b}{t\_1}\\ \mathbf{elif}\;z \leq 10^{+126}:\\ \;\;\;\;a \cdot \left(x \cdot \frac{\frac{z}{a}}{x + t} + \frac{t}{x + t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -1.85e+56)
     t_2
     (if (<= z -2e-45)
       (+ a (/ (* y (- z b)) (+ t y)))
       (if (<= z -1.1e-145)
         (* a (/ (+ t y) t_1))
         (if (<= z -1.85e-149)
           (- b)
           (if (<= z 1.95e-101)
             (/ (- (* a (+ t y)) (* y b)) t_1)
             (if (<= z 1e+126)
               (* a (+ (* x (/ (/ z a) (+ x t))) (/ t (+ x t))))
               t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -1.85e+56) {
		tmp = t_2;
	} else if (z <= -2e-45) {
		tmp = a + ((y * (z - b)) / (t + y));
	} else if (z <= -1.1e-145) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= -1.85e-149) {
		tmp = -b;
	} else if (z <= 1.95e-101) {
		tmp = ((a * (t + y)) - (y * b)) / t_1;
	} else if (z <= 1e+126) {
		tmp = a * ((x * ((z / a) / (x + t))) + (t / (x + t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * ((x + y) / t_1)
    if (z <= (-1.85d+56)) then
        tmp = t_2
    else if (z <= (-2d-45)) then
        tmp = a + ((y * (z - b)) / (t + y))
    else if (z <= (-1.1d-145)) then
        tmp = a * ((t + y) / t_1)
    else if (z <= (-1.85d-149)) then
        tmp = -b
    else if (z <= 1.95d-101) then
        tmp = ((a * (t + y)) - (y * b)) / t_1
    else if (z <= 1d+126) then
        tmp = a * ((x * ((z / a) / (x + t))) + (t / (x + t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -1.85e+56) {
		tmp = t_2;
	} else if (z <= -2e-45) {
		tmp = a + ((y * (z - b)) / (t + y));
	} else if (z <= -1.1e-145) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= -1.85e-149) {
		tmp = -b;
	} else if (z <= 1.95e-101) {
		tmp = ((a * (t + y)) - (y * b)) / t_1;
	} else if (z <= 1e+126) {
		tmp = a * ((x * ((z / a) / (x + t))) + (t / (x + t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -1.85e+56:
		tmp = t_2
	elif z <= -2e-45:
		tmp = a + ((y * (z - b)) / (t + y))
	elif z <= -1.1e-145:
		tmp = a * ((t + y) / t_1)
	elif z <= -1.85e-149:
		tmp = -b
	elif z <= 1.95e-101:
		tmp = ((a * (t + y)) - (y * b)) / t_1
	elif z <= 1e+126:
		tmp = a * ((x * ((z / a) / (x + t))) + (t / (x + t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -1.85e+56)
		tmp = t_2;
	elseif (z <= -2e-45)
		tmp = Float64(a + Float64(Float64(y * Float64(z - b)) / Float64(t + y)));
	elseif (z <= -1.1e-145)
		tmp = Float64(a * Float64(Float64(t + y) / t_1));
	elseif (z <= -1.85e-149)
		tmp = Float64(-b);
	elseif (z <= 1.95e-101)
		tmp = Float64(Float64(Float64(a * Float64(t + y)) - Float64(y * b)) / t_1);
	elseif (z <= 1e+126)
		tmp = Float64(a * Float64(Float64(x * Float64(Float64(z / a) / Float64(x + t))) + Float64(t / Float64(x + t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -1.85e+56)
		tmp = t_2;
	elseif (z <= -2e-45)
		tmp = a + ((y * (z - b)) / (t + y));
	elseif (z <= -1.1e-145)
		tmp = a * ((t + y) / t_1);
	elseif (z <= -1.85e-149)
		tmp = -b;
	elseif (z <= 1.95e-101)
		tmp = ((a * (t + y)) - (y * b)) / t_1;
	elseif (z <= 1e+126)
		tmp = a * ((x * ((z / a) / (x + t))) + (t / (x + t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+56], t$95$2, If[LessEqual[z, -2e-45], N[(a + N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-145], N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.85e-149], (-b), If[LessEqual[z, 1.95e-101], N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 1e+126], N[(a * N[(N[(x * N[(N[(z / a), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.84999999999999998e56 or 9.99999999999999925e125 < z

   1. Initial program 35.7%

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

   3. Taylor expanded in z around inf 27.5%

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

      1. associate-/l* 73.0%

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

      2. +-commutative 73.0%

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

      3. +-commutative 73.0%

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

      4. associate-+r+ 73.0%

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

      5. +-commutative 73.0%

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

      6. associate-+l+ 73.0%

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

   5. Simplified 73.0%

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

   if -1.84999999999999998e56 < z < -1.99999999999999997e-45

   1. Initial program 88.4%

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

   3. Taylor expanded in b around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. +-commutative 88.4%

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

      3. associate-+l+ 88.4%

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

      4. associate-/l* 95.8%

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

      5. +-commutative 95.8%

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

      6. associate-+r+ 95.8%

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

      7. +-commutative 95.8%

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

      8. associate-+l+ 95.8%

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

      9. sub-neg 95.8%

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

      10. div-sub 95.8%

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

   5. Simplified 95.8%

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

   6. Taylor expanded in t around inf 88.0%

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

   7. Taylor expanded in x around 0 72.2%

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

      1. +-commutative 72.2%

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

   9. Simplified 72.2%

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

   if -1.99999999999999997e-45 < z < -1.1e-145

   1. Initial program 49.0%

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

   3. Taylor expanded in a around inf 33.8%

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

      1. associate-/l* 70.1%

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

      2. +-commutative 70.1%

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

      3. associate-+r+ 70.1%

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

      4. +-commutative 70.1%

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

      5. associate-+l+ 70.1%

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

   5. Simplified 70.1%

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

   if -1.1e-145 < z < -1.84999999999999995e-149

   1. Initial program 51.8%

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

   3. Taylor expanded in b around inf 51.8%

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

      1. associate-*r* 51.8%

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

      2. neg-mul-1 51.8%

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

      3. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

   if -1.84999999999999995e-149 < z < 1.95000000000000008e-101

   1. Initial program 86.0%

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

   3. Taylor expanded in z around 0 76.7%

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

      1. *-commutative 76.7%

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

   5. Simplified 76.7%

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

   if 1.95000000000000008e-101 < z < 9.99999999999999925e125

   1. Initial program 75.1%

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

   3. Taylor expanded in a around inf 84.6%

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

      1. associate--l+ 84.6%

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

      2. +-commutative 84.6%

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

      3. +-commutative 84.6%

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

      4. associate-/l* 87.3%

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

      5. +-commutative 87.3%

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

      6. +-commutative 87.3%

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

      7. *-commutative 87.3%

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

      8. +-commutative 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in y around 0 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-/l* 77.4%

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

      3. associate-/r* 77.5%

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

      4. +-commutative 77.5%

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

      5. +-commutative 77.5%

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

   8. Simplified 77.5%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-45}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t + y}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-145}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-149}:\\ \;\;\;\;-b\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-101}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 10^{+126}:\\ \;\;\;\;a \cdot \left(x \cdot \frac{\frac{z}{a}}{x + t} + \frac{t}{x + t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \frac{t + y}{t\_1} + \frac{z \cdot x}{x + t}\\ t_3 := a + \frac{z \cdot x + y \cdot \left(z - b\right)}{t\_1}\\ t_4 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+154}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-39}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-50}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ (* a (/ (+ t y) t_1)) (/ (* z x) (+ x t))))
        (t_3 (+ a (/ (+ (* z x) (* y (- z b))) t_1)))
        (t_4 (* z (/ (+ x y) t_1))))
   (if (<= z -5.3e+154)
     t_4
     (if (<= z -2.1e-39)
       t_3
       (if (<= z -4.7e-143)
         t_2
         (if (<= z 1.15e-50) t_3 (if (<= z 1.05e+126) t_2 t_4)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (a * ((t + y) / t_1)) + ((z * x) / (x + t));
	double t_3 = a + (((z * x) + (y * (z - b))) / t_1);
	double t_4 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -5.3e+154) {
		tmp = t_4;
	} else if (z <= -2.1e-39) {
		tmp = t_3;
	} else if (z <= -4.7e-143) {
		tmp = t_2;
	} else if (z <= 1.15e-50) {
		tmp = t_3;
	} else if (z <= 1.05e+126) {
		tmp = 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 = y + (x + t)
    t_2 = (a * ((t + y) / t_1)) + ((z * x) / (x + t))
    t_3 = a + (((z * x) + (y * (z - b))) / t_1)
    t_4 = z * ((x + y) / t_1)
    if (z <= (-5.3d+154)) then
        tmp = t_4
    else if (z <= (-2.1d-39)) then
        tmp = t_3
    else if (z <= (-4.7d-143)) then
        tmp = t_2
    else if (z <= 1.15d-50) then
        tmp = t_3
    else if (z <= 1.05d+126) then
        tmp = 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 = y + (x + t);
	double t_2 = (a * ((t + y) / t_1)) + ((z * x) / (x + t));
	double t_3 = a + (((z * x) + (y * (z - b))) / t_1);
	double t_4 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -5.3e+154) {
		tmp = t_4;
	} else if (z <= -2.1e-39) {
		tmp = t_3;
	} else if (z <= -4.7e-143) {
		tmp = t_2;
	} else if (z <= 1.15e-50) {
		tmp = t_3;
	} else if (z <= 1.05e+126) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (a * ((t + y) / t_1)) + ((z * x) / (x + t))
	t_3 = a + (((z * x) + (y * (z - b))) / t_1)
	t_4 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -5.3e+154:
		tmp = t_4
	elif z <= -2.1e-39:
		tmp = t_3
	elif z <= -4.7e-143:
		tmp = t_2
	elif z <= 1.15e-50:
		tmp = t_3
	elif z <= 1.05e+126:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(a * Float64(Float64(t + y) / t_1)) + Float64(Float64(z * x) / Float64(x + t)))
	t_3 = Float64(a + Float64(Float64(Float64(z * x) + Float64(y * Float64(z - b))) / t_1))
	t_4 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -5.3e+154)
		tmp = t_4;
	elseif (z <= -2.1e-39)
		tmp = t_3;
	elseif (z <= -4.7e-143)
		tmp = t_2;
	elseif (z <= 1.15e-50)
		tmp = t_3;
	elseif (z <= 1.05e+126)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (a * ((t + y) / t_1)) + ((z * x) / (x + t));
	t_3 = a + (((z * x) + (y * (z - b))) / t_1);
	t_4 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -5.3e+154)
		tmp = t_4;
	elseif (z <= -2.1e-39)
		tmp = t_3;
	elseif (z <= -4.7e-143)
		tmp = t_2;
	elseif (z <= 1.15e-50)
		tmp = t_3;
	elseif (z <= 1.05e+126)
		tmp = t_2;
	else
		tmp = t_4;
	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[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(z * x), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(N[(N[(z * x), $MachinePrecision] + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e+154], t$95$4, If[LessEqual[z, -2.1e-39], t$95$3, If[LessEqual[z, -4.7e-143], t$95$2, If[LessEqual[z, 1.15e-50], t$95$3, If[LessEqual[z, 1.05e+126], t$95$2, t$95$4]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.30000000000000024e154 or 1.05e126 < z

   1. Initial program 30.6%

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

   3. Taylor expanded in z around inf 25.1%

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

      1. associate-/l* 81.2%

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

      2. +-commutative 81.2%

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

      3. +-commutative 81.2%

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

      4. associate-+r+ 81.2%

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

      5. +-commutative 81.2%

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

      6. associate-+l+ 81.2%

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

   5. Simplified 81.2%

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

   if -5.30000000000000024e154 < z < -2.09999999999999993e-39 or -4.70000000000000045e-143 < z < 1.1500000000000001e-50

   1. Initial program 79.8%

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

   3. Taylor expanded in b around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. +-commutative 79.8%

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

      3. associate-+l+ 79.8%

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

      4. associate-/l* 89.9%

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

      5. +-commutative 89.9%

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

      6. associate-+r+ 89.9%

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

      7. +-commutative 89.9%

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

      8. associate-+l+ 89.9%

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

      9. sub-neg 89.9%

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

      10. div-sub 89.9%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in t around inf 76.7%

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

   if -2.09999999999999993e-39 < z < -4.70000000000000045e-143 or 1.1500000000000001e-50 < z < 1.05e126

   1. Initial program 66.6%

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

   3. Taylor expanded in b around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. +-commutative 66.6%

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

      3. associate-+l+ 66.6%

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

      4. associate-/l* 85.0%

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

      5. +-commutative 85.0%

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

      6. associate-+r+ 85.0%

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

      7. +-commutative 85.0%

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

      8. associate-+l+ 85.0%

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

      9. sub-neg 85.0%

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

      10. div-sub 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in y around 0 85.0%

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

      1. *-commutative 85.0%

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

   8. Simplified 85.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-39}:\\ \;\;\;\;a + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + \frac{z \cdot x}{x + t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-50}:\\ \;\;\;\;a + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + \frac{z \cdot x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-40}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t + y}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-145}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_1}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-149}:\\ \;\;\;\;-b\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-103}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) - y \cdot b}{t\_1}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+22}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -1.55e+56)
     t_2
     (if (<= z -2e-40)
       (+ a (/ (* y (- z b)) (+ t y)))
       (if (<= z -1.1e-145)
         (* a (/ (+ t y) t_1))
         (if (<= z -1.85e-149)
           (- b)
           (if (<= z 4.4e-103)
             (/ (- (* a (+ t y)) (* y b)) t_1)
             (if (<= z 5.9e+22) (/ (+ (* z x) (* t a)) (+ x t)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -1.55e+56) {
		tmp = t_2;
	} else if (z <= -2e-40) {
		tmp = a + ((y * (z - b)) / (t + y));
	} else if (z <= -1.1e-145) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= -1.85e-149) {
		tmp = -b;
	} else if (z <= 4.4e-103) {
		tmp = ((a * (t + y)) - (y * b)) / t_1;
	} else if (z <= 5.9e+22) {
		tmp = ((z * x) + (t * a)) / (x + t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * ((x + y) / t_1)
    if (z <= (-1.55d+56)) then
        tmp = t_2
    else if (z <= (-2d-40)) then
        tmp = a + ((y * (z - b)) / (t + y))
    else if (z <= (-1.1d-145)) then
        tmp = a * ((t + y) / t_1)
    else if (z <= (-1.85d-149)) then
        tmp = -b
    else if (z <= 4.4d-103) then
        tmp = ((a * (t + y)) - (y * b)) / t_1
    else if (z <= 5.9d+22) then
        tmp = ((z * x) + (t * a)) / (x + t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -1.55e+56) {
		tmp = t_2;
	} else if (z <= -2e-40) {
		tmp = a + ((y * (z - b)) / (t + y));
	} else if (z <= -1.1e-145) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= -1.85e-149) {
		tmp = -b;
	} else if (z <= 4.4e-103) {
		tmp = ((a * (t + y)) - (y * b)) / t_1;
	} else if (z <= 5.9e+22) {
		tmp = ((z * x) + (t * a)) / (x + t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -1.55e+56:
		tmp = t_2
	elif z <= -2e-40:
		tmp = a + ((y * (z - b)) / (t + y))
	elif z <= -1.1e-145:
		tmp = a * ((t + y) / t_1)
	elif z <= -1.85e-149:
		tmp = -b
	elif z <= 4.4e-103:
		tmp = ((a * (t + y)) - (y * b)) / t_1
	elif z <= 5.9e+22:
		tmp = ((z * x) + (t * a)) / (x + t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -1.55e+56)
		tmp = t_2;
	elseif (z <= -2e-40)
		tmp = Float64(a + Float64(Float64(y * Float64(z - b)) / Float64(t + y)));
	elseif (z <= -1.1e-145)
		tmp = Float64(a * Float64(Float64(t + y) / t_1));
	elseif (z <= -1.85e-149)
		tmp = Float64(-b);
	elseif (z <= 4.4e-103)
		tmp = Float64(Float64(Float64(a * Float64(t + y)) - Float64(y * b)) / t_1);
	elseif (z <= 5.9e+22)
		tmp = Float64(Float64(Float64(z * x) + Float64(t * a)) / Float64(x + t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -1.55e+56)
		tmp = t_2;
	elseif (z <= -2e-40)
		tmp = a + ((y * (z - b)) / (t + y));
	elseif (z <= -1.1e-145)
		tmp = a * ((t + y) / t_1);
	elseif (z <= -1.85e-149)
		tmp = -b;
	elseif (z <= 4.4e-103)
		tmp = ((a * (t + y)) - (y * b)) / t_1;
	elseif (z <= 5.9e+22)
		tmp = ((z * x) + (t * a)) / (x + t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+56], t$95$2, If[LessEqual[z, -2e-40], N[(a + N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-145], N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.85e-149], (-b), If[LessEqual[z, 4.4e-103], N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 5.9e+22], N[(N[(N[(z * x), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.55000000000000002e56 or 5.9000000000000002e22 < z

   1. Initial program 39.9%

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

   3. Taylor expanded in z around inf 30.3%

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

      1. associate-/l* 70.6%

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

      2. +-commutative 70.6%

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

      3. +-commutative 70.6%

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

      4. associate-+r+ 70.6%

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

      5. +-commutative 70.6%

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

      6. associate-+l+ 70.6%

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

   5. Simplified 70.6%

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

   if -1.55000000000000002e56 < z < -1.9999999999999999e-40

   1. Initial program 88.4%

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

   3. Taylor expanded in b around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. +-commutative 88.4%

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

      3. associate-+l+ 88.4%

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

      4. associate-/l* 95.8%

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

      5. +-commutative 95.8%

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

      6. associate-+r+ 95.8%

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

      7. +-commutative 95.8%

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

      8. associate-+l+ 95.8%

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

      9. sub-neg 95.8%

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

      10. div-sub 95.8%

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

   5. Simplified 95.8%

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

   6. Taylor expanded in t around inf 88.0%

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

   7. Taylor expanded in x around 0 72.2%

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

      1. +-commutative 72.2%

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

   9. Simplified 72.2%

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

   if -1.9999999999999999e-40 < z < -1.1e-145

   1. Initial program 49.0%

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

   3. Taylor expanded in a around inf 33.8%

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

      1. associate-/l* 70.1%

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

      2. +-commutative 70.1%

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

      3. associate-+r+ 70.1%

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

      4. +-commutative 70.1%

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

      5. associate-+l+ 70.1%

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

   5. Simplified 70.1%

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

   if -1.1e-145 < z < -1.84999999999999995e-149

   1. Initial program 51.8%

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

   3. Taylor expanded in b around inf 51.8%

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

      1. associate-*r* 51.8%

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

      2. neg-mul-1 51.8%

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

      3. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

   if -1.84999999999999995e-149 < z < 4.3999999999999999e-103

   1. Initial program 86.0%

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

   3. Taylor expanded in z around 0 76.7%

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

      1. *-commutative 76.7%

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

   5. Simplified 76.7%

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

   if 4.3999999999999999e-103 < z < 5.9000000000000002e22

   1. Initial program 80.0%

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

   3. Taylor expanded in y around 0 83.7%

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-40}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t + y}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-145}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-149}:\\ \;\;\;\;-b\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-103}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+22}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{x + t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a + \frac{z \cdot x + y \cdot \left(z - b\right)}{t\_1}\\ t_3 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+154}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_1}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ a (/ (+ (* z x) (* y (- z b))) t_1)))
        (t_3 (* z (/ (+ x y) t_1))))
   (if (<= z -2.5e+154)
     t_3
     (if (<= z -2.5e-46)
       t_2
       (if (<= z -7.5e-143)
         (* a (/ (+ t y) t_1))
         (if (<= z 1.2e+125) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a + (((z * x) + (y * (z - b))) / t_1);
	double t_3 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -2.5e+154) {
		tmp = t_3;
	} else if (z <= -2.5e-46) {
		tmp = t_2;
	} else if (z <= -7.5e-143) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= 1.2e+125) {
		tmp = 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 = y + (x + t)
    t_2 = a + (((z * x) + (y * (z - b))) / t_1)
    t_3 = z * ((x + y) / t_1)
    if (z <= (-2.5d+154)) then
        tmp = t_3
    else if (z <= (-2.5d-46)) then
        tmp = t_2
    else if (z <= (-7.5d-143)) then
        tmp = a * ((t + y) / t_1)
    else if (z <= 1.2d+125) then
        tmp = 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 = y + (x + t);
	double t_2 = a + (((z * x) + (y * (z - b))) / t_1);
	double t_3 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -2.5e+154) {
		tmp = t_3;
	} else if (z <= -2.5e-46) {
		tmp = t_2;
	} else if (z <= -7.5e-143) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= 1.2e+125) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a + (((z * x) + (y * (z - b))) / t_1)
	t_3 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -2.5e+154:
		tmp = t_3
	elif z <= -2.5e-46:
		tmp = t_2
	elif z <= -7.5e-143:
		tmp = a * ((t + y) / t_1)
	elif z <= 1.2e+125:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a + Float64(Float64(Float64(z * x) + Float64(y * Float64(z - b))) / t_1))
	t_3 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -2.5e+154)
		tmp = t_3;
	elseif (z <= -2.5e-46)
		tmp = t_2;
	elseif (z <= -7.5e-143)
		tmp = Float64(a * Float64(Float64(t + y) / t_1));
	elseif (z <= 1.2e+125)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a + (((z * x) + (y * (z - b))) / t_1);
	t_3 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -2.5e+154)
		tmp = t_3;
	elseif (z <= -2.5e-46)
		tmp = t_2;
	elseif (z <= -7.5e-143)
		tmp = a * ((t + y) / t_1);
	elseif (z <= 1.2e+125)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(N[(N[(z * x), $MachinePrecision] + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+154], t$95$3, If[LessEqual[z, -2.5e-46], t$95$2, If[LessEqual[z, -7.5e-143], N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+125], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000002e154 or 1.2e125 < z

   1. Initial program 30.6%

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

   3. Taylor expanded in z around inf 25.1%

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

      1. associate-/l* 81.2%

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

      2. +-commutative 81.2%

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

      3. +-commutative 81.2%

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

      4. associate-+r+ 81.2%

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

      5. +-commutative 81.2%

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

      6. associate-+l+ 81.2%

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

   5. Simplified 81.2%

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

   if -2.50000000000000002e154 < z < -2.49999999999999996e-46 or -7.5000000000000003e-143 < z < 1.2e125

   1. Initial program 78.5%

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

   3. Taylor expanded in b around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. +-commutative 78.6%

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

      3. associate-+l+ 78.6%

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

      4. associate-/l* 88.9%

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

      5. +-commutative 88.9%

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

      6. associate-+r+ 88.9%

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

      7. +-commutative 88.9%

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

      8. associate-+l+ 88.9%

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

      9. sub-neg 88.9%

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

      10. div-sub 88.9%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in t around inf 75.9%

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

   if -2.49999999999999996e-46 < z < -7.5000000000000003e-143

   1. Initial program 49.0%

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

   3. Taylor expanded in a around inf 33.8%

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

      1. associate-/l* 70.1%

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

      2. +-commutative 70.1%

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

      3. associate-+r+ 70.1%

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

      4. +-commutative 70.1%

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

      5. associate-+l+ 70.1%

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

   5. Simplified 70.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-46}:\\ \;\;\;\;a + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+125}:\\ \;\;\;\;a + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \frac{x + y}{t\_2}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{t\_1 + z \cdot \left(x + y\right)}{t\_2}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-101}:\\ \;\;\;\;\frac{t\_1 - y \cdot b}{t\_2}\\ \mathbf{elif}\;z \leq 10^{+126}:\\ \;\;\;\;a \cdot \left(x \cdot \frac{\frac{z}{a}}{x + t} + \frac{t}{x + t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t y))) (t_2 (+ y (+ x t))) (t_3 (* z (/ (+ x y) t_2))))
   (if (<= z -1.6e+96)
     t_3
     (if (<= z -3.5e-143)
       (/ (+ t_1 (* z (+ x y))) t_2)
       (if (<= z 1.2e-101)
         (/ (- t_1 (* y b)) t_2)
         (if (<= z 1e+126)
           (* a (+ (* x (/ (/ z a) (+ x t))) (/ t (+ x t))))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + y);
	double t_2 = y + (x + t);
	double t_3 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -1.6e+96) {
		tmp = t_3;
	} else if (z <= -3.5e-143) {
		tmp = (t_1 + (z * (x + y))) / t_2;
	} else if (z <= 1.2e-101) {
		tmp = (t_1 - (y * b)) / t_2;
	} else if (z <= 1e+126) {
		tmp = a * ((x * ((z / a) / (x + t))) + (t / (x + t)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (t + y)
    t_2 = y + (x + t)
    t_3 = z * ((x + y) / t_2)
    if (z <= (-1.6d+96)) then
        tmp = t_3
    else if (z <= (-3.5d-143)) then
        tmp = (t_1 + (z * (x + y))) / t_2
    else if (z <= 1.2d-101) then
        tmp = (t_1 - (y * b)) / t_2
    else if (z <= 1d+126) then
        tmp = a * ((x * ((z / a) / (x + t))) + (t / (x + t)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + y);
	double t_2 = y + (x + t);
	double t_3 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -1.6e+96) {
		tmp = t_3;
	} else if (z <= -3.5e-143) {
		tmp = (t_1 + (z * (x + y))) / t_2;
	} else if (z <= 1.2e-101) {
		tmp = (t_1 - (y * b)) / t_2;
	} else if (z <= 1e+126) {
		tmp = a * ((x * ((z / a) / (x + t))) + (t / (x + t)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + y)
	t_2 = y + (x + t)
	t_3 = z * ((x + y) / t_2)
	tmp = 0
	if z <= -1.6e+96:
		tmp = t_3
	elif z <= -3.5e-143:
		tmp = (t_1 + (z * (x + y))) / t_2
	elif z <= 1.2e-101:
		tmp = (t_1 - (y * b)) / t_2
	elif z <= 1e+126:
		tmp = a * ((x * ((z / a) / (x + t))) + (t / (x + t)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z * Float64(Float64(x + y) / t_2))
	tmp = 0.0
	if (z <= -1.6e+96)
		tmp = t_3;
	elseif (z <= -3.5e-143)
		tmp = Float64(Float64(t_1 + Float64(z * Float64(x + y))) / t_2);
	elseif (z <= 1.2e-101)
		tmp = Float64(Float64(t_1 - Float64(y * b)) / t_2);
	elseif (z <= 1e+126)
		tmp = Float64(a * Float64(Float64(x * Float64(Float64(z / a) / Float64(x + t))) + Float64(t / Float64(x + t))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + y);
	t_2 = y + (x + t);
	t_3 = z * ((x + y) / t_2);
	tmp = 0.0;
	if (z <= -1.6e+96)
		tmp = t_3;
	elseif (z <= -3.5e-143)
		tmp = (t_1 + (z * (x + y))) / t_2;
	elseif (z <= 1.2e-101)
		tmp = (t_1 - (y * b)) / t_2;
	elseif (z <= 1e+126)
		tmp = a * ((x * ((z / a) / (x + t))) + (t / (x + t)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+96], t$95$3, If[LessEqual[z, -3.5e-143], N[(N[(t$95$1 + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 1.2e-101], N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 1e+126], N[(a * N[(N[(x * N[(N[(z / a), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.60000000000000003e96 or 9.99999999999999925e125 < z

   1. Initial program 33.2%

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

   3. Taylor expanded in z around inf 26.5%

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

      1. associate-/l* 74.8%

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

      2. +-commutative 74.8%

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

      3. +-commutative 74.8%

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

      4. associate-+r+ 74.8%

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

      5. +-commutative 74.8%

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

      6. associate-+l+ 74.8%

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

   5. Simplified 74.8%

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

   if -1.60000000000000003e96 < z < -3.50000000000000005e-143

   1. Initial program 72.7%

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

   3. Taylor expanded in b around 0 66.1%

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

   if -3.50000000000000005e-143 < z < 1.2e-101

   1. Initial program 85.2%

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

   3. Taylor expanded in z around 0 76.1%

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

      1. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   if 1.2e-101 < z < 9.99999999999999925e125

   1. Initial program 75.1%

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

   3. Taylor expanded in a around inf 84.6%

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

      1. associate--l+ 84.6%

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

      2. +-commutative 84.6%

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

      3. +-commutative 84.6%

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

      4. associate-/l* 87.3%

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

      5. +-commutative 87.3%

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

      6. +-commutative 87.3%

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

      7. *-commutative 87.3%

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

      8. +-commutative 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in y around 0 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-/l* 77.4%

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

      3. associate-/r* 77.5%

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

      4. +-commutative 77.5%

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

      5. +-commutative 77.5%

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

   8. Simplified 77.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) + z \cdot \left(x + y\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-101}:\\ \;\;\;\;\frac{a \cdot \left(t + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 10^{+126}:\\ \;\;\;\;a \cdot \left(x \cdot \frac{\frac{z}{a}}{x + t} + \frac{t}{x + t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+160} \lor \neg \left(z \leq 2.4 \cdot 10^{+126}\right):\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_1} + \frac{z \cdot x + y \cdot \left(z - b\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (or (<= z -1.12e+160) (not (<= z 2.4e+126)))
     (* z (/ (+ x y) t_1))
     (+ (* a (/ (+ t y) t_1)) (/ (+ (* z x) (* y (- z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((z <= -1.12e+160) || !(z <= 2.4e+126)) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = (a * ((t + y) / t_1)) + (((z * x) + (y * (z - b))) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if ((z <= (-1.12d+160)) .or. (.not. (z <= 2.4d+126))) then
        tmp = z * ((x + y) / t_1)
    else
        tmp = (a * ((t + y) / t_1)) + (((z * x) + (y * (z - b))) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((z <= -1.12e+160) || !(z <= 2.4e+126)) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = (a * ((t + y) / t_1)) + (((z * x) + (y * (z - b))) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if (z <= -1.12e+160) or not (z <= 2.4e+126):
		tmp = z * ((x + y) / t_1)
	else:
		tmp = (a * ((t + y) / t_1)) + (((z * x) + (y * (z - b))) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if ((z <= -1.12e+160) || !(z <= 2.4e+126))
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	else
		tmp = Float64(Float64(a * Float64(Float64(t + y) / t_1)) + Float64(Float64(Float64(z * x) + Float64(y * Float64(z - b))) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if ((z <= -1.12e+160) || ~((z <= 2.4e+126)))
		tmp = z * ((x + y) / t_1);
	else
		tmp = (a * ((t + y) / t_1)) + (((z * x) + (y * (z - b))) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.12e+160], N[Not[LessEqual[z, 2.4e+126]], $MachinePrecision]], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * x), $MachinePrecision] + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e160 or 2.40000000000000012e126 < z

   1. Initial program 28.7%

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

   3. Taylor expanded in z around inf 23.7%

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

      1. associate-/l* 81.3%

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

      2. +-commutative 81.3%

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

      3. +-commutative 81.3%

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

      4. associate-+r+ 81.3%

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

      5. +-commutative 81.3%

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

      6. associate-+l+ 81.3%

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

   5. Simplified 81.3%

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

   if -1.12e160 < z < 2.40000000000000012e126

   1. Initial program 76.7%

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

   3. Taylor expanded in b around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. +-commutative 76.7%

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

      3. associate-+l+ 76.7%

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

      4. associate-/l* 88.8%

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

      5. +-commutative 88.8%

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

      6. associate-+r+ 88.8%

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

      7. +-commutative 88.8%

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

      8. associate-+l+ 88.8%

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

      9. sub-neg 88.8%

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

      10. div-sub 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+160} \lor \neg \left(z \leq 2.4 \cdot 10^{+126}\right):\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+144}:\\ \;\;\;\;z \cdot \left(\frac{\frac{a \cdot \left(t + y\right) - y \cdot b}{t\_1}}{z} + t\_2\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_1} + \frac{z \cdot x + y \cdot \left(z - b\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ (+ x y) t_1)))
   (if (<= z -8.5e+144)
     (* z (+ (/ (/ (- (* a (+ t y)) (* y b)) t_1) z) t_2))
     (if (<= z 2e+127)
       (+ (* a (/ (+ t y) t_1)) (/ (+ (* z x) (* y (- z b))) t_1))
       (* z 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 = (x + y) / t_1;
	double tmp;
	if (z <= -8.5e+144) {
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_2);
	} else if (z <= 2e+127) {
		tmp = (a * ((t + y) / t_1)) + (((z * x) + (y * (z - b))) / t_1);
	} else {
		tmp = z * 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 = (x + y) / t_1
    if (z <= (-8.5d+144)) then
        tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_2)
    else if (z <= 2d+127) then
        tmp = (a * ((t + y) / t_1)) + (((z * x) + (y * (z - b))) / t_1)
    else
        tmp = z * 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 = (x + y) / t_1;
	double tmp;
	if (z <= -8.5e+144) {
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_2);
	} else if (z <= 2e+127) {
		tmp = (a * ((t + y) / t_1)) + (((z * x) + (y * (z - b))) / t_1);
	} else {
		tmp = z * t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (x + y) / t_1
	tmp = 0
	if z <= -8.5e+144:
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_2)
	elif z <= 2e+127:
		tmp = (a * ((t + y) / t_1)) + (((z * x) + (y * (z - b))) / t_1)
	else:
		tmp = z * t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(x + y) / t_1)
	tmp = 0.0
	if (z <= -8.5e+144)
		tmp = Float64(z * Float64(Float64(Float64(Float64(Float64(a * Float64(t + y)) - Float64(y * b)) / t_1) / z) + t_2));
	elseif (z <= 2e+127)
		tmp = Float64(Float64(a * Float64(Float64(t + y) / t_1)) + Float64(Float64(Float64(z * x) + Float64(y * Float64(z - b))) / t_1));
	else
		tmp = Float64(z * t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (x + y) / t_1;
	tmp = 0.0;
	if (z <= -8.5e+144)
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_2);
	elseif (z <= 2e+127)
		tmp = (a * ((t + y) / t_1)) + (((z * x) + (y * (z - b))) / t_1);
	else
		tmp = z * 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[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[z, -8.5e+144], N[(z * N[(N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] / z), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+127], N[(N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * x), $MachinePrecision] + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(z * t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999998e144

   1. Initial program 34.7%

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

   3. Taylor expanded in z around -inf 81.9%

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

      1. associate-*r* 81.9%

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

      2. mul-1-neg 81.9%

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

      3. mul-1-neg 81.9%

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

      4. unsub-neg 81.9%

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

      5. associate-*r/ 81.9%

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

      6. distribute-lft-in 81.9%

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

      7. neg-mul-1 81.9%

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

      8. unsub-neg 81.9%

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

      9. neg-mul-1 81.9%

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

      10. +-commutative 81.9%

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

      11. associate-+r+ 81.9%

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

      12. +-commutative 81.9%

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

      13. associate-+l+ 81.9%

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

   5. Simplified 81.9%

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

   if -8.4999999999999998e144 < z < 1.99999999999999991e127

   1. Initial program 76.7%

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

   3. Taylor expanded in b around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. +-commutative 76.7%

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

      3. associate-+l+ 76.7%

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

      4. associate-/l* 89.1%

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

      5. +-commutative 89.1%

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

      6. associate-+r+ 89.1%

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

      7. +-commutative 89.1%

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

      8. associate-+l+ 89.1%

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

      9. sub-neg 89.1%

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

      10. div-sub 89.1%

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

   5. Simplified 89.1%

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

   if 1.99999999999999991e127 < z

   1. Initial program 26.8%

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

   3. Taylor expanded in z around inf 27.3%

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

      1. associate-/l* 86.0%

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

      2. +-commutative 86.0%

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

      3. +-commutative 86.0%

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

      4. associate-+r+ 86.0%

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

      5. +-commutative 86.0%

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

      6. associate-+l+ 86.0%

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

   5. Simplified 86.0%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+144}:\\ \;\;\;\;z \cdot \left(\frac{\frac{a \cdot \left(t + y\right) - y \cdot b}{y + \left(x + t\right)}}{z} + \frac{x + y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-144}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_1}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-90}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t + y}\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+17}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -8.8e+46)
     t_2
     (if (<= z -1.55e-144)
       (* a (/ (+ t y) t_1))
       (if (<= z 6.8e-90)
         (* b (- (/ a b) (/ y (+ t y))))
         (if (<= z 1.05e+17) (/ (+ (* z x) (* t a)) (+ x t)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -8.8e+46) {
		tmp = t_2;
	} else if (z <= -1.55e-144) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= 6.8e-90) {
		tmp = b * ((a / b) - (y / (t + y)));
	} else if (z <= 1.05e+17) {
		tmp = ((z * x) + (t * a)) / (x + t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * ((x + y) / t_1)
    if (z <= (-8.8d+46)) then
        tmp = t_2
    else if (z <= (-1.55d-144)) then
        tmp = a * ((t + y) / t_1)
    else if (z <= 6.8d-90) then
        tmp = b * ((a / b) - (y / (t + y)))
    else if (z <= 1.05d+17) then
        tmp = ((z * x) + (t * a)) / (x + t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -8.8e+46) {
		tmp = t_2;
	} else if (z <= -1.55e-144) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= 6.8e-90) {
		tmp = b * ((a / b) - (y / (t + y)));
	} else if (z <= 1.05e+17) {
		tmp = ((z * x) + (t * a)) / (x + t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -8.8e+46:
		tmp = t_2
	elif z <= -1.55e-144:
		tmp = a * ((t + y) / t_1)
	elif z <= 6.8e-90:
		tmp = b * ((a / b) - (y / (t + y)))
	elif z <= 1.05e+17:
		tmp = ((z * x) + (t * a)) / (x + t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -8.8e+46)
		tmp = t_2;
	elseif (z <= -1.55e-144)
		tmp = Float64(a * Float64(Float64(t + y) / t_1));
	elseif (z <= 6.8e-90)
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / Float64(t + y))));
	elseif (z <= 1.05e+17)
		tmp = Float64(Float64(Float64(z * x) + Float64(t * a)) / Float64(x + t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -8.8e+46)
		tmp = t_2;
	elseif (z <= -1.55e-144)
		tmp = a * ((t + y) / t_1);
	elseif (z <= 6.8e-90)
		tmp = b * ((a / b) - (y / (t + y)));
	elseif (z <= 1.05e+17)
		tmp = ((z * x) + (t * a)) / (x + t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+46], t$95$2, If[LessEqual[z, -1.55e-144], N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-90], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+17], N[(N[(N[(z * x), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.8000000000000001e46 or 1.05e17 < z

   1. Initial program 40.1%

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

   3. Taylor expanded in z around inf 30.6%

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

      1. associate-/l* 70.3%

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

      2. +-commutative 70.3%

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

      3. +-commutative 70.3%

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

      4. associate-+r+ 70.3%

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

      5. +-commutative 70.3%

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

      6. associate-+l+ 70.3%

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

   5. Simplified 70.3%

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

   if -8.8000000000000001e46 < z < -1.55e-144

   1. Initial program 75.7%

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

   3. Taylor expanded in a around inf 37.1%

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

      1. associate-/l* 55.7%

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

      2. +-commutative 55.7%

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

      3. associate-+r+ 55.7%

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

      4. +-commutative 55.7%

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

      5. associate-+l+ 55.7%

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

   5. Simplified 55.7%

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

   if -1.55e-144 < z < 6.79999999999999988e-90

   1. Initial program 84.5%

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

   3. Taylor expanded in z around 0 74.7%

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

      1. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in x around 0 56.4%

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

   7. Taylor expanded in b around inf 63.8%

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

      1. +-commutative 63.8%

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

      2. mul-1-neg 63.8%

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

      3. unsub-neg 63.8%

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

      4. +-commutative 63.8%

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

   9. Simplified 63.8%

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

   if 6.79999999999999988e-90 < z < 1.05e17

   1. Initial program 81.7%

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

   3. Taylor expanded in y around 0 86.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-144}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-90}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t + y}\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+17}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{x + t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-144}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_1}\\ \mathbf{elif}\;z \leq 13600000000000:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t + y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -1.65e+43)
     t_2
     (if (<= z -2.7e-144)
       (* a (/ (+ t y) t_1))
       (if (<= z 13600000000000.0) (* b (- (/ a b) (/ y (+ t y)))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -1.65e+43) {
		tmp = t_2;
	} else if (z <= -2.7e-144) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= 13600000000000.0) {
		tmp = b * ((a / b) - (y / (t + y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * ((x + y) / t_1)
    if (z <= (-1.65d+43)) then
        tmp = t_2
    else if (z <= (-2.7d-144)) then
        tmp = a * ((t + y) / t_1)
    else if (z <= 13600000000000.0d0) then
        tmp = b * ((a / b) - (y / (t + y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -1.65e+43) {
		tmp = t_2;
	} else if (z <= -2.7e-144) {
		tmp = a * ((t + y) / t_1);
	} else if (z <= 13600000000000.0) {
		tmp = b * ((a / b) - (y / (t + y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -1.65e+43:
		tmp = t_2
	elif z <= -2.7e-144:
		tmp = a * ((t + y) / t_1)
	elif z <= 13600000000000.0:
		tmp = b * ((a / b) - (y / (t + y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -1.65e+43)
		tmp = t_2;
	elseif (z <= -2.7e-144)
		tmp = Float64(a * Float64(Float64(t + y) / t_1));
	elseif (z <= 13600000000000.0)
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / Float64(t + y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -1.65e+43)
		tmp = t_2;
	elseif (z <= -2.7e-144)
		tmp = a * ((t + y) / t_1);
	elseif (z <= 13600000000000.0)
		tmp = b * ((a / b) - (y / (t + y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+43], t$95$2, If[LessEqual[z, -2.7e-144], N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 13600000000000.0], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6500000000000001e43 or 1.36e13 < z

   1. Initial program 40.1%

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

   3. Taylor expanded in z around inf 30.6%

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

      1. associate-/l* 70.3%

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

      2. +-commutative 70.3%

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

      3. +-commutative 70.3%

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

      4. associate-+r+ 70.3%

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

      5. +-commutative 70.3%

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

      6. associate-+l+ 70.3%

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

   5. Simplified 70.3%

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

   if -1.6500000000000001e43 < z < -2.69999999999999975e-144

   1. Initial program 75.7%

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

   3. Taylor expanded in a around inf 37.1%

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

      1. associate-/l* 55.7%

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

      2. +-commutative 55.7%

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

      3. associate-+r+ 55.7%

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

      4. +-commutative 55.7%

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

      5. associate-+l+ 55.7%

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

   5. Simplified 55.7%

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

   if -2.69999999999999975e-144 < z < 1.36e13

   1. Initial program 84.0%

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

   3. Taylor expanded in z around 0 69.6%

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

      1. *-commutative 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in x around 0 54.0%

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

   7. Taylor expanded in b around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. +-commutative 61.8%

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

   9. Simplified 61.8%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-144}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 13600000000000:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t + y}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+125}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-235}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t + y}\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= x -8.5e+125)
     z
     (if (<= x -1.75e-189)
       t_1
       (if (<= x 1.52e-235)
         (* b (- (/ a b) (/ y (+ t y))))
         (if (<= x 1.6e+216) t_1 z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (x <= -8.5e+125) {
		tmp = z;
	} else if (x <= -1.75e-189) {
		tmp = t_1;
	} else if (x <= 1.52e-235) {
		tmp = b * ((a / b) - (y / (t + y)));
	} else if (x <= 1.6e+216) {
		tmp = t_1;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (x <= (-8.5d+125)) then
        tmp = z
    else if (x <= (-1.75d-189)) then
        tmp = t_1
    else if (x <= 1.52d-235) then
        tmp = b * ((a / b) - (y / (t + y)))
    else if (x <= 1.6d+216) then
        tmp = t_1
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (x <= -8.5e+125) {
		tmp = z;
	} else if (x <= -1.75e-189) {
		tmp = t_1;
	} else if (x <= 1.52e-235) {
		tmp = b * ((a / b) - (y / (t + y)));
	} else if (x <= 1.6e+216) {
		tmp = t_1;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if x <= -8.5e+125:
		tmp = z
	elif x <= -1.75e-189:
		tmp = t_1
	elif x <= 1.52e-235:
		tmp = b * ((a / b) - (y / (t + y)))
	elif x <= 1.6e+216:
		tmp = t_1
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (x <= -8.5e+125)
		tmp = z;
	elseif (x <= -1.75e-189)
		tmp = t_1;
	elseif (x <= 1.52e-235)
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / Float64(t + y))));
	elseif (x <= 1.6e+216)
		tmp = t_1;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (x <= -8.5e+125)
		tmp = z;
	elseif (x <= -1.75e-189)
		tmp = t_1;
	elseif (x <= 1.52e-235)
		tmp = b * ((a / b) - (y / (t + y)));
	elseif (x <= 1.6e+216)
		tmp = t_1;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[x, -8.5e+125], z, If[LessEqual[x, -1.75e-189], t$95$1, If[LessEqual[x, 1.52e-235], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+216], t$95$1, z]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.49999999999999974e125 or 1.59999999999999985e216 < x

   1. Initial program 46.3%

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

   3. Taylor expanded in x around inf 62.6%

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

   if -8.49999999999999974e125 < x < -1.7500000000000001e-189 or 1.52e-235 < x < 1.59999999999999985e216

   1. Initial program 68.0%

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

   3. Taylor expanded in y around inf 57.6%

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

   if -1.7500000000000001e-189 < x < 1.52e-235

   1. Initial program 69.7%

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

   3. Taylor expanded in z around 0 64.5%

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

      1. *-commutative 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in x around 0 64.5%

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

   7. Taylor expanded in b around inf 81.1%

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

      1. +-commutative 81.1%

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

      2. mul-1-neg 81.1%

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

      3. unsub-neg 81.1%

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

      4. +-commutative 81.1%

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

   9. Simplified 81.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+125}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-189}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-235}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t + y}\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+216}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-49}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-204} \lor \neg \left(x \leq 2.7 \cdot 10^{-189}\right) \land x \leq 5.5 \cdot 10^{+167}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.8e-49)
   z
   (if (or (<= x 1.5e-204) (and (not (<= x 2.7e-189)) (<= x 5.5e+167)))
     (- a b)
     z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.8e-49) {
		tmp = z;
	} else if ((x <= 1.5e-204) || (!(x <= 2.7e-189) && (x <= 5.5e+167))) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.8d-49)) then
        tmp = z
    else if ((x <= 1.5d-204) .or. (.not. (x <= 2.7d-189)) .and. (x <= 5.5d+167)) then
        tmp = a - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.8e-49) {
		tmp = z;
	} else if ((x <= 1.5e-204) || (!(x <= 2.7e-189) && (x <= 5.5e+167))) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.8e-49:
		tmp = z
	elif (x <= 1.5e-204) or (not (x <= 2.7e-189) and (x <= 5.5e+167)):
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.8e-49)
		tmp = z;
	elseif ((x <= 1.5e-204) || (!(x <= 2.7e-189) && (x <= 5.5e+167)))
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.8e-49)
		tmp = z;
	elseif ((x <= 1.5e-204) || (~((x <= 2.7e-189)) && (x <= 5.5e+167)))
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.8e-49], z, If[Or[LessEqual[x, 1.5e-204], And[N[Not[LessEqual[x, 2.7e-189]], $MachinePrecision], LessEqual[x, 5.5e+167]]], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999985e-49 or 1.4999999999999999e-204 < x < 2.6999999999999999e-189 or 5.5000000000000005e167 < x

   1. Initial program 56.3%

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

   3. Taylor expanded in x around inf 55.5%

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

   if -4.79999999999999985e-49 < x < 1.4999999999999999e-204 or 2.6999999999999999e-189 < x < 5.5000000000000005e167

   1. Initial program 68.3%

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

   3. Taylor expanded in z around 0 54.7%

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

      1. *-commutative 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in y around inf 50.4%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-49}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-204} \lor \neg \left(x \leq 2.7 \cdot 10^{-189}\right) \land x \leq 5.5 \cdot 10^{+167}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7400000000000 \lor \neg \left(x \leq 2.65 \cdot 10^{+157}\right):\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -7400000000000.0) (not (<= x 2.65e+157)))
   (* z (/ (+ x y) (+ y (+ x t))))
   (+ a (/ (* y (- z b)) (+ t y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -7400000000000.0) || !(x <= 2.65e+157)) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else {
		tmp = a + ((y * (z - b)) / (t + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-7400000000000.0d0)) .or. (.not. (x <= 2.65d+157))) then
        tmp = z * ((x + y) / (y + (x + t)))
    else
        tmp = a + ((y * (z - b)) / (t + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -7400000000000.0) || !(x <= 2.65e+157)) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else {
		tmp = a + ((y * (z - b)) / (t + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -7400000000000.0) or not (x <= 2.65e+157):
		tmp = z * ((x + y) / (y + (x + t)))
	else:
		tmp = a + ((y * (z - b)) / (t + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -7400000000000.0) || !(x <= 2.65e+157))
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	else
		tmp = Float64(a + Float64(Float64(y * Float64(z - b)) / Float64(t + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -7400000000000.0) || ~((x <= 2.65e+157)))
		tmp = z * ((x + y) / (y + (x + t)));
	else
		tmp = a + ((y * (z - b)) / (t + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -7400000000000.0], N[Not[LessEqual[x, 2.65e+157]], $MachinePrecision]], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.4e12 or 2.6499999999999999e157 < x

   1. Initial program 48.9%

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

   3. Taylor expanded in z around inf 33.2%

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

      1. associate-/l* 63.5%

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

      2. +-commutative 63.5%

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

      3. +-commutative 63.5%

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

      4. associate-+r+ 63.5%

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

      5. +-commutative 63.5%

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

      6. associate-+l+ 63.5%

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

   5. Simplified 63.5%

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

   if -7.4e12 < x < 2.6499999999999999e157

   1. Initial program 71.0%

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

   3. Taylor expanded in b around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. +-commutative 71.0%

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

      3. associate-+l+ 71.0%

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

      4. associate-/l* 80.0%

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

      5. +-commutative 80.0%

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

      6. associate-+r+ 80.0%

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

      7. +-commutative 80.0%

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

      8. associate-+l+ 80.0%

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

      9. sub-neg 80.0%

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

      10. div-sub 80.0%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around inf 74.9%

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

   7. Taylor expanded in x around 0 68.1%

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

      1. +-commutative 68.1%

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

   9. Simplified 68.1%

      \[\leadsto a \cdot 1 + \color{blue}{\frac{y \cdot \left(z - b\right)}{y + t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7400000000000 \lor \neg \left(x \leq 2.65 \cdot 10^{+157}\right):\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+125}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+216}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.55e+125) z (if (<= x 1.45e+216) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.55e+125) {
		tmp = z;
	} else if (x <= 1.45e+216) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.55d+125)) then
        tmp = z
    else if (x <= 1.45d+216) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.55e+125) {
		tmp = z;
	} else if (x <= 1.45e+216) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.55e+125:
		tmp = z
	elif x <= 1.45e+216:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.55e+125)
		tmp = z;
	elseif (x <= 1.45e+216)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.55e+125)
		tmp = z;
	elseif (x <= 1.45e+216)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.55e+125], z, If[LessEqual[x, 1.45e+216], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5499999999999999e125 or 1.45e216 < x

   1. Initial program 46.3%

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

   3. Taylor expanded in x around inf 62.6%

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

   if -2.5499999999999999e125 < x < 1.45e216

   1. Initial program 68.3%

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

   3. Taylor expanded in y around inf 58.1%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+125}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+216}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 43.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{-36}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+167}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.55e-36) z (if (<= x 5.5e+167) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.55e-36) {
		tmp = z;
	} else if (x <= 5.5e+167) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.55d-36)) then
        tmp = z
    else if (x <= 5.5d+167) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.55e-36) {
		tmp = z;
	} else if (x <= 5.5e+167) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.55e-36:
		tmp = z
	elif x <= 5.5e+167:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.55e-36)
		tmp = z;
	elseif (x <= 5.5e+167)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.55e-36)
		tmp = z;
	elseif (x <= 5.5e+167)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.55e-36], z, If[LessEqual[x, 5.5e+167], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -2.54999999999999987e-36 or 5.5000000000000005e167 < x

   1. Initial program 53.0%

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

   3. Taylor expanded in x around inf 56.0%

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

   if -2.54999999999999987e-36 < x < 5.5000000000000005e167

   1. Initial program 69.5%

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

   3. Taylor expanded in t around inf 43.8%

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

Alternative 17: 32.3% 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 63.0%

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

3. Taylor expanded in t around inf 32.3%

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

Developer target: 81.8% 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 2024085 
(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)))