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

Percentage Accurate: 60.5% → 92.9%

Time: 17.3s

Alternatives: 20

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.5% 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: 92.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := x + \left(t + y\right)\\ \mathbf{if}\;z \leq -1.76 \cdot 10^{-71} \lor \neg \left(z \leq 6.4 \cdot 10^{-41}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\left(\frac{y}{t\_1} + \frac{a}{z} \cdot \frac{t + y}{t\_1}\right) - \frac{b \cdot \frac{y}{z}}{t\_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + b \cdot \left(\left(x + y\right) \cdot \frac{\frac{z}{b}}{t\_2} - \frac{y}{t\_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (+ x (+ t y))))
   (if (or (<= z -1.76e-71) (not (<= z 6.4e-41)))
     (*
      z
      (+
       (/ x t_1)
       (- (+ (/ y t_1) (* (/ a z) (/ (+ t y) t_1))) (/ (* b (/ y z)) t_1))))
     (+
      (* a (/ (+ t y) (+ y (+ x t))))
      (* b (- (* (+ x y) (/ (/ z b) t_2)) (/ y 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 = x + (t + y);
	double tmp;
	if ((z <= -1.76e-71) || !(z <= 6.4e-41)) {
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)));
	} else {
		tmp = (a * ((t + y) / (y + (x + t)))) + (b * (((x + y) * ((z / b) / t_2)) - (y / 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 = x + (t + y)
    if ((z <= (-1.76d-71)) .or. (.not. (z <= 6.4d-41))) 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) / (y + (x + t)))) + (b * (((x + y) * ((z / b) / t_2)) - (y / 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 = x + (t + y);
	double tmp;
	if ((z <= -1.76e-71) || !(z <= 6.4e-41)) {
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)));
	} else {
		tmp = (a * ((t + y) / (y + (x + t)))) + (b * (((x + y) * ((z / b) / t_2)) - (y / t_2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = x + (t + y)
	tmp = 0
	if (z <= -1.76e-71) or not (z <= 6.4e-41):
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)))
	else:
		tmp = (a * ((t + y) / (y + (x + t)))) + (b * (((x + y) * ((z / b) / t_2)) - (y / t_2)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(x + Float64(t + y))
	tmp = 0.0
	if ((z <= -1.76e-71) || !(z <= 6.4e-41))
		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) / Float64(y + Float64(x + t)))) + Float64(b * Float64(Float64(Float64(x + y) * Float64(Float64(z / b) / t_2)) - Float64(y / t_2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = x + (t + y);
	tmp = 0.0;
	if ((z <= -1.76e-71) || ~((z <= 6.4e-41)))
		tmp = z * ((x / t_1) + (((y / t_1) + ((a / z) * ((t + y) / t_1))) - ((b * (y / z)) / t_1)));
	else
		tmp = (a * ((t + y) / (y + (x + t)))) + (b * (((x + y) * ((z / b) / t_2)) - (y / 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[(x + N[(t + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.76e-71], N[Not[LessEqual[z, 6.4e-41]], $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] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(N[(x + y), $MachinePrecision] * N[(N[(z / b), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.76000000000000002e-71 or 6.40000000000000024e-41 < z

   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 z around inf 69.1%

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

      1. associate--l+ 69.1%

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

      2. +-commutative 69.1%

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

      3. +-commutative 69.1%

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

      4. times-frac 87.5%

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

      5. +-commutative 87.5%

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

      6. associate-/r* 88.4%

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

      7. associate-/l* 95.2%

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

      8. +-commutative 95.2%

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

   5. Simplified 95.2%

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

   if -1.76000000000000002e-71 < z < 6.40000000000000024e-41

   1. Initial program 68.2%

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

   3. Taylor expanded in b around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. +-commutative 68.2%

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

      3. associate-+l+ 68.2%

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

      4. associate-/l* 89.8%

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

      5. +-commutative 89.8%

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

      6. associate-+r+ 89.8%

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

      7. +-commutative 89.8%

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

      8. associate-+l+ 89.8%

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

      9. sub-neg 89.8%

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

      10. div-sub 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in b around inf 94.7%

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

      1. +-commutative 94.7%

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

      2. mul-1-neg 94.7%

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

      3. unsub-neg 94.7%

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

   8. Simplified 91.9%

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

   9. Taylor expanded in b around inf 94.7%

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

       1. +-commutative 94.7%

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

       2. mul-1-neg 94.7%

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

       3. sub-neg 94.7%

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

       4. +-commutative 94.7%

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

       5. associate-+r+ 94.7%

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

       6. associate-*r/ 91.9%

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

       7. +-commutative 91.9%

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

       8. associate-+r+ 91.9%

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

       9. associate-*r/ 91.9%

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

       10. distribute-rgt-in 91.9%

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

   11. Simplified 92.8%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.76 \cdot 10^{-71} \lor \neg \left(z \leq 6.4 \cdot 10^{-41}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t + \left(x + y\right)} + \left(\left(\frac{y}{t + \left(x + y\right)} + \frac{a}{z} \cdot \frac{t + y}{t + \left(x + y\right)}\right) - \frac{b \cdot \frac{y}{z}}{t + \left(x + y\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + b \cdot \left(\left(x + y\right) \cdot \frac{\frac{z}{b}}{x + \left(t + y\right)} - \frac{y}{x + \left(t + y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{t\_2}\\ t_4 := a \cdot \frac{t + y}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty \lor \neg \left(t\_3 \leq 4 \cdot 10^{+245}\right):\\ \;\;\;\;t\_4 + b \cdot \left(\left(x + y\right) \cdot \frac{\frac{z}{b}}{t\_1} - \frac{y}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4 + \frac{z \cdot x + y \cdot \left(z - b\right)}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ t y)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* a (+ t y)) (* z (+ x y))) (* y b)) t_2))
        (t_4 (* a (/ (+ t y) t_2))))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 4e+245)))
     (+ t_4 (* b (- (* (+ x y) (/ (/ z b) t_1)) (/ y t_1))))
     (+ t_4 (/ (+ (* 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 = x + (t + y);
	double t_2 = y + (x + t);
	double t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2;
	double t_4 = a * ((t + y) / t_2);
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 4e+245)) {
		tmp = t_4 + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)));
	} else {
		tmp = t_4 + (((z * x) + (y * (z - b))) / t_2);
	}
	return tmp;
}

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 = y + (x + t);
	double t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2;
	double t_4 = a * ((t + y) / t_2);
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 4e+245)) {
		tmp = t_4 + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)));
	} else {
		tmp = t_4 + (((z * x) + (y * (z - b))) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t + y)
	t_2 = y + (x + t)
	t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2
	t_4 = a * ((t + y) / t_2)
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 4e+245):
		tmp = t_4 + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)))
	else:
		tmp = t_4 + (((z * x) + (y * (z - b))) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(a * Float64(t + y)) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_2)
	t_4 = Float64(a * Float64(Float64(t + y) / t_2))
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 4e+245))
		tmp = Float64(t_4 + Float64(b * Float64(Float64(Float64(x + y) * Float64(Float64(z / b) / t_1)) - Float64(y / t_1))));
	else
		tmp = Float64(t_4 + 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 = x + (t + y);
	t_2 = y + (x + t);
	t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2;
	t_4 = a * ((t + y) / t_2);
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 4e+245)))
		tmp = t_4 + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)));
	else
		tmp = t_4 + (((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[(x + N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 4e+245]], $MachinePrecision]], N[(t$95$4 + N[(b * N[(N[(N[(x + y), $MachinePrecision] * N[(N[(z / b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$4 + 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 (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.00000000000000018e245 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.2%

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

   3. Taylor expanded in b around 0 6.2%

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

      1. mul-1-neg 6.2%

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

      2. +-commutative 6.2%

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

      3. associate-+l+ 6.2%

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

      4. associate-/l* 38.0%

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

      5. +-commutative 38.0%

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

      6. associate-+r+ 38.0%

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

      7. +-commutative 38.0%

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

      8. associate-+l+ 38.0%

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

      9. sub-neg 38.0%

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

      10. div-sub 38.0%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in b around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. mul-1-neg 49.7%

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

      3. unsub-neg 49.7%

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

   8. Simplified 68.9%

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

   9. Taylor expanded in b around inf 49.7%

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

       1. +-commutative 49.7%

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

       2. mul-1-neg 49.7%

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

       3. sub-neg 49.7%

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

       4. +-commutative 49.7%

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

       5. associate-+r+ 49.7%

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

       6. associate-*r/ 56.3%

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

       7. +-commutative 56.3%

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

       8. associate-+r+ 56.3%

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

       9. associate-*r/ 68.9%

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

       10. distribute-rgt-in 69.4%

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

   11. Simplified 81.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000018e245

   1. Initial program 99.7%

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

   3. Taylor expanded in b around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-/l* 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-+r+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l+ 99.7%

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

      9. sub-neg 99.7%

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

      10. div-sub 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+245}\right):\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + b \cdot \left(\left(x + y\right) \cdot \frac{\frac{z}{b}}{x + \left(t + y\right)} - \frac{y}{x + \left(t + y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{t\_2}\\ t_4 := a \cdot \frac{t + y}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;a + b \cdot \left(\left(x + y\right) \cdot \frac{\frac{z}{b}}{t\_1} - \frac{y}{t\_1}\right)\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+235}:\\ \;\;\;\;t\_4 + \frac{z \cdot x + y \cdot \left(z - b\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;z + t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ t y)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* a (+ t y)) (* z (+ x y))) (* y b)) t_2))
        (t_4 (* a (/ (+ t y) t_2))))
   (if (<= t_3 (- INFINITY))
     (+ a (* b (- (* (+ x y) (/ (/ z b) t_1)) (/ y t_1))))
     (if (<= t_3 4e+235)
       (+ t_4 (/ (+ (* z x) (* y (- z b))) t_2))
       (+ z 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 = y + (x + t);
	double t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2;
	double t_4 = a * ((t + y) / t_2);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = a + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)));
	} else if (t_3 <= 4e+235) {
		tmp = t_4 + (((z * x) + (y * (z - b))) / t_2);
	} else {
		tmp = z + t_4;
	}
	return tmp;
}

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 = y + (x + t);
	double t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2;
	double t_4 = a * ((t + y) / t_2);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = a + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)));
	} else if (t_3 <= 4e+235) {
		tmp = t_4 + (((z * x) + (y * (z - b))) / t_2);
	} else {
		tmp = z + t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t + y)
	t_2 = y + (x + t)
	t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2
	t_4 = a * ((t + y) / t_2)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = a + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)))
	elif t_3 <= 4e+235:
		tmp = t_4 + (((z * x) + (y * (z - b))) / t_2)
	else:
		tmp = z + t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(a * Float64(t + y)) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_2)
	t_4 = Float64(a * Float64(Float64(t + y) / t_2))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(a + Float64(b * Float64(Float64(Float64(x + y) * Float64(Float64(z / b) / t_1)) - Float64(y / t_1))));
	elseif (t_3 <= 4e+235)
		tmp = Float64(t_4 + Float64(Float64(Float64(z * x) + Float64(y * Float64(z - b))) / t_2));
	else
		tmp = Float64(z + t_4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t + y);
	t_2 = y + (x + t);
	t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2;
	t_4 = a * ((t + y) / t_2);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = a + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)));
	elseif (t_3 <= 4e+235)
		tmp = t_4 + (((z * x) + (y * (z - b))) / t_2);
	else
		tmp = z + t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(a + N[(b * N[(N[(N[(x + y), $MachinePrecision] * N[(N[(z / b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e+235], N[(t$95$4 + N[(N[(N[(z * x), $MachinePrecision] + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], N[(z + t$95$4), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.3%

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

   3. Taylor expanded in b around 0 6.3%

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

      1. mul-1-neg 6.3%

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

      2. +-commutative 6.3%

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

      3. associate-+l+ 6.3%

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

      4. associate-/l* 41.6%

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

      5. +-commutative 41.6%

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

      6. associate-+r+ 41.6%

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

      7. +-commutative 41.6%

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

      8. associate-+l+ 41.6%

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

      9. sub-neg 41.6%

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

      10. div-sub 41.6%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in b around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

   8. Simplified 80.1%

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

   9. Taylor expanded in b around inf 56.2%

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

       1. +-commutative 56.2%

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

       2. mul-1-neg 56.2%

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

       3. sub-neg 56.2%

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

       4. +-commutative 56.2%

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

       5. associate-+r+ 56.2%

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

       6. associate-*r/ 66.0%

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

       7. +-commutative 66.0%

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

       8. associate-+r+ 66.0%

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

       9. associate-*r/ 80.1%

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

       10. distribute-rgt-in 80.1%

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

   11. Simplified 86.3%

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

   12. Taylor expanded in t around inf 80.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000002e235

   1. Initial program 99.7%

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

   3. Taylor expanded in b around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-/l* 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-+r+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l+ 99.7%

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

      9. sub-neg 99.7%

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

      10. div-sub 99.7%

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

   5. Simplified 99.7%

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

   if 4.0000000000000002e235 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.6%

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

   3. Taylor expanded in b around 0 7.6%

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

      1. mul-1-neg 7.6%

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

      2. +-commutative 7.6%

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

      3. associate-+l+ 7.6%

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

      4. associate-/l* 36.3%

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

      5. +-commutative 36.3%

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

      6. associate-+r+ 36.3%

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

      7. +-commutative 36.3%

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

      8. associate-+l+ 36.3%

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

      9. sub-neg 36.3%

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

      10. div-sub 36.3%

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

   5. Simplified 36.8%

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

   6. Taylor expanded in x around inf 74.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;a + b \cdot \left(\left(x + y\right) \cdot \frac{\frac{z}{b}}{x + \left(t + y\right)} - \frac{y}{x + \left(t + y\right)}\right)\\ \mathbf{elif}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+235}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+291}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+235}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t + y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* a (+ t y)) (* z (+ x y))) (* y b)) t_1)))
   (if (<= t_2 -5e+291)
     (- (+ z a) b)
     (if (<= t_2 4e+235) t_2 (+ z (* a (/ (+ t y) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -5e+291) {
		tmp = (z + a) - b;
	} else if (t_2 <= 4e+235) {
		tmp = t_2;
	} else {
		tmp = z + (a * ((t + y) / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_1
    if (t_2 <= (-5d+291)) then
        tmp = (z + a) - b
    else if (t_2 <= 4d+235) then
        tmp = t_2
    else
        tmp = z + (a * ((t + y) / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -5e+291) {
		tmp = (z + a) - b;
	} else if (t_2 <= 4e+235) {
		tmp = t_2;
	} else {
		tmp = z + (a * ((t + y) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_1
	tmp = 0
	if t_2 <= -5e+291:
		tmp = (z + a) - b
	elif t_2 <= 4e+235:
		tmp = t_2
	else:
		tmp = z + (a * ((t + y) / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(a * Float64(t + y)) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= -5e+291)
		tmp = Float64(Float64(z + a) - b);
	elseif (t_2 <= 4e+235)
		tmp = t_2;
	else
		tmp = Float64(z + Float64(a * Float64(Float64(t + y) / t_1)));
	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)) + (z * (x + y))) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_2 <= -5e+291)
		tmp = (z + a) - b;
	elseif (t_2 <= 4e+235)
		tmp = t_2;
	else
		tmp = z + (a * ((t + y) / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+291], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$2, 4e+235], t$95$2, N[(z + N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.0000000000000001e291

   1. Initial program 10.0%

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

   3. Taylor expanded in y around inf 78.4%

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

   if -5.0000000000000001e291 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000002e235

   1. Initial program 99.7%

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

   if 4.0000000000000002e235 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.6%

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

   3. Taylor expanded in b around 0 7.6%

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

      1. mul-1-neg 7.6%

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

      2. +-commutative 7.6%

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

      3. associate-+l+ 7.6%

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

      4. associate-/l* 36.3%

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

      5. +-commutative 36.3%

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

      6. associate-+r+ 36.3%

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

      7. +-commutative 36.3%

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

      8. associate-+l+ 36.3%

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

      9. sub-neg 36.3%

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

      10. div-sub 36.3%

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

   5. Simplified 36.8%

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

   6. Taylor expanded in x around inf 74.3%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+291}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+235}:\\ \;\;\;\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;a + b \cdot \left(\left(x + y\right) \cdot \frac{\frac{z}{b}}{t\_1} - \frac{y}{t\_1}\right)\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+235}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t + y}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ t y)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* a (+ t y)) (* z (+ x y))) (* y b)) t_2)))
   (if (<= t_3 (- INFINITY))
     (+ a (* b (- (* (+ x y) (/ (/ z b) t_1)) (/ y t_1))))
     (if (<= t_3 4e+235) t_3 (+ z (* a (/ (+ t y) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t + y);
	double t_2 = y + (x + t);
	double t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = a + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)));
	} else if (t_3 <= 4e+235) {
		tmp = t_3;
	} else {
		tmp = z + (a * ((t + y) / t_2));
	}
	return tmp;
}

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 = y + (x + t);
	double t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = a + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)));
	} else if (t_3 <= 4e+235) {
		tmp = t_3;
	} else {
		tmp = z + (a * ((t + y) / t_2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t + y)
	t_2 = y + (x + t)
	t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = a + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)))
	elif t_3 <= 4e+235:
		tmp = t_3
	else:
		tmp = z + (a * ((t + y) / t_2))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(a * Float64(t + y)) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(a + Float64(b * Float64(Float64(Float64(x + y) * Float64(Float64(z / b) / t_1)) - Float64(y / t_1))));
	elseif (t_3 <= 4e+235)
		tmp = t_3;
	else
		tmp = Float64(z + Float64(a * Float64(Float64(t + y) / t_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t + y);
	t_2 = y + (x + t);
	t_3 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = a + (b * (((x + y) * ((z / b) / t_1)) - (y / t_1)));
	elseif (t_3 <= 4e+235)
		tmp = t_3;
	else
		tmp = z + (a * ((t + y) / t_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(a + N[(b * N[(N[(N[(x + y), $MachinePrecision] * N[(N[(z / b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e+235], t$95$3, N[(z + N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.3%

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

   3. Taylor expanded in b around 0 6.3%

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

      1. mul-1-neg 6.3%

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

      2. +-commutative 6.3%

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

      3. associate-+l+ 6.3%

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

      4. associate-/l* 41.6%

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

      5. +-commutative 41.6%

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

      6. associate-+r+ 41.6%

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

      7. +-commutative 41.6%

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

      8. associate-+l+ 41.6%

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

      9. sub-neg 41.6%

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

      10. div-sub 41.6%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in b around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

   8. Simplified 80.1%

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

   9. Taylor expanded in b around inf 56.2%

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

       1. +-commutative 56.2%

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

       2. mul-1-neg 56.2%

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

       3. sub-neg 56.2%

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

       4. +-commutative 56.2%

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

       5. associate-+r+ 56.2%

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

       6. associate-*r/ 66.0%

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

       7. +-commutative 66.0%

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

       8. associate-+r+ 66.0%

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

       9. associate-*r/ 80.1%

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

       10. distribute-rgt-in 80.1%

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

   11. Simplified 86.3%

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

   12. Taylor expanded in t around inf 80.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.0000000000000002e235

   1. Initial program 99.7%

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

   if 4.0000000000000002e235 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.6%

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

   3. Taylor expanded in b around 0 7.6%

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

      1. mul-1-neg 7.6%

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

      2. +-commutative 7.6%

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

      3. associate-+l+ 7.6%

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

      4. associate-/l* 36.3%

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

      5. +-commutative 36.3%

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

      6. associate-+r+ 36.3%

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

      7. +-commutative 36.3%

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

      8. associate-+l+ 36.3%

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

      9. sub-neg 36.3%

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

      10. div-sub 36.3%

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

   5. Simplified 36.8%

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

   6. Taylor expanded in x around inf 74.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;a + b \cdot \left(\left(x + y\right) \cdot \frac{\frac{z}{b}}{x + \left(t + y\right)} - \frac{y}{x + \left(t + y\right)}\right)\\ \mathbf{elif}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+235}:\\ \;\;\;\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z \cdot \frac{x + y}{y + \left(x + t\right)}\\ t_3 := a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-283}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-192}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (* z (/ (+ x y) (+ y (+ x t)))))
        (t_3 (+ a (* y (- (/ z t) (/ b t))))))
   (if (<= x -7.8e+74)
     t_2
     (if (<= x -3.6e-146)
       t_1
       (if (<= x -5e-283)
         t_3
         (if (<= x 2.9e-262)
           t_1
           (if (<= x 3.25e-192) t_3 (if (<= x 9e+27) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z * ((x + y) / (y + (x + t)));
	double t_3 = a + (y * ((z / t) - (b / t)));
	double tmp;
	if (x <= -7.8e+74) {
		tmp = t_2;
	} else if (x <= -3.6e-146) {
		tmp = t_1;
	} else if (x <= -5e-283) {
		tmp = t_3;
	} else if (x <= 2.9e-262) {
		tmp = t_1;
	} else if (x <= 3.25e-192) {
		tmp = t_3;
	} else if (x <= 9e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z * ((x + y) / (y + (x + t)))
    t_3 = a + (y * ((z / t) - (b / t)))
    if (x <= (-7.8d+74)) then
        tmp = t_2
    else if (x <= (-3.6d-146)) then
        tmp = t_1
    else if (x <= (-5d-283)) then
        tmp = t_3
    else if (x <= 2.9d-262) then
        tmp = t_1
    else if (x <= 3.25d-192) then
        tmp = t_3
    else if (x <= 9d+27) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z * ((x + y) / (y + (x + t)));
	double t_3 = a + (y * ((z / t) - (b / t)));
	double tmp;
	if (x <= -7.8e+74) {
		tmp = t_2;
	} else if (x <= -3.6e-146) {
		tmp = t_1;
	} else if (x <= -5e-283) {
		tmp = t_3;
	} else if (x <= 2.9e-262) {
		tmp = t_1;
	} else if (x <= 3.25e-192) {
		tmp = t_3;
	} else if (x <= 9e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z * ((x + y) / (y + (x + t)))
	t_3 = a + (y * ((z / t) - (b / t)))
	tmp = 0
	if x <= -7.8e+74:
		tmp = t_2
	elif x <= -3.6e-146:
		tmp = t_1
	elif x <= -5e-283:
		tmp = t_3
	elif x <= 2.9e-262:
		tmp = t_1
	elif x <= 3.25e-192:
		tmp = t_3
	elif x <= 9e+27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))))
	t_3 = Float64(a + Float64(y * Float64(Float64(z / t) - Float64(b / t))))
	tmp = 0.0
	if (x <= -7.8e+74)
		tmp = t_2;
	elseif (x <= -3.6e-146)
		tmp = t_1;
	elseif (x <= -5e-283)
		tmp = t_3;
	elseif (x <= 2.9e-262)
		tmp = t_1;
	elseif (x <= 3.25e-192)
		tmp = t_3;
	elseif (x <= 9e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = z * ((x + y) / (y + (x + t)));
	t_3 = a + (y * ((z / t) - (b / t)));
	tmp = 0.0;
	if (x <= -7.8e+74)
		tmp = t_2;
	elseif (x <= -3.6e-146)
		tmp = t_1;
	elseif (x <= -5e-283)
		tmp = t_3;
	elseif (x <= 2.9e-262)
		tmp = t_1;
	elseif (x <= 3.25e-192)
		tmp = t_3;
	elseif (x <= 9e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(y * N[(N[(z / t), $MachinePrecision] - N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e+74], t$95$2, If[LessEqual[x, -3.6e-146], t$95$1, If[LessEqual[x, -5e-283], t$95$3, If[LessEqual[x, 2.9e-262], t$95$1, If[LessEqual[x, 3.25e-192], t$95$3, If[LessEqual[x, 9e+27], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.80000000000000015e74 or 8.9999999999999998e27 < x

   1. Initial program 50.0%

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

   3. Taylor expanded in z around inf 29.8%

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

      1. associate-/l* 60.0%

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

      2. +-commutative 60.0%

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

      3. +-commutative 60.0%

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

      4. associate-+r+ 60.0%

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

      5. +-commutative 60.0%

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

      6. associate-+l+ 60.0%

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

   5. Simplified 60.0%

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

   if -7.80000000000000015e74 < x < -3.59999999999999978e-146 or -5.0000000000000001e-283 < x < 2.89999999999999996e-262 or 3.24999999999999983e-192 < x < 8.9999999999999998e27

   1. Initial program 63.3%

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

   3. Taylor expanded in y around inf 74.7%

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

   if -3.59999999999999978e-146 < x < -5.0000000000000001e-283 or 2.89999999999999996e-262 < x < 3.24999999999999983e-192

   1. Initial program 69.9%

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

   3. Taylor expanded in x around 0 65.9%

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

   4. Taylor expanded in y around 0 72.9%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-146}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-283}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-262}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-192}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+27}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a + \frac{z \cdot x + y \cdot \left(z - b\right)}{t\_1}\\ t_3 := a \cdot \frac{t + y}{t\_1} + x \cdot \frac{z}{x + t}\\ \mathbf{if}\;x \leq -145000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-285}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-273}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-35}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (+ (* a (/ (+ t y) t_1)) (* x (/ z (+ x t))))))
   (if (<= x -145000000.0)
     t_3
     (if (<= x -1.25e-285)
       t_2
       (if (<= x 7e-273) (- (+ z a) b) (if (<= x 4.6e-35) 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 = (a * ((t + y) / t_1)) + (x * (z / (x + t)));
	double tmp;
	if (x <= -145000000.0) {
		tmp = t_3;
	} else if (x <= -1.25e-285) {
		tmp = t_2;
	} else if (x <= 7e-273) {
		tmp = (z + a) - b;
	} else if (x <= 4.6e-35) {
		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 = (a * ((t + y) / t_1)) + (x * (z / (x + t)))
    if (x <= (-145000000.0d0)) then
        tmp = t_3
    else if (x <= (-1.25d-285)) then
        tmp = t_2
    else if (x <= 7d-273) then
        tmp = (z + a) - b
    else if (x <= 4.6d-35) 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 = (a * ((t + y) / t_1)) + (x * (z / (x + t)));
	double tmp;
	if (x <= -145000000.0) {
		tmp = t_3;
	} else if (x <= -1.25e-285) {
		tmp = t_2;
	} else if (x <= 7e-273) {
		tmp = (z + a) - b;
	} else if (x <= 4.6e-35) {
		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 = (a * ((t + y) / t_1)) + (x * (z / (x + t)))
	tmp = 0
	if x <= -145000000.0:
		tmp = t_3
	elif x <= -1.25e-285:
		tmp = t_2
	elif x <= 7e-273:
		tmp = (z + a) - b
	elif x <= 4.6e-35:
		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(Float64(a * Float64(Float64(t + y) / t_1)) + Float64(x * Float64(z / Float64(x + t))))
	tmp = 0.0
	if (x <= -145000000.0)
		tmp = t_3;
	elseif (x <= -1.25e-285)
		tmp = t_2;
	elseif (x <= 7e-273)
		tmp = Float64(Float64(z + a) - b);
	elseif (x <= 4.6e-35)
		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 = (a * ((t + y) / t_1)) + (x * (z / (x + t)));
	tmp = 0.0;
	if (x <= -145000000.0)
		tmp = t_3;
	elseif (x <= -1.25e-285)
		tmp = t_2;
	elseif (x <= 7e-273)
		tmp = (z + a) - b;
	elseif (x <= 4.6e-35)
		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[(N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -145000000.0], t$95$3, If[LessEqual[x, -1.25e-285], t$95$2, If[LessEqual[x, 7e-273], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[x, 4.6e-35], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45e8 or 4.5999999999999998e-35 < x

   1. Initial program 51.9%

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

   3. Taylor expanded in b around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. +-commutative 52.0%

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

      3. associate-+l+ 52.0%

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

      4. associate-/l* 64.3%

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

      5. +-commutative 64.3%

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

      6. associate-+r+ 64.3%

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

      7. +-commutative 64.3%

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

      8. associate-+l+ 64.3%

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

      9. sub-neg 64.3%

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

      10. div-sub 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in y around 0 61.8%

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

      1. associate-/l* 78.4%

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

   8. Simplified 78.4%

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

   if -1.45e8 < x < -1.25000000000000005e-285 or 6.99999999999999984e-273 < x < 4.5999999999999998e-35

   1. Initial program 69.8%

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

   3. Taylor expanded in b around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. +-commutative 69.9%

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

      3. associate-+l+ 69.9%

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

      4. associate-/l* 84.9%

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

      5. +-commutative 84.9%

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

      6. associate-+r+ 84.9%

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

      7. +-commutative 84.9%

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

      8. associate-+l+ 84.9%

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

      9. sub-neg 84.9%

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

      10. div-sub 84.9%

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

   5. Simplified 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 t around inf 82.4%

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

   if -1.25000000000000005e-285 < x < 6.99999999999999984e-273

   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 y around inf 93.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -145000000:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-285}:\\ \;\;\;\;a + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-273}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-35}:\\ \;\;\;\;a + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)} + x \cdot \frac{z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ t_3 := z + a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{-130}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-283}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-191}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ a (* y (- (/ z t) (/ b t)))))
        (t_3 (+ z (* a (/ (+ t y) (+ y (+ x t)))))))
   (if (<= x -2.1e-130)
     t_3
     (if (<= x -4.5e-283)
       t_2
       (if (<= x 4.4e-262)
         t_1
         (if (<= x 1.6e-191) t_2 (if (<= x 2.5e-54) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (y * ((z / t) - (b / t)));
	double t_3 = z + (a * ((t + y) / (y + (x + t))));
	double tmp;
	if (x <= -2.1e-130) {
		tmp = t_3;
	} else if (x <= -4.5e-283) {
		tmp = t_2;
	} else if (x <= 4.4e-262) {
		tmp = t_1;
	} else if (x <= 1.6e-191) {
		tmp = t_2;
	} else if (x <= 2.5e-54) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a + (y * ((z / t) - (b / t)))
    t_3 = z + (a * ((t + y) / (y + (x + t))))
    if (x <= (-2.1d-130)) then
        tmp = t_3
    else if (x <= (-4.5d-283)) then
        tmp = t_2
    else if (x <= 4.4d-262) then
        tmp = t_1
    else if (x <= 1.6d-191) then
        tmp = t_2
    else if (x <= 2.5d-54) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + (y * ((z / t) - (b / t)));
	double t_3 = z + (a * ((t + y) / (y + (x + t))));
	double tmp;
	if (x <= -2.1e-130) {
		tmp = t_3;
	} else if (x <= -4.5e-283) {
		tmp = t_2;
	} else if (x <= 4.4e-262) {
		tmp = t_1;
	} else if (x <= 1.6e-191) {
		tmp = t_2;
	} else if (x <= 2.5e-54) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a + (y * ((z / t) - (b / t)))
	t_3 = z + (a * ((t + y) / (y + (x + t))))
	tmp = 0
	if x <= -2.1e-130:
		tmp = t_3
	elif x <= -4.5e-283:
		tmp = t_2
	elif x <= 4.4e-262:
		tmp = t_1
	elif x <= 1.6e-191:
		tmp = t_2
	elif x <= 2.5e-54:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a + Float64(y * Float64(Float64(z / t) - Float64(b / t))))
	t_3 = Float64(z + Float64(a * Float64(Float64(t + y) / Float64(y + Float64(x + t)))))
	tmp = 0.0
	if (x <= -2.1e-130)
		tmp = t_3;
	elseif (x <= -4.5e-283)
		tmp = t_2;
	elseif (x <= 4.4e-262)
		tmp = t_1;
	elseif (x <= 1.6e-191)
		tmp = t_2;
	elseif (x <= 2.5e-54)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a + (y * ((z / t) - (b / t)));
	t_3 = z + (a * ((t + y) / (y + (x + t))));
	tmp = 0.0;
	if (x <= -2.1e-130)
		tmp = t_3;
	elseif (x <= -4.5e-283)
		tmp = t_2;
	elseif (x <= 4.4e-262)
		tmp = t_1;
	elseif (x <= 1.6e-191)
		tmp = t_2;
	elseif (x <= 2.5e-54)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(y * N[(N[(z / t), $MachinePrecision] - N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z + N[(a * N[(N[(t + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e-130], t$95$3, If[LessEqual[x, -4.5e-283], t$95$2, If[LessEqual[x, 4.4e-262], t$95$1, If[LessEqual[x, 1.6e-191], t$95$2, If[LessEqual[x, 2.5e-54], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.10000000000000002e-130 or 2.50000000000000008e-54 < x

   1. Initial program 55.4%

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

   3. Taylor expanded in b around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. +-commutative 55.4%

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

      3. associate-+l+ 55.4%

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

      4. associate-/l* 68.1%

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

      5. +-commutative 68.1%

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

      6. associate-+r+ 68.1%

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

      7. +-commutative 68.1%

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

      8. associate-+l+ 68.1%

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

      9. sub-neg 68.1%

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

      10. div-sub 68.1%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in x around inf 72.4%

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

   if -2.10000000000000002e-130 < x < -4.4999999999999997e-283 or 4.39999999999999977e-262 < x < 1.6000000000000002e-191

   1. Initial program 67.9%

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

   3. Taylor expanded in x around 0 63.7%

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

   4. Taylor expanded in y around 0 72.0%

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

   if -4.4999999999999997e-283 < x < 4.39999999999999977e-262 or 1.6000000000000002e-191 < x < 2.50000000000000008e-54

   1. Initial program 64.0%

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

   3. Taylor expanded in y around inf 84.8%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-130}:\\ \;\;\;\;z + a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-283}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-262}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-191}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-54}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a + \frac{z \cdot x + y \cdot \left(z - b\right)}{t\_1}\\ t_3 := z + a \cdot \frac{t + y}{t\_1}\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+81}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-285}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-273}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (* a (/ (+ t y) t_1)))))
   (if (<= x -1.2e+81)
     t_3
     (if (<= x -1.25e-285)
       t_2
       (if (<= x 7e-273) (- (+ z a) b) (if (<= x 2.75e-33) 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 + (a * ((t + y) / t_1));
	double tmp;
	if (x <= -1.2e+81) {
		tmp = t_3;
	} else if (x <= -1.25e-285) {
		tmp = t_2;
	} else if (x <= 7e-273) {
		tmp = (z + a) - b;
	} else if (x <= 2.75e-33) {
		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 + (a * ((t + y) / t_1))
    if (x <= (-1.2d+81)) then
        tmp = t_3
    else if (x <= (-1.25d-285)) then
        tmp = t_2
    else if (x <= 7d-273) then
        tmp = (z + a) - b
    else if (x <= 2.75d-33) 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 + (a * ((t + y) / t_1));
	double tmp;
	if (x <= -1.2e+81) {
		tmp = t_3;
	} else if (x <= -1.25e-285) {
		tmp = t_2;
	} else if (x <= 7e-273) {
		tmp = (z + a) - b;
	} else if (x <= 2.75e-33) {
		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 + (a * ((t + y) / t_1))
	tmp = 0
	if x <= -1.2e+81:
		tmp = t_3
	elif x <= -1.25e-285:
		tmp = t_2
	elif x <= 7e-273:
		tmp = (z + a) - b
	elif x <= 2.75e-33:
		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(a * Float64(Float64(t + y) / t_1)))
	tmp = 0.0
	if (x <= -1.2e+81)
		tmp = t_3;
	elseif (x <= -1.25e-285)
		tmp = t_2;
	elseif (x <= 7e-273)
		tmp = Float64(Float64(z + a) - b);
	elseif (x <= 2.75e-33)
		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 + (a * ((t + y) / t_1));
	tmp = 0.0;
	if (x <= -1.2e+81)
		tmp = t_3;
	elseif (x <= -1.25e-285)
		tmp = t_2;
	elseif (x <= 7e-273)
		tmp = (z + a) - b;
	elseif (x <= 2.75e-33)
		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[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+81], t$95$3, If[LessEqual[x, -1.25e-285], t$95$2, If[LessEqual[x, 7e-273], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[x, 2.75e-33], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.19999999999999995e81 or 2.75e-33 < x

   1. Initial program 50.7%

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

   3. Taylor expanded in b around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. +-commutative 50.7%

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

      3. associate-+l+ 50.7%

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

      4. associate-/l* 61.6%

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

      5. +-commutative 61.6%

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

      6. associate-+r+ 61.6%

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

      7. +-commutative 61.6%

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

      8. associate-+l+ 61.6%

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

      9. sub-neg 61.6%

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

      10. div-sub 61.6%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in x around inf 76.3%

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

   if -1.19999999999999995e81 < x < -1.25000000000000005e-285 or 6.99999999999999984e-273 < x < 2.75e-33

   1. Initial program 68.5%

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

   3. Taylor expanded in b around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. +-commutative 68.6%

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

      3. associate-+l+ 68.6%

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

      4. associate-/l* 84.6%

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

      5. +-commutative 84.6%

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

      6. associate-+r+ 84.6%

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

      7. +-commutative 84.6%

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

      8. associate-+l+ 84.6%

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

      9. sub-neg 84.6%

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

      10. div-sub 84.6%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in t around inf 82.4%

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

   if -1.25000000000000005e-285 < x < 6.99999999999999984e-273

   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 y around inf 93.8%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+81}:\\ \;\;\;\;z + a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-285}:\\ \;\;\;\;a + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-273}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-33}:\\ \;\;\;\;a + \frac{z \cdot x + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq -23000000 \lor \neg \left(a \leq -4.4 \cdot 10^{-17} \lor \neg \left(a \leq -9 \cdot 10^{-116}\right) \land a \leq 1.12 \cdot 10^{-54}\right):\\ \;\;\;\;z + a \cdot \frac{t + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (or (<= a -23000000.0)
           (not
            (or (<= a -4.4e-17) (and (not (<= a -9e-116)) (<= a 1.12e-54)))))
     (+ z (* a (/ (+ t y) t_1)))
     (/ (- (* z (+ x y)) (* y 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 ((a <= -23000000.0) || !((a <= -4.4e-17) || (!(a <= -9e-116) && (a <= 1.12e-54)))) {
		tmp = z + (a * ((t + y) / t_1));
	} else {
		tmp = ((z * (x + y)) - (y * 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 ((a <= (-23000000.0d0)) .or. (.not. (a <= (-4.4d-17)) .or. (.not. (a <= (-9d-116))) .and. (a <= 1.12d-54))) then
        tmp = z + (a * ((t + y) / t_1))
    else
        tmp = ((z * (x + y)) - (y * 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 ((a <= -23000000.0) || !((a <= -4.4e-17) || (!(a <= -9e-116) && (a <= 1.12e-54)))) {
		tmp = z + (a * ((t + y) / t_1));
	} else {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if (a <= -23000000.0) or not ((a <= -4.4e-17) or (not (a <= -9e-116) and (a <= 1.12e-54))):
		tmp = z + (a * ((t + y) / t_1))
	else:
		tmp = ((z * (x + y)) - (y * 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 ((a <= -23000000.0) || !((a <= -4.4e-17) || (!(a <= -9e-116) && (a <= 1.12e-54))))
		tmp = Float64(z + Float64(a * Float64(Float64(t + y) / t_1)));
	else
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * 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 ((a <= -23000000.0) || ~(((a <= -4.4e-17) || (~((a <= -9e-116)) && (a <= 1.12e-54)))))
		tmp = z + (a * ((t + y) / t_1));
	else
		tmp = ((z * (x + y)) - (y * 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[a, -23000000.0], N[Not[Or[LessEqual[a, -4.4e-17], And[N[Not[LessEqual[a, -9e-116]], $MachinePrecision], LessEqual[a, 1.12e-54]]]], $MachinePrecision]], N[(z + N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.3e7 or -4.4e-17 < a < -9.00000000000000023e-116 or 1.11999999999999994e-54 < a

   1. Initial program 47.5%

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

   3. Taylor expanded in b around 0 47.5%

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

      1. mul-1-neg 47.5%

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

      2. +-commutative 47.5%

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

      3. associate-+l+ 47.5%

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

      4. associate-/l* 70.5%

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

      5. +-commutative 70.5%

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

      6. associate-+r+ 70.5%

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

      7. +-commutative 70.5%

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

      8. associate-+l+ 70.5%

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

      9. sub-neg 70.5%

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

      10. div-sub 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in x around inf 80.7%

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

   if -2.3e7 < a < -4.4e-17 or -9.00000000000000023e-116 < a < 1.11999999999999994e-54

   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 a around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. *-commutative 70.7%

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

   5. Simplified 70.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -23000000 \lor \neg \left(a \leq -4.4 \cdot 10^{-17} \lor \neg \left(a \leq -9 \cdot 10^{-116}\right) \land a \leq 1.12 \cdot 10^{-54}\right):\\ \;\;\;\;z + a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \frac{x}{x + \left(t + y\right)}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* a (/ (+ t y) (+ y (+ x t))))))
   (if (<= a -8e+71)
     t_2
     (if (<= a 2.85e-210)
       t_1
       (if (<= a 3.1e-86)
         (* z (/ x (+ x (+ t y))))
         (if (<= a 3.8e+80) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((t + y) / (y + (x + t)));
	double tmp;
	if (a <= -8e+71) {
		tmp = t_2;
	} else if (a <= 2.85e-210) {
		tmp = t_1;
	} else if (a <= 3.1e-86) {
		tmp = z * (x / (x + (t + y)));
	} else if (a <= 3.8e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a * ((t + y) / (y + (x + t)))
    if (a <= (-8d+71)) then
        tmp = t_2
    else if (a <= 2.85d-210) then
        tmp = t_1
    else if (a <= 3.1d-86) then
        tmp = z * (x / (x + (t + y)))
    else if (a <= 3.8d+80) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((t + y) / (y + (x + t)));
	double tmp;
	if (a <= -8e+71) {
		tmp = t_2;
	} else if (a <= 2.85e-210) {
		tmp = t_1;
	} else if (a <= 3.1e-86) {
		tmp = z * (x / (x + (t + y)));
	} else if (a <= 3.8e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a * ((t + y) / (y + (x + t)))
	tmp = 0
	if a <= -8e+71:
		tmp = t_2
	elif a <= 2.85e-210:
		tmp = t_1
	elif a <= 3.1e-86:
		tmp = z * (x / (x + (t + y)))
	elif a <= 3.8e+80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a * Float64(Float64(t + y) / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (a <= -8e+71)
		tmp = t_2;
	elseif (a <= 2.85e-210)
		tmp = t_1;
	elseif (a <= 3.1e-86)
		tmp = Float64(z * Float64(x / Float64(x + Float64(t + y))));
	elseif (a <= 3.8e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a * ((t + y) / (y + (x + t)));
	tmp = 0.0;
	if (a <= -8e+71)
		tmp = t_2;
	elseif (a <= 2.85e-210)
		tmp = t_1;
	elseif (a <= 3.1e-86)
		tmp = z * (x / (x + (t + y)));
	elseif (a <= 3.8e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(t + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+71], t$95$2, If[LessEqual[a, 2.85e-210], t$95$1, If[LessEqual[a, 3.1e-86], N[(z * N[(x / N[(x + N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+80], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.0000000000000003e71 or 3.79999999999999997e80 < a

   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 a around inf 34.1%

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

      1. associate-/l* 75.5%

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

      2. +-commutative 75.5%

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

      3. associate-+r+ 75.5%

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

      4. +-commutative 75.5%

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

      5. associate-+l+ 75.5%

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

   5. Simplified 75.5%

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

   if -8.0000000000000003e71 < a < 2.84999999999999985e-210 or 3.09999999999999989e-86 < a < 3.79999999999999997e80

   1. Initial program 70.4%

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

   3. Taylor expanded in y around inf 58.2%

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

   if 2.84999999999999985e-210 < a < 3.09999999999999989e-86

   1. Initial program 76.5%

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

   3. Taylor expanded in x around inf 50.0%

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

      1. *-commutative 50.0%

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

   5. Simplified 50.0%

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

      1. associate-/l* 57.6%

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

      2. associate-+l+ 57.6%

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

      3. +-commutative 57.6%

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

   7. Applied egg-rr 57.6%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-210}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \frac{x}{x + \left(t + y\right)}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-234}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* z (/ (+ x y) (+ y (+ x t))))))
   (if (<= x -1.65e+77)
     t_2
     (if (<= x -4e-151)
       t_1
       (if (<= x -3.8e-234)
         (- a (* b (/ y t)))
         (if (<= x 1.02e+27) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z * ((x + y) / (y + (x + t)));
	double tmp;
	if (x <= -1.65e+77) {
		tmp = t_2;
	} else if (x <= -4e-151) {
		tmp = t_1;
	} else if (x <= -3.8e-234) {
		tmp = a - (b * (y / t));
	} else if (x <= 1.02e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z * ((x + y) / (y + (x + t)))
    if (x <= (-1.65d+77)) then
        tmp = t_2
    else if (x <= (-4d-151)) then
        tmp = t_1
    else if (x <= (-3.8d-234)) then
        tmp = a - (b * (y / t))
    else if (x <= 1.02d+27) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z * ((x + y) / (y + (x + t)));
	double tmp;
	if (x <= -1.65e+77) {
		tmp = t_2;
	} else if (x <= -4e-151) {
		tmp = t_1;
	} else if (x <= -3.8e-234) {
		tmp = a - (b * (y / t));
	} else if (x <= 1.02e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z * ((x + y) / (y + (x + t)))
	tmp = 0
	if x <= -1.65e+77:
		tmp = t_2
	elif x <= -4e-151:
		tmp = t_1
	elif x <= -3.8e-234:
		tmp = a - (b * (y / t))
	elif x <= 1.02e+27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (x <= -1.65e+77)
		tmp = t_2;
	elseif (x <= -4e-151)
		tmp = t_1;
	elseif (x <= -3.8e-234)
		tmp = Float64(a - Float64(b * Float64(y / t)));
	elseif (x <= 1.02e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = z * ((x + y) / (y + (x + t)));
	tmp = 0.0;
	if (x <= -1.65e+77)
		tmp = t_2;
	elseif (x <= -4e-151)
		tmp = t_1;
	elseif (x <= -3.8e-234)
		tmp = a - (b * (y / t));
	elseif (x <= 1.02e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+77], t$95$2, If[LessEqual[x, -4e-151], t$95$1, If[LessEqual[x, -3.8e-234], N[(a - N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e+27], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6499999999999999e77 or 1.0199999999999999e27 < x

   1. Initial program 50.0%

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

   3. Taylor expanded in z around inf 29.8%

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

      1. associate-/l* 60.0%

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

      2. +-commutative 60.0%

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

      3. +-commutative 60.0%

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

      4. associate-+r+ 60.0%

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

      5. +-commutative 60.0%

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

      6. associate-+l+ 60.0%

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

   5. Simplified 60.0%

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

   if -1.6499999999999999e77 < x < -3.9999999999999998e-151 or -3.79999999999999984e-234 < x < 1.0199999999999999e27

   1. Initial program 65.2%

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

   3. Taylor expanded in y around inf 68.8%

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

   if -3.9999999999999998e-151 < x < -3.79999999999999984e-234

   1. Initial program 66.7%

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

   3. Taylor expanded in x around 0 60.1%

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

   4. Taylor expanded in z around 0 58.2%

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

      1. *-commutative 58.2%

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

      2. +-commutative 58.2%

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

      3. +-commutative 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in y around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. unsub-neg 77.9%

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

      3. associate-/l* 78.5%

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

   9. Simplified 78.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-234}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+27}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a - b \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (- a (* b (/ y t)))))
   (if (<= t -5e+129)
     t_2
     (if (<= t 1.5e+133)
       t_1
       (if (<= t 1.6e+154)
         (* z (/ (+ x y) t))
         (if (<= t 9.8e+163) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a - (b * (y / t));
	double tmp;
	if (t <= -5e+129) {
		tmp = t_2;
	} else if (t <= 1.5e+133) {
		tmp = t_1;
	} else if (t <= 1.6e+154) {
		tmp = z * ((x + y) / t);
	} else if (t <= 9.8e+163) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a - (b * (y / t))
    if (t <= (-5d+129)) then
        tmp = t_2
    else if (t <= 1.5d+133) then
        tmp = t_1
    else if (t <= 1.6d+154) then
        tmp = z * ((x + y) / t)
    else if (t <= 9.8d+163) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a - (b * (y / t));
	double tmp;
	if (t <= -5e+129) {
		tmp = t_2;
	} else if (t <= 1.5e+133) {
		tmp = t_1;
	} else if (t <= 1.6e+154) {
		tmp = z * ((x + y) / t);
	} else if (t <= 9.8e+163) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a - (b * (y / t))
	tmp = 0
	if t <= -5e+129:
		tmp = t_2
	elif t <= 1.5e+133:
		tmp = t_1
	elif t <= 1.6e+154:
		tmp = z * ((x + y) / t)
	elif t <= 9.8e+163:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a - Float64(b * Float64(y / t)))
	tmp = 0.0
	if (t <= -5e+129)
		tmp = t_2;
	elseif (t <= 1.5e+133)
		tmp = t_1;
	elseif (t <= 1.6e+154)
		tmp = Float64(z * Float64(Float64(x + y) / t));
	elseif (t <= 9.8e+163)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a - (b * (y / t));
	tmp = 0.0;
	if (t <= -5e+129)
		tmp = t_2;
	elseif (t <= 1.5e+133)
		tmp = t_1;
	elseif (t <= 1.6e+154)
		tmp = z * ((x + y) / t);
	elseif (t <= 9.8e+163)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+129], t$95$2, If[LessEqual[t, 1.5e+133], t$95$1, If[LessEqual[t, 1.6e+154], N[(z * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e+163], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000003e129 or 9.8e163 < t

   1. Initial program 46.1%

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

   3. Taylor expanded in x around 0 30.6%

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

   4. Taylor expanded in z around 0 28.6%

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

      1. *-commutative 28.6%

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

      2. +-commutative 28.6%

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

      3. +-commutative 28.6%

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

   6. Simplified 28.6%

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

   7. Taylor expanded in y around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

      3. associate-/l* 56.4%

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

   9. Simplified 56.4%

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

   if -5.0000000000000003e129 < t < 1.50000000000000003e133 or 1.6e154 < t < 9.8e163

   1. Initial program 61.8%

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

   3. Taylor expanded in y around inf 66.9%

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

   if 1.50000000000000003e133 < t < 1.6e154

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 63.8%

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

      1. +-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in t around inf 63.5%

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

      1. associate-/l* 63.3%

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

      2. +-commutative 63.3%

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

   8. Simplified 63.3%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+129}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \frac{x + y}{t}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+163}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a - b \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+154}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (- a (* b (/ y t)))))
   (if (<= t -3.7e+130)
     t_2
     (if (<= t 1.5e+133)
       t_1
       (if (<= t 1.6e+154) (/ (* z (+ x y)) t) (if (<= t 3e+162) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a - (b * (y / t));
	double tmp;
	if (t <= -3.7e+130) {
		tmp = t_2;
	} else if (t <= 1.5e+133) {
		tmp = t_1;
	} else if (t <= 1.6e+154) {
		tmp = (z * (x + y)) / t;
	} else if (t <= 3e+162) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a - (b * (y / t))
    if (t <= (-3.7d+130)) then
        tmp = t_2
    else if (t <= 1.5d+133) then
        tmp = t_1
    else if (t <= 1.6d+154) then
        tmp = (z * (x + y)) / t
    else if (t <= 3d+162) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a - (b * (y / t));
	double tmp;
	if (t <= -3.7e+130) {
		tmp = t_2;
	} else if (t <= 1.5e+133) {
		tmp = t_1;
	} else if (t <= 1.6e+154) {
		tmp = (z * (x + y)) / t;
	} else if (t <= 3e+162) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a - (b * (y / t))
	tmp = 0
	if t <= -3.7e+130:
		tmp = t_2
	elif t <= 1.5e+133:
		tmp = t_1
	elif t <= 1.6e+154:
		tmp = (z * (x + y)) / t
	elif t <= 3e+162:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a - Float64(b * Float64(y / t)))
	tmp = 0.0
	if (t <= -3.7e+130)
		tmp = t_2;
	elseif (t <= 1.5e+133)
		tmp = t_1;
	elseif (t <= 1.6e+154)
		tmp = Float64(Float64(z * Float64(x + y)) / t);
	elseif (t <= 3e+162)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a - (b * (y / t));
	tmp = 0.0;
	if (t <= -3.7e+130)
		tmp = t_2;
	elseif (t <= 1.5e+133)
		tmp = t_1;
	elseif (t <= 1.6e+154)
		tmp = (z * (x + y)) / t;
	elseif (t <= 3e+162)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+130], t$95$2, If[LessEqual[t, 1.5e+133], t$95$1, If[LessEqual[t, 1.6e+154], N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 3e+162], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7000000000000001e130 or 2.9999999999999998e162 < t

   1. Initial program 46.1%

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

   3. Taylor expanded in x around 0 30.6%

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

   4. Taylor expanded in z around 0 28.6%

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

      1. *-commutative 28.6%

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

      2. +-commutative 28.6%

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

      3. +-commutative 28.6%

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

   6. Simplified 28.6%

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

   7. Taylor expanded in y around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

      3. associate-/l* 56.4%

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

   9. Simplified 56.4%

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

   if -3.7000000000000001e130 < t < 1.50000000000000003e133 or 1.6e154 < t < 2.9999999999999998e162

   1. Initial program 61.8%

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

   3. Taylor expanded in y around inf 66.9%

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

   if 1.50000000000000003e133 < t < 1.6e154

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 63.8%

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

      1. +-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in t around inf 63.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+130}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+154}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+162}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a - \frac{y \cdot b}{t}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+154}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{t}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (- a (/ (* y b) t))))
   (if (<= t -1.7e+130)
     t_2
     (if (<= t 1.5e+133)
       t_1
       (if (<= t 1.6e+154)
         (/ (* z (+ x y)) t)
         (if (<= t 8.8e+163) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a - ((y * b) / t);
	double tmp;
	if (t <= -1.7e+130) {
		tmp = t_2;
	} else if (t <= 1.5e+133) {
		tmp = t_1;
	} else if (t <= 1.6e+154) {
		tmp = (z * (x + y)) / t;
	} else if (t <= 8.8e+163) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a - ((y * b) / t)
    if (t <= (-1.7d+130)) then
        tmp = t_2
    else if (t <= 1.5d+133) then
        tmp = t_1
    else if (t <= 1.6d+154) then
        tmp = (z * (x + y)) / t
    else if (t <= 8.8d+163) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a - ((y * b) / t);
	double tmp;
	if (t <= -1.7e+130) {
		tmp = t_2;
	} else if (t <= 1.5e+133) {
		tmp = t_1;
	} else if (t <= 1.6e+154) {
		tmp = (z * (x + y)) / t;
	} else if (t <= 8.8e+163) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a - ((y * b) / t)
	tmp = 0
	if t <= -1.7e+130:
		tmp = t_2
	elif t <= 1.5e+133:
		tmp = t_1
	elif t <= 1.6e+154:
		tmp = (z * (x + y)) / t
	elif t <= 8.8e+163:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a - Float64(Float64(y * b) / t))
	tmp = 0.0
	if (t <= -1.7e+130)
		tmp = t_2;
	elseif (t <= 1.5e+133)
		tmp = t_1;
	elseif (t <= 1.6e+154)
		tmp = Float64(Float64(z * Float64(x + y)) / t);
	elseif (t <= 8.8e+163)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a - ((y * b) / t);
	tmp = 0.0;
	if (t <= -1.7e+130)
		tmp = t_2;
	elseif (t <= 1.5e+133)
		tmp = t_1;
	elseif (t <= 1.6e+154)
		tmp = (z * (x + y)) / t;
	elseif (t <= 8.8e+163)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+130], t$95$2, If[LessEqual[t, 1.5e+133], t$95$1, If[LessEqual[t, 1.6e+154], N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 8.8e+163], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e130 or 8.79999999999999945e163 < t

   1. Initial program 46.1%

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

   3. Taylor expanded in x around 0 30.6%

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

   4. Taylor expanded in z around 0 28.6%

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

      1. *-commutative 28.6%

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

      2. +-commutative 28.6%

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

      3. +-commutative 28.6%

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

   6. Simplified 28.6%

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

   7. Taylor expanded in y around 0 58.1%

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

      1. associate-*r/ 58.1%

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

      2. neg-mul-1 58.1%

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

      3. distribute-rgt-neg-in 58.1%

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

   9. Simplified 58.1%

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

   if -1.7e130 < t < 1.50000000000000003e133 or 1.6e154 < t < 8.79999999999999945e163

   1. Initial program 61.8%

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

   3. Taylor expanded in y around inf 66.9%

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

   if 1.50000000000000003e133 < t < 1.6e154

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 63.8%

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

      1. +-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in t around inf 63.5%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+130}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+154}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{t}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+163}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+154}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-151} \lor \neg \left(x \leq -1.5 \cdot 10^{-233}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.5e+154)
   z
   (if (or (<= x -5.2e-151) (not (<= x -1.5e-233)))
     (- (+ z a) b)
     (* a (/ t (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.5e+154) {
		tmp = z;
	} else if ((x <= -5.2e-151) || !(x <= -1.5e-233)) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.5d+154)) then
        tmp = z
    else if ((x <= (-5.2d-151)) .or. (.not. (x <= (-1.5d-233)))) then
        tmp = (z + a) - b
    else
        tmp = a * (t / (x + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.5e+154) {
		tmp = z;
	} else if ((x <= -5.2e-151) || !(x <= -1.5e-233)) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.5e+154:
		tmp = z
	elif (x <= -5.2e-151) or not (x <= -1.5e-233):
		tmp = (z + a) - b
	else:
		tmp = a * (t / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.5e+154)
		tmp = z;
	elseif ((x <= -5.2e-151) || !(x <= -1.5e-233))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(t / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.5e+154)
		tmp = z;
	elseif ((x <= -5.2e-151) || ~((x <= -1.5e-233)))
		tmp = (z + a) - b;
	else
		tmp = a * (t / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.5e+154], z, If[Or[LessEqual[x, -5.2e-151], N[Not[LessEqual[x, -1.5e-233]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5000000000000002e154

   1. Initial program 42.7%

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

   3. Taylor expanded in x around inf 71.9%

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

   if -8.5000000000000002e154 < x < -5.2000000000000001e-151 or -1.49999999999999999e-233 < x

   1. Initial program 60.6%

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

   3. Taylor expanded in y around inf 60.1%

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

   if -5.2000000000000001e-151 < x < -1.49999999999999999e-233

   1. Initial program 66.7%

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

   3. Taylor expanded in y around 0 50.1%

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

   4. Taylor expanded in a around inf 50.4%

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

      1. associate-/l* 70.6%

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

      2. +-commutative 70.6%

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

   6. Simplified 70.6%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+154}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-151} \lor \neg \left(x \leq -1.5 \cdot 10^{-233}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+32}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.4e+32) a (if (<= a 9e+86) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.4e+32) {
		tmp = a;
	} else if (a <= 9e+86) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-6.4d+32)) then
        tmp = a
    else if (a <= 9d+86) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.4e+32) {
		tmp = a;
	} else if (a <= 9e+86) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.4e+32:
		tmp = a
	elif a <= 9e+86:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.4e+32)
		tmp = a;
	elseif (a <= 9e+86)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6.4e+32)
		tmp = a;
	elseif (a <= 9e+86)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.4e+32], a, If[LessEqual[a, 9e+86], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -6.3999999999999998e32 or 8.99999999999999986e86 < a

   1. Initial program 41.1%

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

   3. Taylor expanded in t around inf 57.8%

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

   if -6.3999999999999998e32 < a < 8.99999999999999986e86

   1. Initial program 71.7%

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

   3. Taylor expanded in x around inf 43.9%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+32}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 45.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{+17}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+84}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.22e+17) (- a b) (if (<= a 7.8e+84) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.22e+17) {
		tmp = a - b;
	} else if (a <= 7.8e+84) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.22d+17)) then
        tmp = a - b
    else if (a <= 7.8d+84) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.22e+17) {
		tmp = a - b;
	} else if (a <= 7.8e+84) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.22e+17:
		tmp = a - b
	elif a <= 7.8e+84:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.22e+17)
		tmp = Float64(a - b);
	elseif (a <= 7.8e+84)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.22e+17)
		tmp = a - b;
	elseif (a <= 7.8e+84)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.22e+17], N[(a - b), $MachinePrecision], If[LessEqual[a, 7.8e+84], z, a]]

Derivation

1. Split input into 3 regimes

2. if a < -1.22e17

   1. Initial program 42.6%

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

   3. Taylor expanded in x around 0 28.1%

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

   4. Taylor expanded in z around 0 23.0%

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

      1. *-commutative 23.0%

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

      2. +-commutative 23.0%

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

      3. +-commutative 23.0%

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

   6. Simplified 23.0%

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

   7. Taylor expanded in y around inf 54.8%

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

   if -1.22e17 < a < 7.80000000000000032e84

   1. Initial program 71.4%

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

   3. Taylor expanded in x around inf 44.6%

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

   if 7.80000000000000032e84 < a

   1. Initial program 44.7%

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

   3. Taylor expanded in t around inf 62.1%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{+17}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+84}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 58.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{+162}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= t 3.8e+162) (- (+ z a) b) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 3.8e+162) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 3.8d+162) then
        tmp = (z + a) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 3.8e+162) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 3.8e+162:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 3.8e+162)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 3.8e+162)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 3.8e+162], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if t < 3.80000000000000024e162

   1. Initial program 61.0%

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

   3. Taylor expanded in y around inf 60.1%

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

   if 3.80000000000000024e162 < t

   1. Initial program 46.1%

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

   3. Taylor expanded in t around inf 57.7%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{+162}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 33.0% 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 59.1%

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

3. Taylor expanded in t around inf 31.3%

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

4. Final simplification 31.3%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.9% 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 2024050 
(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)))