Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.0% → 83.3%

Time: 22.1s

Alternatives: 16

Speedup: 1.6×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Initial Program: 56.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{if}\;t\_1 \leq 10^{+289}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
           t)
          (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))
   (if (<= t_1 1e+289) t_1 (+ x (- (/ z y) (* a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	double tmp;
	if (t_1 <= 1e+289) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    if (t_1 <= 1d+289) then
        tmp = t_1
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	double tmp;
	if (t_1 <= 1e+289) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	tmp = 0
	if t_1 <= 1e+289:
		tmp = t_1
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i))
	tmp = 0.0
	if (t_1 <= 1e+289)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	tmp = 0.0;
	if (t_1 <= 1e+289)
		tmp = t_1;
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+289], t$95$1, N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 1.0000000000000001e289

   1. Initial program 95.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   if 1.0000000000000001e289 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 3.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.5%

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

      1. associate--l+ 65.5%

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

      2. associate-/l* 71.6%

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

   5. Simplified 71.6%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq 10^{+289}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+50} \lor \neg \left(y \leq 1.1 \cdot 10^{+47}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.95e+50) (not (<= y 1.1e+47)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/
    (+ (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)) t)
    (+ i (* y (+ c (* y (+ b (* y a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.95e+50) || !(y <= 1.1e+47)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.95d+50)) .or. (.not. (y <= 1.1d+47))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) + t) / (i + (y * (c + (y * (b + (y * 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 c, double i) {
	double tmp;
	if ((y <= -2.95e+50) || !(y <= 1.1e+47)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.95e+50) or not (y <= 1.1e+47):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.95e+50) || !(y <= 1.1e+47))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.95e+50) || ~((y <= 1.1e+47)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.95e+50], N[Not[LessEqual[y, 1.1e+47]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9499999999999999e50 or 1.1e47 < y

   1. Initial program 3.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.1%

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

      1. associate--l+ 66.1%

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

      2. associate-/l* 72.4%

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

   5. Simplified 72.4%

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

   if -2.9499999999999999e50 < y < 1.1e47

   1. Initial program 94.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 92.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot \left(b + a \cdot y\right)\right)} + i} \]
   4. Step-by-step derivation

      1. *-commutative 92.5%

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{y \cdot \left(c + y \cdot \left(b + \color{blue}{y \cdot a}\right)\right) + i} \]

   5. Simplified 92.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)} + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+50} \lor \neg \left(y \leq 1.1 \cdot 10^{+47}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -5.5e+73)
     t_1
     (if (<= y 1.15e+26)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (if (<= y 6.2e+104)
         (+ (* y (+ (/ z b) (/ (* x y) b))) (* 27464.7644705 (/ 1.0 b)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.5e+73) {
		tmp = t_1;
	} else if (y <= 1.15e+26) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-5.5d+73)) then
        tmp = t_1
    else if (y <= 1.15d+26) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= 6.2d+104) then
        tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705d0 * (1.0d0 / b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.5e+73) {
		tmp = t_1;
	} else if (y <= 1.15e+26) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -5.5e+73:
		tmp = t_1
	elif y <= 1.15e+26:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= 6.2e+104:
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -5.5e+73)
		tmp = t_1;
	elseif (y <= 1.15e+26)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= 6.2e+104)
		tmp = Float64(Float64(y * Float64(Float64(z / b) + Float64(Float64(x * y) / b))) + Float64(27464.7644705 * Float64(1.0 / b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -5.5e+73)
		tmp = t_1;
	elseif (y <= 1.15e+26)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= 6.2e+104)
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+73], t$95$1, If[LessEqual[y, 1.15e+26], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+104], N[(N[(y * N[(N[(z / b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(27464.7644705 * N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000003e73 or 6.20000000000000033e104 < y

   1. Initial program 1.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

   if -5.5000000000000003e73 < y < 1.15e26

   1. Initial program 96.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.8%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 1.15e26 < y < 6.20000000000000033e104

   1. Initial program 16.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 9.9%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{b \cdot {y}^{2}}} \]

   4. Taylor expanded in y around -inf 51.6%

      \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{z}{b} - 27464.7644705 \cdot \frac{1}{b \cdot y}}{y} + \frac{x}{b}\right)} \]

   5. Taylor expanded in y around 0 49.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+73}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-40}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{t\_1}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t\_1 + i}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* y (+ (* y (+ (* y (+ y a)) b)) c)))
        (t_2 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -5.5e+73)
     t_2
     (if (<= y -1.3e-40)
       (/ (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))) t_1)
       (if (<= y 1.1e+26)
         (/ (+ t (* y 230661.510616)) (+ t_1 i))
         (if (<= y 6.2e+104)
           (+ (* y (+ (/ z b) (/ (* x y) b))) (* 27464.7644705 (/ 1.0 b)))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * ((y * ((y * (y + a)) + b)) + c);
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.5e+73) {
		tmp = t_2;
	} else if (y <= -1.3e-40) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	} else if (y <= 1.1e+26) {
		tmp = (t + (y * 230661.510616)) / (t_1 + i);
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((y * ((y * (y + a)) + b)) + c)
    t_2 = x + ((z / y) - (a * (x / y)))
    if (y <= (-5.5d+73)) then
        tmp = t_2
    else if (y <= (-1.3d-40)) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / t_1
    else if (y <= 1.1d+26) then
        tmp = (t + (y * 230661.510616d0)) / (t_1 + i)
    else if (y <= 6.2d+104) then
        tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705d0 * (1.0d0 / b))
    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 c, double i) {
	double t_1 = y * ((y * ((y * (y + a)) + b)) + c);
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.5e+73) {
		tmp = t_2;
	} else if (y <= -1.3e-40) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	} else if (y <= 1.1e+26) {
		tmp = (t + (y * 230661.510616)) / (t_1 + i);
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = y * ((y * ((y * (y + a)) + b)) + c)
	t_2 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -5.5e+73:
		tmp = t_2
	elif y <= -1.3e-40:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1
	elif y <= 1.1e+26:
		tmp = (t + (y * 230661.510616)) / (t_1 + i)
	elif y <= 6.2e+104:
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -5.5e+73)
		tmp = t_2;
	elseif (y <= -1.3e-40)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / t_1);
	elseif (y <= 1.1e+26)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(t_1 + i));
	elseif (y <= 6.2e+104)
		tmp = Float64(Float64(y * Float64(Float64(z / b) + Float64(Float64(x * y) / b))) + Float64(27464.7644705 * Float64(1.0 / b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = y * ((y * ((y * (y + a)) + b)) + c);
	t_2 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -5.5e+73)
		tmp = t_2;
	elseif (y <= -1.3e-40)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	elseif (y <= 1.1e+26)
		tmp = (t + (y * 230661.510616)) / (t_1 + i);
	elseif (y <= 6.2e+104)
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+73], t$95$2, If[LessEqual[y, -1.3e-40], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 1.1e+26], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+104], N[(N[(y * N[(N[(z / b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(27464.7644705 * N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.5000000000000003e73 or 6.20000000000000033e104 < y

   1. Initial program 1.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

   if -5.5000000000000003e73 < y < -1.3000000000000001e-40

   1. Initial program 81.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.8%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in i around 0 54.9%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   if -1.3000000000000001e-40 < y < 1.10000000000000004e26

   1. Initial program 99.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 91.5%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 91.5%

         \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 91.5%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 1.10000000000000004e26 < y < 6.20000000000000033e104

   1. Initial program 16.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 9.9%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{b \cdot {y}^{2}}} \]

   4. Taylor expanded in y around -inf 51.6%

      \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{z}{b} - 27464.7644705 \cdot \frac{1}{b \cdot y}}{y} + \frac{x}{b}\right)} \]

   5. Taylor expanded in y around 0 49.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+73}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-40}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -6e+47)
     t_1
     (if (<= y 7.5e+26)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
        (+ i (* y (+ c (* y (+ b (* y a)))))))
       (if (<= y 6.2e+104)
         (+ (* y (+ (/ z b) (/ (* x y) b))) (* 27464.7644705 (/ 1.0 b)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -6e+47) {
		tmp = t_1;
	} else if (y <= 7.5e+26) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-6d+47)) then
        tmp = t_1
    else if (y <= 7.5d+26) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
    else if (y <= 6.2d+104) then
        tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705d0 * (1.0d0 / b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -6e+47) {
		tmp = t_1;
	} else if (y <= 7.5e+26) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -6e+47:
		tmp = t_1
	elif y <= 7.5e+26:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
	elif y <= 6.2e+104:
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -6e+47)
		tmp = t_1;
	elseif (y <= 7.5e+26)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * a)))))));
	elseif (y <= 6.2e+104)
		tmp = Float64(Float64(y * Float64(Float64(z / b) + Float64(Float64(x * y) / b))) + Float64(27464.7644705 * Float64(1.0 / b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -6e+47)
		tmp = t_1;
	elseif (y <= 7.5e+26)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	elseif (y <= 6.2e+104)
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+47], t$95$1, If[LessEqual[y, 7.5e+26], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+104], N[(N[(y * N[(N[(z / b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(27464.7644705 * N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.0000000000000003e47 or 6.20000000000000033e104 < y

   1. Initial program 3.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

   if -6.0000000000000003e47 < y < 7.49999999999999941e26

   1. Initial program 97.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.8%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot \left(b + a \cdot y\right)\right)} + i} \]
   4. Step-by-step derivation

      1. *-commutative 95.8%

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{y \cdot \left(c + y \cdot \left(b + \color{blue}{y \cdot a}\right)\right) + i} \]

   5. Simplified 95.8%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)} + i} \]

   6. Taylor expanded in x around 0 91.4%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right) + i} \]

   if 7.49999999999999941e26 < y < 6.20000000000000033e104

   1. Initial program 16.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 9.9%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{b \cdot {y}^{2}}} \]

   4. Taylor expanded in y around -inf 51.6%

      \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{z}{b} - 27464.7644705 \cdot \frac{1}{b \cdot y}}{y} + \frac{x}{b}\right)} \]

   5. Taylor expanded in y around 0 49.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+47}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -2.4e+19)
     t_1
     (if (<= y 4.6e+26)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (if (<= y 6.2e+104)
         (+ (* y (+ (/ z b) (/ (* x y) b))) (* 27464.7644705 (/ 1.0 b)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.4e+19) {
		tmp = t_1;
	} else if (y <= 4.6e+26) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-2.4d+19)) then
        tmp = t_1
    else if (y <= 4.6d+26) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= 6.2d+104) then
        tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705d0 * (1.0d0 / b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.4e+19) {
		tmp = t_1;
	} else if (y <= 4.6e+26) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -2.4e+19:
		tmp = t_1
	elif y <= 4.6e+26:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= 6.2e+104:
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -2.4e+19)
		tmp = t_1;
	elseif (y <= 4.6e+26)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= 6.2e+104)
		tmp = Float64(Float64(y * Float64(Float64(z / b) + Float64(Float64(x * y) / b))) + Float64(27464.7644705 * Float64(1.0 / b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -2.4e+19)
		tmp = t_1;
	elseif (y <= 4.6e+26)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= 6.2e+104)
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+19], t$95$1, If[LessEqual[y, 4.6e+26], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+104], N[(N[(y * N[(N[(z / b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(27464.7644705 * N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e19 or 6.20000000000000033e104 < y

   1. Initial program 6.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.8%

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

      1. associate--l+ 66.8%

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

      2. associate-/l* 73.1%

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

   5. Simplified 73.1%

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

   if -2.4e19 < y < 4.6000000000000001e26

   1. Initial program 99.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 86.4%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705 \cdot y} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 86.4%

         \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 86.4%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 4.6000000000000001e26 < y < 6.20000000000000033e104

   1. Initial program 16.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 9.9%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{b \cdot {y}^{2}}} \]

   4. Taylor expanded in y around -inf 51.6%

      \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{z}{b} - 27464.7644705 \cdot \frac{1}{b \cdot y}}{y} + \frac{x}{b}\right)} \]

   5. Taylor expanded in y around 0 49.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -2.4e+19)
     t_1
     (if (<= y 2.4e+26)
       (/
        (+ t (* y 230661.510616))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (if (<= y 6.2e+104)
         (+ (* y (+ (/ z b) (/ (* x y) b))) (* 27464.7644705 (/ 1.0 b)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.4e+19) {
		tmp = t_1;
	} else if (y <= 2.4e+26) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-2.4d+19)) then
        tmp = t_1
    else if (y <= 2.4d+26) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= 6.2d+104) then
        tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705d0 * (1.0d0 / b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.4e+19) {
		tmp = t_1;
	} else if (y <= 2.4e+26) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -2.4e+19:
		tmp = t_1
	elif y <= 2.4e+26:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= 6.2e+104:
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -2.4e+19)
		tmp = t_1;
	elseif (y <= 2.4e+26)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= 6.2e+104)
		tmp = Float64(Float64(y * Float64(Float64(z / b) + Float64(Float64(x * y) / b))) + Float64(27464.7644705 * Float64(1.0 / b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -2.4e+19)
		tmp = t_1;
	elseif (y <= 2.4e+26)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= 6.2e+104)
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+19], t$95$1, If[LessEqual[y, 2.4e+26], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+104], N[(N[(y * N[(N[(z / b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(27464.7644705 * N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e19 or 6.20000000000000033e104 < y

   1. Initial program 6.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.8%

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

      1. associate--l+ 66.8%

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

      2. associate-/l* 73.1%

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

   5. Simplified 73.1%

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

   if -2.4e19 < y < 2.40000000000000005e26

   1. Initial program 99.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 85.7%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. *-commutative 85.7%

         \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Simplified 85.7%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 2.40000000000000005e26 < y < 6.20000000000000033e104

   1. Initial program 16.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 9.9%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{b \cdot {y}^{2}}} \]

   4. Taylor expanded in y around -inf 51.6%

      \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{z}{b} - 27464.7644705 \cdot \frac{1}{b \cdot y}}{y} + \frac{x}{b}\right)} \]

   5. Taylor expanded in y around 0 49.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -2.3e+19)
     t_1
     (if (<= y 2e+26)
       (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ b (* y a)))))))
       (if (<= y 6.2e+104)
         (+ (* y (+ (/ z b) (/ (* x y) b))) (* 27464.7644705 (/ 1.0 b)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.3e+19) {
		tmp = t_1;
	} else if (y <= 2e+26) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * a))))));
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-2.3d+19)) then
        tmp = t_1
    else if (y <= 2d+26) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * a))))))
    else if (y <= 6.2d+104) then
        tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705d0 * (1.0d0 / b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.3e+19) {
		tmp = t_1;
	} else if (y <= 2e+26) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * a))))));
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -2.3e+19:
		tmp = t_1
	elif y <= 2e+26:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * a))))))
	elif y <= 6.2e+104:
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -2.3e+19)
		tmp = t_1;
	elseif (y <= 2e+26)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * a)))))));
	elseif (y <= 6.2e+104)
		tmp = Float64(Float64(y * Float64(Float64(z / b) + Float64(Float64(x * y) / b))) + Float64(27464.7644705 * Float64(1.0 / b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -2.3e+19)
		tmp = t_1;
	elseif (y <= 2e+26)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * a))))));
	elseif (y <= 6.2e+104)
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+19], t$95$1, If[LessEqual[y, 2e+26], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+104], N[(N[(y * N[(N[(z / b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(27464.7644705 * N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3e19 or 6.20000000000000033e104 < y

   1. Initial program 6.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.8%

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

      1. associate--l+ 66.8%

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

      2. associate-/l* 73.1%

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

   5. Simplified 73.1%

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

   if -2.3e19 < y < 2.0000000000000001e26

   1. Initial program 99.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 97.1%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot \left(b + a \cdot y\right)\right)} + i} \]
   4. Step-by-step derivation

      1. *-commutative 97.1%

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{y \cdot \left(c + y \cdot \left(b + \color{blue}{y \cdot a}\right)\right) + i} \]

   5. Simplified 97.1%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)} + i} \]

   6. Taylor expanded in y around 0 84.4%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right) + i} \]
   7. Step-by-step derivation

      1. *-commutative 85.7%

         \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   8. Simplified 84.4%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right) + i} \]

   if 2.0000000000000001e26 < y < 6.20000000000000033e104

   1. Initial program 16.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 9.9%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{b \cdot {y}^{2}}} \]

   4. Taylor expanded in y around -inf 51.6%

      \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{z}{b} - 27464.7644705 \cdot \frac{1}{b \cdot y}}{y} + \frac{x}{b}\right)} \]

   5. Taylor expanded in y around 0 49.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -5000000000.0)
     t_1
     (if (<= y 1.25e+26)
       (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
       (if (<= y 6.2e+104)
         (+ (* y (+ (/ z b) (/ (* x y) b))) (* 27464.7644705 (/ 1.0 b)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5000000000.0) {
		tmp = t_1;
	} else if (y <= 1.25e+26) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-5000000000.0d0)) then
        tmp = t_1
    else if (y <= 1.25d+26) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else if (y <= 6.2d+104) then
        tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705d0 * (1.0d0 / b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5000000000.0) {
		tmp = t_1;
	} else if (y <= 1.25e+26) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else if (y <= 6.2e+104) {
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -5000000000.0:
		tmp = t_1
	elif y <= 1.25e+26:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	elif y <= 6.2e+104:
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -5000000000.0)
		tmp = t_1;
	elseif (y <= 1.25e+26)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 6.2e+104)
		tmp = Float64(Float64(y * Float64(Float64(z / b) + Float64(Float64(x * y) / b))) + Float64(27464.7644705 * Float64(1.0 / b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -5000000000.0)
		tmp = t_1;
	elseif (y <= 1.25e+26)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	elseif (y <= 6.2e+104)
		tmp = (y * ((z / b) + ((x * y) / b))) + (27464.7644705 * (1.0 / b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5000000000.0], t$95$1, If[LessEqual[y, 1.25e+26], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+104], N[(N[(y * N[(N[(z / b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(27464.7644705 * N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5e9 or 6.20000000000000033e104 < y

   1. Initial program 9.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-/l* 71.1%

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

   5. Simplified 71.1%

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

   if -5e9 < y < 1.25e26

   1. Initial program 99.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 90.0%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + b \cdot y\right)} + i} \]
   4. Step-by-step derivation

      1. *-commutative 90.0%

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{y \cdot \left(c + \color{blue}{y \cdot b}\right) + i} \]

   5. Simplified 90.0%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot b\right)} + i} \]

   6. Taylor expanded in y around 0 81.6%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{y \cdot \left(c + y \cdot b\right) + i} \]
   7. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   8. Simplified 81.6%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{y \cdot \left(c + y \cdot b\right) + i} \]

   if 1.25e26 < y < 6.20000000000000033e104

   1. Initial program 16.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 9.9%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{b \cdot {y}^{2}}} \]

   4. Taylor expanded in y around -inf 51.6%

      \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{z}{b} - 27464.7644705 \cdot \frac{1}{b \cdot y}}{y} + \frac{x}{b}\right)} \]

   5. Taylor expanded in y around 0 49.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5000000000:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\frac{z}{b} + \frac{x \cdot y}{b}\right) + 27464.7644705 \cdot \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5000000000 \lor \neg \left(y \leq 3.55 \cdot 10^{+21}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5000000000.0) (not (<= y 3.55e+21)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5000000000.0) || !(y <= 3.55e+21)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-5000000000.0d0)) .or. (.not. (y <= 3.55d+21))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5000000000.0) || !(y <= 3.55e+21)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5000000000.0) or not (y <= 3.55e+21):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5000000000.0) || !(y <= 3.55e+21))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5000000000.0) || ~((y <= 3.55e+21)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5000000000.0], N[Not[LessEqual[y, 3.55e+21]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e9 or 3.55e21 < y

   1. Initial program 11.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 58.0%

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

      1. associate--l+ 58.0%

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

      2. associate-/l* 63.3%

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

   5. Simplified 63.3%

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

   if -5e9 < y < 3.55e21

   1. Initial program 99.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 90.6%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + b \cdot y\right)} + i} \]
   4. Step-by-step derivation

      1. *-commutative 90.6%

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{y \cdot \left(c + \color{blue}{y \cdot b}\right) + i} \]

   5. Simplified 90.6%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot b\right)} + i} \]

   6. Taylor expanded in y around 0 82.2%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y} + t}{y \cdot \left(c + y \cdot b\right) + i} \]
   7. Step-by-step derivation

      1. *-commutative 87.3%

         \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   8. Simplified 82.2%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{y \cdot \left(c + y \cdot b\right) + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5000000000 \lor \neg \left(y \leq 3.55 \cdot 10^{+21}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+19} \lor \neg \left(y \leq 6.9 \cdot 10^{+25}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.35e+19) (not (<= y 6.9e+25)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ t (+ i (* y (+ c (* y (+ b (* y a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.35e+19) || !(y <= 6.9e+25)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.35d+19)) .or. (.not. (y <= 6.9d+25))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = t / (i + (y * (c + (y * (b + (y * 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 c, double i) {
	double tmp;
	if ((y <= -2.35e+19) || !(y <= 6.9e+25)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.35e+19) or not (y <= 6.9e+25):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = t / (i + (y * (c + (y * (b + (y * a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.35e+19) || !(y <= 6.9e+25))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.35e+19) || ~((y <= 6.9e+25)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = t / (i + (y * (c + (y * (b + (y * a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.35e+19], N[Not[LessEqual[y, 6.9e+25]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.35e19 or 6.8999999999999998e25 < y

   1. Initial program 9.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.4%

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

      1. associate--l+ 59.4%

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

      2. associate-/l* 64.8%

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

   5. Simplified 64.8%

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

   if -2.35e19 < y < 6.8999999999999998e25

   1. Initial program 99.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 97.8%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot \left(b + a \cdot y\right)\right)} + i} \]
   4. Step-by-step derivation

      1. *-commutative 97.8%

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{y \cdot \left(c + y \cdot \left(b + \color{blue}{y \cdot a}\right)\right) + i} \]

   5. Simplified 97.8%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)} + i} \]

   6. Taylor expanded in t around inf 69.7%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+19} \lor \neg \left(y \leq 6.9 \cdot 10^{+25}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -820000000 \lor \neg \left(y \leq 2.05 \cdot 10^{+25}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -820000000.0) (not (<= y 2.05e+25)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ t (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -820000000.0) || !(y <= 2.05e+25)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-820000000.0d0)) .or. (.not. (y <= 2.05d+25))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = t / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -820000000.0) || !(y <= 2.05e+25)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -820000000.0) or not (y <= 2.05e+25):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -820000000.0) || !(y <= 2.05e+25))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -820000000.0) || ~((y <= 2.05e+25)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -820000000.0], N[Not[LessEqual[y, 2.05e+25]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2e8 or 2.04999999999999983e25 < y

   1. Initial program 11.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 58.0%

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

      1. associate--l+ 58.0%

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

      2. associate-/l* 63.3%

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

   5. Simplified 63.3%

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

   if -8.2e8 < y < 2.04999999999999983e25

   1. Initial program 99.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 90.6%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + b \cdot y\right)} + i} \]
   4. Step-by-step derivation

      1. *-commutative 90.6%

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{y \cdot \left(c + \color{blue}{y \cdot b}\right) + i} \]

   5. Simplified 90.6%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot b\right)} + i} \]

   6. Taylor expanded in t around inf 67.4%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -820000000 \lor \neg \left(y \leq 2.05 \cdot 10^{+25}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-5} \lor \neg \left(y \leq 30000000000000\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7.5e-5) (not (<= y 30000000000000.0)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ (+ t (* y 230661.510616)) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7.5e-5) || !(y <= 30000000000000.0)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-7.5d-5)) .or. (.not. (y <= 30000000000000.0d0))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * 230661.510616d0)) / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7.5e-5) || !(y <= 30000000000000.0)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -7.5e-5) or not (y <= 30000000000000.0):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * 230661.510616)) / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -7.5e-5) || !(y <= 30000000000000.0))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -7.5e-5) || ~((y <= 30000000000000.0)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * 230661.510616)) / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -7.5e-5], N[Not[LessEqual[y, 30000000000000.0]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999934e-5 or 3e13 < y

   1. Initial program 14.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 56.0%

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

      1. associate--l+ 56.0%

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

      2. associate-/l* 61.1%

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

   5. Simplified 61.1%

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

   if -7.49999999999999934e-5 < y < 3e13

   1. Initial program 99.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 63.4%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i}} \]

   4. Taylor expanded in y around 0 60.4%

      \[\leadsto \frac{t + \color{blue}{230661.510616 \cdot y}}{i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-5} \lor \neg \left(y \leq 30000000000000\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1650000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.1e-9)
   x
   (if (<= y 1650000000000.0) (/ (+ t (* y 230661.510616)) i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.1e-9) {
		tmp = x;
	} else if (y <= 1650000000000.0) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.1d-9)) then
        tmp = x
    else if (y <= 1650000000000.0d0) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.1e-9) {
		tmp = x;
	} else if (y <= 1650000000000.0) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.1e-9:
		tmp = x
	elif y <= 1650000000000.0:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.1e-9)
		tmp = x;
	elseif (y <= 1650000000000.0)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.1e-9)
		tmp = x;
	elseif (y <= 1650000000000.0)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.1e-9], x, If[LessEqual[y, 1650000000000.0], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000019e-9 or 1.65e12 < y

   1. Initial program 16.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 45.1%

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

   if -2.10000000000000019e-9 < y < 1.65e12

   1. Initial program 99.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 64.7%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i}} \]

   4. Taylor expanded in y around 0 61.6%

      \[\leadsto \frac{t + \color{blue}{230661.510616 \cdot y}}{i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1650000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.1e-5) x (if (<= y 4.8e+17) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.1e-5) {
		tmp = x;
	} else if (y <= 4.8e+17) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.1d-5)) then
        tmp = x
    else if (y <= 4.8d+17) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.1e-5) {
		tmp = x;
	} else if (y <= 4.8e+17) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.1e-5:
		tmp = x
	elif y <= 4.8e+17:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.1e-5)
		tmp = x;
	elseif (y <= 4.8e+17)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.1e-5)
		tmp = x;
	elseif (y <= 4.8e+17)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.1e-5], x, If[LessEqual[y, 4.8e+17], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.09999999999999988e-5 or 4.8e17 < y

   1. Initial program 14.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 46.2%

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

   if -2.09999999999999988e-5 < y < 4.8e17

   1. Initial program 99.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 53.8%

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

Alternative 16: 25.7% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := x

Derivation

1. Initial program 61.8%

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 22.4%

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

Reproduce

herbie shell --seed 2024089 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))