Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.8% → 84.7%

Time: 22.4s

Alternatives: 16

Speedup: 2.5×

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: 55.8% 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: 84.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+53} \lor \neg \left(y \leq 1.58 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(z + y \cdot x\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7.5e+53) (not (<= y 1.58e+65)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/
    (+ (* y (+ (* y (+ (* y (+ z (* y x))) 27464.7644705)) 230661.510616)) t)
    (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) 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+53) || !(y <= 1.58e+65)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = ((y * ((y * ((y * (z + (y * x))) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + 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+53)) .or. (.not. (y <= 1.58d+65))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = ((y * ((y * ((y * (z + (y * x))) + 27464.7644705d0)) + 230661.510616d0)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + 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+53) || !(y <= 1.58e+65)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = ((y * ((y * ((y * (z + (y * x))) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -7.5e+53) or not (y <= 1.58e+65):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = ((y * ((y * ((y * (z + (y * x))) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -7.5e+53) || !(y <= 1.58e+65))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(z + Float64(y * x))) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + 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+53) || ~((y <= 1.58e+65)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = ((y * ((y * ((y * (z + (y * x))) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -7.5e+53], N[Not[LessEqual[y, 1.58e+65]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(z + N[(y * x), $MachinePrecision]), $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]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999997e53 or 1.5800000000000001e65 < y

   1. Initial program 0.5%

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

   2. Taylor expanded in y around inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. associate-/l* 75.7%

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

   4. Simplified 75.7%

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

   if -7.4999999999999997e53 < y < 1.5800000000000001e65

   1. Initial program 94.6%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+53} \lor \neg \left(y \leq 1.58 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(z + y \cdot x\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 2: 80.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-50}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+115}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
        (t_2 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -4e+53)
     t_2
     (if (<= y -6.6e-50)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* y y)))))))
        t_1)
       (if (<= y 1.05e+48)
         (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) t_1)
         (if (<= y 5.6e+115)
           (/ 1.0 (+ (/ 1.0 x) (/ (- (/ a x) (/ z (* x x))) y)))
           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)) + i;
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -4e+53) {
		tmp = t_2;
	} else if (y <= -6.6e-50) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_1;
	} else if (y <= 1.05e+48) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1;
	} else if (y <= 5.6e+115) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} 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)) + i
    t_2 = (z / y) + (x - (a / (y / x)))
    if (y <= (-4d+53)) then
        tmp = t_2
    else if (y <= (-6.6d-50)) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (y * y))))))) / t_1
    else if (y <= 1.05d+48) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / t_1
    else if (y <= 5.6d+115) then
        tmp = 1.0d0 / ((1.0d0 / x) + (((a / x) - (z / (x * x))) / y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -4e+53) {
		tmp = t_2;
	} else if (y <= -6.6e-50) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_1;
	} else if (y <= 1.05e+48) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1;
	} else if (y <= 5.6e+115) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} 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)) + i
	t_2 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -4e+53:
		tmp = t_2
	elif y <= -6.6e-50:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_1
	elif y <= 1.05e+48:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1
	elif y <= 5.6e+115:
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -4e+53)
		tmp = t_2;
	elseif (y <= -6.6e-50)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * Float64(y * y))))))) / t_1);
	elseif (y <= 1.05e+48)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / t_1);
	elseif (y <= 5.6e+115)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) + Float64(Float64(Float64(a / x) - Float64(z / Float64(x * x))) / y)));
	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)) + i;
	t_2 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -4e+53)
		tmp = t_2;
	elseif (y <= -6.6e-50)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_1;
	elseif (y <= 1.05e+48)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1;
	elseif (y <= 5.6e+115)
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+53], t$95$2, If[LessEqual[y, -6.6e-50], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 1.05e+48], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 5.6e+115], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] + N[(N[(N[(a / x), $MachinePrecision] - N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4e53 or 5.6000000000000001e115 < y

   1. Initial program 0.3%

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

   2. Taylor expanded in y around inf 74.6%

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

      1. associate--l+ 74.6%

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

      2. associate-/l* 80.6%

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

   4. Simplified 80.6%

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

   if -4e53 < y < -6.5999999999999997e-50

   1. Initial program 83.0%

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

   2. Taylor expanded in x around inf 78.9%

      \[\leadsto \frac{\left(\left(\color{blue}{{y}^{2} \cdot x} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

      1. *-commutative 78.9%

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

      2. unpow2 78.9%

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

   4. Simplified 78.9%

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

   if -6.5999999999999997e-50 < y < 1.0499999999999999e48

   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. Taylor expanded in z around inf 95.9%

      \[\leadsto \frac{\left(\color{blue}{{y}^{2} \cdot z} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

      1. *-commutative 95.9%

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

      2. unpow2 95.9%

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

   4. Simplified 95.9%

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

   if 1.0499999999999999e48 < y < 5.6000000000000001e115

   1. Initial program 8.4%

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

      1. clear-num 8.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \]

      2. inv-pow 8.4%

         \[\leadsto \color{blue}{{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{-1}} \]

   3. Applied egg-rr 8.4%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 8.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

      2. fma-udef 8.4%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      3. *-commutative 8.4%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, 27464.7644705\right), 230661.510616\right), t\right)}} \]

      4. fma-def 8.4%

         \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, 27464.7644705\right), 230661.510616\right), t\right)}} \]

   5. Simplified 8.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}} \]

   6. Taylor expanded in y around -inf 39.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 39.8%

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

      2. distribute-lft-out-- 39.8%

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

      3. unpow2 39.8%

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

   8. Simplified 39.8%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+53}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-50}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+115}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 3: 80.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+53} \lor \neg \left(y \leq 1.55 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5e+53) (not (<= y 1.55e+59)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* z (* y y)))))
    (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5e+53) || !(y <= 1.55e+59)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + 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 <= (-5d+53)) .or. (.not. (y <= 1.55d+59))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + 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 <= -5e+53) || !(y <= 1.55e+59)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5e+53) or not (y <= 1.55e+59):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5e+53) || !(y <= 1.55e+59))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5e+53) || ~((y <= 1.55e+59)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5e+53], N[Not[LessEqual[y, 1.55e+59]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $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]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000004e53 or 1.55000000000000007e59 < 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. Taylor expanded in y around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. associate-/l* 74.4%

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

   4. Simplified 74.4%

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

   if -5.0000000000000004e53 < y < 1.55000000000000007e59

   1. Initial program 95.2%

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

   2. Taylor expanded in z around inf 89.2%

      \[\leadsto \frac{\left(\color{blue}{{y}^{2} \cdot z} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

      1. *-commutative 89.2%

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

      2. unpow2 89.2%

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

   4. Simplified 89.2%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+53} \lor \neg \left(y \leq 1.55 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 4: 76.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+53} \lor \neg \left(y \leq 1.25 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.4e+53) (not (<= y 1.25e+56)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.4e+53) || !(y <= 1.25e+56)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + 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 <= (-5.4d+53)) .or. (.not. (y <= 1.25d+56))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + 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 <= -5.4e+53) || !(y <= 1.25e+56)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5.4e+53) or not (y <= 1.25e+56):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5.4e+53) || !(y <= 1.25e+56))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		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));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5.4e+53) || ~((y <= 1.25e+56)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5.4e+53], N[Not[LessEqual[y, 1.25e+56]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if y < -5.40000000000000039e53 or 1.25000000000000006e56 < 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. Taylor expanded in y around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. associate-/l* 74.4%

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

   4. Simplified 74.4%

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

   if -5.40000000000000039e53 < y < 1.25000000000000006e56

   1. Initial program 95.2%

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

   2. Taylor expanded in y around 0 84.2%

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

      1. *-commutative 84.2%

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

   4. Simplified 84.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+53} \lor \neg \left(y \leq 1.25 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 5: 75.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+53} \lor \neg \left(y \leq 1.4 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.8e+53) (not (<= y 1.4e+57)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.8e+53) || !(y <= 1.4e+57)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + 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 <= (-3.8d+53)) .or. (.not. (y <= 1.4d+57))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + 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 <= -3.8e+53) || !(y <= 1.4e+57)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.8e+53) or not (y <= 1.4e+57):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.8e+53) || !(y <= 1.4e+57))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.8e+53) || ~((y <= 1.4e+57)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.8e+53], N[Not[LessEqual[y, 1.4e+57]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if y < -3.79999999999999997e53 or 1.4e57 < 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. Taylor expanded in y around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. associate-/l* 74.4%

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

   4. Simplified 74.4%

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

   if -3.79999999999999997e53 < y < 1.4e57

   1. Initial program 95.2%

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

   2. Taylor expanded in y around 0 82.7%

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

      1. *-commutative 82.7%

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

   4. Simplified 82.7%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+53} \lor \neg \left(y \leq 1.4 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 6: 74.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+53} \lor \neg \left(y \leq 1.8 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.9e+53) (not (<= y 1.8e+61)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ b (* y y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.9e+53) || !(y <= 1.8e+61)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * 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) :: tmp
    if ((y <= (-2.9d+53)) .or. (.not. (y <= 1.8d+61))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * 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 tmp;
	if ((y <= -2.9e+53) || !(y <= 1.8e+61)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * y))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.9e+53) or not (y <= 1.8e+61):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * y))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.9e+53) || !(y <= 1.8e+61))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * y)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.9e+53) || ~((y <= 1.8e+61)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * y))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.9e+53], N[Not[LessEqual[y, 1.8e+61]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000002e53 or 1.80000000000000005e61 < 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. Taylor expanded in y around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. associate-/l* 75.0%

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

   4. Simplified 75.0%

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

   if -2.9000000000000002e53 < y < 1.80000000000000005e61

   1. Initial program 94.5%

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

   2. Taylor expanded in y around 0 82.2%

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

      1. *-commutative 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in a around 0 79.1%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\left(\color{blue}{\left({y}^{2} + b\right) \cdot y} + c\right) \cdot y + i} \]
   6. Step-by-step derivation

      1. *-commutative 79.1%

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

      2. +-commutative 79.1%

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

      3. unpow2 79.1%

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

   7. Simplified 79.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+53} \lor \neg \left(y \leq 1.8 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \end{array} \]

Alternative 7: 73.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+53} \lor \neg \left(y \leq 1.05 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.9e+53) (not (<= y 1.05e+49)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ 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 <= -2.9e+53) || !(y <= 1.05e+49)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} 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 <= (-2.9d+53)) .or. (.not. (y <= 1.05d+49))) then
        tmp = (z / y) + (x - (a / (y / x)))
    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 <= -2.9e+53) || !(y <= 1.05e+49)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} 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 <= -2.9e+53) or not (y <= 1.05e+49):
		tmp = (z / y) + (x - (a / (y / x)))
	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 <= -2.9e+53) || !(y <= 1.05e+49))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	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 <= -2.9e+53) || ~((y <= 1.05e+49)))
		tmp = (z / y) + (x - (a / (y / x)));
	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, -2.9e+53], N[Not[LessEqual[y, 1.05e+49]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $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 < -2.9000000000000002e53 or 1.05000000000000005e49 < y

   1. Initial program 1.5%

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

   2. Taylor expanded in y around inf 66.7%

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

      1. associate--l+ 66.7%

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

      2. associate-/l* 73.7%

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

   4. Simplified 73.7%

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

   if -2.9000000000000002e53 < y < 1.05000000000000005e49

   1. Initial program 95.8%

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

   2. Taylor expanded in y around 0 83.2%

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

      1. *-commutative 83.2%

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

   4. Simplified 83.2%

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

   5. Taylor expanded in y around 0 79.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+53} \lor \neg \left(y \leq 1.05 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 8: 60.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+37} \lor \neg \left(y \leq 7.2 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i} + y \cdot \frac{230661.510616}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6e+37) (not (<= y 7.2e-25)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (+ (/ t i) (* 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 <= -6e+37) || !(y <= 7.2e-25)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t / i) + (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 <= (-6d+37)) .or. (.not. (y <= 7.2d-25))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t / i) + (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 <= -6e+37) || !(y <= 7.2e-25)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t / i) + (y * (230661.510616 / i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6e+37) or not (y <= 7.2e-25):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t / i) + (y * (230661.510616 / i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6e+37) || !(y <= 7.2e-25))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t / i) + Float64(y * Float64(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 <= -6e+37) || ~((y <= 7.2e-25)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t / i) + (y * (230661.510616 / i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6e+37], N[Not[LessEqual[y, 7.2e-25]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / i), $MachinePrecision] + N[(y * N[(230661.510616 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.00000000000000043e37 or 7.1999999999999998e-25 < y

   1. Initial program 11.0%

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

   2. Taylor expanded in y around inf 59.8%

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

      1. associate--l+ 59.8%

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

      2. associate-/l* 66.0%

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

   4. Simplified 66.0%

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

   if -6.00000000000000043e37 < y < 7.1999999999999998e-25

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 48.8%

      \[\leadsto \color{blue}{\frac{t}{i} + \left(230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) \cdot y} \]

   3. Taylor expanded in i around inf 58.1%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+37} \lor \neg \left(y \leq 7.2 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i} + y \cdot \frac{230661.510616}{i}\\ \end{array} \]

Alternative 9: 70.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+53} \lor \neg \left(y \leq 1.96 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.9e+53) (not (<= y 1.96e+31)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ i (* y c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.9e+53) || !(y <= 1.96e+31)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	}
	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 <= (-2.9d+53)) .or. (.not. (y <= 1.96d+31))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    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 <= -2.9e+53) || !(y <= 1.96e+31)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.9e+53) or not (y <= 1.96e+31):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.9e+53) || !(y <= 1.96e+31))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.9e+53) || ~((y <= 1.96e+31)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.9e+53], N[Not[LessEqual[y, 1.96e+31]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000002e53 or 1.95999999999999994e31 < y

   1. Initial program 2.4%

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

   2. Taylor expanded in y around inf 65.6%

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

      1. associate--l+ 65.6%

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

      2. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

   if -2.9000000000000002e53 < y < 1.95999999999999994e31

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 83.7%

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

      1. *-commutative 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in y around 0 71.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+53} \lor \neg \left(y \leq 1.96 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \end{array} \]

Alternative 10: 58.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+33} \lor \neg \left(y \leq 6.8 \cdot 10^{-25}\right):\\ \;\;\;\;x - \frac{x \cdot a - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i} + y \cdot \frac{230661.510616}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.6e+33) (not (<= y 6.8e-25)))
   (- x (/ (- (* x a) z) y))
   (+ (/ t i) (* 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 <= -5.6e+33) || !(y <= 6.8e-25)) {
		tmp = x - (((x * a) - z) / y);
	} else {
		tmp = (t / i) + (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 <= (-5.6d+33)) .or. (.not. (y <= 6.8d-25))) then
        tmp = x - (((x * a) - z) / y)
    else
        tmp = (t / i) + (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 <= -5.6e+33) || !(y <= 6.8e-25)) {
		tmp = x - (((x * a) - z) / y);
	} else {
		tmp = (t / i) + (y * (230661.510616 / i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5.6e+33) or not (y <= 6.8e-25):
		tmp = x - (((x * a) - z) / y)
	else:
		tmp = (t / i) + (y * (230661.510616 / i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5.6e+33) || !(y <= 6.8e-25))
		tmp = Float64(x - Float64(Float64(Float64(x * a) - z) / y));
	else
		tmp = Float64(Float64(t / i) + Float64(y * Float64(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 <= -5.6e+33) || ~((y <= 6.8e-25)))
		tmp = x - (((x * a) - z) / y);
	else
		tmp = (t / i) + (y * (230661.510616 / i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5.6e+33], N[Not[LessEqual[y, 6.8e-25]], $MachinePrecision]], N[(x - N[(N[(N[(x * a), $MachinePrecision] - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t / i), $MachinePrecision] + N[(y * N[(230661.510616 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6000000000000002e33 or 6.80000000000000003e-25 < y

   1. Initial program 11.0%

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

      1. div-inv 10.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \]

      2. *-commutative 10.9%

         \[\leadsto \left(\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right)} + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. fma-def 10.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616, t\right)} \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. *-commutative 10.9%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{y \cdot \left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right)} + 230661.510616, t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. fma-def 10.9%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \left(x \cdot y + z\right) \cdot y + 27464.7644705, 230661.510616\right)}, t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. *-commutative 10.9%

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(x \cdot y + z\right)} + 27464.7644705, 230661.510616\right), t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 10.9%

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}, 230661.510616\right), t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. fma-def 10.9%

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right), 230661.510616\right), t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. *-commutative 10.9%

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right) \cdot \frac{1}{\color{blue}{y \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)} + i} \]

      10. fma-def 10.9%

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right) \cdot \frac{1}{\color{blue}{\mathsf{fma}\left(y, \left(\left(y + a\right) \cdot y + b\right) \cdot y + c, i\right)}} \]

   3. Applied egg-rr 10.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right) \cdot \frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]

   4. Taylor expanded in y around -inf 59.8%

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

      1. +-commutative 59.8%

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

      2. associate-*r/ 59.8%

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

      3. mul-1-neg 59.8%

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

      4. *-commutative 59.8%

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

      5. fma-neg 59.8%

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

      6. mul-1-neg 59.8%

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

      7. remove-double-neg 59.8%

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

      8. *-commutative 59.8%

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

      9. distribute-neg-frac 59.8%

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

      10. unsub-neg 59.8%

          \[\leadsto \color{blue}{x - \frac{\mathsf{fma}\left(z, -1, x \cdot a\right)}{y}} \]

      11. fma-udef 59.8%

          \[\leadsto x - \frac{\color{blue}{z \cdot -1 + x \cdot a}}{y} \]

      12. *-commutative 59.8%

          \[\leadsto x - \frac{\color{blue}{-1 \cdot z} + x \cdot a}{y} \]

      13. *-commutative 59.8%

          \[\leadsto x - \frac{-1 \cdot z + \color{blue}{a \cdot x}}{y} \]

      14. +-commutative 59.8%

          \[\leadsto x - \frac{\color{blue}{a \cdot x + -1 \cdot z}}{y} \]

      15. mul-1-neg 59.8%

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

      16. unsub-neg 59.8%

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

   6. Simplified 59.8%

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

   if -5.6000000000000002e33 < y < 6.80000000000000003e-25

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 48.8%

      \[\leadsto \color{blue}{\frac{t}{i} + \left(230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) \cdot y} \]

   3. Taylor expanded in i around inf 58.1%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+33} \lor \neg \left(y \leq 6.8 \cdot 10^{-25}\right):\\ \;\;\;\;x - \frac{x \cdot a - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i} + y \cdot \frac{230661.510616}{i}\\ \end{array} \]

Alternative 11: 53.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{i} + y \cdot \frac{230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.2e+38)
   (- x (/ a (/ y x)))
   (if (<= y 2.8e-29) (+ (/ t i) (* 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 <= -6.2e+38) {
		tmp = x - (a / (y / x));
	} else if (y <= 2.8e-29) {
		tmp = (t / i) + (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 <= (-6.2d+38)) then
        tmp = x - (a / (y / x))
    else if (y <= 2.8d-29) then
        tmp = (t / i) + (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 <= -6.2e+38) {
		tmp = x - (a / (y / x));
	} else if (y <= 2.8e-29) {
		tmp = (t / i) + (y * (230661.510616 / i));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.2e+38:
		tmp = x - (a / (y / x))
	elif y <= 2.8e-29:
		tmp = (t / i) + (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 <= -6.2e+38)
		tmp = Float64(x - Float64(a / Float64(y / x)));
	elseif (y <= 2.8e-29)
		tmp = Float64(Float64(t / i) + Float64(y * Float64(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 <= -6.2e+38)
		tmp = x - (a / (y / x));
	elseif (y <= 2.8e-29)
		tmp = (t / i) + (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, -6.2e+38], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-29], N[(N[(t / i), $MachinePrecision] + N[(y * N[(230661.510616 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000035e38

   1. Initial program 2.4%

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

   2. Taylor expanded in x around inf 2.5%

      \[\leadsto \frac{\left(\left(\color{blue}{{y}^{2} \cdot x} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

      1. *-commutative 2.5%

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

      2. unpow2 2.5%

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

   4. Simplified 2.5%

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

   5. Taylor expanded in y around inf 55.7%

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

      1. +-commutative 55.7%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot x}{y}} \]

      2. mul-1-neg 55.7%

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

      3. sub-neg 55.7%

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

      4. associate-/l* 58.9%

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

   7. Simplified 58.9%

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

   if -6.20000000000000035e38 < y < 2.8000000000000002e-29

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 49.1%

      \[\leadsto \color{blue}{\frac{t}{i} + \left(230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) \cdot y} \]

   3. Taylor expanded in i around inf 58.6%

      \[\leadsto \frac{t}{i} + \color{blue}{\frac{230661.510616}{i}} \cdot y \]

   if 2.8000000000000002e-29 < y

   1. Initial program 19.0%

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

   2. Taylor expanded in y around inf 47.2%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{i} + y \cdot \frac{230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 53.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+33}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.9e+33)
   (- x (/ a (/ y x)))
   (if (<= y 2.8e-29) (/ (+ 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 <= -4.9e+33) {
		tmp = x - (a / (y / x));
	} else if (y <= 2.8e-29) {
		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 <= (-4.9d+33)) then
        tmp = x - (a / (y / x))
    else if (y <= 2.8d-29) 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 <= -4.9e+33) {
		tmp = x - (a / (y / x));
	} else if (y <= 2.8e-29) {
		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 <= -4.9e+33:
		tmp = x - (a / (y / x))
	elif y <= 2.8e-29:
		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 <= -4.9e+33)
		tmp = Float64(x - Float64(a / Float64(y / x)));
	elseif (y <= 2.8e-29)
		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 <= -4.9e+33)
		tmp = x - (a / (y / x));
	elseif (y <= 2.8e-29)
		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, -4.9e+33], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-29], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < -4.90000000000000014e33

   1. Initial program 2.4%

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

   2. Taylor expanded in x around inf 2.5%

      \[\leadsto \frac{\left(\left(\color{blue}{{y}^{2} \cdot x} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

      1. *-commutative 2.5%

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

      2. unpow2 2.5%

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

   4. Simplified 2.5%

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

   5. Taylor expanded in y around inf 55.7%

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

      1. +-commutative 55.7%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot x}{y}} \]

      2. mul-1-neg 55.7%

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

      3. sub-neg 55.7%

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

      4. associate-/l* 58.9%

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

   7. Simplified 58.9%

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

   if -4.90000000000000014e33 < y < 2.8000000000000002e-29

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 89.2%

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

      1. *-commutative 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in i around inf 58.6%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]

   if 2.8000000000000002e-29 < y

   1. Initial program 19.0%

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

   2. Taylor expanded in y around inf 47.2%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+33}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 48.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-147}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.2e+44)
   x
   (if (<= y -6.9e-147) (/ t (* y c)) (if (<= y 2.8e-29) (/ 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 <= -6.2e+44) {
		tmp = x;
	} else if (y <= -6.9e-147) {
		tmp = t / (y * c);
	} else if (y <= 2.8e-29) {
		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 <= (-6.2d+44)) then
        tmp = x
    else if (y <= (-6.9d-147)) then
        tmp = t / (y * c)
    else if (y <= 2.8d-29) 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 <= -6.2e+44) {
		tmp = x;
	} else if (y <= -6.9e-147) {
		tmp = t / (y * c);
	} else if (y <= 2.8e-29) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.2e+44:
		tmp = x
	elif y <= -6.9e-147:
		tmp = t / (y * c)
	elif y <= 2.8e-29:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.2e+44)
		tmp = x;
	elseif (y <= -6.9e-147)
		tmp = Float64(t / Float64(y * c));
	elseif (y <= 2.8e-29)
		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 <= -6.2e+44)
		tmp = x;
	elseif (y <= -6.9e-147)
		tmp = t / (y * c);
	elseif (y <= 2.8e-29)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.2e+44], x, If[LessEqual[y, -6.9e-147], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-29], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.19999999999999991e44 or 2.8000000000000002e-29 < y

   1. Initial program 10.9%

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

   2. Taylor expanded in y around inf 52.6%

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

   if -6.19999999999999991e44 < y < -6.89999999999999999e-147

   1. Initial program 92.7%

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

   2. Taylor expanded in c around inf 38.0%

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

   3. Taylor expanded in y around 0 31.0%

      \[\leadsto \color{blue}{\frac{t}{c \cdot y}} \]

   if -6.89999999999999999e-147 < y < 2.8000000000000002e-29

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 65.9%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-147}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 48.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+53}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-146}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.3e+53)
   (- x (/ a (/ y x)))
   (if (<= y -3.2e-146) (/ t (* y c)) (if (<= y 2.8e-29) (/ 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 <= -3.3e+53) {
		tmp = x - (a / (y / x));
	} else if (y <= -3.2e-146) {
		tmp = t / (y * c);
	} else if (y <= 2.8e-29) {
		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 <= (-3.3d+53)) then
        tmp = x - (a / (y / x))
    else if (y <= (-3.2d-146)) then
        tmp = t / (y * c)
    else if (y <= 2.8d-29) 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 <= -3.3e+53) {
		tmp = x - (a / (y / x));
	} else if (y <= -3.2e-146) {
		tmp = t / (y * c);
	} else if (y <= 2.8e-29) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.3e+53:
		tmp = x - (a / (y / x))
	elif y <= -3.2e-146:
		tmp = t / (y * c)
	elif y <= 2.8e-29:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.3e+53)
		tmp = Float64(x - Float64(a / Float64(y / x)));
	elseif (y <= -3.2e-146)
		tmp = Float64(t / Float64(y * c));
	elseif (y <= 2.8e-29)
		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 <= -3.3e+53)
		tmp = x - (a / (y / x));
	elseif (y <= -3.2e-146)
		tmp = t / (y * c);
	elseif (y <= 2.8e-29)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.3e+53], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-146], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-29], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.3000000000000002e53

   1. Initial program 0.6%

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

   2. Taylor expanded in x around inf 0.7%

      \[\leadsto \frac{\left(\left(\color{blue}{{y}^{2} \cdot x} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

      1. *-commutative 0.7%

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

      2. unpow2 0.7%

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

   4. Simplified 0.7%

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

   5. Taylor expanded in y around inf 57.7%

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

      1. +-commutative 57.7%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot x}{y}} \]

      2. mul-1-neg 57.7%

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

      3. sub-neg 57.7%

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

      4. associate-/l* 60.9%

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

   7. Simplified 60.9%

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

   if -3.3000000000000002e53 < y < -3.1999999999999999e-146

   1. Initial program 90.6%

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

   2. Taylor expanded in c around inf 37.2%

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

   3. Taylor expanded in y around 0 30.3%

      \[\leadsto \color{blue}{\frac{t}{c \cdot y}} \]

   if -3.1999999999999999e-146 < y < 2.8000000000000002e-29

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 65.9%

      \[\leadsto \color{blue}{\frac{t}{i}} \]

   if 2.8000000000000002e-29 < y

   1. Initial program 19.0%

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

   2. Taylor expanded in y around inf 47.2%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+53}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-146}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 50.3% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1150:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1150.0) x (if (<= y 2.8e-29) (/ 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 <= -1150.0) {
		tmp = x;
	} else if (y <= 2.8e-29) {
		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 <= (-1150.0d0)) then
        tmp = x
    else if (y <= 2.8d-29) 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 <= -1150.0) {
		tmp = x;
	} else if (y <= 2.8e-29) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1150.0:
		tmp = x
	elif y <= 2.8e-29:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1150.0)
		tmp = x;
	elseif (y <= 2.8e-29)
		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 <= -1150.0)
		tmp = x;
	elseif (y <= 2.8e-29)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1150.0], x, If[LessEqual[y, 2.8e-29], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1150 or 2.8000000000000002e-29 < y

   1. Initial program 14.8%

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

   2. Taylor expanded in y around inf 49.3%

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

   if -1150 < y < 2.8000000000000002e-29

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 53.9%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1150:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 55.3%

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

2. Taylor expanded in y around inf 27.3%

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

3. Final simplification 27.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023181 
(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)))