Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.5% → 83.0%

Time: 23.8s

Alternatives: 15

Speedup: 1.9×

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: 55.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+48}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+48}:\\ \;\;\;\;\frac{t}{t\_1} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ b (* y (+ y a)))))))))
   (if (<= y -2.4e+48)
     (- (+ x (/ z y)) (/ (* x a) y))
     (if (<= y 1.65e+48)
       (+
        (/ t t_1)
        (/
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
         t_1))
       (+ x (/ (+ z (/ (- 27464.7644705 (* z a)) y)) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * (b + (y * (y + a))))));
	double tmp;
	if (y <= -2.4e+48) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 1.65e+48) {
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / 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) :: t_1
    real(8) :: tmp
    t_1 = i + (y * (c + (y * (b + (y * (y + a))))))
    if (y <= (-2.4d+48)) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else if (y <= 1.65d+48) then
        tmp = (t / t_1) + ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))) / t_1)
    else
        tmp = x + ((z + ((27464.7644705d0 - (z * a)) / 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 t_1 = i + (y * (c + (y * (b + (y * (y + a))))));
	double tmp;
	if (y <= -2.4e+48) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 1.65e+48) {
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * (b + (y * (y + a))))))
	tmp = 0
	if y <= -2.4e+48:
		tmp = (x + (z / y)) - ((x * a) / y)
	elif y <= 1.65e+48:
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1)
	else:
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))
	tmp = 0.0
	if (y <= -2.4e+48)
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	elseif (y <= 1.65e+48)
		tmp = Float64(Float64(t / t_1) + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_1));
	else
		tmp = Float64(x + Float64(Float64(z + Float64(Float64(27464.7644705 - Float64(z * a)) / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * (b + (y * (y + a))))));
	tmp = 0.0;
	if (y <= -2.4e+48)
		tmp = (x + (z / y)) - ((x * a) / y);
	elseif (y <= 1.65e+48)
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	else
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+48], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+48], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z + N[(N[(27464.7644705 - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4000000000000001e48

   1. Initial program 0.7%

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

   3. Taylor expanded in y around inf 71.9%

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

   if -2.4000000000000001e48 < y < 1.65000000000000011e48

   1. Initial program 97.7%

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

   3. Taylor expanded in t around 0 97.7%

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

   if 1.65000000000000011e48 < y

   1. Initial program 0.8%

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

   3. Taylor expanded in y around -inf 59.3%

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

   4. Taylor expanded in x around 0 72.8%

      \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot z + -1 \cdot \frac{27464.7644705 - a \cdot z}{y}}{y}} \]
   5. Step-by-step derivation

      1. distribute-lft-out 72.8%

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

      2. *-commutative 72.8%

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

   6. Simplified 72.8%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+48}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+48}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.8e+44)
   (- (+ x (/ z y)) (/ (* x a) y))
   (if (<= y 3.25e+47)
     (/
      (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
      (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
     (+ x (/ (+ z (/ (- 27464.7644705 (* z a)) 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 <= -2.8e+44) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 3.25e+47) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / 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 <= (-2.8d+44)) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else if (y <= 3.25d+47) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else
        tmp = x + ((z + ((27464.7644705d0 - (z * a)) / 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 <= -2.8e+44) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 3.25e+47) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.8e+44:
		tmp = (x + (z / y)) - ((x * a) / y)
	elif y <= 3.25e+47:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.8e+44)
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	elseif (y <= 3.25e+47)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = Float64(x + Float64(Float64(z + Float64(Float64(27464.7644705 - Float64(z * a)) / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.8e+44)
		tmp = (x + (z / y)) - ((x * a) / y);
	elseif (y <= 3.25e+47)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	else
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.8e+44], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.25e+47], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z + N[(N[(27464.7644705 - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8000000000000001e44

   1. Initial program 0.7%

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

   3. Taylor expanded in y around inf 71.9%

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

   if -2.8000000000000001e44 < y < 3.24999999999999994e47

   1. Initial program 97.7%

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

   if 3.24999999999999994e47 < y

   1. Initial program 0.8%

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

   3. Taylor expanded in y around -inf 59.3%

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

   4. Taylor expanded in x around 0 72.8%

      \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot z + -1 \cdot \frac{27464.7644705 - a \cdot z}{y}}{y}} \]
   5. Step-by-step derivation

      1. distribute-lft-out 72.8%

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

      2. *-commutative 72.8%

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

   6. Simplified 72.8%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+46}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+16}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.5e+46)
   (- (+ x (/ z y)) (/ (* x a) y))
   (if (<= y 1.45e+16)
     (/
      (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
      (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
     (+ x (/ (+ z (/ (- 27464.7644705 (* z a)) 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 <= -3.5e+46) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 1.45e+16) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / 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 <= (-3.5d+46)) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else if (y <= 1.45d+16) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else
        tmp = x + ((z + ((27464.7644705d0 - (z * a)) / 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 <= -3.5e+46) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 1.45e+16) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.5e+46:
		tmp = (x + (z / y)) - ((x * a) / y)
	elif y <= 1.45e+16:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.5e+46)
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	elseif (y <= 1.45e+16)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = Float64(x + Float64(Float64(z + Float64(Float64(27464.7644705 - Float64(z * a)) / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.5e+46)
		tmp = (x + (z / y)) - ((x * a) / y);
	elseif (y <= 1.45e+16)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	else
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.5e+46], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+16], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z + N[(N[(27464.7644705 - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.49999999999999985e46

   1. Initial program 0.7%

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

   3. Taylor expanded in y around inf 71.9%

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

   if -3.49999999999999985e46 < y < 1.45e16

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 92.8%

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

   if 1.45e16 < y

   1. Initial program 2.6%

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

   3. Taylor expanded in y around -inf 56.3%

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

   4. Taylor expanded in x around 0 69.2%

      \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot z + -1 \cdot \frac{27464.7644705 - a \cdot z}{y}}{y}} \]
   5. Step-by-step derivation

      1. distribute-lft-out 69.2%

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

      2. *-commutative 69.2%

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

   6. Simplified 69.2%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+46}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+16}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+35} \lor \neg \left(y \leq 1.45 \cdot 10^{+16}\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.1e+35) (not (<= y 1.45e+16)))
   (+ x (/ (+ z (/ (- 27464.7644705 (* z a)) y)) y))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y (+ b (* y a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.1e+35) || !(y <= 1.45e+16)) {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-5.1d+35)) .or. (.not. (y <= 1.45d+16))) then
        tmp = x + ((z + ((27464.7644705d0 - (z * a)) / y)) / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.1e+35) || !(y <= 1.45e+16)) {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5.1e+35) or not (y <= 1.45e+16):
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5.1e+35) || !(y <= 1.45e+16))
		tmp = Float64(x + Float64(Float64(z + Float64(Float64(27464.7644705 - Float64(z * a)) / y)) / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5.1e+35) || ~((y <= 1.45e+16)))
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5.1e+35], N[Not[LessEqual[y, 1.45e+16]], $MachinePrecision]], N[(x + N[(N[(z + N[(N[(27464.7644705 - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.10000000000000017e35 or 1.45e16 < y

   1. Initial program 2.5%

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

   3. Taylor expanded in y around -inf 57.4%

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

   4. Taylor expanded in x around 0 70.1%

      \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot z + -1 \cdot \frac{27464.7644705 - a \cdot z}{y}}{y}} \]
   5. Step-by-step derivation

      1. distribute-lft-out 70.1%

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

      2. *-commutative 70.1%

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

   6. Simplified 70.1%

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

   if -5.10000000000000017e35 < y < 1.45e16

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 92.8%

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

   4. Taylor expanded in y around 0 92.1%

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

      1. *-commutative 92.1%

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

   6. Simplified 92.1%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+35} \lor \neg \left(y \leq 1.45 \cdot 10^{+16}\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+31} \lor \neg \left(y \leq 4.2 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.5e+31) (not (<= y 4.2e+15)))
   (+ x (/ (+ z (/ (- 27464.7644705 (* z a)) y)) y))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ 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 <= -4.5e+31) || !(y <= 4.2e+15)) {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (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 <= (-4.5d+31)) .or. (.not. (y <= 4.2d+15))) then
        tmp = x + ((z + ((27464.7644705d0 - (z * a)) / y)) / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (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 <= -4.5e+31) || !(y <= 4.2e+15)) {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.5e+31) or not (y <= 4.2e+15):
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.5e+31) || !(y <= 4.2e+15))
		tmp = Float64(x + Float64(Float64(z + Float64(Float64(27464.7644705 - Float64(z * a)) / y)) / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.5e+31) || ~((y <= 4.2e+15)))
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.5e+31], N[Not[LessEqual[y, 4.2e+15]], $MachinePrecision]], N[(x + N[(N[(z + N[(N[(27464.7644705 - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999996e31 or 4.2e15 < y

   1. Initial program 3.3%

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

   3. Taylor expanded in y around -inf 56.9%

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

   4. Taylor expanded in x around 0 69.5%

      \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot z + -1 \cdot \frac{27464.7644705 - a \cdot z}{y}}{y}} \]
   5. Step-by-step derivation

      1. distribute-lft-out 69.5%

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

      2. *-commutative 69.5%

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

   6. Simplified 69.5%

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

   if -4.4999999999999996e31 < y < 4.2e15

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 92.8%

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

   4. Taylor expanded in y around 0 90.7%

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

      1. *-commutative 90.7%

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

   6. Simplified 90.7%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+31} \lor \neg \left(y \leq 4.2 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+36} \lor \neg \left(y \leq 1.45 \cdot 10^{+16}\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6.8e+36) (not (<= y 1.45e+16)))
   (+ x (/ (+ z (/ (- 27464.7644705 (* z a)) y)) y))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.8e+36) || !(y <= 1.45e+16)) {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-6.8d+36)) .or. (.not. (y <= 1.45d+16))) then
        tmp = x + ((z + ((27464.7644705d0 - (z * a)) / y)) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.8e+36) || !(y <= 1.45e+16)) {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6.8e+36) or not (y <= 1.45e+16):
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y)
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6.8e+36) || !(y <= 1.45e+16))
		tmp = Float64(x + Float64(Float64(z + Float64(Float64(27464.7644705 - Float64(z * a)) / y)) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -6.8e+36) || ~((y <= 1.45e+16)))
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6.8e+36], N[Not[LessEqual[y, 1.45e+16]], $MachinePrecision]], N[(x + N[(N[(z + N[(N[(27464.7644705 - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.7999999999999996e36 or 1.45e16 < y

   1. Initial program 2.5%

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

   3. Taylor expanded in y around -inf 57.4%

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

   4. Taylor expanded in x around 0 70.1%

      \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot z + -1 \cdot \frac{27464.7644705 - a \cdot z}{y}}{y}} \]
   5. Step-by-step derivation

      1. distribute-lft-out 70.1%

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

      2. *-commutative 70.1%

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

   6. Simplified 70.1%

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

   if -6.7999999999999996e36 < y < 1.45e16

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 86.9%

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

      1. *-commutative 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+36} \lor \neg \left(y \leq 1.45 \cdot 10^{+16}\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -96000000 \lor \neg \left(y \leq 1.35 \cdot 10^{+16}\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -96000000.0) (not (<= y 1.35e+16)))
   (+ x (/ (+ z (/ (- 27464.7644705 (* z a)) y)) y))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ 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 <= -96000000.0) || !(y <= 1.35e+16)) {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (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 <= (-96000000.0d0)) .or. (.not. (y <= 1.35d+16))) then
        tmp = x + ((z + ((27464.7644705d0 - (z * a)) / y)) / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (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 <= -96000000.0) || !(y <= 1.35e+16)) {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -96000000.0) or not (y <= 1.35e+16):
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -96000000.0) || !(y <= 1.35e+16))
		tmp = Float64(x + Float64(Float64(z + Float64(Float64(27464.7644705 - Float64(z * a)) / y)) / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / 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 <= -96000000.0) || ~((y <= 1.35e+16)))
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -96000000.0], N[Not[LessEqual[y, 1.35e+16]], $MachinePrecision]], N[(x + N[(N[(z + N[(N[(27464.7644705 - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $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 < -9.6e7 or 1.35e16 < y

   1. Initial program 4.9%

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

   3. Taylor expanded in y around -inf 56.3%

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

   4. Taylor expanded in x around 0 68.7%

      \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot z + -1 \cdot \frac{27464.7644705 - a \cdot z}{y}}{y}} \]
   5. Step-by-step derivation

      1. distribute-lft-out 68.7%

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

      2. *-commutative 68.7%

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

   6. Simplified 68.7%

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

   if -9.6e7 < y < 1.35e16

   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. Add Preprocessing

   3. Taylor expanded in x around 0 94.0%

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

   4. Taylor expanded in y around 0 91.9%

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

      1. *-commutative 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in z around 0 87.3%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -96000000 \lor \neg \left(y \leq 1.35 \cdot 10^{+16}\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -75000000 \lor \neg \left(y \leq 8 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -75000000.0) (not (<= y 8e+15)))
   (+ x (/ (+ z (/ (- 27464.7644705 (* z a)) y)) y))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -75000000.0) || !(y <= 8e+15)) {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-75000000.0d0)) .or. (.not. (y <= 8d+15))) then
        tmp = x + ((z + ((27464.7644705d0 - (z * a)) / y)) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -75000000.0) || !(y <= 8e+15)) {
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -75000000.0) or not (y <= 8e+15):
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y)
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -75000000.0) || !(y <= 8e+15))
		tmp = Float64(x + Float64(Float64(z + Float64(Float64(27464.7644705 - Float64(z * a)) / y)) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -75000000.0) || ~((y <= 8e+15)))
		tmp = x + ((z + ((27464.7644705 - (z * a)) / y)) / y);
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -75000000.0], N[Not[LessEqual[y, 8e+15]], $MachinePrecision]], N[(x + N[(N[(z + N[(N[(27464.7644705 - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $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 < -7.5e7 or 8e15 < y

   1. Initial program 4.9%

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

   3. Taylor expanded in y around -inf 56.3%

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

   4. Taylor expanded in x around 0 68.7%

      \[\leadsto x + -1 \cdot \color{blue}{\frac{-1 \cdot z + -1 \cdot \frac{27464.7644705 - a \cdot z}{y}}{y}} \]
   5. Step-by-step derivation

      1. distribute-lft-out 68.7%

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

      2. *-commutative 68.7%

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

   6. Simplified 68.7%

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

   if -7.5e7 < y < 8e15

   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. Add Preprocessing

   3. Taylor expanded in y around 0 88.6%

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

      1. *-commutative 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in y around 0 87.2%

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

      1. *-commutative 91.9%

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

   8. Simplified 87.2%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -75000000 \lor \neg \left(y \leq 8 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z + \frac{27464.7644705 - z \cdot a}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -100000000 \lor \neg \left(y \leq 5.5 \cdot 10^{+16}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -100000000.0) (not (<= y 5.5e+16)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -100000000.0) || !(y <= 5.5e+16)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-100000000.0d0)) .or. (.not. (y <= 5.5d+16))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -100000000.0) || !(y <= 5.5e+16)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -100000000.0) or not (y <= 5.5e+16):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -100000000.0) || !(y <= 5.5e+16))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -100000000.0) || ~((y <= 5.5e+16)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -100000000.0], N[Not[LessEqual[y, 5.5e+16]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $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 < -1e8 or 5.5e16 < y

   1. Initial program 4.9%

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

   3. Taylor expanded in y around inf 66.9%

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

   if -1e8 < y < 5.5e16

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 88.0%

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

      1. *-commutative 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in y around 0 86.6%

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

      1. *-commutative 91.2%

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

   8. Simplified 86.6%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -100000000 \lor \neg \left(y \leq 5.5 \cdot 10^{+16}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -31500000 \lor \neg \left(y \leq 5.7 \cdot 10^{+16}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -31500000.0) (not (<= y 5.7e+16)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/ (+ 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 <= -31500000.0) || !(y <= 5.7e+16)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} 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 <= (-31500000.0d0)) .or. (.not. (y <= 5.7d+16))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    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 <= -31500000.0) || !(y <= 5.7e+16)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} 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 <= -31500000.0) or not (y <= 5.7e+16):
		tmp = (x + (z / y)) - ((x * a) / y)
	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 <= -31500000.0) || !(y <= 5.7e+16))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	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 <= -31500000.0) || ~((y <= 5.7e+16)))
		tmp = (x + (z / y)) - ((x * a) / y);
	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, -31500000.0], N[Not[LessEqual[y, 5.7e+16]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $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 < -3.15e7 or 5.7e16 < y

   1. Initial program 4.9%

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

   3. Taylor expanded in y around inf 66.9%

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

   if -3.15e7 < y < 5.7e16

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 88.0%

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

      1. *-commutative 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in y around 0 78.7%

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

      1. *-commutative 78.7%

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

   8. Simplified 78.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31500000 \lor \neg \left(y \leq 5.7 \cdot 10^{+16}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5000000 \lor \neg \left(y \leq 1.9 \cdot 10^{+15}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5000000.0) (not (<= y 1.9e+15)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/ t (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5000000.0) || !(y <= 1.9e+15)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-5000000.0d0)) .or. (.not. (y <= 1.9d+15))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = t / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5000000.0) || !(y <= 1.9e+15)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5000000.0) or not (y <= 1.9e+15):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5000000.0) || !(y <= 1.9e+15))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5000000.0) || ~((y <= 1.9e+15)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5000000.0], N[Not[LessEqual[y, 1.9e+15]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e6 or 1.9e15 < y

   1. Initial program 5.7%

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

   3. Taylor expanded in y around inf 65.8%

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

   if -5e6 < y < 1.9e15

   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. Add Preprocessing

   3. Taylor expanded in t around inf 76.0%

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

   4. Taylor expanded in y around 0 74.6%

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

      1. *-commutative 74.6%

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

   6. Simplified 74.6%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5000000 \lor \neg \left(y \leq 1.9 \cdot 10^{+15}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -32000000 \lor \neg \left(y \leq 4.3 \cdot 10^{+15}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -32000000.0) (not (<= y 4.3e+15)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/ t (+ 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 <= -32000000.0) || !(y <= 4.3e+15)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = t / (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 <= (-32000000.0d0)) .or. (.not. (y <= 4.3d+15))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = t / (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 <= -32000000.0) || !(y <= 4.3e+15)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -32000000.0) or not (y <= 4.3e+15):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = t / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -32000000.0) || !(y <= 4.3e+15))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(t / 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 <= -32000000.0) || ~((y <= 4.3e+15)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = t / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -32000000.0], N[Not[LessEqual[y, 4.3e+15]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e7 or 4.3e15 < y

   1. Initial program 5.7%

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

   3. Taylor expanded in y around inf 65.8%

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

   if -3.2e7 < y < 4.3e15

   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. Add Preprocessing

   3. Taylor expanded in t around inf 76.0%

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

   4. Taylor expanded in y around 0 69.5%

      \[\leadsto \frac{t}{i + \color{blue}{c \cdot y}} \]
   5. Step-by-step derivation

      1. *-commutative 69.5%

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

   6. Simplified 69.5%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -32000000 \lor \neg \left(y \leq 4.3 \cdot 10^{+15}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -100000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -100000000.0) x (if (<= y 3e+15) (/ t (+ i (* y c))) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -100000000.0) {
		tmp = x;
	} else if (y <= 3e+15) {
		tmp = t / (i + (y * c));
	} 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 <= (-100000000.0d0)) then
        tmp = x
    else if (y <= 3d+15) then
        tmp = t / (i + (y * c))
    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 <= -100000000.0) {
		tmp = x;
	} else if (y <= 3e+15) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -100000000.0:
		tmp = x
	elif y <= 3e+15:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -100000000.0)
		tmp = x;
	elseif (y <= 3e+15)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	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 <= -100000000.0)
		tmp = x;
	elseif (y <= 3e+15)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -100000000.0], x, If[LessEqual[y, 3e+15], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1e8 or 3e15 < y

   1. Initial program 5.7%

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

   3. Taylor expanded in y around inf 56.0%

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

   if -1e8 < y < 3e15

   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. Add Preprocessing

   3. Taylor expanded in t around inf 76.0%

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

   4. Taylor expanded in y around 0 69.5%

      \[\leadsto \frac{t}{i + \color{blue}{c \cdot y}} \]
   5. Step-by-step derivation

      1. *-commutative 69.5%

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

   6. Simplified 69.5%

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

Alternative 14: 50.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.55e-39) x (if (<= y 4e+15) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.55e-39) {
		tmp = x;
	} else if (y <= 4e+15) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.55d-39)) then
        tmp = x
    else if (y <= 4d+15) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.55e-39) {
		tmp = x;
	} else if (y <= 4e+15) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.55e-39:
		tmp = x
	elif y <= 4e+15:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.55e-39)
		tmp = x;
	elseif (y <= 4e+15)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.55e-39)
		tmp = x;
	elseif (y <= 4e+15)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.55e-39], x, If[LessEqual[y, 4e+15], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.54999999999999994e-39 or 4e15 < y

   1. Initial program 12.1%

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

   3. Taylor expanded in y around inf 53.2%

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

   if -2.54999999999999994e-39 < y < 4e15

   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. Add Preprocessing

   3. Taylor expanded in y around 0 55.2%

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

Alternative 15: 25.9% 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 54.9%

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

3. Taylor expanded in y around inf 28.7%

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

Reproduce

herbie shell --seed 2024102 
(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)))