Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.0% → 82.7%

Time: 31.1s

Alternatives: 17

Speedup: 3.0×

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: 55.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ t_2 := y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - t_1\right)\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{t_2} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)) (t_2 (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i)))
   (if (<= y -6.2e+48)
     (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) t_1))
     (if (<= y 5.3e+45)
       (+
        (/ t t_2)
        (/
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
         t_2))
       (- (+ (/ z y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i;
	double tmp;
	if (y <= -6.2e+48) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 5.3e+45) {
		tmp = (t / t_2) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_2);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * a) / y
    t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i
    if (y <= (-6.2d+48)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - t_1)
    else if (y <= 5.3d+45) then
        tmp = (t / t_2) + ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))) / t_2)
    else
        tmp = ((z / y) + x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i;
	double tmp;
	if (y <= -6.2e+48) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 5.3e+45) {
		tmp = (t / t_2) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_2);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i
	tmp = 0
	if y <= -6.2e+48:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1)
	elif y <= 5.3e+45:
		tmp = (t / t_2) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_2)
	else:
		tmp = ((z / y) + x) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	t_2 = Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i)
	tmp = 0.0
	if (y <= -6.2e+48)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - t_1));
	elseif (y <= 5.3e+45)
		tmp = Float64(Float64(t / t_2) + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_2));
	else
		tmp = Float64(Float64(Float64(z / y) + x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i;
	tmp = 0.0;
	if (y <= -6.2e+48)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	elseif (y <= 5.3e+45)
		tmp = (t / t_2) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_2);
	else
		tmp = ((z / y) + x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -6.2e+48], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e+45], N[(N[(t / t$95$2), $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$2), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000011e48

   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 y around inf 52.2%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 52.2%

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

      2. +-commutative 52.2%

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

      3. associate-*r/ 52.2%

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

      4. metadata-eval 52.2%

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

      5. unpow2 52.2%

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

      6. associate-/l* 55.8%

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

      7. unpow2 55.8%

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

      8. associate-/l* 55.7%

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

      9. unpow2 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -6.20000000000000011e48 < y < 5.29999999999999991e45

   1. Initial program 95.0%

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

   2. Taylor expanded in t around inf 95.0%

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

   if 5.29999999999999991e45 < y

   1. Initial program 3.9%

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

   2. Taylor expanded in y around inf 75.0%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\right)\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 2: 82.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - t_1\right)\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)))
   (if (<= y -1.02e+49)
     (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) t_1))
     (if (<= y 1.14e+46)
       (/
        (+
         t
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
        (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))
       (- (+ (/ z y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.02e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 1.14e+46) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * a) / y
    if (y <= (-1.02d+49)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - t_1)
    else if (y <= 1.14d+46) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
    else
        tmp = ((z / y) + x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.02e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 1.14e+46) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	tmp = 0
	if y <= -1.02e+49:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1)
	elif y <= 1.14e+46:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	else:
		tmp = ((z / y) + x) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	tmp = 0.0
	if (y <= -1.02e+49)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - t_1));
	elseif (y <= 1.14e+46)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	else
		tmp = Float64(Float64(Float64(z / y) + x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	tmp = 0.0;
	if (y <= -1.02e+49)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	elseif (y <= 1.14e+46)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	else
		tmp = ((z / y) + x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.02e+49], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.14e+46], 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[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02e49

   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 y around inf 52.2%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 52.2%

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

      2. +-commutative 52.2%

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

      3. associate-*r/ 52.2%

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

      4. metadata-eval 52.2%

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

      5. unpow2 52.2%

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

      6. associate-/l* 55.8%

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

      7. unpow2 55.8%

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

      8. associate-/l* 55.7%

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

      9. unpow2 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -1.02e49 < y < 1.14000000000000005e46

   1. Initial program 95.0%

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

   if 1.14000000000000005e46 < y

   1. Initial program 3.9%

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

   2. Taylor expanded in y around inf 75.0%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\right)\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 3: 78.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - t_1\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)))
   (if (<= y -1.7e+49)
     (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) t_1))
     (if (<= y 5.4e+43)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* y y)))))))
        (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))
       (- (+ (/ z y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.7e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 5.4e+43) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * a) / y
    if (y <= (-1.7d+49)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - t_1)
    else if (y <= 5.4d+43) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (y * y))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
    else
        tmp = ((z / y) + x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.7e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 5.4e+43) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	tmp = 0
	if y <= -1.7e+49:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1)
	elif y <= 5.4e+43:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	else:
		tmp = ((z / y) + x) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	tmp = 0.0
	if (y <= -1.7e+49)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - t_1));
	elseif (y <= 5.4e+43)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * Float64(y * y))))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	else
		tmp = Float64(Float64(Float64(z / y) + x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	tmp = 0.0;
	if (y <= -1.7e+49)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	elseif (y <= 5.4e+43)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	else
		tmp = ((z / y) + x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.7e+49], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+43], 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] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e49

   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 y around inf 53.1%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 53.1%

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

      2. +-commutative 53.1%

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

      3. associate-*r/ 53.1%

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

      4. metadata-eval 53.1%

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

      5. unpow2 53.1%

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

      6. associate-/l* 56.7%

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

      7. unpow2 56.7%

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

      8. associate-/l* 56.6%

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

      9. unpow2 56.6%

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

   4. Simplified 56.6%

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

   5. Taylor expanded in y around inf 63.9%

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

   if -1.7e49 < y < 5.4000000000000004e43

   1. Initial program 94.3%

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

   2. Taylor expanded in x around inf 88.5%

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

      1. *-commutative 88.5%

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

      2. unpow2 88.5%

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

   4. Simplified 88.5%

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

   if 5.4000000000000004e43 < y

   1. Initial program 3.9%

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

   2. Taylor expanded in y around inf 75.0%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 4: 79.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - t_1\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)))
   (if (<= y -1e+49)
     (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) t_1))
     (if (<= y 2.5e+32)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
        (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))
       (- (+ (/ z y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2.5e+32) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * a) / y
    if (y <= (-1d+49)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - t_1)
    else if (y <= 2.5d+32) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
    else
        tmp = ((z / y) + x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2.5e+32) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	tmp = 0
	if y <= -1e+49:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1)
	elif y <= 2.5e+32:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	else:
		tmp = ((z / y) + x) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	tmp = 0.0
	if (y <= -1e+49)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - t_1));
	elseif (y <= 2.5e+32)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	else
		tmp = Float64(Float64(Float64(z / y) + x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	tmp = 0.0;
	if (y <= -1e+49)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	elseif (y <= 2.5e+32)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	else
		tmp = ((z / y) + x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1e+49], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+32], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999946e48

   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 y around inf 52.2%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 52.2%

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

      2. +-commutative 52.2%

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

      3. associate-*r/ 52.2%

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

      4. metadata-eval 52.2%

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

      5. unpow2 52.2%

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

      6. associate-/l* 55.8%

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

      7. unpow2 55.8%

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

      8. associate-/l* 55.7%

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

      9. unpow2 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -9.99999999999999946e48 < y < 2.4999999999999999e32

   1. Initial program 95.5%

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

   2. Taylor expanded in x around 0 88.1%

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

   if 2.4999999999999999e32 < y

   1. Initial program 7.4%

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

   2. Taylor expanded in y around inf 72.9%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 5: 78.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - t_1\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)))
   (if (<= y -5.2e+48)
     (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) t_1))
     (if (<= y 2.5e+32)
       (/
        (+ t (* y (+ 230661.510616 (* z (* y y)))))
        (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))
       (- (+ (/ z y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -5.2e+48) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2.5e+32) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * a) / y
    if (y <= (-5.2d+48)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - t_1)
    else if (y <= 2.5d+32) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
    else
        tmp = ((z / y) + x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -5.2e+48) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2.5e+32) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	tmp = 0
	if y <= -5.2e+48:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1)
	elif y <= 2.5e+32:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	else:
		tmp = ((z / y) + x) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	tmp = 0.0
	if (y <= -5.2e+48)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - t_1));
	elseif (y <= 2.5e+32)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	else
		tmp = Float64(Float64(Float64(z / y) + x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	tmp = 0.0;
	if (y <= -5.2e+48)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	elseif (y <= 2.5e+32)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	else
		tmp = ((z / y) + x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -5.2e+48], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+32], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.1999999999999999e48

   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 y around inf 52.2%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 52.2%

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

      2. +-commutative 52.2%

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

      3. associate-*r/ 52.2%

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

      4. metadata-eval 52.2%

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

      5. unpow2 52.2%

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

      6. associate-/l* 55.8%

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

      7. unpow2 55.8%

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

      8. associate-/l* 55.7%

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

      9. unpow2 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -5.1999999999999999e48 < y < 2.4999999999999999e32

   1. Initial program 95.5%

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

   2. Taylor expanded in z around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. unpow2 87.2%

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

   4. Simplified 87.2%

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

   if 2.4999999999999999e32 < y

   1. Initial program 7.4%

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

   2. Taylor expanded in y around inf 72.9%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 6: 75.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - t_1\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)))
   (if (<= y -1.5e+49)
     (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) t_1))
     (if (<= y 2e+32)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))
       (- (+ (/ z y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.5e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2e+32) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * a) / y
    if (y <= (-1.5d+49)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - t_1)
    else if (y <= 2d+32) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
    else
        tmp = ((z / y) + x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.5e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2e+32) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	tmp = 0
	if y <= -1.5e+49:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1)
	elif y <= 2e+32:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	else:
		tmp = ((z / y) + x) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	tmp = 0.0
	if (y <= -1.5e+49)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - t_1));
	elseif (y <= 2e+32)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	else
		tmp = Float64(Float64(Float64(z / y) + x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	tmp = 0.0;
	if (y <= -1.5e+49)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	elseif (y <= 2e+32)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	else
		tmp = ((z / y) + x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.5e+49], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+32], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e49

   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 y around inf 53.1%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 53.1%

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

      2. +-commutative 53.1%

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

      3. associate-*r/ 53.1%

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

      4. metadata-eval 53.1%

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

      5. unpow2 53.1%

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

      6. associate-/l* 56.7%

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

      7. unpow2 56.7%

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

      8. associate-/l* 56.6%

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

      9. unpow2 56.6%

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

   4. Simplified 56.6%

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

   5. Taylor expanded in y around inf 63.9%

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

   if -1.5000000000000001e49 < y < 2.00000000000000011e32

   1. Initial program 94.8%

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

   2. Taylor expanded in y around 0 82.1%

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

      1. *-commutative 82.1%

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

   4. Simplified 82.1%

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

   if 2.00000000000000011e32 < y

   1. Initial program 7.4%

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

   2. Taylor expanded in y around inf 72.9%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 7: 74.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - t_1\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)))
   (if (<= y -1.6e+49)
     (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) t_1))
     (if (<= y 1.95e+32)
       (/
        (+ t (* y 230661.510616))
        (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))
       (- (+ (/ z y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.6e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 1.95e+32) {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * a) / y
    if (y <= (-1.6d+49)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - t_1)
    else if (y <= 1.95d+32) then
        tmp = (t + (y * 230661.510616d0)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
    else
        tmp = ((z / y) + x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.6e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 1.95e+32) {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	tmp = 0
	if y <= -1.6e+49:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1)
	elif y <= 1.95e+32:
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	else:
		tmp = ((z / y) + x) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	tmp = 0.0
	if (y <= -1.6e+49)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - t_1));
	elseif (y <= 1.95e+32)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	else
		tmp = Float64(Float64(Float64(z / y) + x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	tmp = 0.0;
	if (y <= -1.6e+49)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	elseif (y <= 1.95e+32)
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	else
		tmp = ((z / y) + x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.6e+49], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+32], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.60000000000000007e49

   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 y around inf 53.1%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 53.1%

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

      2. +-commutative 53.1%

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

      3. associate-*r/ 53.1%

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

      4. metadata-eval 53.1%

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

      5. unpow2 53.1%

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

      6. associate-/l* 56.7%

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

      7. unpow2 56.7%

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

      8. associate-/l* 56.6%

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

      9. unpow2 56.6%

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

   4. Simplified 56.6%

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

   5. Taylor expanded in y around inf 63.9%

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

   if -1.60000000000000007e49 < y < 1.95e32

   1. Initial program 94.8%

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

   2. Taylor expanded in y around 0 81.5%

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

      1. *-commutative 81.5%

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

   4. Simplified 81.5%

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

   if 1.95e32 < y

   1. Initial program 7.4%

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

   2. Taylor expanded in y around inf 72.9%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 8: 72.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - t_1\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)))
   (if (<= y -1.75e+49)
     (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) t_1))
     (if (<= y 2.5e+32)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ i (* y (+ c (* y b)))))
       (- (+ (/ z y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.75e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2.5e+32) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * a) / y
    if (y <= (-1.75d+49)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - t_1)
    else if (y <= 2.5d+32) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * b))))
    else
        tmp = ((z / y) + x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.75e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2.5e+32) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	tmp = 0
	if y <= -1.75e+49:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1)
	elif y <= 2.5e+32:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	else:
		tmp = ((z / y) + x) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	tmp = 0.0
	if (y <= -1.75e+49)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - t_1));
	elseif (y <= 2.5e+32)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(Float64(Float64(z / y) + x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	tmp = 0.0;
	if (y <= -1.75e+49)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	elseif (y <= 2.5e+32)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	else
		tmp = ((z / y) + x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.75e+49], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+32], 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], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.74999999999999987e49

   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 y around inf 53.1%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 53.1%

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

      2. +-commutative 53.1%

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

      3. associate-*r/ 53.1%

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

      4. metadata-eval 53.1%

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

      5. unpow2 53.1%

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

      6. associate-/l* 56.7%

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

      7. unpow2 56.7%

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

      8. associate-/l* 56.6%

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

      9. unpow2 56.6%

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

   4. Simplified 56.6%

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

   5. Taylor expanded in y around inf 63.9%

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

   if -1.74999999999999987e49 < y < 2.4999999999999999e32

   1. Initial program 94.8%

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

   2. Taylor expanded in x around 0 87.5%

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

   3. Taylor expanded in y around 0 77.9%

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

   4. Taylor expanded in z around 0 74.9%

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

   if 2.4999999999999999e32 < y

   1. Initial program 7.4%

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

   2. Taylor expanded in y around inf 72.9%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 9: 67.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - t_1\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)))
   (if (<= y -1.5e+49)
     (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) t_1))
     (if (<= y 2.05e+32)
       (/ t (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))
       (- (+ (/ z y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.5e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2.05e+32) {
		tmp = t / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * a) / y
    if (y <= (-1.5d+49)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - t_1)
    else if (y <= 2.05d+32) then
        tmp = t / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
    else
        tmp = ((z / y) + x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.5e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2.05e+32) {
		tmp = t / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	tmp = 0
	if y <= -1.5e+49:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1)
	elif y <= 2.05e+32:
		tmp = t / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	else:
		tmp = ((z / y) + x) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	tmp = 0.0
	if (y <= -1.5e+49)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - t_1));
	elseif (y <= 2.05e+32)
		tmp = Float64(t / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	else
		tmp = Float64(Float64(Float64(z / y) + x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	tmp = 0.0;
	if (y <= -1.5e+49)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	elseif (y <= 2.05e+32)
		tmp = t / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	else
		tmp = ((z / y) + x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.5e+49], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+32], N[(t / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e49

   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 y around inf 53.1%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 53.1%

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

      2. +-commutative 53.1%

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

      3. associate-*r/ 53.1%

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

      4. metadata-eval 53.1%

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

      5. unpow2 53.1%

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

      6. associate-/l* 56.7%

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

      7. unpow2 56.7%

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

      8. associate-/l* 56.6%

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

      9. unpow2 56.6%

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

   4. Simplified 56.6%

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

   5. Taylor expanded in y around inf 63.9%

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

   if -1.5000000000000001e49 < y < 2.0499999999999999e32

   1. Initial program 94.8%

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

   2. Taylor expanded in t around inf 67.3%

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

   if 2.0499999999999999e32 < y

   1. Initial program 7.4%

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

   2. Taylor expanded in y around inf 72.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 10: 64.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+49} \lor \neg \left(y \leq 1.35 \cdot 10^{+31}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.35e+49) (not (<= y 1.35e+31)))
   (- (+ (/ z y) x) (/ (* x a) y))
   (/ t (+ i (* y (+ c (* y (* 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 <= -1.35e+49) || !(y <= 1.35e+31)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + (y * (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 <= (-1.35d+49)) .or. (.not. (y <= 1.35d+31))) then
        tmp = ((z / y) + x) - ((x * a) / y)
    else
        tmp = t / (i + (y * (c + (y * (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 <= -1.35e+49) || !(y <= 1.35e+31)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + (y * (y * (y + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.35e+49) or not (y <= 1.35e+31):
		tmp = ((z / y) + x) - ((x * a) / y)
	else:
		tmp = t / (i + (y * (c + (y * (y * (y + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.35e+49) || !(y <= 1.35e+31))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * 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 <= -1.35e+49) || ~((y <= 1.35e+31)))
		tmp = ((z / y) + x) - ((x * a) / y);
	else
		tmp = t / (i + (y * (c + (y * (y * (y + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.35e+49], N[Not[LessEqual[y, 1.35e+31]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35000000000000005e49 or 1.34999999999999993e31 < y

   1. Initial program 4.0%

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

   2. Taylor expanded in y around inf 67.0%

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

   if -1.35000000000000005e49 < y < 1.34999999999999993e31

   1. Initial program 94.8%

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

   2. Taylor expanded in t around inf 67.3%

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

   3. Taylor expanded in b around 0 63.2%

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

      1. *-commutative 63.2%

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

      2. +-commutative 63.2%

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

      3. *-commutative 63.2%

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

      4. unpow2 63.2%

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

      5. +-commutative 63.2%

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

      6. associate-*r* 63.2%

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

   5. Simplified 63.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+49} \lor \neg \left(y \leq 1.35 \cdot 10^{+31}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 11: 64.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - t_1\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)))
   (if (<= y -1.5e+49)
     (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) t_1))
     (if (<= y 2.2e+32)
       (/ t (+ i (* y (+ c (* y (* y (+ y a)))))))
       (- (+ (/ z y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.5e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2.2e+32) {
		tmp = t / (i + (y * (c + (y * (y * (y + a))))));
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * a) / y
    if (y <= (-1.5d+49)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - t_1)
    else if (y <= 2.2d+32) then
        tmp = t / (i + (y * (c + (y * (y * (y + a))))))
    else
        tmp = ((z / y) + x) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * a) / y;
	double tmp;
	if (y <= -1.5e+49) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	} else if (y <= 2.2e+32) {
		tmp = t / (i + (y * (c + (y * (y * (y + a))))));
	} else {
		tmp = ((z / y) + x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	tmp = 0
	if y <= -1.5e+49:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1)
	elif y <= 2.2e+32:
		tmp = t / (i + (y * (c + (y * (y * (y + a))))))
	else:
		tmp = ((z / y) + x) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	tmp = 0.0
	if (y <= -1.5e+49)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - t_1));
	elseif (y <= 2.2e+32)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(y * Float64(y + a)))))));
	else
		tmp = Float64(Float64(Float64(z / y) + x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	tmp = 0.0;
	if (y <= -1.5e+49)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - t_1);
	elseif (y <= 2.2e+32)
		tmp = t / (i + (y * (c + (y * (y * (y + a))))));
	else
		tmp = ((z / y) + x) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.5e+49], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+32], N[(t / N[(i + N[(y * N[(c + N[(y * N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e49

   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 y around inf 53.1%

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 53.1%

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

      2. +-commutative 53.1%

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

      3. associate-*r/ 53.1%

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

      4. metadata-eval 53.1%

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

      5. unpow2 53.1%

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

      6. associate-/l* 56.7%

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

      7. unpow2 56.7%

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

      8. associate-/l* 56.6%

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

      9. unpow2 56.6%

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

   4. Simplified 56.6%

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

   5. Taylor expanded in y around inf 63.9%

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

   if -1.5000000000000001e49 < y < 2.20000000000000001e32

   1. Initial program 94.8%

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

   2. Taylor expanded in t around inf 67.3%

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

   3. Taylor expanded in b around 0 63.2%

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

      1. *-commutative 63.2%

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

      2. +-commutative 63.2%

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

      3. *-commutative 63.2%

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

      4. unpow2 63.2%

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

      5. +-commutative 63.2%

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

      6. associate-*r* 63.2%

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

   5. Simplified 63.2%

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

   if 2.20000000000000001e32 < y

   1. Initial program 7.4%

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

   2. Taylor expanded in y around inf 72.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 12: 64.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+49} \lor \neg \left(y \leq 2.45 \cdot 10^{+27}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + \left(y \cdot y\right) \cdot a\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.3e+49) (not (<= y 2.45e+27)))
   (- (+ (/ z y) x) (/ (* x a) y))
   (/ t (+ i (* y (+ c (* (* 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 <= -1.3e+49) || !(y <= 2.45e+27)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + ((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 <= (-1.3d+49)) .or. (.not. (y <= 2.45d+27))) then
        tmp = ((z / y) + x) - ((x * a) / y)
    else
        tmp = t / (i + (y * (c + ((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 <= -1.3e+49) || !(y <= 2.45e+27)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + ((y * y) * a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.3e+49) or not (y <= 2.45e+27):
		tmp = ((z / y) + x) - ((x * a) / y)
	else:
		tmp = t / (i + (y * (c + ((y * y) * a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.3e+49) || !(y <= 2.45e+27))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(Float64(y * y) * a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.3e+49) || ~((y <= 2.45e+27)))
		tmp = ((z / y) + x) - ((x * a) / y);
	else
		tmp = t / (i + (y * (c + ((y * y) * a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.3e+49], N[Not[LessEqual[y, 2.45e+27]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(N[(y * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999994e49 or 2.45000000000000007e27 < y

   1. Initial program 4.0%

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

   2. Taylor expanded in y around inf 67.0%

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

   if -1.29999999999999994e49 < y < 2.45000000000000007e27

   1. Initial program 94.8%

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

   2. Taylor expanded in t around inf 67.3%

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

   3. Taylor expanded in a around inf 63.1%

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

      1. unpow2 63.1%

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

   5. Simplified 63.1%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+49} \lor \neg \left(y \leq 2.45 \cdot 10^{+27}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + \left(y \cdot y\right) \cdot a\right)}\\ \end{array} \]

Alternative 13: 63.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+48} \lor \neg \left(y \leq 7 \cdot 10^{+31}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.8e+48) (not (<= y 7e+31)))
   (- (+ (/ z y) x) (/ (* 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 <= -3.8e+48) || !(y <= 7e+31)) {
		tmp = ((z / y) + x) - ((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 <= (-3.8d+48)) .or. (.not. (y <= 7d+31))) then
        tmp = ((z / y) + x) - ((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 <= -3.8e+48) || !(y <= 7e+31)) {
		tmp = ((z / y) + x) - ((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 <= -3.8e+48) or not (y <= 7e+31):
		tmp = ((z / y) + x) - ((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 <= -3.8e+48) || !(y <= 7e+31))
		tmp = Float64(Float64(Float64(z / y) + x) - 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 <= -3.8e+48) || ~((y <= 7e+31)))
		tmp = ((z / y) + x) - ((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, -3.8e+48], N[Not[LessEqual[y, 7e+31]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $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 < -3.8e48 or 7e31 < y

   1. Initial program 3.9%

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

   2. Taylor expanded in y around inf 66.5%

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

   if -3.8e48 < y < 7e31

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf 67.8%

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

   3. Taylor expanded in y around 0 58.2%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+48} \lor \neg \left(y \leq 7 \cdot 10^{+31}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]

Alternative 14: 65.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+49} \lor \neg \left(y \leq 1.85 \cdot 10^{+32}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.3e+49) (not (<= y 1.85e+32)))
   (- (+ (/ z y) x) (/ (* 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 <= -1.3e+49) || !(y <= 1.85e+32)) {
		tmp = ((z / y) + x) - ((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 <= (-1.3d+49)) .or. (.not. (y <= 1.85d+32))) then
        tmp = ((z / y) + x) - ((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 <= -1.3e+49) || !(y <= 1.85e+32)) {
		tmp = ((z / y) + x) - ((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 <= -1.3e+49) or not (y <= 1.85e+32):
		tmp = ((z / y) + x) - ((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 <= -1.3e+49) || !(y <= 1.85e+32))
		tmp = Float64(Float64(Float64(z / y) + x) - 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 <= -1.3e+49) || ~((y <= 1.85e+32)))
		tmp = ((z / y) + x) - ((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, -1.3e+49], N[Not[LessEqual[y, 1.85e+32]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $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 < -1.29999999999999994e49 or 1.85e32 < y

   1. Initial program 4.0%

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

   2. Taylor expanded in y around inf 67.0%

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

   if -1.29999999999999994e49 < y < 1.85e32

   1. Initial program 94.8%

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

   2. Taylor expanded in x around 0 87.5%

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

   3. Taylor expanded in y around 0 77.9%

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

   4. Taylor expanded in t around inf 61.8%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+49} \lor \neg \left(y \leq 1.85 \cdot 10^{+32}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 15: 58.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.6e+35) x (if (<= y 4.4e-8) (/ 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 <= -1.6e+35) {
		tmp = x;
	} else if (y <= 4.4e-8) {
		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 <= (-1.6d+35)) then
        tmp = x
    else if (y <= 4.4d-8) 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 <= -1.6e+35) {
		tmp = x;
	} else if (y <= 4.4e-8) {
		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 <= -1.6e+35:
		tmp = x
	elif y <= 4.4e-8:
		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 <= -1.6e+35)
		tmp = x;
	elseif (y <= 4.4e-8)
		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 <= -1.6e+35)
		tmp = x;
	elseif (y <= 4.4e-8)
		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, -1.6e+35], x, If[LessEqual[y, 4.4e-8], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999991e35 or 4.3999999999999997e-8 < y

   1. Initial program 9.9%

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

   2. Taylor expanded in y around inf 47.9%

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

   if -1.59999999999999991e35 < y < 4.3999999999999997e-8

   1. Initial program 97.4%

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

   2. Taylor expanded in t around inf 71.8%

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

   3. Taylor expanded in y around 0 62.9%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 50.6% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.3e+21) x (if (<= y 3e-8) (/ 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 <= -2.3e+21) {
		tmp = x;
	} else if (y <= 3e-8) {
		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 <= (-2.3d+21)) then
        tmp = x
    else if (y <= 3d-8) 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 <= -2.3e+21) {
		tmp = x;
	} else if (y <= 3e-8) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.3e+21:
		tmp = x
	elif y <= 3e-8:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.3e+21)
		tmp = x;
	elseif (y <= 3e-8)
		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 <= -2.3e+21)
		tmp = x;
	elseif (y <= 3e-8)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.3e+21], x, If[LessEqual[y, 3e-8], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e21 or 2.99999999999999973e-8 < y

   1. Initial program 10.4%

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

   2. Taylor expanded in y around inf 46.9%

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

   if -2.3e21 < y < 2.99999999999999973e-8

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 51.7%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 26.3% 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 53.3%

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

2. Taylor expanded in y around inf 25.8%

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

3. Final simplification 25.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023274 
(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)))