Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.6% → 83.9%

Time: 29.2s

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: 55.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -6 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+46}:\\ \;\;\;\;\frac{\left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right) + t}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t_1} + \left(\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (<= y -6e+46)
     (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
     (if (<= y 1.65e+46)
       (/
        (+
         (+
          (* x (pow y 4.0))
          (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
         t)
        t_1)
       (+ (/ t t_1) (- (+ x (/ z y)) (/ (* x a) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -6e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.65e+46) {
		tmp = (((x * pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) + t) / t_1;
	} else {
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    if (y <= (-6d+46)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 1.65d+46) then
        tmp = (((x * (y ** 4.0d0)) + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) + t) / t_1
    else
        tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -6e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.65e+46) {
		tmp = (((x * Math.pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) + t) / t_1;
	} else {
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	tmp = 0
	if y <= -6e+46:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 1.65e+46:
		tmp = (((x * math.pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) + t) / t_1
	else:
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if (y <= -6e+46)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 1.65e+46)
		tmp = Float64(Float64(Float64(Float64(x * (y ^ 4.0)) + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) + t) / t_1);
	else
		tmp = Float64(Float64(t / t_1) + Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	tmp = 0.0;
	if (y <= -6e+46)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 1.65e+46)
		tmp = (((x * (y ^ 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) + t) / t_1;
	else
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -6e+46], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+46], N[(N[(N[(N[(x * N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000047e46

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 56.3%

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

      1. associate--l+ 56.3%

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

      2. +-commutative 56.3%

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

      3. associate-*r/ 56.3%

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

      4. metadata-eval 56.3%

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

      5. unpow2 56.3%

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

      6. unpow2 56.3%

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

      7. unpow2 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in b around 0 62.4%

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

      1. associate--l+ 62.4%

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

      2. associate-*r/ 62.4%

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

      3. metadata-eval 62.4%

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

      4. unpow2 62.4%

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

      5. associate-/l* 62.3%

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

      6. associate--r+ 62.3%

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

      7. associate-/l* 62.4%

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

      8. div-sub 62.4%

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

      9. associate-/l* 64.5%

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

      10. unpow2 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in a around 0 70.5%

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

      1. +-commutative 70.5%

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

      2. associate-*r/ 70.5%

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

      3. metadata-eval 70.5%

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

      4. unpow2 70.5%

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

      5. associate-/r* 70.5%

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

   10. Simplified 70.5%

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

   if -6.00000000000000047e46 < y < 1.6499999999999999e46

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0 96.8%

      \[\leadsto \frac{\color{blue}{\left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 1.6499999999999999e46 < y

   1. Initial program 2.9%

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

   2. Taylor expanded in t around 0 2.9%

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

   3. Taylor expanded in y around inf 75.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+46}:\\ \;\;\;\;\frac{\left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \left(\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\right)\\ \end{array} \]

Alternative 2: 84.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -6 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t_1} + \left(\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (<= y -6e+46)
     (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
     (if (<= y 1.65e+46)
       (/
        (+
         t
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
        t_1)
       (+ (/ t t_1) (- (+ x (/ z y)) (/ (* x a) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -6e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.65e+46) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	} else {
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    if (y <= (-6d+46)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 1.65d+46) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / t_1
    else
        tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -6e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.65e+46) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	} else {
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	tmp = 0
	if y <= -6e+46:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 1.65e+46:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1
	else:
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if (y <= -6e+46)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 1.65e+46)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / t_1);
	else
		tmp = Float64(Float64(t / t_1) + Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	tmp = 0.0;
	if (y <= -6e+46)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 1.65e+46)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	else
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -6e+46], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+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] / t$95$1), $MachinePrecision], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000047e46

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 56.3%

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

      1. associate--l+ 56.3%

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

      2. +-commutative 56.3%

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

      3. associate-*r/ 56.3%

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

      4. metadata-eval 56.3%

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

      5. unpow2 56.3%

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

      6. unpow2 56.3%

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

      7. unpow2 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in b around 0 62.4%

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

      1. associate--l+ 62.4%

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

      2. associate-*r/ 62.4%

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

      3. metadata-eval 62.4%

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

      4. unpow2 62.4%

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

      5. associate-/l* 62.3%

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

      6. associate--r+ 62.3%

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

      7. associate-/l* 62.4%

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

      8. div-sub 62.4%

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

      9. associate-/l* 64.5%

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

      10. unpow2 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in a around 0 70.5%

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

      1. +-commutative 70.5%

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

      2. associate-*r/ 70.5%

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

      3. metadata-eval 70.5%

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

      4. unpow2 70.5%

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

      5. associate-/r* 70.5%

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

   10. Simplified 70.5%

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

   if -6.00000000000000047e46 < y < 1.6499999999999999e46

   1. Initial program 96.7%

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

   if 1.6499999999999999e46 < y

   1. Initial program 2.9%

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

   2. Taylor expanded in t around 0 2.9%

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

   3. Taylor expanded in y around inf 75.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \left(\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\right)\\ \end{array} \]

Alternative 3: 80.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+47}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{1}{\frac{t_1}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right) + t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t_1} + \left(\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (<= y -2.35e+47)
     (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
     (if (<= y 3.8e+43)
       (/
        1.0
        (/ t_1 (+ (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))) t)))
       (+ (/ t t_1) (- (+ x (/ z y)) (/ (* x a) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -2.35e+47) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 3.8e+43) {
		tmp = 1.0 / (t_1 / ((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) + t));
	} else {
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    if (y <= (-2.35d+47)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 3.8d+43) then
        tmp = 1.0d0 / (t_1 / ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z))))) + t))
    else
        tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -2.35e+47) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 3.8e+43) {
		tmp = 1.0 / (t_1 / ((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) + t));
	} else {
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	tmp = 0
	if y <= -2.35e+47:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 3.8e+43:
		tmp = 1.0 / (t_1 / ((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) + t))
	else:
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if (y <= -2.35e+47)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 3.8e+43)
		tmp = Float64(1.0 / Float64(t_1 / Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z))))) + t)));
	else
		tmp = Float64(Float64(t / t_1) + Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	tmp = 0.0;
	if (y <= -2.35e+47)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 3.8e+43)
		tmp = 1.0 / (t_1 / ((y * (230661.510616 + (y * (27464.7644705 + (y * z))))) + t));
	else
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -2.35e+47], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+43], N[(1.0 / N[(t$95$1 / N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.34999999999999982e47

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. associate--l+ 57.4%

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

      2. +-commutative 57.4%

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

      3. associate-*r/ 57.4%

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

      4. metadata-eval 57.4%

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

      5. unpow2 57.4%

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

      6. unpow2 57.4%

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

      7. unpow2 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in b around 0 63.6%

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

      1. associate--l+ 63.6%

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

      2. associate-*r/ 63.6%

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

      3. metadata-eval 63.6%

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

      4. unpow2 63.6%

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

      5. associate-/l* 63.5%

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

      6. associate--r+ 63.5%

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

      7. associate-/l* 63.6%

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

      8. div-sub 63.6%

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

      9. associate-/l* 65.8%

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

      10. unpow2 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*r/ 71.9%

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

      3. metadata-eval 71.9%

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

      4. unpow2 71.9%

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

      5. associate-/r* 71.9%

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

   10. Simplified 71.9%

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

   if -2.34999999999999982e47 < y < 3.80000000000000008e43

   1. Initial program 96.1%

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

      1. clear-num 95.9%

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

      2. inv-pow 95.9%

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

   3. Applied egg-rr 95.9%

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

      1. unpow-1 95.9%

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

      2. fma-udef 95.9%

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

      3. *-commutative 95.9%

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

      4. fma-def 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in x around 0 91.2%

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

   if 3.80000000000000008e43 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in t around 0 5.1%

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

   3. Taylor expanded in y around inf 73.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+47}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right) + t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \left(\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\right)\\ \end{array} \]

Alternative 4: 79.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t_1} + \left(\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (<= y -5.5e+46)
     (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
     (if (<= y 1.32e+46)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* y y)))))))
        t_1)
       (+ (/ t t_1) (- (+ x (/ z y)) (/ (* x a) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -5.5e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.32e+46) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_1;
	} else {
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    if (y <= (-5.5d+46)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 1.32d+46) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (y * y))))))) / t_1
    else
        tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -5.5e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.32e+46) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_1;
	} else {
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	tmp = 0
	if y <= -5.5e+46:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 1.32e+46:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_1
	else:
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if (y <= -5.5e+46)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 1.32e+46)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * Float64(y * y))))))) / t_1);
	else
		tmp = Float64(Float64(t / t_1) + Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	tmp = 0.0;
	if (y <= -5.5e+46)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 1.32e+46)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_1;
	else
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -5.5e+46], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e+46], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999998e46

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 56.3%

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

      1. associate--l+ 56.3%

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

      2. +-commutative 56.3%

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

      3. associate-*r/ 56.3%

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

      4. metadata-eval 56.3%

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

      5. unpow2 56.3%

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

      6. unpow2 56.3%

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

      7. unpow2 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in b around 0 62.4%

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

      1. associate--l+ 62.4%

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

      2. associate-*r/ 62.4%

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

      3. metadata-eval 62.4%

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

      4. unpow2 62.4%

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

      5. associate-/l* 62.3%

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

      6. associate--r+ 62.3%

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

      7. associate-/l* 62.4%

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

      8. div-sub 62.4%

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

      9. associate-/l* 64.5%

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

      10. unpow2 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in a around 0 70.5%

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

      1. +-commutative 70.5%

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

      2. associate-*r/ 70.5%

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

      3. metadata-eval 70.5%

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

      4. unpow2 70.5%

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

      5. associate-/r* 70.5%

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

   10. Simplified 70.5%

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

   if -5.4999999999999998e46 < y < 1.32e46

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0 92.2%

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

      1. unpow2 92.2%

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

   4. Simplified 92.2%

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

   if 1.32e46 < y

   1. Initial program 2.9%

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

   2. Taylor expanded in t around 0 2.9%

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

   3. Taylor expanded in y around inf 75.1%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \left(\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\right)\\ \end{array} \]

Alternative 5: 79.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t_1} + \left(\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (<= y -1.5e+47)
     (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
     (if (<= y 2.5e+38)
       (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) t_1)
       (+ (/ t t_1) (- (+ x (/ z y)) (/ (* x a) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -1.5e+47) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 2.5e+38) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1;
	} else {
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    if (y <= (-1.5d+47)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 2.5d+38) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / t_1
    else
        tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -1.5e+47) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 2.5e+38) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1;
	} else {
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	tmp = 0
	if y <= -1.5e+47:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 2.5e+38:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1
	else:
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if (y <= -1.5e+47)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 2.5e+38)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / t_1);
	else
		tmp = Float64(Float64(t / t_1) + Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	tmp = 0.0;
	if (y <= -1.5e+47)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 2.5e+38)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1;
	else
		tmp = (t / t_1) + ((x + (z / y)) - ((x * a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -1.5e+47], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+38], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e47

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. associate--l+ 57.4%

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

      2. +-commutative 57.4%

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

      3. associate-*r/ 57.4%

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

      4. metadata-eval 57.4%

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

      5. unpow2 57.4%

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

      6. unpow2 57.4%

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

      7. unpow2 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in b around 0 63.6%

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

      1. associate--l+ 63.6%

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

      2. associate-*r/ 63.6%

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

      3. metadata-eval 63.6%

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

      4. unpow2 63.6%

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

      5. associate-/l* 63.5%

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

      6. associate--r+ 63.5%

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

      7. associate-/l* 63.6%

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

      8. div-sub 63.6%

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

      9. associate-/l* 65.8%

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

      10. unpow2 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*r/ 71.9%

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

      3. metadata-eval 71.9%

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

      4. unpow2 71.9%

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

      5. associate-/r* 71.9%

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

   10. Simplified 71.9%

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

   if -1.5000000000000001e47 < y < 2.49999999999999985e38

   1. Initial program 96.1%

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

   2. Taylor expanded in z around inf 89.4%

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

      1. *-commutative 89.4%

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

      2. unpow2 89.4%

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

   4. Simplified 89.4%

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

   if 2.49999999999999985e38 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in t around 0 5.1%

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

   3. Taylor expanded in y around inf 73.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \left(\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\right)\\ \end{array} \]

Alternative 6: 80.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+47}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.8e+47)
   (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
   (if (<= y 1.5e+42)
     (/
      (+ t (* y (+ 230661.510616 (* z (* y y)))))
      (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
     (+ x (- (/ z y) (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.8e+47) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.5e+42) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.8d+47)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 1.5d+42) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = x + ((z / y) - (a / (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.8e+47) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.5e+42) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.8e+47:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 1.5e+42:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = x + ((z / y) - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.8e+47)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 1.5e+42)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.8e+47)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 1.5e+42)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = x + ((z / y) - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.8e+47], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+42], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000003e47

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. associate--l+ 57.4%

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

      2. +-commutative 57.4%

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

      3. associate-*r/ 57.4%

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

      4. metadata-eval 57.4%

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

      5. unpow2 57.4%

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

      6. unpow2 57.4%

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

      7. unpow2 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in b around 0 63.6%

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

      1. associate--l+ 63.6%

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

      2. associate-*r/ 63.6%

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

      3. metadata-eval 63.6%

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

      4. unpow2 63.6%

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

      5. associate-/l* 63.5%

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

      6. associate--r+ 63.5%

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

      7. associate-/l* 63.6%

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

      8. div-sub 63.6%

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

      9. associate-/l* 65.8%

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

      10. unpow2 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*r/ 71.9%

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

      3. metadata-eval 71.9%

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

      4. unpow2 71.9%

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

      5. associate-/r* 71.9%

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

   10. Simplified 71.9%

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

   if -3.8000000000000003e47 < y < 1.50000000000000014e42

   1. Initial program 96.1%

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

   2. Taylor expanded in z around inf 89.4%

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

      1. *-commutative 89.4%

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

      2. unpow2 89.4%

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

   4. Simplified 89.4%

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

   if 1.50000000000000014e42 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in y around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+47}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 7: 77.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{+47}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.56e+47)
   (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
   (if (<= y 7e+40)
     (/
      (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
      (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
     (+ x (- (/ z y) (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.56e+47) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 7e+40) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a / (y / 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 <= (-1.56d+47)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 7d+40) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = x + ((z / y) - (a / (y / 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 <= -1.56e+47) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 7e+40) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.56e+47:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 7e+40:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = x + ((z / y) - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.56e+47)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 7e+40)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.56e+47)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 7e+40)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = x + ((z / y) - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.56e+47], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+40], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55999999999999998e47

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. associate--l+ 57.4%

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

      2. +-commutative 57.4%

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

      3. associate-*r/ 57.4%

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

      4. metadata-eval 57.4%

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

      5. unpow2 57.4%

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

      6. unpow2 57.4%

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

      7. unpow2 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in b around 0 63.6%

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

      1. associate--l+ 63.6%

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

      2. associate-*r/ 63.6%

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

      3. metadata-eval 63.6%

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

      4. unpow2 63.6%

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

      5. associate-/l* 63.5%

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

      6. associate--r+ 63.5%

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

      7. associate-/l* 63.6%

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

      8. div-sub 63.6%

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

      9. associate-/l* 65.8%

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

      10. unpow2 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*r/ 71.9%

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

      3. metadata-eval 71.9%

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

      4. unpow2 71.9%

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

      5. associate-/r* 71.9%

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

   10. Simplified 71.9%

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

   if -1.55999999999999998e47 < y < 6.9999999999999998e40

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 87.3%

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

      1. *-commutative 87.3%

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

   4. Simplified 87.3%

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

   if 6.9999999999999998e40 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in y around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{+47}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 8: 76.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+39}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.2e+46)
   (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
   (if (<= y 1.85e+39)
     (/ (+ t (* y 230661.510616)) (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
     (+ x (- (/ z y) (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.2e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.85e+39) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-6.2d+46)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 1.85d+39) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = x + ((z / y) - (a / (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.2e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.85e+39) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.2e+46:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 1.85e+39:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = x + ((z / y) - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.2e+46)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 1.85e+39)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -6.2e+46)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 1.85e+39)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = x + ((z / y) - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.2e+46], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+39], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1999999999999995e46

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. associate--l+ 57.4%

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

      2. +-commutative 57.4%

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

      3. associate-*r/ 57.4%

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

      4. metadata-eval 57.4%

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

      5. unpow2 57.4%

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

      6. unpow2 57.4%

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

      7. unpow2 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in b around 0 63.6%

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

      1. associate--l+ 63.6%

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

      2. associate-*r/ 63.6%

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

      3. metadata-eval 63.6%

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

      4. unpow2 63.6%

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

      5. associate-/l* 63.5%

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

      6. associate--r+ 63.5%

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

      7. associate-/l* 63.6%

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

      8. div-sub 63.6%

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

      9. associate-/l* 65.8%

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

      10. unpow2 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*r/ 71.9%

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

      3. metadata-eval 71.9%

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

      4. unpow2 71.9%

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

      5. associate-/r* 71.9%

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

   10. Simplified 71.9%

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

   if -6.1999999999999995e46 < y < 1.85000000000000006e39

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 85.2%

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

      1. *-commutative 85.2%

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

   4. Simplified 85.2%

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

   if 1.85000000000000006e39 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in y around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+39}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 9: 69.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+47}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.9e+47)
   (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
   (if (<= y 2.05e+36)
     (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
     (+ x (- (/ z y) (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.9e+47) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 2.05e+36) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a / (y / 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 <= (-1.9d+47)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 2.05d+36) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = x + ((z / y) - (a / (y / 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 <= -1.9e+47) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 2.05e+36) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.9e+47:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 2.05e+36:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = x + ((z / y) - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.9e+47)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 2.05e+36)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.9e+47)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 2.05e+36)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = x + ((z / y) - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.9e+47], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+36], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000002e47

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. associate--l+ 57.4%

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

      2. +-commutative 57.4%

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

      3. associate-*r/ 57.4%

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

      4. metadata-eval 57.4%

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

      5. unpow2 57.4%

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

      6. unpow2 57.4%

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

      7. unpow2 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in b around 0 63.6%

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

      1. associate--l+ 63.6%

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

      2. associate-*r/ 63.6%

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

      3. metadata-eval 63.6%

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

      4. unpow2 63.6%

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

      5. associate-/l* 63.5%

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

      6. associate--r+ 63.5%

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

      7. associate-/l* 63.6%

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

      8. div-sub 63.6%

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

      9. associate-/l* 65.8%

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

      10. unpow2 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*r/ 71.9%

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

      3. metadata-eval 71.9%

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

      4. unpow2 71.9%

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

      5. associate-/r* 71.9%

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

   10. Simplified 71.9%

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

   if -1.9000000000000002e47 < y < 2.05000000000000006e36

   1. Initial program 96.1%

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

   2. Taylor expanded in t around inf 72.1%

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

   if 2.05000000000000006e36 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in y around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+47}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 10: 65.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.2e+46)
   (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
   (if (<= y 1.9e+29) (/ t (+ i (* y c))) (+ x (- (/ z y) (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.2e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.9e+29) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-6.2d+46)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 1.9d+29) then
        tmp = t / (i + (y * c))
    else
        tmp = x + ((z / y) - (a / (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.2e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 1.9e+29) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.2e+46:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 1.9e+29:
		tmp = t / (i + (y * c))
	else:
		tmp = x + ((z / y) - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.2e+46)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 1.9e+29)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -6.2e+46)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 1.9e+29)
		tmp = t / (i + (y * c));
	else
		tmp = x + ((z / y) - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.2e+46], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+29], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1999999999999995e46

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. associate--l+ 57.4%

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

      2. +-commutative 57.4%

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

      3. associate-*r/ 57.4%

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

      4. metadata-eval 57.4%

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

      5. unpow2 57.4%

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

      6. unpow2 57.4%

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

      7. unpow2 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in b around 0 63.6%

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

      1. associate--l+ 63.6%

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

      2. associate-*r/ 63.6%

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

      3. metadata-eval 63.6%

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

      4. unpow2 63.6%

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

      5. associate-/l* 63.5%

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

      6. associate--r+ 63.5%

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

      7. associate-/l* 63.6%

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

      8. div-sub 63.6%

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

      9. associate-/l* 65.8%

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

      10. unpow2 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*r/ 71.9%

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

      3. metadata-eval 71.9%

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

      4. unpow2 71.9%

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

      5. associate-/r* 71.9%

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

   10. Simplified 71.9%

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

   if -6.1999999999999995e46 < y < 1.89999999999999985e29

   1. Initial program 96.1%

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

   2. Taylor expanded in t around inf 72.1%

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

   3. Taylor expanded in y around 0 64.1%

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

      1. *-commutative 64.1%

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

   5. Simplified 64.1%

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

   if 1.89999999999999985e29 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in y around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 11: 68.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.2e+46)
   (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
   (if (<= y 2.1e+36)
     (/ t (+ i (* y (+ c (* y b)))))
     (+ x (- (/ z y) (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.2e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 2.1e+36) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-6.2d+46)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 2.1d+36) then
        tmp = t / (i + (y * (c + (y * b))))
    else
        tmp = x + ((z / y) - (a / (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.2e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 2.1e+36) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.2e+46:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 2.1e+36:
		tmp = t / (i + (y * (c + (y * b))))
	else:
		tmp = x + ((z / y) - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.2e+46)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 2.1e+36)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -6.2e+46)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 2.1e+36)
		tmp = t / (i + (y * (c + (y * b))));
	else
		tmp = x + ((z / y) - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.2e+46], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+36], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1999999999999995e46

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. associate--l+ 57.4%

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

      2. +-commutative 57.4%

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

      3. associate-*r/ 57.4%

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

      4. metadata-eval 57.4%

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

      5. unpow2 57.4%

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

      6. unpow2 57.4%

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

      7. unpow2 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in b around 0 63.6%

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

      1. associate--l+ 63.6%

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

      2. associate-*r/ 63.6%

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

      3. metadata-eval 63.6%

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

      4. unpow2 63.6%

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

      5. associate-/l* 63.5%

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

      6. associate--r+ 63.5%

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

      7. associate-/l* 63.6%

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

      8. div-sub 63.6%

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

      9. associate-/l* 65.8%

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

      10. unpow2 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*r/ 71.9%

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

      3. metadata-eval 71.9%

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

      4. unpow2 71.9%

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

      5. associate-/r* 71.9%

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

   10. Simplified 71.9%

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

   if -6.1999999999999995e46 < y < 2.10000000000000004e36

   1. Initial program 96.1%

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

   2. Taylor expanded in t around inf 72.1%

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

   3. Taylor expanded in y around 0 69.9%

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

      1. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if 2.10000000000000004e36 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in y around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 12: 63.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+46} \lor \neg \left(y \leq 1.2 \cdot 10^{+37}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6.2e+46) (not (<= y 1.2e+37)))
   (+ x (/ (- z (* 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 <= -6.2e+46) || !(y <= 1.2e+37)) {
		tmp = x + ((z - (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 <= (-6.2d+46)) .or. (.not. (y <= 1.2d+37))) then
        tmp = x + ((z - (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 <= -6.2e+46) || !(y <= 1.2e+37)) {
		tmp = x + ((z - (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 <= -6.2e+46) or not (y <= 1.2e+37):
		tmp = x + ((z - (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 <= -6.2e+46) || !(y <= 1.2e+37))
		tmp = Float64(x + Float64(Float64(z - 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 <= -6.2e+46) || ~((y <= 1.2e+37)))
		tmp = x + ((z - (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, -6.2e+46], N[Not[LessEqual[y, 1.2e+37]], $MachinePrecision]], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999995e46 or 1.2e37 < y

   1. Initial program 2.8%

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

   2. Taylor expanded in y around inf 57.9%

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

      1. associate--l+ 57.9%

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

      2. +-commutative 57.9%

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

      3. associate-*r/ 57.9%

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

      4. metadata-eval 57.9%

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

      5. unpow2 57.9%

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

      6. unpow2 57.9%

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

      7. unpow2 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in y around inf 68.3%

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

   if -6.1999999999999995e46 < y < 1.2e37

   1. Initial program 96.1%

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

   2. Taylor expanded in t around inf 72.1%

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

   3. Taylor expanded in y around 0 64.1%

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

      1. *-commutative 64.1%

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

   5. Simplified 64.1%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+46} \lor \neg \left(y \leq 1.2 \cdot 10^{+37}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]

Alternative 13: 64.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.4e+46)
   (+ x (+ (/ z y) (/ (/ 27464.7644705 y) y)))
   (if (<= y 5.2e+35) (/ t (+ i (* y c))) (+ x (/ (- z (* x a)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.4e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 5.2e+35) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-6.4d+46)) then
        tmp = x + ((z / y) + ((27464.7644705d0 / y) / y))
    else if (y <= 5.2d+35) then
        tmp = t / (i + (y * c))
    else
        tmp = x + ((z - (x * a)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.4e+46) {
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	} else if (y <= 5.2e+35) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.4e+46:
		tmp = x + ((z / y) + ((27464.7644705 / y) / y))
	elif y <= 5.2e+35:
		tmp = t / (i + (y * c))
	else:
		tmp = x + ((z - (x * a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.4e+46)
		tmp = Float64(x + Float64(Float64(z / y) + Float64(Float64(27464.7644705 / y) / y)));
	elseif (y <= 5.2e+35)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -6.4e+46)
		tmp = x + ((z / y) + ((27464.7644705 / y) / y));
	elseif (y <= 5.2e+35)
		tmp = t / (i + (y * c));
	else
		tmp = x + ((z - (x * a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.4e+46], N[(x + N[(N[(z / y), $MachinePrecision] + N[(N[(27464.7644705 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+35], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.3999999999999996e46

   1. Initial program 0.8%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. associate--l+ 57.4%

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

      2. +-commutative 57.4%

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

      3. associate-*r/ 57.4%

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

      4. metadata-eval 57.4%

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

      5. unpow2 57.4%

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

      6. unpow2 57.4%

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

      7. unpow2 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in b around 0 63.6%

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

      1. associate--l+ 63.6%

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

      2. associate-*r/ 63.6%

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

      3. metadata-eval 63.6%

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

      4. unpow2 63.6%

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

      5. associate-/l* 63.5%

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

      6. associate--r+ 63.5%

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

      7. associate-/l* 63.6%

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

      8. div-sub 63.6%

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

      9. associate-/l* 65.8%

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

      10. unpow2 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*r/ 71.9%

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

      3. metadata-eval 71.9%

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

      4. unpow2 71.9%

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

      5. associate-/r* 71.9%

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

   10. Simplified 71.9%

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

   if -6.3999999999999996e46 < y < 5.20000000000000013e35

   1. Initial program 96.1%

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

   2. Taylor expanded in t around inf 72.1%

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

   3. Taylor expanded in y around 0 64.1%

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

      1. *-commutative 64.1%

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

   5. Simplified 64.1%

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

   if 5.20000000000000013e35 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in y around inf 58.5%

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

      1. associate--l+ 58.5%

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

      2. +-commutative 58.5%

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

      3. associate-*r/ 58.5%

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

      4. metadata-eval 58.5%

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

      5. unpow2 58.5%

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

      6. unpow2 58.5%

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

      7. unpow2 58.5%

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

   4. Simplified 58.5%

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

   5. Taylor expanded in y around inf 71.4%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} + \frac{\frac{27464.7644705}{y}}{y}\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]

Alternative 14: 49.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-9}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.7e+87) x (if (<= y 5.1e-9) (/ t i) (- x (/ (* x a) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.7e+87) {
		tmp = x;
	} else if (y <= 5.1e-9) {
		tmp = t / i;
	} else {
		tmp = x - ((x * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.7d+87)) then
        tmp = x
    else if (y <= 5.1d-9) then
        tmp = t / i
    else
        tmp = x - ((x * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.7e+87) {
		tmp = x;
	} else if (y <= 5.1e-9) {
		tmp = t / i;
	} else {
		tmp = x - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.7e+87:
		tmp = x
	elif y <= 5.1e-9:
		tmp = t / i
	else:
		tmp = x - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.7e+87)
		tmp = x;
	elseif (y <= 5.1e-9)
		tmp = Float64(t / i);
	else
		tmp = Float64(x - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.7e+87)
		tmp = x;
	elseif (y <= 5.1e-9)
		tmp = t / i;
	else
		tmp = x - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.7e+87], x, If[LessEqual[y, 5.1e-9], N[(t / i), $MachinePrecision], N[(x - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.70000000000000007e87

   1. Initial program 0.4%

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

   2. Taylor expanded in y around inf 67.4%

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

   if -2.70000000000000007e87 < y < 5.10000000000000017e-9

   1. Initial program 96.0%

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

   2. Taylor expanded in y around 0 49.2%

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

   if 5.10000000000000017e-9 < y

   1. Initial program 20.9%

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

   2. Taylor expanded in x around inf 5.0%

      \[\leadsto \color{blue}{\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   3. Taylor expanded in y around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. unsub-neg 47.3%

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

   5. Simplified 47.3%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-9}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 15: 57.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.7e+87)
   x
   (if (<= y 5e+31) (/ t (+ i (* y c))) (- x (/ (* x a) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.7e+87) {
		tmp = x;
	} else if (y <= 5e+31) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x - ((x * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.7d+87)) then
        tmp = x
    else if (y <= 5d+31) then
        tmp = t / (i + (y * c))
    else
        tmp = x - ((x * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.7e+87) {
		tmp = x;
	} else if (y <= 5e+31) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.7e+87:
		tmp = x
	elif y <= 5e+31:
		tmp = t / (i + (y * c))
	else:
		tmp = x - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.7e+87)
		tmp = x;
	elseif (y <= 5e+31)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = Float64(x - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.7e+87)
		tmp = x;
	elseif (y <= 5e+31)
		tmp = t / (i + (y * c));
	else
		tmp = x - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.7e+87], x, If[LessEqual[y, 5e+31], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.70000000000000007e87

   1. Initial program 0.4%

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

   2. Taylor expanded in y around inf 67.4%

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

   if -2.70000000000000007e87 < y < 5.00000000000000027e31

   1. Initial program 93.9%

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

   2. Taylor expanded in t around inf 70.5%

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

   3. Taylor expanded in y around 0 62.7%

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

      1. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   if 5.00000000000000027e31 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in x around inf 1.2%

      \[\leadsto \color{blue}{\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   3. Taylor expanded in y around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. unsub-neg 60.8%

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

   5. Simplified 60.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 16: 50.4% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-35}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.7e+87) x (if (<= y 1.45e-35) (/ 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 <= -2.7e+87) {
		tmp = x;
	} else if (y <= 1.45e-35) {
		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 <= (-2.7d+87)) then
        tmp = x
    else if (y <= 1.45d-35) 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 <= -2.7e+87) {
		tmp = x;
	} else if (y <= 1.45e-35) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.7e+87:
		tmp = x
	elif y <= 1.45e-35:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.7e+87)
		tmp = x;
	elseif (y <= 1.45e-35)
		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 <= -2.7e+87)
		tmp = x;
	elseif (y <= 1.45e-35)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.7e+87], x, If[LessEqual[y, 1.45e-35], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000007e87 or 1.4500000000000001e-35 < y

   1. Initial program 12.7%

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

   2. Taylor expanded in y around inf 55.6%

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

   if -2.70000000000000007e87 < y < 1.4500000000000001e-35

   1. Initial program 95.9%

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

   2. Taylor expanded in y around 0 49.5%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-35}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 26.1% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.5%

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

2. Taylor expanded in y around inf 25.2%

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

3. Final simplification 25.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023275 
(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)))