Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.3% → 86.1%

Time: 27.5s

Alternatives: 13

Speedup: 1.2×

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: 55.3% 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: 86.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := {t\_1}^{2}\\ t_3 := y \cdot t\_1\\ t_4 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{+20}:\\ \;\;\;\;c \cdot \left(27464.7644705 \cdot \frac{-1}{y \cdot t\_2} - \left(230661.510616 \cdot \frac{1}{t\_2 \cdot {y}^{2}} + \left(\frac{z}{t\_2} + \frac{y \cdot x}{t\_2}\right)\right)\right) + \left(230661.510616 \cdot \frac{1}{t\_3} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{t\_1}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+61}:\\ \;\;\;\;\frac{\left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right) + t}{i + y \cdot \left(c + t\_3\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2 (pow t_1 2.0))
        (t_3 (* y t_1))
        (t_4 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.25e+84)
     t_4
     (if (<= y -1.36e+20)
       (+
        (*
         c
         (-
          (* 27464.7644705 (/ -1.0 (* y t_2)))
          (+
           (* 230661.510616 (/ 1.0 (* t_2 (pow y 2.0))))
           (+ (/ z t_2) (/ (* y x) t_2)))))
        (+
         (* 230661.510616 (/ 1.0 t_3))
         (/ (+ 27464.7644705 (* y (+ z (* y x)))) t_1)))
       (if (<= y 3.8e+61)
         (/
          (+
           (+
            (* x (pow y 4.0))
            (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
           t)
          (+ i (* y (+ c t_3))))
         t_4)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = pow(t_1, 2.0);
	double t_3 = y * t_1;
	double t_4 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.25e+84) {
		tmp = t_4;
	} else if (y <= -1.36e+20) {
		tmp = (c * ((27464.7644705 * (-1.0 / (y * t_2))) - ((230661.510616 * (1.0 / (t_2 * pow(y, 2.0)))) + ((z / t_2) + ((y * x) / t_2))))) + ((230661.510616 * (1.0 / t_3)) + ((27464.7644705 + (y * (z + (y * x)))) / t_1));
	} else if (y <= 3.8e+61) {
		tmp = (((x * pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) + t) / (i + (y * (c + t_3)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b + (y * (y + a))
    t_2 = t_1 ** 2.0d0
    t_3 = y * t_1
    t_4 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.25d+84)) then
        tmp = t_4
    else if (y <= (-1.36d+20)) then
        tmp = (c * ((27464.7644705d0 * ((-1.0d0) / (y * t_2))) - ((230661.510616d0 * (1.0d0 / (t_2 * (y ** 2.0d0)))) + ((z / t_2) + ((y * x) / t_2))))) + ((230661.510616d0 * (1.0d0 / t_3)) + ((27464.7644705d0 + (y * (z + (y * x)))) / t_1))
    else if (y <= 3.8d+61) then
        tmp = (((x * (y ** 4.0d0)) + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) + t) / (i + (y * (c + t_3)))
    else
        tmp = t_4
    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 = b + (y * (y + a));
	double t_2 = Math.pow(t_1, 2.0);
	double t_3 = y * t_1;
	double t_4 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.25e+84) {
		tmp = t_4;
	} else if (y <= -1.36e+20) {
		tmp = (c * ((27464.7644705 * (-1.0 / (y * t_2))) - ((230661.510616 * (1.0 / (t_2 * Math.pow(y, 2.0)))) + ((z / t_2) + ((y * x) / t_2))))) + ((230661.510616 * (1.0 / t_3)) + ((27464.7644705 + (y * (z + (y * x)))) / t_1));
	} else if (y <= 3.8e+61) {
		tmp = (((x * Math.pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) + t) / (i + (y * (c + t_3)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b + (y * (y + a))
	t_2 = math.pow(t_1, 2.0)
	t_3 = y * t_1
	t_4 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.25e+84:
		tmp = t_4
	elif y <= -1.36e+20:
		tmp = (c * ((27464.7644705 * (-1.0 / (y * t_2))) - ((230661.510616 * (1.0 / (t_2 * math.pow(y, 2.0)))) + ((z / t_2) + ((y * x) / t_2))))) + ((230661.510616 * (1.0 / t_3)) + ((27464.7644705 + (y * (z + (y * x)))) / t_1))
	elif y <= 3.8e+61:
		tmp = (((x * math.pow(y, 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) + t) / (i + (y * (c + t_3)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b + Float64(y * Float64(y + a)))
	t_2 = t_1 ^ 2.0
	t_3 = Float64(y * t_1)
	t_4 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.25e+84)
		tmp = t_4;
	elseif (y <= -1.36e+20)
		tmp = Float64(Float64(c * Float64(Float64(27464.7644705 * Float64(-1.0 / Float64(y * t_2))) - Float64(Float64(230661.510616 * Float64(1.0 / Float64(t_2 * (y ^ 2.0)))) + Float64(Float64(z / t_2) + Float64(Float64(y * x) / t_2))))) + Float64(Float64(230661.510616 * Float64(1.0 / t_3)) + Float64(Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))) / t_1)));
	elseif (y <= 3.8e+61)
		tmp = Float64(Float64(Float64(Float64(x * (y ^ 4.0)) + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) + t) / Float64(i + Float64(y * Float64(c + t_3))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b + (y * (y + a));
	t_2 = t_1 ^ 2.0;
	t_3 = y * t_1;
	t_4 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.25e+84)
		tmp = t_4;
	elseif (y <= -1.36e+20)
		tmp = (c * ((27464.7644705 * (-1.0 / (y * t_2))) - ((230661.510616 * (1.0 / (t_2 * (y ^ 2.0)))) + ((z / t_2) + ((y * x) / t_2))))) + ((230661.510616 * (1.0 / t_3)) + ((27464.7644705 + (y * (z + (y * x)))) / t_1));
	elseif (y <= 3.8e+61)
		tmp = (((x * (y ^ 4.0)) + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) + t) / (i + (y * (c + t_3)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[t$95$1, 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(y * t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+84], t$95$4, If[LessEqual[y, -1.36e+20], N[(N[(c * N[(N[(27464.7644705 * N[(-1.0 / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(230661.510616 * N[(1.0 / N[(t$95$2 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t$95$2), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+61], 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] / N[(i + N[(y * N[(c + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e84 or 3.79999999999999995e61 < y

   1. Initial program 0.2%

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

   3. Taylor expanded in y around inf 84.2%

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

      1. associate--l+ 84.2%

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

      2. associate-/l* 86.3%

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

   5. Simplified 86.3%

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

   if -1.25e84 < y < -1.36e20

   1. Initial program 26.1%

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

   3. Taylor expanded in i around 0 26.1%

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

   4. Taylor expanded in t around 0 55.9%

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

   5. Taylor expanded in c around 0 78.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(27464.7644705 \cdot \frac{1}{y \cdot {\left(b + y \cdot \left(a + y\right)\right)}^{2}} + \left(230661.510616 \cdot \frac{1}{{y}^{2} \cdot {\left(b + y \cdot \left(a + y\right)\right)}^{2}} + \left(\frac{z}{{\left(b + y \cdot \left(a + y\right)\right)}^{2}} + \frac{x \cdot y}{{\left(b + y \cdot \left(a + y\right)\right)}^{2}}\right)\right)\right)\right) + \left(230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(a + y\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + x \cdot y\right)}{b + y \cdot \left(a + y\right)}\right)} \]

   if -1.36e20 < y < 3.79999999999999995e61

   1. Initial program 95.2%

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

   3. Taylor expanded in x around 0 95.2%

      \[\leadsto \frac{\color{blue}{\left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{+20}:\\ \;\;\;\;c \cdot \left(27464.7644705 \cdot \frac{-1}{y \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}} - \left(230661.510616 \cdot \frac{1}{{\left(b + y \cdot \left(y + a\right)\right)}^{2} \cdot {y}^{2}} + \left(\frac{z}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \frac{y \cdot x}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}}\right)\right)\right) + \left(230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+61}:\\ \;\;\;\;\frac{\left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right) + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 89.1%

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

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 83.0%

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

      1. associate--l+ 83.0%

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

      2. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

4. Final simplification 87.7%

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

Alternative 3: 79.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -0.059:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t\_1}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.1e+79)
     t_2
     (if (<= y -0.059)
       (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1)
       (if (<= y 8.2e+32)
         (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i (* y t_1)))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.1e+79) {
		tmp = t_2;
	} else if (y <= -0.059) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else if (y <= 8.2e+32) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (y * (b + (y * (y + a))))
    t_2 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.1d+79)) then
        tmp = t_2
    else if (y <= (-0.059d0)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    else if (y <= 8.2d+32) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.1e+79) {
		tmp = t_2;
	} else if (y <= -0.059) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else if (y <= 8.2e+32) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.1e+79:
		tmp = t_2
	elif y <= -0.059:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	elif y <= 8.2e+32:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.1e+79)
		tmp = t_2;
	elseif (y <= -0.059)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1);
	elseif (y <= 8.2e+32)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.1e+79)
		tmp = t_2;
	elseif (y <= -0.059)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	elseif (y <= 8.2e+32)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+79], t$95$2, If[LessEqual[y, -0.059], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 8.2e+32], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0999999999999999e79 or 8.19999999999999961e32 < y

   1. Initial program 2.3%

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

   3. Taylor expanded in y around inf 79.1%

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

      1. associate--l+ 79.1%

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

      2. associate-/l* 81.0%

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

   5. Simplified 81.0%

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

   if -1.0999999999999999e79 < y < -0.058999999999999997

   1. Initial program 39.9%

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

   3. Taylor expanded in i around 0 39.9%

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

   4. Taylor expanded in t around 0 58.5%

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

   if -0.058999999999999997 < y < 8.19999999999999961e32

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 90.0%

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

      1. *-commutative 90.0%

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

   5. Simplified 90.0%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+79}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -0.059:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+53} \lor \neg \left(y \leq 1.05 \cdot 10^{+41}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.7e+53) (not (<= y 1.05e+41)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.7e+53) || !(y <= 1.05e+41)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.7d+53)) .or. (.not. (y <= 1.05d+41))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.7e+53) || !(y <= 1.05e+41)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.7e+53) or not (y <= 1.05e+41):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.7e+53) || !(y <= 1.05e+41))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.7e+53) || ~((y <= 1.05e+41)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.7e+53], N[Not[LessEqual[y, 1.05e+41]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7e53 or 1.05e41 < y

   1. Initial program 2.4%

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

   3. Taylor expanded in y around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. associate-/l* 77.6%

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

   5. Simplified 77.6%

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

   if -3.7e53 < y < 1.05e41

   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. Add Preprocessing

   3. Taylor expanded in x around 0 91.1%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+53} \lor \neg \left(y \leq 1.05 \cdot 10^{+41}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -0.0023:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 10^{-20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* y (+ (/ x a) (/ z (* y a))))))
   (if (<= y -4.2e+106)
     x
     (if (<= y -0.0023)
       t_1
       (if (<= y -3.05e-80)
         (/ t (* y c))
         (if (<= y 1e-20) (/ t i) (if (<= y 1.9e+137) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * ((x / a) + (z / (y * a)));
	double tmp;
	if (y <= -4.2e+106) {
		tmp = x;
	} else if (y <= -0.0023) {
		tmp = t_1;
	} else if (y <= -3.05e-80) {
		tmp = t / (y * c);
	} else if (y <= 1e-20) {
		tmp = t / i;
	} else if (y <= 1.9e+137) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((x / a) + (z / (y * a)))
    if (y <= (-4.2d+106)) then
        tmp = x
    else if (y <= (-0.0023d0)) then
        tmp = t_1
    else if (y <= (-3.05d-80)) then
        tmp = t / (y * c)
    else if (y <= 1d-20) then
        tmp = t / i
    else if (y <= 1.9d+137) then
        tmp = t_1
    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 t_1 = y * ((x / a) + (z / (y * a)));
	double tmp;
	if (y <= -4.2e+106) {
		tmp = x;
	} else if (y <= -0.0023) {
		tmp = t_1;
	} else if (y <= -3.05e-80) {
		tmp = t / (y * c);
	} else if (y <= 1e-20) {
		tmp = t / i;
	} else if (y <= 1.9e+137) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = y * ((x / a) + (z / (y * a)))
	tmp = 0
	if y <= -4.2e+106:
		tmp = x
	elif y <= -0.0023:
		tmp = t_1
	elif y <= -3.05e-80:
		tmp = t / (y * c)
	elif y <= 1e-20:
		tmp = t / i
	elif y <= 1.9e+137:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(y * Float64(Float64(x / a) + Float64(z / Float64(y * a))))
	tmp = 0.0
	if (y <= -4.2e+106)
		tmp = x;
	elseif (y <= -0.0023)
		tmp = t_1;
	elseif (y <= -3.05e-80)
		tmp = Float64(t / Float64(y * c));
	elseif (y <= 1e-20)
		tmp = Float64(t / i);
	elseif (y <= 1.9e+137)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = y * ((x / a) + (z / (y * a)));
	tmp = 0.0;
	if (y <= -4.2e+106)
		tmp = x;
	elseif (y <= -0.0023)
		tmp = t_1;
	elseif (y <= -3.05e-80)
		tmp = t / (y * c);
	elseif (y <= 1e-20)
		tmp = t / i;
	elseif (y <= 1.9e+137)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(N[(x / a), $MachinePrecision] + N[(z / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+106], x, If[LessEqual[y, -0.0023], t$95$1, If[LessEqual[y, -3.05e-80], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-20], N[(t / i), $MachinePrecision], If[LessEqual[y, 1.9e+137], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2000000000000001e106 or 1.89999999999999981e137 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 75.6%

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

   if -4.2000000000000001e106 < y < -0.0023 or 9.99999999999999945e-21 < y < 1.89999999999999981e137

   1. Initial program 37.3%

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

   3. Taylor expanded in a around inf 11.4%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{\left(i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)\right) \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)}{a \cdot {y}^{6}} + \left(\frac{t}{{y}^{3}} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{{y}^{2}}\right)}{a}} \]

   4. Taylor expanded in a around inf 30.6%

      \[\leadsto \frac{\color{blue}{z + \left(27464.7644705 \cdot \frac{1}{y} + \left(230661.510616 \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}}{a} \]

   5. Taylor expanded in y around inf 30.7%

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

      1. *-commutative 30.7%

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

   7. Simplified 30.7%

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

   if -0.0023 < y < -3.0500000000000001e-80

   1. Initial program 99.4%

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

   3. Taylor expanded in i around 0 87.4%

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

   4. Taylor expanded in y around 0 36.0%

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

   if -3.0500000000000001e-80 < y < 9.99999999999999945e-21

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 59.7%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -0.0023:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 10^{-20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+137}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-10}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t\_1}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -6.2e+78)
     t_2
     (if (<= y -2.4e-10)
       (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1)
       (if (<= y 2.8e+30)
         (/ (+ t (* y 230661.510616)) (+ i (* y t_1)))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -6.2e+78) {
		tmp = t_2;
	} else if (y <= -2.4e-10) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else if (y <= 2.8e+30) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (y * (b + (y * (y + a))))
    t_2 = x + ((z / y) - (a * (x / y)))
    if (y <= (-6.2d+78)) then
        tmp = t_2
    else if (y <= (-2.4d-10)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    else if (y <= 2.8d+30) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -6.2e+78) {
		tmp = t_2;
	} else if (y <= -2.4e-10) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else if (y <= 2.8e+30) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -6.2e+78:
		tmp = t_2
	elif y <= -2.4e-10:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	elif y <= 2.8e+30:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -6.2e+78)
		tmp = t_2;
	elseif (y <= -2.4e-10)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1);
	elseif (y <= 2.8e+30)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -6.2e+78)
		tmp = t_2;
	elseif (y <= -2.4e-10)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	elseif (y <= 2.8e+30)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+78], t$95$2, If[LessEqual[y, -2.4e-10], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.8e+30], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2e78 or 2.79999999999999983e30 < y

   1. Initial program 2.3%

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

   3. Taylor expanded in y around inf 79.1%

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

      1. associate--l+ 79.1%

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

      2. associate-/l* 81.0%

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

   5. Simplified 81.0%

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

   if -6.2e78 < y < -2.4e-10

   1. Initial program 43.4%

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

   3. Taylor expanded in i around 0 43.4%

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

   4. Taylor expanded in t around 0 60.9%

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

   if -2.4e-10 < y < 2.79999999999999983e30

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 89.3%

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

      1. *-commutative 89.3%

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

   5. Simplified 89.3%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-10}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.38 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-66}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ t (* y (+ c (* y (+ b (* y (+ y a))))))))
        (t_2 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.38e+38)
     t_2
     (if (<= y -9.5e-171)
       t_1
       (if (<= y 3.4e-66) (/ t i) (if (<= y 2.3e+42) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (y * (c + (y * (b + (y * (y + a))))));
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.38e+38) {
		tmp = t_2;
	} else if (y <= -9.5e-171) {
		tmp = t_1;
	} else if (y <= 3.4e-66) {
		tmp = t / i;
	} else if (y <= 2.3e+42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (y * (c + (y * (b + (y * (y + a))))))
    t_2 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.38d+38)) then
        tmp = t_2
    else if (y <= (-9.5d-171)) then
        tmp = t_1
    else if (y <= 3.4d-66) then
        tmp = t / i
    else if (y <= 2.3d+42) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (y * (c + (y * (b + (y * (y + a))))));
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.38e+38) {
		tmp = t_2;
	} else if (y <= -9.5e-171) {
		tmp = t_1;
	} else if (y <= 3.4e-66) {
		tmp = t / i;
	} else if (y <= 2.3e+42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t / (y * (c + (y * (b + (y * (y + a))))))
	t_2 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.38e+38:
		tmp = t_2
	elif y <= -9.5e-171:
		tmp = t_1
	elif y <= 3.4e-66:
		tmp = t / i
	elif y <= 2.3e+42:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t / Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.38e+38)
		tmp = t_2;
	elseif (y <= -9.5e-171)
		tmp = t_1;
	elseif (y <= 3.4e-66)
		tmp = Float64(t / i);
	elseif (y <= 2.3e+42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t / (y * (c + (y * (b + (y * (y + a))))));
	t_2 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.38e+38)
		tmp = t_2;
	elseif (y <= -9.5e-171)
		tmp = t_1;
	elseif (y <= 3.4e-66)
		tmp = t / i;
	elseif (y <= 2.3e+42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t / N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.38e+38], t$95$2, If[LessEqual[y, -9.5e-171], t$95$1, If[LessEqual[y, 3.4e-66], N[(t / i), $MachinePrecision], If[LessEqual[y, 2.3e+42], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3799999999999999e38 or 2.3e42 < y

   1. Initial program 3.3%

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

   3. Taylor expanded in y around inf 75.4%

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

      1. associate--l+ 75.4%

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

      2. associate-/l* 77.2%

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

   5. Simplified 77.2%

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

   if -1.3799999999999999e38 < y < -9.4999999999999994e-171 or 3.39999999999999997e-66 < y < 2.3e42

   1. Initial program 91.8%

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

   3. Taylor expanded in i around 0 66.6%

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

   4. Taylor expanded in t around inf 44.0%

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

   if -9.4999999999999994e-171 < y < 3.39999999999999997e-66

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 69.4%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+38}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-171}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-66}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+42}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.9e-10)
     t_1
     (if (<= y -3.8e-80)
       (/ t (* y c))
       (if (<= y 1.75e-20)
         (/ t i)
         (if (<= y 8e+73) (* y (+ (/ x a) (/ z (* y a)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.9e-10) {
		tmp = t_1;
	} else if (y <= -3.8e-80) {
		tmp = t / (y * c);
	} else if (y <= 1.75e-20) {
		tmp = t / i;
	} else if (y <= 8e+73) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.9d-10)) then
        tmp = t_1
    else if (y <= (-3.8d-80)) then
        tmp = t / (y * c)
    else if (y <= 1.75d-20) then
        tmp = t / i
    else if (y <= 8d+73) then
        tmp = y * ((x / a) + (z / (y * a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.9e-10) {
		tmp = t_1;
	} else if (y <= -3.8e-80) {
		tmp = t / (y * c);
	} else if (y <= 1.75e-20) {
		tmp = t / i;
	} else if (y <= 8e+73) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.9e-10:
		tmp = t_1
	elif y <= -3.8e-80:
		tmp = t / (y * c)
	elif y <= 1.75e-20:
		tmp = t / i
	elif y <= 8e+73:
		tmp = y * ((x / a) + (z / (y * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.9e-10)
		tmp = t_1;
	elseif (y <= -3.8e-80)
		tmp = Float64(t / Float64(y * c));
	elseif (y <= 1.75e-20)
		tmp = Float64(t / i);
	elseif (y <= 8e+73)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(z / Float64(y * a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.9e-10)
		tmp = t_1;
	elseif (y <= -3.8e-80)
		tmp = t / (y * c);
	elseif (y <= 1.75e-20)
		tmp = t / i;
	elseif (y <= 8e+73)
		tmp = y * ((x / a) + (z / (y * a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e-10], t$95$1, If[LessEqual[y, -3.8e-80], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-20], N[(t / i), $MachinePrecision], If[LessEqual[y, 8e+73], N[(y * N[(N[(x / a), $MachinePrecision] + N[(z / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.8999999999999999e-10 or 7.99999999999999986e73 < y

   1. Initial program 6.9%

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

   3. Taylor expanded in y around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. associate-/l* 76.9%

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

   5. Simplified 76.9%

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

   if -1.8999999999999999e-10 < y < -3.79999999999999967e-80

   1. Initial program 99.4%

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

   3. Taylor expanded in i around 0 86.5%

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

   4. Taylor expanded in y around 0 38.2%

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

   if -3.79999999999999967e-80 < y < 1.75000000000000002e-20

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 59.7%

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

   if 1.75000000000000002e-20 < y < 7.99999999999999986e73

   1. Initial program 60.0%

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

   3. Taylor expanded in a around inf 13.8%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{\left(i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)\right) \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)}{a \cdot {y}^{6}} + \left(\frac{t}{{y}^{3}} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{{y}^{2}}\right)}{a}} \]

   4. Taylor expanded in a around inf 29.8%

      \[\leadsto \frac{\color{blue}{z + \left(27464.7644705 \cdot \frac{1}{y} + \left(230661.510616 \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}}{a} \]

   5. Taylor expanded in y around inf 30.0%

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

      1. *-commutative 30.0%

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

   7. Simplified 30.0%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-10}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+38} \lor \neg \left(y \leq 1.4 \cdot 10^{+31}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.3e+38) (not (<= y 1.4e+31)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.3e+38) || !(y <= 1.4e+31)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.3d+38)) .or. (.not. (y <= 1.4d+31))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.3e+38) || !(y <= 1.4e+31)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.3e+38) or not (y <= 1.4e+31):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.3e+38) || !(y <= 1.4e+31))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.3e+38) || ~((y <= 1.4e+31)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.3e+38], N[Not[LessEqual[y, 1.4e+31]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e38 or 1.40000000000000008e31 < y

   1. Initial program 4.1%

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

   3. Taylor expanded in y around inf 74.7%

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

      1. associate--l+ 74.7%

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

      2. associate-/l* 76.5%

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

   5. Simplified 76.5%

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

   if -1.3e38 < y < 1.40000000000000008e31

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 85.6%

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

      1. *-commutative 85.6%

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

   5. Simplified 85.6%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+38} \lor \neg \left(y \leq 1.4 \cdot 10^{+31}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+38} \lor \neg \left(y \leq 1.2 \cdot 10^{+37}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.38e+38) (not (<= y 1.2e+37)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ t (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.38e+38) || !(y <= 1.2e+37)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.38d+38)) .or. (.not. (y <= 1.2d+37))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.38e+38) || !(y <= 1.2e+37)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.38e+38) or not (y <= 1.2e+37):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.38e+38) || !(y <= 1.2e+37))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.38e+38) || ~((y <= 1.2e+37)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.38e+38], N[Not[LessEqual[y, 1.2e+37]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3799999999999999e38 or 1.2e37 < y

   1. Initial program 4.1%

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

   3. Taylor expanded in y around inf 74.7%

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

      1. associate--l+ 74.7%

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

      2. associate-/l* 76.5%

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

   5. Simplified 76.5%

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

   if -1.3799999999999999e38 < y < 1.2e37

   1. Initial program 96.4%

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

   3. Taylor expanded in t around inf 71.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+38} \lor \neg \left(y \leq 1.2 \cdot 10^{+37}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 0.00015:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.4e-7)
   x
   (if (<= y -3.5e-80) (/ t (* y c)) (if (<= y 0.00015) (/ 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 <= -1.4e-7) {
		tmp = x;
	} else if (y <= -3.5e-80) {
		tmp = t / (y * c);
	} else if (y <= 0.00015) {
		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 <= (-1.4d-7)) then
        tmp = x
    else if (y <= (-3.5d-80)) then
        tmp = t / (y * c)
    else if (y <= 0.00015d0) 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 <= -1.4e-7) {
		tmp = x;
	} else if (y <= -3.5e-80) {
		tmp = t / (y * c);
	} else if (y <= 0.00015) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.4e-7:
		tmp = x
	elif y <= -3.5e-80:
		tmp = t / (y * c)
	elif y <= 0.00015:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.4e-7)
		tmp = x;
	elseif (y <= -3.5e-80)
		tmp = Float64(t / Float64(y * c));
	elseif (y <= 0.00015)
		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 <= -1.4e-7)
		tmp = x;
	elseif (y <= -3.5e-80)
		tmp = t / (y * c);
	elseif (y <= 0.00015)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.4e-7], x, If[LessEqual[y, -3.5e-80], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00015], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4000000000000001e-7 or 1.49999999999999987e-4 < y

   1. Initial program 13.1%

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

   3. Taylor expanded in y around inf 50.2%

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

   if -1.4000000000000001e-7 < y < -3.50000000000000015e-80

   1. Initial program 99.4%

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

   3. Taylor expanded in i around 0 86.5%

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

   4. Taylor expanded in y around 0 38.2%

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

   if -3.50000000000000015e-80 < y < 1.49999999999999987e-4

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 57.8%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 0.00015:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.00165:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.8e-80) x (if (<= y 0.00165) (/ 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 <= -4.8e-80) {
		tmp = x;
	} else if (y <= 0.00165) {
		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 <= (-4.8d-80)) then
        tmp = x
    else if (y <= 0.00165d0) 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 <= -4.8e-80) {
		tmp = x;
	} else if (y <= 0.00165) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.8e-80:
		tmp = x
	elif y <= 0.00165:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.8e-80)
		tmp = x;
	elseif (y <= 0.00165)
		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 <= -4.8e-80)
		tmp = x;
	elseif (y <= 0.00165)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.8e-80], x, If[LessEqual[y, 0.00165], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7999999999999998e-80 or 0.00165 < y

   1. Initial program 22.1%

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

   3. Taylor expanded in y around inf 45.4%

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

   if -4.7999999999999998e-80 < y < 0.00165

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 57.8%

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

Alternative 13: 26.9% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.4%

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

3. Taylor expanded in y around inf 27.0%

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

Reproduce

herbie shell --seed 2024094 
(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)))