Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.4% → 79.4%

Time: 22.0s

Alternatives: 17

Speedup: 3.6×

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: 55.4% 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: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+47}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.7e+94)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y -6.8e+47)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 1.05e+55)
       (/
        (+ t (* y (+ 230661.510616 (* z (* y y)))))
        (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
       (if (<= y 1.7e+99)
         (+ (/ z a) (+ (* 27464.7644705 (/ 1.0 (* y a))) (/ (* x y) a)))
         (+ x (/ z 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+94) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -6.8e+47) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 1.05e+55) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else if (y <= 1.7e+99) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / 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+94)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-6.8d+47)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 1.05d+55) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    else if (y <= 1.7d+99) then
        tmp = (z / a) + ((27464.7644705d0 * (1.0d0 / (y * a))) + ((x * y) / a))
    else
        tmp = x + (z / 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+94) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -6.8e+47) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 1.05e+55) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else if (y <= 1.7e+99) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.7e+94:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -6.8e+47:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 1.05e+55:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	elif y <= 1.7e+99:
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.7e+94)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -6.8e+47)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 1.05e+55)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	elseif (y <= 1.7e+99)
		tmp = Float64(Float64(z / a) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * a))) + Float64(Float64(x * y) / a)));
	else
		tmp = Float64(x + Float64(z / 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+94)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -6.8e+47)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 1.05e+55)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	elseif (y <= 1.7e+99)
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.7e+94], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.8e+47], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+55], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+99], N[(N[(z / a), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7000000000000001e94

   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. Taylor expanded in y around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -2.7000000000000001e94 < y < -6.7999999999999996e47

   1. Initial program 12.4%

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

   2. Taylor expanded in a around inf 1.3%

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

   3. Taylor expanded in y around inf 75.9%

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

      1. +-commutative 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-+r+ 75.9%

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

      4. associate-*r/ 75.9%

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

      5. metadata-eval 75.9%

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

      6. +-commutative 75.9%

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

      7. associate-/l* 75.9%

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

   5. Simplified 75.9%

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

   if -6.7999999999999996e47 < y < 1.05e55

   1. Initial program 96.2%

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

   2. Taylor expanded in z around inf 90.6%

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

      1. *-commutative 90.6%

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

      2. unpow2 90.6%

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

   4. Simplified 90.6%

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

   if 1.05e55 < y < 1.69999999999999992e99

   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 a around inf 11.8%

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

   3. Taylor expanded in y around inf 71.2%

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

   if 1.69999999999999992e99 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 80.6%

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

   3. Taylor expanded in a around 0 85.1%

      \[\leadsto \color{blue}{\frac{z}{y} + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+47}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]

Alternative 2: 83.8% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.0%

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

      1. fma-def 93.1%

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

      2. fma-def 93.1%

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

      3. fma-def 93.1%

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

      4. fma-def 93.1%

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

      5. fma-def 93.1%

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

      6. fma-def 93.1%

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

      7. fma-def 93.1%

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

   3. Simplified 93.1%

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

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) 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. Taylor expanded in y around inf 63.9%

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

   3. Taylor expanded in a around 0 71.6%

      \[\leadsto \color{blue}{\frac{z}{y} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.0%

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

Alternative 3: 83.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
           t)
          (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))))
   (if (<= t_1 INFINITY) t_1 (+ x (/ z 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 * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x + (z / 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 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.0%

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

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) 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. Taylor expanded in y around inf 63.9%

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

   3. Taylor expanded in a around 0 71.6%

      \[\leadsto \color{blue}{\frac{z}{y} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.0%

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

Alternative 4: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+92}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -7200000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-7}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.7e+92)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y -7200000000.0)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 1.02e-7)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
       (if (<= y 3.9e+102)
         (+ (/ z a) (+ (* 27464.7644705 (/ 1.0 (* y a))) (/ (* x y) a)))
         (+ x (/ z 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+92) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -7200000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 1.02e-7) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else if (y <= 3.9e+102) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / 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+92)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-7200000000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 1.02d-7) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    else if (y <= 3.9d+102) then
        tmp = (z / a) + ((27464.7644705d0 * (1.0d0 / (y * a))) + ((x * y) / a))
    else
        tmp = x + (z / 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+92) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -7200000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 1.02e-7) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else if (y <= 3.9e+102) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.7e+92:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -7200000000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 1.02e-7:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	elif y <= 3.9e+102:
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.7e+92)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -7200000000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 1.02e-7)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	elseif (y <= 3.9e+102)
		tmp = Float64(Float64(z / a) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * a))) + Float64(Float64(x * y) / a)));
	else
		tmp = Float64(x + Float64(z / 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+92)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -7200000000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 1.02e-7)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	elseif (y <= 3.9e+102)
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.7e+92], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7200000000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e-7], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+102], N[(N[(z / a), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.6999999999999999e92

   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. Taylor expanded in y around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -2.6999999999999999e92 < y < -7.2e9

   1. Initial program 41.3%

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

   2. Taylor expanded in a around inf 7.8%

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

   3. Taylor expanded in y around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. *-commutative 50.8%

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

      3. associate-+r+ 50.8%

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

      4. associate-*r/ 50.8%

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

      5. metadata-eval 50.8%

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

      6. +-commutative 50.8%

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

      7. associate-/l* 55.5%

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

   5. Simplified 55.5%

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

   if -7.2e9 < y < 1.02e-7

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 91.3%

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

      1. *-commutative 91.3%

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

   4. Simplified 91.3%

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

   if 1.02e-7 < y < 3.8999999999999998e102

   1. Initial program 50.8%

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

   2. Taylor expanded in a around inf 20.3%

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

   3. Taylor expanded in y around inf 50.2%

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

   if 3.8999999999999998e102 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 80.6%

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

   3. Taylor expanded in a around 0 85.1%

      \[\leadsto \color{blue}{\frac{z}{y} + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+92}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -7200000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-7}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]

Alternative 5: 76.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z a) (+ (* 27464.7644705 (/ 1.0 (* y a))) (/ (* x y) a)))))
   (if (<= y -9.6e+95)
     (+ (/ z y) (- x (/ a (/ y x))))
     (if (<= y -1.1e+32)
       t_1
       (if (<= y 1.02e+55)
         (/
          (+ t (* y (+ 230661.510616 (* z (* y y)))))
          (+ i (* y (+ c (* y (+ b (* y y)))))))
         (if (<= y 3.1e+102) t_1 (+ x (/ z y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	double tmp;
	if (y <= -9.6e+95) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -1.1e+32) {
		tmp = t_1;
	} else if (y <= 1.02e+55) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * (b + (y * y))))));
	} else if (y <= 3.1e+102) {
		tmp = t_1;
	} else {
		tmp = x + (z / 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 = (z / a) + ((27464.7644705d0 * (1.0d0 / (y * a))) + ((x * y) / a))
    if (y <= (-9.6d+95)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-1.1d+32)) then
        tmp = t_1
    else if (y <= 1.02d+55) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / (i + (y * (c + (y * (b + (y * y))))))
    else if (y <= 3.1d+102) then
        tmp = t_1
    else
        tmp = x + (z / 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 = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	double tmp;
	if (y <= -9.6e+95) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -1.1e+32) {
		tmp = t_1;
	} else if (y <= 1.02e+55) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * (b + (y * y))))));
	} else if (y <= 3.1e+102) {
		tmp = t_1;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a))
	tmp = 0
	if y <= -9.6e+95:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -1.1e+32:
		tmp = t_1
	elif y <= 1.02e+55:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * (b + (y * y))))))
	elif y <= 3.1e+102:
		tmp = t_1
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / a) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * a))) + Float64(Float64(x * y) / a)))
	tmp = 0.0
	if (y <= -9.6e+95)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -1.1e+32)
		tmp = t_1;
	elseif (y <= 1.02e+55)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * y)))))));
	elseif (y <= 3.1e+102)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	tmp = 0.0;
	if (y <= -9.6e+95)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -1.1e+32)
		tmp = t_1;
	elseif (y <= 1.02e+55)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * (b + (y * y))))));
	elseif (y <= 3.1e+102)
		tmp = t_1;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / a), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+95], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e+32], t$95$1, If[LessEqual[y, 1.02e+55], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+102], t$95$1, N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.6000000000000002e95

   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. Taylor expanded in y around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -9.6000000000000002e95 < y < -1.1e32 or 1.02000000000000002e55 < y < 3.09999999999999987e102

   1. Initial program 25.4%

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

   2. Taylor expanded in a around inf 9.9%

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

   3. Taylor expanded in y around inf 68.1%

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

   if -1.1e32 < y < 1.02000000000000002e55

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf 92.1%

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

      1. *-commutative 92.1%

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

      2. unpow2 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in a around 0 87.7%

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

      1. *-commutative 87.7%

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

      2. +-commutative 87.7%

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

      3. unpow2 87.7%

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

   7. Simplified 87.7%

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

   if 3.09999999999999987e102 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 80.6%

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

   3. Taylor expanded in a around 0 85.1%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+102}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]

Alternative 6: 71.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+96}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -3400000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-105}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.5e+96)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y -3400000000.0)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y -1.9e-105)
       (/ t (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
       (if (<= y 5.6e-16)
         (/ (+ t (* y 230661.510616)) (+ i (* y c)))
         (if (<= y 1.65e+99)
           (+ (/ z a) (+ (* 27464.7644705 (/ 1.0 (* y a))) (/ (* x y) a)))
           (+ x (/ z y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.5e+96) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -3400000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= -1.9e-105) {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else if (y <= 5.6e-16) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 1.65e+99) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / 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 <= (-4.5d+96)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-3400000000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= (-1.9d-105)) then
        tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    else if (y <= 5.6d-16) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else if (y <= 1.65d+99) then
        tmp = (z / a) + ((27464.7644705d0 * (1.0d0 / (y * a))) + ((x * y) / a))
    else
        tmp = x + (z / 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 <= -4.5e+96) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -3400000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= -1.9e-105) {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else if (y <= 5.6e-16) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 1.65e+99) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.5e+96:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -3400000000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= -1.9e-105:
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	elif y <= 5.6e-16:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	elif y <= 1.65e+99:
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.5e+96)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -3400000000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= -1.9e-105)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	elseif (y <= 5.6e-16)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	elseif (y <= 1.65e+99)
		tmp = Float64(Float64(z / a) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * a))) + Float64(Float64(x * y) / a)));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.5e+96)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -3400000000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= -1.9e-105)
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	elseif (y <= 5.6e-16)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	elseif (y <= 1.65e+99)
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.5e+96], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3400000000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-105], N[(t / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-16], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+99], N[(N[(z / a), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.49999999999999957e96

   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. Taylor expanded in y around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -4.49999999999999957e96 < y < -3.4e9

   1. Initial program 41.3%

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

   2. Taylor expanded in a around inf 7.8%

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

   3. Taylor expanded in y around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. *-commutative 50.8%

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

      3. associate-+r+ 50.8%

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

      4. associate-*r/ 50.8%

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

      5. metadata-eval 50.8%

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

      6. +-commutative 50.8%

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

      7. associate-/l* 55.5%

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

   5. Simplified 55.5%

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

   if -3.4e9 < y < -1.8999999999999999e-105

   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. Taylor expanded in t around inf 57.5%

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

   if -1.8999999999999999e-105 < y < 5.6000000000000003e-16

   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. Taylor expanded in z around inf 98.1%

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

      1. *-commutative 98.1%

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

      2. unpow2 98.1%

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

   4. Simplified 98.1%

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

   5. Taylor expanded in y around 0 93.1%

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

   6. Taylor expanded in z around 0 92.1%

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

   if 5.6000000000000003e-16 < y < 1.65e99

   1. Initial program 57.1%

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

   2. Taylor expanded in a around inf 22.1%

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

   3. Taylor expanded in y around inf 44.3%

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

   if 1.65e99 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 80.6%

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

   3. Taylor expanded in a around 0 85.1%

      \[\leadsto \color{blue}{\frac{z}{y} + x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+96}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -3400000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-105}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]

Alternative 7: 75.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+92}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -2400000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7.5e+92)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y -2400000000.0)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 4.5e-6)
       (/
        (+ t (* y 230661.510616))
        (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
       (if (<= y 1.25e+99)
         (+ (/ z a) (+ (* 27464.7644705 (/ 1.0 (* y a))) (/ (* x y) a)))
         (+ x (/ z y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7.5e+92) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -2400000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 4.5e-6) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else if (y <= 1.25e+99) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / 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 <= (-7.5d+92)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-2400000000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 4.5d-6) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    else if (y <= 1.25d+99) then
        tmp = (z / a) + ((27464.7644705d0 * (1.0d0 / (y * a))) + ((x * y) / a))
    else
        tmp = x + (z / 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 <= -7.5e+92) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -2400000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 4.5e-6) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else if (y <= 1.25e+99) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7.5e+92:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -2400000000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 4.5e-6:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	elif y <= 1.25e+99:
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7.5e+92)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -2400000000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 4.5e-6)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	elseif (y <= 1.25e+99)
		tmp = Float64(Float64(z / a) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * a))) + Float64(Float64(x * y) / a)));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -7.5e+92)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -2400000000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 4.5e-6)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	elseif (y <= 1.25e+99)
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7.5e+92], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2400000000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-6], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+99], N[(N[(z / a), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.49999999999999946e92

   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. Taylor expanded in y around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -7.49999999999999946e92 < y < -2.4e9

   1. Initial program 41.3%

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

   2. Taylor expanded in a around inf 7.8%

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

   3. Taylor expanded in y around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. *-commutative 50.8%

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

      3. associate-+r+ 50.8%

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

      4. associate-*r/ 50.8%

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

      5. metadata-eval 50.8%

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

      6. +-commutative 50.8%

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

      7. associate-/l* 55.5%

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

   5. Simplified 55.5%

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

   if -2.4e9 < y < 4.50000000000000011e-6

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 91.2%

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

      1. *-commutative 91.2%

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

   4. Simplified 91.2%

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

   if 4.50000000000000011e-6 < y < 1.25000000000000002e99

   1. Initial program 50.8%

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

   2. Taylor expanded in a around inf 20.3%

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

   3. Taylor expanded in y around inf 50.2%

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

   if 1.25000000000000002e99 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 80.6%

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

   3. Taylor expanded in a around 0 85.1%

      \[\leadsto \color{blue}{\frac{z}{y} + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+92}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -2400000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]

Alternative 8: 70.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+92}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.6e+92)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y -1000000.0)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 6.5e-16)
       (/ (+ t (* y 230661.510616)) (+ i (* y c)))
       (if (<= y 1.25e+99)
         (+ (/ z a) (+ (* 27464.7644705 (/ 1.0 (* y a))) (/ (* x y) a)))
         (+ x (/ z y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.6e+92) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -1000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 6.5e-16) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 1.25e+99) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.6d+92)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-1000000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 6.5d-16) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else if (y <= 1.25d+99) then
        tmp = (z / a) + ((27464.7644705d0 * (1.0d0 / (y * a))) + ((x * y) / a))
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.6e+92) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -1000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 6.5e-16) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 1.25e+99) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.6e+92:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -1000000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 6.5e-16:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	elif y <= 1.25e+99:
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.6e+92)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -1000000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 6.5e-16)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	elseif (y <= 1.25e+99)
		tmp = Float64(Float64(z / a) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * a))) + Float64(Float64(x * y) / a)));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.6e+92)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -1000000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 6.5e-16)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	elseif (y <= 1.25e+99)
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.6e+92], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1000000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-16], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+99], N[(N[(z / a), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.6e92

   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. Taylor expanded in y around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -3.6e92 < y < -1e6

   1. Initial program 46.6%

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

   2. Taylor expanded in a around inf 11.6%

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

   3. Taylor expanded in y around inf 46.4%

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

      1. +-commutative 46.4%

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

      2. *-commutative 46.4%

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

      3. associate-+r+ 46.4%

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

      4. associate-*r/ 46.4%

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

      5. metadata-eval 46.4%

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

      6. +-commutative 46.4%

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

      7. associate-/l* 50.6%

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

   5. Simplified 50.6%

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

   if -1e6 < y < 6.50000000000000011e-16

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 96.9%

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

      1. *-commutative 96.9%

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

      2. unpow2 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in y around 0 87.5%

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

   6. Taylor expanded in z around 0 83.8%

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

   if 6.50000000000000011e-16 < y < 1.25000000000000002e99

   1. Initial program 57.1%

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

   2. Taylor expanded in a around inf 22.1%

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

   3. Taylor expanded in y around inf 44.3%

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

   if 1.25000000000000002e99 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 80.6%

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

   3. Taylor expanded in a around 0 85.1%

      \[\leadsto \color{blue}{\frac{z}{y} + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+92}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]

Alternative 9: 72.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -2800000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.7e+94)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y -2800000000.0)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 6.5e-16)
       (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) (+ i (* y c)))
       (if (<= y 3e+99)
         (+ (/ z a) (+ (* 27464.7644705 (/ 1.0 (* y a))) (/ (* x y) a)))
         (+ x (/ z 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+94) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -2800000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 6.5e-16) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c));
	} else if (y <= 3e+99) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / 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+94)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-2800000000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 6.5d-16) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / (i + (y * c))
    else if (y <= 3d+99) then
        tmp = (z / a) + ((27464.7644705d0 * (1.0d0 / (y * a))) + ((x * y) / a))
    else
        tmp = x + (z / 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+94) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -2800000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 6.5e-16) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c));
	} else if (y <= 3e+99) {
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.7e+94:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -2800000000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 6.5e-16:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c))
	elif y <= 3e+99:
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.7e+94)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -2800000000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 6.5e-16)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(i + Float64(y * c)));
	elseif (y <= 3e+99)
		tmp = Float64(Float64(z / a) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * a))) + Float64(Float64(x * y) / a)));
	else
		tmp = Float64(x + Float64(z / 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+94)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -2800000000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 6.5e-16)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c));
	elseif (y <= 3e+99)
		tmp = (z / a) + ((27464.7644705 * (1.0 / (y * a))) + ((x * y) / a));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.7e+94], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2800000000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-16], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+99], N[(N[(z / a), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7000000000000001e94

   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. Taylor expanded in y around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -2.7000000000000001e94 < y < -2.8e9

   1. Initial program 41.3%

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

   2. Taylor expanded in a around inf 7.8%

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

   3. Taylor expanded in y around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. *-commutative 50.8%

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

      3. associate-+r+ 50.8%

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

      4. associate-*r/ 50.8%

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

      5. metadata-eval 50.8%

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

      6. +-commutative 50.8%

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

      7. associate-/l* 55.5%

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

   5. Simplified 55.5%

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

   if -2.8e9 < y < 6.50000000000000011e-16

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 96.9%

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

      1. *-commutative 96.9%

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

      2. unpow2 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in y around 0 86.3%

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

   if 6.50000000000000011e-16 < y < 3.00000000000000014e99

   1. Initial program 57.1%

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

   2. Taylor expanded in a around inf 22.1%

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

   3. Taylor expanded in y around inf 44.3%

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

   if 3.00000000000000014e99 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 80.6%

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

   3. Taylor expanded in a around 0 85.1%

      \[\leadsto \color{blue}{\frac{z}{y} + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -2800000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \left(27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{x \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]

Alternative 10: 70.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+92}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -45000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.7e+92)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y -45000.0)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 6.5e-16)
       (/ (+ t (* y 230661.510616)) (+ i (* y c)))
       (if (<= y 1.25e+99) (+ (/ z a) (/ (* x y) a)) (+ x (/ z 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+92) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -45000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 6.5e-16) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 1.25e+99) {
		tmp = (z / a) + ((x * y) / a);
	} else {
		tmp = x + (z / 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+92)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-45000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 6.5d-16) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else if (y <= 1.25d+99) then
        tmp = (z / a) + ((x * y) / a)
    else
        tmp = x + (z / 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+92) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -45000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 6.5e-16) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 1.25e+99) {
		tmp = (z / a) + ((x * y) / a);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.7e+92:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -45000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 6.5e-16:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	elif y <= 1.25e+99:
		tmp = (z / a) + ((x * y) / a)
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.7e+92)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -45000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 6.5e-16)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	elseif (y <= 1.25e+99)
		tmp = Float64(Float64(z / a) + Float64(Float64(x * y) / a));
	else
		tmp = Float64(x + Float64(z / 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+92)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -45000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 6.5e-16)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	elseif (y <= 1.25e+99)
		tmp = (z / a) + ((x * y) / a);
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.7e+92], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -45000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-16], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+99], N[(N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.6999999999999999e92

   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. Taylor expanded in y around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -2.6999999999999999e92 < y < -45000

   1. Initial program 46.6%

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

   2. Taylor expanded in a around inf 11.6%

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

   3. Taylor expanded in y around inf 46.4%

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

      1. +-commutative 46.4%

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

      2. *-commutative 46.4%

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

      3. associate-+r+ 46.4%

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

      4. associate-*r/ 46.4%

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

      5. metadata-eval 46.4%

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

      6. +-commutative 46.4%

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

      7. associate-/l* 50.6%

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

   5. Simplified 50.6%

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

   if -45000 < y < 6.50000000000000011e-16

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 96.9%

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

      1. *-commutative 96.9%

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

      2. unpow2 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in y around 0 87.5%

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

   6. Taylor expanded in z around 0 83.8%

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

   if 6.50000000000000011e-16 < y < 1.25000000000000002e99

   1. Initial program 57.1%

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

   2. Taylor expanded in a around inf 22.1%

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

   3. Taylor expanded in y around inf 43.7%

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

   if 1.25000000000000002e99 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 80.6%

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

   3. Taylor expanded in a around 0 85.1%

      \[\leadsto \color{blue}{\frac{z}{y} + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+92}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -45000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]

Alternative 11: 65.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a} + \frac{x \cdot y}{a}\\ t_2 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -5.1 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -260:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z a) (/ (* x y) a))) (t_2 (+ x (/ z y))))
   (if (<= y -5.1e+92)
     t_2
     (if (<= y -260.0)
       t_1
       (if (<= y 4.2e-16) (/ t (+ i (* y c))) (if (<= y 3.7e+101) 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 = (z / a) + ((x * y) / a);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -5.1e+92) {
		tmp = t_2;
	} else if (y <= -260.0) {
		tmp = t_1;
	} else if (y <= 4.2e-16) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.7e+101) {
		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 = (z / a) + ((x * y) / a)
    t_2 = x + (z / y)
    if (y <= (-5.1d+92)) then
        tmp = t_2
    else if (y <= (-260.0d0)) then
        tmp = t_1
    else if (y <= 4.2d-16) then
        tmp = t / (i + (y * c))
    else if (y <= 3.7d+101) 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 = (z / a) + ((x * y) / a);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -5.1e+92) {
		tmp = t_2;
	} else if (y <= -260.0) {
		tmp = t_1;
	} else if (y <= 4.2e-16) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.7e+101) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / a) + ((x * y) / a)
	t_2 = x + (z / y)
	tmp = 0
	if y <= -5.1e+92:
		tmp = t_2
	elif y <= -260.0:
		tmp = t_1
	elif y <= 4.2e-16:
		tmp = t / (i + (y * c))
	elif y <= 3.7e+101:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / a) + Float64(Float64(x * y) / a))
	t_2 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -5.1e+92)
		tmp = t_2;
	elseif (y <= -260.0)
		tmp = t_1;
	elseif (y <= 4.2e-16)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	elseif (y <= 3.7e+101)
		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 = (z / a) + ((x * y) / a);
	t_2 = x + (z / y);
	tmp = 0.0;
	if (y <= -5.1e+92)
		tmp = t_2;
	elseif (y <= -260.0)
		tmp = t_1;
	elseif (y <= 4.2e-16)
		tmp = t / (i + (y * c));
	elseif (y <= 3.7e+101)
		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[(N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.1e+92], t$95$2, If[LessEqual[y, -260.0], t$95$1, If[LessEqual[y, 4.2e-16], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+101], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.1000000000000003e92 or 3.6999999999999997e101 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 72.4%

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

   3. Taylor expanded in a around 0 80.9%

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

   if -5.1000000000000003e92 < y < -260 or 4.2000000000000002e-16 < y < 3.6999999999999997e101

   1. Initial program 52.0%

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

   2. Taylor expanded in a around inf 17.0%

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

   3. Taylor expanded in y around inf 43.0%

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

   if -260 < y < 4.2000000000000002e-16

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 96.9%

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

      1. *-commutative 96.9%

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

      2. unpow2 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in y around 0 87.5%

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

   6. Taylor expanded in y around 0 72.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+92}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -260:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+101}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]

Alternative 12: 65.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+93}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -280:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z a) (/ (* x y) a))))
   (if (<= y -1.6e+93)
     (+ (/ z y) (- x (/ a (/ y x))))
     (if (<= y -280.0)
       t_1
       (if (<= y 6.5e-16)
         (/ t (+ i (* y c)))
         (if (<= y 3.3e+99) t_1 (+ x (/ z y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / a) + ((x * y) / a);
	double tmp;
	if (y <= -1.6e+93) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -280.0) {
		tmp = t_1;
	} else if (y <= 6.5e-16) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.3e+99) {
		tmp = t_1;
	} else {
		tmp = x + (z / 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 = (z / a) + ((x * y) / a)
    if (y <= (-1.6d+93)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-280.0d0)) then
        tmp = t_1
    else if (y <= 6.5d-16) then
        tmp = t / (i + (y * c))
    else if (y <= 3.3d+99) then
        tmp = t_1
    else
        tmp = x + (z / 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 = (z / a) + ((x * y) / a);
	double tmp;
	if (y <= -1.6e+93) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -280.0) {
		tmp = t_1;
	} else if (y <= 6.5e-16) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.3e+99) {
		tmp = t_1;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / a) + ((x * y) / a)
	tmp = 0
	if y <= -1.6e+93:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -280.0:
		tmp = t_1
	elif y <= 6.5e-16:
		tmp = t / (i + (y * c))
	elif y <= 3.3e+99:
		tmp = t_1
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / a) + Float64(Float64(x * y) / a))
	tmp = 0.0
	if (y <= -1.6e+93)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -280.0)
		tmp = t_1;
	elseif (y <= 6.5e-16)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	elseif (y <= 3.3e+99)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / a) + ((x * y) / a);
	tmp = 0.0;
	if (y <= -1.6e+93)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -280.0)
		tmp = t_1;
	elseif (y <= 6.5e-16)
		tmp = t / (i + (y * c));
	elseif (y <= 3.3e+99)
		tmp = t_1;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+93], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -280.0], t$95$1, If[LessEqual[y, 6.5e-16], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+99], t$95$1, N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6000000000000001e93

   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. Taylor expanded in y around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -1.6000000000000001e93 < y < -280 or 6.50000000000000011e-16 < y < 3.2999999999999999e99

   1. Initial program 52.0%

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

   2. Taylor expanded in a around inf 17.0%

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

   3. Taylor expanded in y around inf 43.0%

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

   if -280 < y < 6.50000000000000011e-16

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 96.9%

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

      1. *-commutative 96.9%

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

      2. unpow2 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in y around 0 87.5%

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

   6. Taylor expanded in y around 0 72.3%

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

   if 3.2999999999999999e99 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 80.6%

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

   3. Taylor expanded in a around 0 85.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+93}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -280:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]

Alternative 13: 70.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4200:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z a) (/ (* x y) a))))
   (if (<= y -1.1e+95)
     (+ (/ z y) (- x (/ a (/ y x))))
     (if (<= y -4200.0)
       t_1
       (if (<= y 4.8e-16)
         (/ (+ t (* y 230661.510616)) (+ i (* y c)))
         (if (<= y 2.4e+102) t_1 (+ x (/ z y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / a) + ((x * y) / a);
	double tmp;
	if (y <= -1.1e+95) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -4200.0) {
		tmp = t_1;
	} else if (y <= 4.8e-16) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 2.4e+102) {
		tmp = t_1;
	} else {
		tmp = x + (z / 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 = (z / a) + ((x * y) / a)
    if (y <= (-1.1d+95)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-4200.0d0)) then
        tmp = t_1
    else if (y <= 4.8d-16) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else if (y <= 2.4d+102) then
        tmp = t_1
    else
        tmp = x + (z / 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 = (z / a) + ((x * y) / a);
	double tmp;
	if (y <= -1.1e+95) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -4200.0) {
		tmp = t_1;
	} else if (y <= 4.8e-16) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 2.4e+102) {
		tmp = t_1;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / a) + ((x * y) / a)
	tmp = 0
	if y <= -1.1e+95:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -4200.0:
		tmp = t_1
	elif y <= 4.8e-16:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	elif y <= 2.4e+102:
		tmp = t_1
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / a) + Float64(Float64(x * y) / a))
	tmp = 0.0
	if (y <= -1.1e+95)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -4200.0)
		tmp = t_1;
	elseif (y <= 4.8e-16)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	elseif (y <= 2.4e+102)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / a) + ((x * y) / a);
	tmp = 0.0;
	if (y <= -1.1e+95)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -4200.0)
		tmp = t_1;
	elseif (y <= 4.8e-16)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	elseif (y <= 2.4e+102)
		tmp = t_1;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+95], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4200.0], t$95$1, If[LessEqual[y, 4.8e-16], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+102], t$95$1, N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.0999999999999999e95

   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. Taylor expanded in y around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -1.0999999999999999e95 < y < -4200 or 4.8000000000000001e-16 < y < 2.39999999999999994e102

   1. Initial program 52.0%

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

   2. Taylor expanded in a around inf 17.0%

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

   3. Taylor expanded in y around inf 43.0%

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

   if -4200 < y < 4.8000000000000001e-16

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 96.9%

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

      1. *-commutative 96.9%

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

      2. unpow2 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in y around 0 87.5%

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

   6. Taylor expanded in z around 0 83.8%

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

   if 2.39999999999999994e102 < y

   1. Initial program 0.1%

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

   2. Taylor expanded in y around inf 80.6%

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

   3. Taylor expanded in a around 0 85.1%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4200:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+102}:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]

Alternative 14: 64.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -130 \lor \neg \left(y \leq 6.5 \cdot 10^{-16}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -130.0) (not (<= y 6.5e-16)))
   (+ x (/ z 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 <= -130.0) || !(y <= 6.5e-16)) {
		tmp = x + (z / 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 <= (-130.0d0)) .or. (.not. (y <= 6.5d-16))) then
        tmp = x + (z / 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 <= -130.0) || !(y <= 6.5e-16)) {
		tmp = x + (z / y);
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -130.0) or not (y <= 6.5e-16):
		tmp = x + (z / 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 <= -130.0) || !(y <= 6.5e-16))
		tmp = Float64(x + Float64(z / 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 <= -130.0) || ~((y <= 6.5e-16)))
		tmp = x + (z / 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, -130.0], N[Not[LessEqual[y, 6.5e-16]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -130 or 6.50000000000000011e-16 < y

   1. Initial program 21.0%

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

   2. Taylor expanded in y around inf 50.0%

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

   3. Taylor expanded in a around 0 55.5%

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

   if -130 < y < 6.50000000000000011e-16

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 96.9%

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

      1. *-commutative 96.9%

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

      2. unpow2 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in y around 0 88.7%

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

   6. Taylor expanded in y around 0 73.3%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -130 \lor \neg \left(y \leq 6.5 \cdot 10^{-16}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]

Alternative 15: 57.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \lor \neg \left(y \leq 4.8 \cdot 10^{-16}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.7) (not (<= y 4.8e-16))) (+ x (/ z y)) (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.7) || !(y <= 4.8e-16)) {
		tmp = x + (z / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.7d0)) .or. (.not. (y <= 4.8d-16))) then
        tmp = x + (z / y)
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.7) || !(y <= 4.8e-16)) {
		tmp = x + (z / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.7) or not (y <= 4.8e-16):
		tmp = x + (z / y)
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.7) || !(y <= 4.8e-16))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.7) || ~((y <= 4.8e-16)))
		tmp = x + (z / y);
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.7], N[Not[LessEqual[y, 4.8e-16]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7000000000000002 or 4.8000000000000001e-16 < y

   1. Initial program 21.0%

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

   2. Taylor expanded in y around inf 50.0%

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

   3. Taylor expanded in a around 0 55.5%

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

   if -3.7000000000000002 < y < 4.8000000000000001e-16

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 52.3%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \lor \neg \left(y \leq 4.8 \cdot 10^{-16}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]

Alternative 16: 49.4% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5600000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5600000000.0) x (if (<= y 6.5e+64) (/ 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 <= -5600000000.0) {
		tmp = x;
	} else if (y <= 6.5e+64) {
		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 <= (-5600000000.0d0)) then
        tmp = x
    else if (y <= 6.5d+64) 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 <= -5600000000.0) {
		tmp = x;
	} else if (y <= 6.5e+64) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5600000000.0:
		tmp = x
	elif y <= 6.5e+64:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5600000000.0)
		tmp = x;
	elseif (y <= 6.5e+64)
		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 <= -5600000000.0)
		tmp = x;
	elseif (y <= 6.5e+64)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5600000000.0], x, If[LessEqual[y, 6.5e+64], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6e9 or 6.50000000000000007e64 < y

   1. Initial program 10.1%

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

   2. Taylor expanded in y around inf 45.7%

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

   if -5.6e9 < y < 6.50000000000000007e64

   1. Initial program 97.8%

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

   2. Taylor expanded in y around 0 46.9%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5600000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 25.4% 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 62.5%

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

2. Taylor expanded in y around inf 20.3%

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

3. Final simplification 20.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023199 
(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)))