Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.6% → 85.4%

Time: 32.9s

Alternatives: 16

Speedup: 1.6×

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: 56.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+63}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -7.6e+46)
     t_1
     (if (<= y 7.8e+63)
       (/
        (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))
       (if (<= y 3.8e+151) (/ x (/ (+ (+ y a) (/ b y)) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -7.6e+46) {
		tmp = t_1;
	} else if (y <= 7.8e+63) {
		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 if (y <= 3.8e+151) {
		tmp = x / (((y + a) + (b / y)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -7.6e+46)
		tmp = t_1;
	elseif (y <= 7.8e+63)
		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));
	elseif (y <= 3.8e+151)
		tmp = Float64(x / Float64(Float64(Float64(y + a) + Float64(b / y)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.6e+46], t$95$1, If[LessEqual[y, 7.8e+63], 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], If[LessEqual[y, 3.8e+151], N[(x / N[(N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5999999999999998e46 or 3.8e151 < y

   1. Initial program 1.2%

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

   3. Taylor expanded in y around inf 80.0%

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

      1. associate--l+ 80.0%

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

      2. associate-/l* 87.0%

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

   5. Simplified 87.0%

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

   if -7.5999999999999998e46 < y < 7.8e63

   1. Initial program 90.2%

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

      1. fma-def 90.2%

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

      2. fma-def 90.2%

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

      3. fma-def 90.2%

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

      4. fma-def 90.2%

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

      5. fma-def 90.2%

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

      6. fma-def 90.2%

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

      7. fma-def 90.2%

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

   3. Simplified 90.2%

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

   if 7.8e63 < y < 3.8e151

   1. Initial program 0.5%

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

   3. Taylor expanded in t around 0 0.5%

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

   5. Simplified 1.4%

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

   6. Taylor expanded in y around -inf 74.9%

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

   8. Simplified 74.9%

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

   9. Taylor expanded in x around inf 62.0%

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

       1. associate-/l* 85.7%

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

       2. associate-+r+ 85.7%

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

       3. +-commutative 85.7%

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

   11. Simplified 85.7%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+63}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.9 \cdot 10^{+61}:\\ \;\;\;\;\frac{t}{t_1} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
        (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -7.6e+46)
     t_2
     (if (<= y 8.9e+61)
       (+
        (/ t t_1)
        (/
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
         t_1))
       (if (<= y 3e+154) (/ x (/ (+ (+ y a) (/ b y)) y)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * (b + (y * (y + a))))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -7.6e+46) {
		tmp = t_2;
	} else if (y <= 8.9e+61) {
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else if (y <= 3e+154) {
		tmp = x / (((y + a) + (b / y)) / y);
	} 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 = i + (y * (c + (y * (b + (y * (y + a))))))
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-7.6d+46)) then
        tmp = t_2
    else if (y <= 8.9d+61) then
        tmp = (t / t_1) + ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))) / t_1)
    else if (y <= 3d+154) then
        tmp = x / (((y + a) + (b / y)) / y)
    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 = i + (y * (c + (y * (b + (y * (y + a))))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -7.6e+46) {
		tmp = t_2;
	} else if (y <= 8.9e+61) {
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else if (y <= 3e+154) {
		tmp = x / (((y + a) + (b / y)) / y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * (b + (y * (y + a))))))
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -7.6e+46:
		tmp = t_2
	elif y <= 8.9e+61:
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1)
	elif y <= 3e+154:
		tmp = x / (((y + a) + (b / y)) / y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -7.6e+46)
		tmp = t_2;
	elseif (y <= 8.9e+61)
		tmp = Float64(Float64(t / t_1) + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_1));
	elseif (y <= 3e+154)
		tmp = Float64(x / Float64(Float64(Float64(y + a) + Float64(b / y)) / y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * (b + (y * (y + a))))));
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -7.6e+46)
		tmp = t_2;
	elseif (y <= 8.9e+61)
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	elseif (y <= 3e+154)
		tmp = x / (((y + a) + (b / y)) / y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.6e+46], t$95$2, If[LessEqual[y, 8.9e+61], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+154], N[(x / N[(N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5999999999999998e46 or 3.00000000000000026e154 < y

   1. Initial program 1.2%

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

   3. Taylor expanded in y around inf 80.0%

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

      1. associate--l+ 80.0%

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

      2. associate-/l* 87.0%

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

   5. Simplified 87.0%

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

   if -7.5999999999999998e46 < y < 8.90000000000000005e61

   1. Initial program 90.2%

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

   3. Taylor expanded in t around 0 90.2%

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

   if 8.90000000000000005e61 < y < 3.00000000000000026e154

   1. Initial program 0.5%

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

   3. Taylor expanded in t around 0 0.5%

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

   5. Simplified 1.4%

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

   6. Taylor expanded in y around -inf 74.9%

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

   8. Simplified 74.9%

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

   9. Taylor expanded in x around inf 62.0%

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

       1. associate-/l* 85.7%

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

       2. associate-+r+ 85.7%

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

       3. +-commutative 85.7%

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

   11. Simplified 85.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 8.9 \cdot 10^{+61}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 660000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ x (/ (+ (+ y a) (/ b y)) y)))
        (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -1e+129)
     t_2
     (if (<= y -3.6e+20)
       t_1
       (if (<= y 660000.0)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
         (if (<= y 5.5e+151) 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 = x / (((y + a) + (b / y)) / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1e+129) {
		tmp = t_2;
	} else if (y <= -3.6e+20) {
		tmp = t_1;
	} else if (y <= 660000.0) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 5.5e+151) {
		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 = x / (((y + a) + (b / y)) / y)
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-1d+129)) then
        tmp = t_2
    else if (y <= (-3.6d+20)) then
        tmp = t_1
    else if (y <= 660000.0d0) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else if (y <= 5.5d+151) 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 = x / (((y + a) + (b / y)) / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1e+129) {
		tmp = t_2;
	} else if (y <= -3.6e+20) {
		tmp = t_1;
	} else if (y <= 660000.0) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 5.5e+151) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x / (((y + a) + (b / y)) / y)
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -1e+129:
		tmp = t_2
	elif y <= -3.6e+20:
		tmp = t_1
	elif y <= 660000.0:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	elif y <= 5.5e+151:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x / Float64(Float64(Float64(y + a) + Float64(b / y)) / y))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1e+129)
		tmp = t_2;
	elseif (y <= -3.6e+20)
		tmp = t_1;
	elseif (y <= 660000.0)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	elseif (y <= 5.5e+151)
		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 = x / (((y + a) + (b / y)) / y);
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1e+129)
		tmp = t_2;
	elseif (y <= -3.6e+20)
		tmp = t_1;
	elseif (y <= 660000.0)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	elseif (y <= 5.5e+151)
		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[(x / N[(N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+129], t$95$2, If[LessEqual[y, -3.6e+20], t$95$1, If[LessEqual[y, 660000.0], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+151], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e129 or 5.4999999999999994e151 < y

   1. Initial program 1.2%

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

   3. Taylor expanded in y around inf 82.5%

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

      1. associate--l+ 82.5%

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

      2. associate-/l* 90.2%

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

   5. Simplified 90.2%

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

   if -1e129 < y < -3.6e20 or 6.6e5 < y < 5.4999999999999994e151

   1. Initial program 18.6%

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

   3. Taylor expanded in t around 0 15.0%

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

   5. Simplified 17.5%

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

   6. Taylor expanded in y around -inf 56.5%

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

   8. Simplified 56.5%

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

   9. Taylor expanded in x around inf 47.4%

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

       1. associate-/l* 63.8%

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

       2. associate-+r+ 63.8%

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

       3. +-commutative 63.8%

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

   11. Simplified 63.8%

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

   if -3.6e20 < y < 6.6e5

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 93.4%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+129}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{elif}\;y \leq 660000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.9 \cdot 10^{+61}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -4.3e+46)
     t_1
     (if (<= y 8.9e+61)
       (/
        (+
         t
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
        (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
       (if (<= y 9.5e+155) (/ x (/ (+ (+ y a) (/ b y)) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -4.3e+46) {
		tmp = t_1;
	} else if (y <= 8.9e+61) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 9.5e+155) {
		tmp = x / (((y + a) + (b / y)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    if (y <= (-4.3d+46)) then
        tmp = t_1
    else if (y <= 8.9d+61) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else if (y <= 9.5d+155) then
        tmp = x / (((y + a) + (b / y)) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -4.3e+46) {
		tmp = t_1;
	} else if (y <= 8.9e+61) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 9.5e+155) {
		tmp = x / (((y + a) + (b / y)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -4.3e+46:
		tmp = t_1
	elif y <= 8.9e+61:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	elif y <= 9.5e+155:
		tmp = x / (((y + a) + (b / y)) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -4.3e+46)
		tmp = t_1;
	elseif (y <= 8.9e+61)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	elseif (y <= 9.5e+155)
		tmp = Float64(x / Float64(Float64(Float64(y + a) + Float64(b / y)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -4.3e+46)
		tmp = t_1;
	elseif (y <= 8.9e+61)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	elseif (y <= 9.5e+155)
		tmp = x / (((y + a) + (b / y)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+46], t$95$1, If[LessEqual[y, 8.9e+61], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+155], N[(x / N[(N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.30000000000000005e46 or 9.5000000000000006e155 < y

   1. Initial program 1.2%

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

   3. Taylor expanded in y around inf 80.0%

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

      1. associate--l+ 80.0%

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

      2. associate-/l* 87.0%

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

   5. Simplified 87.0%

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

   if -4.30000000000000005e46 < y < 8.90000000000000005e61

   1. Initial program 90.2%

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

   if 8.90000000000000005e61 < y < 9.5000000000000006e155

   1. Initial program 0.5%

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

   3. Taylor expanded in t around 0 0.5%

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

   5. Simplified 1.4%

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

   6. Taylor expanded in y around -inf 74.9%

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

   8. Simplified 74.9%

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

   9. Taylor expanded in x around inf 62.0%

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

       1. associate-/l* 85.7%

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

       2. associate-+r+ 85.7%

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

       3. +-commutative 85.7%

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

   11. Simplified 85.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+46}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 8.9 \cdot 10^{+61}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 115000000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ x (/ (+ (+ y a) (/ b y)) y)))
        (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.5e+124)
     t_2
     (if (<= y -8.2e+17)
       t_1
       (if (<= y 115000000000.0)
         (/
          (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
         (if (<= y 4.7e+151) 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 = x / (((y + a) + (b / y)) / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.5e+124) {
		tmp = t_2;
	} else if (y <= -8.2e+17) {
		tmp = t_1;
	} else if (y <= 115000000000.0) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 4.7e+151) {
		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 = x / (((y + a) + (b / y)) / y)
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-2.5d+124)) then
        tmp = t_2
    else if (y <= (-8.2d+17)) then
        tmp = t_1
    else if (y <= 115000000000.0d0) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else if (y <= 4.7d+151) 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 = x / (((y + a) + (b / y)) / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.5e+124) {
		tmp = t_2;
	} else if (y <= -8.2e+17) {
		tmp = t_1;
	} else if (y <= 115000000000.0) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 4.7e+151) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x / (((y + a) + (b / y)) / y)
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -2.5e+124:
		tmp = t_2
	elif y <= -8.2e+17:
		tmp = t_1
	elif y <= 115000000000.0:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	elif y <= 4.7e+151:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x / Float64(Float64(Float64(y + a) + Float64(b / y)) / y))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.5e+124)
		tmp = t_2;
	elseif (y <= -8.2e+17)
		tmp = t_1;
	elseif (y <= 115000000000.0)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	elseif (y <= 4.7e+151)
		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 = x / (((y + a) + (b / y)) / y);
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.5e+124)
		tmp = t_2;
	elseif (y <= -8.2e+17)
		tmp = t_1;
	elseif (y <= 115000000000.0)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	elseif (y <= 4.7e+151)
		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[(x / N[(N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+124], t$95$2, If[LessEqual[y, -8.2e+17], t$95$1, If[LessEqual[y, 115000000000.0], 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[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+151], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999998e124 or 4.69999999999999989e151 < y

   1. Initial program 1.2%

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

   3. Taylor expanded in y around inf 82.5%

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

      1. associate--l+ 82.5%

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

      2. associate-/l* 90.2%

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

   5. Simplified 90.2%

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

   if -2.4999999999999998e124 < y < -8.2e17 or 1.15e11 < y < 4.69999999999999989e151

   1. Initial program 17.3%

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

   3. Taylor expanded in t around 0 15.4%

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

   5. Simplified 18.0%

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

   6. Taylor expanded in y around -inf 56.7%

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

   8. Simplified 56.7%

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

   9. Taylor expanded in x around inf 47.3%

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

       1. associate-/l* 64.3%

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

       2. associate-+r+ 64.3%

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

       3. +-commutative 64.3%

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

   11. Simplified 64.3%

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

   if -8.2e17 < y < 1.15e11

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 88.8%

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

      1. *-commutative 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+124}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{elif}\;y \leq 115000000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ x (/ (+ (+ y a) (/ b y)) y)))
        (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -6.5e+127)
     t_2
     (if (<= y -5.2e+16)
       t_1
       (if (<= y 3000000000.0)
         (/
          (+ t (* y 230661.510616))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
         (if (<= y 1.4e+154) 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 = x / (((y + a) + (b / y)) / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -6.5e+127) {
		tmp = t_2;
	} else if (y <= -5.2e+16) {
		tmp = t_1;
	} else if (y <= 3000000000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 1.4e+154) {
		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 = x / (((y + a) + (b / y)) / y)
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-6.5d+127)) then
        tmp = t_2
    else if (y <= (-5.2d+16)) then
        tmp = t_1
    else if (y <= 3000000000.0d0) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else if (y <= 1.4d+154) 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 = x / (((y + a) + (b / y)) / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -6.5e+127) {
		tmp = t_2;
	} else if (y <= -5.2e+16) {
		tmp = t_1;
	} else if (y <= 3000000000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 1.4e+154) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x / (((y + a) + (b / y)) / y)
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -6.5e+127:
		tmp = t_2
	elif y <= -5.2e+16:
		tmp = t_1
	elif y <= 3000000000.0:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	elif y <= 1.4e+154:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x / Float64(Float64(Float64(y + a) + Float64(b / y)) / y))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -6.5e+127)
		tmp = t_2;
	elseif (y <= -5.2e+16)
		tmp = t_1;
	elseif (y <= 3000000000.0)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	elseif (y <= 1.4e+154)
		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 = x / (((y + a) + (b / y)) / y);
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -6.5e+127)
		tmp = t_2;
	elseif (y <= -5.2e+16)
		tmp = t_1;
	elseif (y <= 3000000000.0)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	elseif (y <= 1.4e+154)
		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[(x / N[(N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+127], t$95$2, If[LessEqual[y, -5.2e+16], t$95$1, If[LessEqual[y, 3000000000.0], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+154], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5e127 or 1.4e154 < y

   1. Initial program 1.2%

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

   3. Taylor expanded in y around inf 82.5%

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

      1. associate--l+ 82.5%

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

      2. associate-/l* 90.2%

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

   5. Simplified 90.2%

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

   if -6.5e127 < y < -5.2e16 or 3e9 < y < 1.4e154

   1. Initial program 17.3%

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

   3. Taylor expanded in t around 0 15.4%

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

   5. Simplified 18.0%

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

   6. Taylor expanded in y around -inf 56.7%

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

   8. Simplified 56.7%

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

   9. Taylor expanded in x around inf 47.3%

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

       1. associate-/l* 64.3%

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

       2. associate-+r+ 64.3%

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

       3. +-commutative 64.3%

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

   11. Simplified 64.3%

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

   if -5.2e16 < y < 3e9

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 88.0%

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

      1. *-commutative 88.0%

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

   5. Simplified 88.0%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+127}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{elif}\;y \leq 3000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + a\right) + \frac{b}{y}\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{\frac{t_1}{x}}\\ \mathbf{elif}\;y \leq 10^{-8}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{\frac{t_1}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ y a) (/ b y))) (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -9.8e+125)
     t_2
     (if (<= y -1.2e-24)
       (/ y (/ t_1 x))
       (if (<= y 1e-8)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y c)))
         (if (<= y 5e+155) (/ x (/ t_1 y)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y + a) + (b / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -9.8e+125) {
		tmp = t_2;
	} else if (y <= -1.2e-24) {
		tmp = y / (t_1 / x);
	} else if (y <= 1e-8) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c));
	} else if (y <= 5e+155) {
		tmp = x / (t_1 / y);
	} 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 = (y + a) + (b / y)
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-9.8d+125)) then
        tmp = t_2
    else if (y <= (-1.2d-24)) then
        tmp = y / (t_1 / x)
    else if (y <= 1d-8) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * c))
    else if (y <= 5d+155) then
        tmp = x / (t_1 / y)
    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 = (y + a) + (b / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -9.8e+125) {
		tmp = t_2;
	} else if (y <= -1.2e-24) {
		tmp = y / (t_1 / x);
	} else if (y <= 1e-8) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c));
	} else if (y <= 5e+155) {
		tmp = x / (t_1 / y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y + a) + (b / y)
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -9.8e+125:
		tmp = t_2
	elif y <= -1.2e-24:
		tmp = y / (t_1 / x)
	elif y <= 1e-8:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c))
	elif y <= 5e+155:
		tmp = x / (t_1 / y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y + a) + Float64(b / y))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -9.8e+125)
		tmp = t_2;
	elseif (y <= -1.2e-24)
		tmp = Float64(y / Float64(t_1 / x));
	elseif (y <= 1e-8)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * c)));
	elseif (y <= 5e+155)
		tmp = Float64(x / Float64(t_1 / y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y + a) + (b / y);
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -9.8e+125)
		tmp = t_2;
	elseif (y <= -1.2e-24)
		tmp = y / (t_1 / x);
	elseif (y <= 1e-8)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c));
	elseif (y <= 5e+155)
		tmp = x / (t_1 / y);
	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[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.8e+125], t$95$2, If[LessEqual[y, -1.2e-24], N[(y / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-8], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+155], N[(x / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.80000000000000032e125 or 4.9999999999999999e155 < y

   1. Initial program 1.2%

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

   3. Taylor expanded in y around inf 82.5%

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

      1. associate--l+ 82.5%

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

      2. associate-/l* 90.2%

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

   5. Simplified 90.2%

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

   if -9.80000000000000032e125 < y < -1.1999999999999999e-24

   1. Initial program 48.5%

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

   3. Taylor expanded in t around 0 39.4%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in y around -inf 49.4%

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

   8. Simplified 49.4%

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

   9. Taylor expanded in x around inf 55.6%

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

       1. associate-+r+ 55.6%

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

       2. +-commutative 55.6%

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

   11. Simplified 55.6%

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

   if -1.1999999999999999e-24 < y < 1e-8

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 95.4%

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

   4. Taylor expanded in y around 0 85.2%

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

      1. *-commutative 85.2%

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

   6. Simplified 85.2%

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

   if 1e-8 < y < 4.9999999999999999e155

   1. Initial program 20.1%

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

   3. Taylor expanded in t around 0 12.4%

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

   5. Simplified 15.6%

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

   6. Taylor expanded in y around -inf 49.3%

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

   8. Simplified 49.3%

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

   9. Taylor expanded in x around inf 42.9%

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

       1. associate-/l* 55.7%

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

       2. associate-+r+ 55.7%

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

       3. +-commutative 55.7%

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

   11. Simplified 55.7%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+125}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{\frac{\left(y + a\right) + \frac{b}{y}}{x}}\\ \mathbf{elif}\;y \leq 10^{-8}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{\frac{b}{y \cdot x}}\\ \mathbf{elif}\;y \leq 1600000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.1e+158)
   x
   (if (<= y -9.8e+109)
     (/ z y)
     (if (<= y -4.6e+27)
       x
       (if (<= y -1.75e-51)
         (/ y (/ b (* y x)))
         (if (<= y 1600000000.0) (/ t (+ i (* y c))) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.1e+158) {
		tmp = x;
	} else if (y <= -9.8e+109) {
		tmp = z / y;
	} else if (y <= -4.6e+27) {
		tmp = x;
	} else if (y <= -1.75e-51) {
		tmp = y / (b / (y * x));
	} else if (y <= 1600000000.0) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.1d+158)) then
        tmp = x
    else if (y <= (-9.8d+109)) then
        tmp = z / y
    else if (y <= (-4.6d+27)) then
        tmp = x
    else if (y <= (-1.75d-51)) then
        tmp = y / (b / (y * x))
    else if (y <= 1600000000.0d0) then
        tmp = t / (i + (y * c))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.1e+158) {
		tmp = x;
	} else if (y <= -9.8e+109) {
		tmp = z / y;
	} else if (y <= -4.6e+27) {
		tmp = x;
	} else if (y <= -1.75e-51) {
		tmp = y / (b / (y * x));
	} else if (y <= 1600000000.0) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.1e+158:
		tmp = x
	elif y <= -9.8e+109:
		tmp = z / y
	elif y <= -4.6e+27:
		tmp = x
	elif y <= -1.75e-51:
		tmp = y / (b / (y * x))
	elif y <= 1600000000.0:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.1e+158)
		tmp = x;
	elseif (y <= -9.8e+109)
		tmp = Float64(z / y);
	elseif (y <= -4.6e+27)
		tmp = x;
	elseif (y <= -1.75e-51)
		tmp = Float64(y / Float64(b / Float64(y * x)));
	elseif (y <= 1600000000.0)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.1e+158)
		tmp = x;
	elseif (y <= -9.8e+109)
		tmp = z / y;
	elseif (y <= -4.6e+27)
		tmp = x;
	elseif (y <= -1.75e-51)
		tmp = y / (b / (y * x));
	elseif (y <= 1600000000.0)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.1e+158], x, If[LessEqual[y, -9.8e+109], N[(z / y), $MachinePrecision], If[LessEqual[y, -4.6e+27], x, If[LessEqual[y, -1.75e-51], N[(y / N[(b / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1600000000.0], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.1000000000000002e158 or -9.8000000000000007e109 < y < -4.6000000000000001e27 or 1.6e9 < y

   1. Initial program 6.2%

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

   3. Taylor expanded in y around inf 56.3%

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

   if -3.1000000000000002e158 < y < -9.8000000000000007e109

   1. Initial program 10.0%

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

   3. Taylor expanded in x around 0 10.0%

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

   4. Taylor expanded in y around inf 72.1%

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

   if -4.6000000000000001e27 < y < -1.7499999999999999e-51

   1. Initial program 78.4%

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

   3. Taylor expanded in t around 0 62.2%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in y around -inf 23.3%

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

   8. Simplified 23.3%

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

   9. Taylor expanded in b around inf 21.9%

      \[\leadsto \frac{y}{\color{blue}{\frac{b}{x \cdot y}}} \]
   10. Step-by-step derivation

       1. *-commutative 21.9%

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

   11. Simplified 21.9%

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

   if -1.7499999999999999e-51 < y < 1.6e9

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 95.4%

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

   4. Taylor expanded in y around 0 83.6%

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

      1. *-commutative 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in t around inf 75.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{\frac{b}{y \cdot x}}\\ \mathbf{elif}\;y \leq 1600000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0018:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ x (/ (+ (+ y a) (/ b y)) y)))
        (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.2e+128)
     t_2
     (if (<= y -1.75e-51)
       t_1
       (if (<= y 0.0018) (/ t (+ i (* y c))) (if (<= y 3.1e+153) 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 = x / (((y + a) + (b / y)) / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+128) {
		tmp = t_2;
	} else if (y <= -1.75e-51) {
		tmp = t_1;
	} else if (y <= 0.0018) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.1e+153) {
		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 = x / (((y + a) + (b / y)) / y)
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-2.2d+128)) then
        tmp = t_2
    else if (y <= (-1.75d-51)) then
        tmp = t_1
    else if (y <= 0.0018d0) then
        tmp = t / (i + (y * c))
    else if (y <= 3.1d+153) 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 = x / (((y + a) + (b / y)) / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+128) {
		tmp = t_2;
	} else if (y <= -1.75e-51) {
		tmp = t_1;
	} else if (y <= 0.0018) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.1e+153) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x / (((y + a) + (b / y)) / y)
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -2.2e+128:
		tmp = t_2
	elif y <= -1.75e-51:
		tmp = t_1
	elif y <= 0.0018:
		tmp = t / (i + (y * c))
	elif y <= 3.1e+153:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x / Float64(Float64(Float64(y + a) + Float64(b / y)) / y))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.2e+128)
		tmp = t_2;
	elseif (y <= -1.75e-51)
		tmp = t_1;
	elseif (y <= 0.0018)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	elseif (y <= 3.1e+153)
		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 = x / (((y + a) + (b / y)) / y);
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.2e+128)
		tmp = t_2;
	elseif (y <= -1.75e-51)
		tmp = t_1;
	elseif (y <= 0.0018)
		tmp = t / (i + (y * c));
	elseif (y <= 3.1e+153)
		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[(x / N[(N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+128], t$95$2, If[LessEqual[y, -1.75e-51], t$95$1, If[LessEqual[y, 0.0018], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+153], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.20000000000000017e128 or 3.1e153 < y

   1. Initial program 1.2%

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

   3. Taylor expanded in y around inf 82.5%

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

      1. associate--l+ 82.5%

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

      2. associate-/l* 90.2%

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

   5. Simplified 90.2%

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

   if -2.20000000000000017e128 < y < -1.7499999999999999e-51 or 0.0018 < y < 3.1e153

   1. Initial program 32.6%

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

   3. Taylor expanded in t around 0 24.5%

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

   5. Simplified 26.6%

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

   6. Taylor expanded in y around -inf 48.5%

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

   8. Simplified 48.5%

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

   9. Taylor expanded in x around inf 41.3%

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

       1. associate-/l* 53.3%

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

       2. associate-+r+ 53.3%

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

       3. +-commutative 53.3%

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

   11. Simplified 53.3%

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

   if -1.7499999999999999e-51 < y < 0.0018

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 96.2%

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

   4. Taylor expanded in y around 0 85.0%

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

      1. *-commutative 85.0%

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

   6. Simplified 85.0%

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

   7. Taylor expanded in t around inf 76.8%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{elif}\;y \leq 0.0018:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+153}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + a\right) + \frac{b}{y}\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{\frac{t_1}{x}}\\ \mathbf{elif}\;y \leq 0.0215:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{\frac{t_1}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ y a) (/ b y))) (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -1.45e+116)
     t_2
     (if (<= y -1.75e-51)
       (/ y (/ t_1 x))
       (if (<= y 0.0215)
         (/ t (+ i (* y c)))
         (if (<= y 2.1e+154) (/ x (/ t_1 y)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y + a) + (b / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1.45e+116) {
		tmp = t_2;
	} else if (y <= -1.75e-51) {
		tmp = y / (t_1 / x);
	} else if (y <= 0.0215) {
		tmp = t / (i + (y * c));
	} else if (y <= 2.1e+154) {
		tmp = x / (t_1 / y);
	} 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 = (y + a) + (b / y)
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-1.45d+116)) then
        tmp = t_2
    else if (y <= (-1.75d-51)) then
        tmp = y / (t_1 / x)
    else if (y <= 0.0215d0) then
        tmp = t / (i + (y * c))
    else if (y <= 2.1d+154) then
        tmp = x / (t_1 / y)
    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 = (y + a) + (b / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1.45e+116) {
		tmp = t_2;
	} else if (y <= -1.75e-51) {
		tmp = y / (t_1 / x);
	} else if (y <= 0.0215) {
		tmp = t / (i + (y * c));
	} else if (y <= 2.1e+154) {
		tmp = x / (t_1 / y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y + a) + (b / y)
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -1.45e+116:
		tmp = t_2
	elif y <= -1.75e-51:
		tmp = y / (t_1 / x)
	elif y <= 0.0215:
		tmp = t / (i + (y * c))
	elif y <= 2.1e+154:
		tmp = x / (t_1 / y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y + a) + Float64(b / y))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.45e+116)
		tmp = t_2;
	elseif (y <= -1.75e-51)
		tmp = Float64(y / Float64(t_1 / x));
	elseif (y <= 0.0215)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	elseif (y <= 2.1e+154)
		tmp = Float64(x / Float64(t_1 / y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y + a) + (b / y);
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.45e+116)
		tmp = t_2;
	elseif (y <= -1.75e-51)
		tmp = y / (t_1 / x);
	elseif (y <= 0.0215)
		tmp = t / (i + (y * c));
	elseif (y <= 2.1e+154)
		tmp = x / (t_1 / y);
	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[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+116], t$95$2, If[LessEqual[y, -1.75e-51], N[(y / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0215], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+154], N[(x / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.4500000000000001e116 or 2.09999999999999994e154 < y

   1. Initial program 1.2%

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

   3. Taylor expanded in y around inf 82.5%

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

      1. associate--l+ 82.5%

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

      2. associate-/l* 90.2%

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

   5. Simplified 90.2%

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

   if -1.4500000000000001e116 < y < -1.7499999999999999e-51

   1. Initial program 52.3%

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

   3. Taylor expanded in t around 0 43.9%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in y around -inf 45.8%

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

   8. Simplified 45.8%

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

   9. Taylor expanded in x around inf 51.8%

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

       1. associate-+r+ 51.8%

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

       2. +-commutative 51.8%

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

   11. Simplified 51.8%

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

   if -1.7499999999999999e-51 < y < 0.021499999999999998

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 96.2%

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

   4. Taylor expanded in y around 0 85.0%

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

      1. *-commutative 85.0%

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

   6. Simplified 85.0%

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

   7. Taylor expanded in t around inf 76.8%

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

   if 0.021499999999999998 < y < 2.09999999999999994e154

   1. Initial program 17.9%

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

   3. Taylor expanded in t around 0 10.0%

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

   5. Simplified 13.3%

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

   6. Taylor expanded in y around -inf 50.6%

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

   8. Simplified 50.6%

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

   9. Taylor expanded in x around inf 43.9%

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

       1. associate-/l* 57.1%

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

       2. associate-+r+ 57.1%

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

       3. +-commutative 57.1%

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

   11. Simplified 57.1%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+116}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{\frac{\left(y + a\right) + \frac{b}{y}}{x}}\\ \mathbf{elif}\;y \leq 0.0215:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + a\right) + \frac{b}{y}\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{\frac{t_1}{x}}\\ \mathbf{elif}\;y \leq 62000000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{t_1}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ y a) (/ b y))) (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -4.8e+125)
     t_2
     (if (<= y -1.3e-24)
       (/ y (/ t_1 x))
       (if (<= y 62000000000.0)
         (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i (* y c)))
         (if (<= y 1.02e+152) (/ x (/ t_1 y)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y + a) + (b / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -4.8e+125) {
		tmp = t_2;
	} else if (y <= -1.3e-24) {
		tmp = y / (t_1 / x);
	} else if (y <= 62000000000.0) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c));
	} else if (y <= 1.02e+152) {
		tmp = x / (t_1 / y);
	} 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 = (y + a) + (b / y)
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-4.8d+125)) then
        tmp = t_2
    else if (y <= (-1.3d-24)) then
        tmp = y / (t_1 / x)
    else if (y <= 62000000000.0d0) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * c))
    else if (y <= 1.02d+152) then
        tmp = x / (t_1 / y)
    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 = (y + a) + (b / y);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -4.8e+125) {
		tmp = t_2;
	} else if (y <= -1.3e-24) {
		tmp = y / (t_1 / x);
	} else if (y <= 62000000000.0) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c));
	} else if (y <= 1.02e+152) {
		tmp = x / (t_1 / y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y + a) + (b / y)
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -4.8e+125:
		tmp = t_2
	elif y <= -1.3e-24:
		tmp = y / (t_1 / x)
	elif y <= 62000000000.0:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c))
	elif y <= 1.02e+152:
		tmp = x / (t_1 / y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y + a) + Float64(b / y))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -4.8e+125)
		tmp = t_2;
	elseif (y <= -1.3e-24)
		tmp = Float64(y / Float64(t_1 / x));
	elseif (y <= 62000000000.0)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * c)));
	elseif (y <= 1.02e+152)
		tmp = Float64(x / Float64(t_1 / y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y + a) + (b / y);
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -4.8e+125)
		tmp = t_2;
	elseif (y <= -1.3e-24)
		tmp = y / (t_1 / x);
	elseif (y <= 62000000000.0)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c));
	elseif (y <= 1.02e+152)
		tmp = x / (t_1 / y);
	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[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+125], t$95$2, If[LessEqual[y, -1.3e-24], N[(y / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 62000000000.0], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+152], N[(x / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.7999999999999999e125 or 1.01999999999999999e152 < y

   1. Initial program 1.2%

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

   3. Taylor expanded in y around inf 82.5%

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

      1. associate--l+ 82.5%

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

      2. associate-/l* 90.2%

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

   5. Simplified 90.2%

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

   if -4.7999999999999999e125 < y < -1.3e-24

   1. Initial program 48.5%

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

   3. Taylor expanded in t around 0 39.4%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in y around -inf 49.4%

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

   8. Simplified 49.4%

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

   9. Taylor expanded in x around inf 55.6%

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

       1. associate-+r+ 55.6%

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

       2. +-commutative 55.6%

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

   11. Simplified 55.6%

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

   if -1.3e-24 < y < 6.2e10

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 94.7%

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

   4. Taylor expanded in y around 0 83.0%

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

      1. *-commutative 83.0%

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

   6. Simplified 83.0%

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

   7. Taylor expanded in z around 0 82.3%

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

      1. *-commutative 82.3%

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

   9. Simplified 82.3%

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

   if 6.2e10 < y < 1.01999999999999999e152

   1. Initial program 13.4%

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

   3. Taylor expanded in t around 0 10.6%

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

   5. Simplified 14.2%

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

   6. Taylor expanded in y around -inf 52.1%

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

   8. Simplified 52.1%

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

   9. Taylor expanded in x around inf 44.8%

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

       1. associate-/l* 59.1%

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

       2. associate-+r+ 59.1%

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

       3. +-commutative 59.1%

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

   11. Simplified 59.1%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+125}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{\frac{\left(y + a\right) + \frac{b}{y}}{x}}\\ \mathbf{elif}\;y \leq 62000000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{\left(y + a\right) + \frac{b}{y}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 3100000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.1e+158)
   x
   (if (<= y -1.3e-24)
     (/ z y)
     (if (<= y 3100000000.0) (/ t (+ i (* y c))) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.1e+158) {
		tmp = x;
	} else if (y <= -1.3e-24) {
		tmp = z / y;
	} else if (y <= 3100000000.0) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.1d+158)) then
        tmp = x
    else if (y <= (-1.3d-24)) then
        tmp = z / y
    else if (y <= 3100000000.0d0) then
        tmp = t / (i + (y * c))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.1e+158) {
		tmp = x;
	} else if (y <= -1.3e-24) {
		tmp = z / y;
	} else if (y <= 3100000000.0) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.1e+158:
		tmp = x
	elif y <= -1.3e-24:
		tmp = z / y
	elif y <= 3100000000.0:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.1e+158)
		tmp = x;
	elseif (y <= -1.3e-24)
		tmp = Float64(z / y);
	elseif (y <= 3100000000.0)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.1e+158)
		tmp = x;
	elseif (y <= -1.3e-24)
		tmp = z / y;
	elseif (y <= 3100000000.0)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.1e+158], x, If[LessEqual[y, -1.3e-24], N[(z / y), $MachinePrecision], If[LessEqual[y, 3100000000.0], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1000000000000002e158 or 3.1e9 < y

   1. Initial program 4.0%

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

   3. Taylor expanded in y around inf 58.5%

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

   if -3.1000000000000002e158 < y < -1.3e-24

   1. Initial program 38.6%

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

   3. Taylor expanded in x around 0 19.5%

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

   4. Taylor expanded in y around inf 29.0%

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

   if -1.3e-24 < y < 3.1e9

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 94.7%

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

   4. Taylor expanded in y around 0 83.0%

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

      1. *-commutative 83.0%

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

   6. Simplified 83.0%

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

   7. Taylor expanded in t around inf 74.3%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 3100000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+14} \lor \neg \left(y \leq 6.4 \cdot 10^{+30}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.05e+14) (not (<= y 6.4e+30)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/ 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 <= -1.05e+14) || !(y <= 6.4e+30)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} 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 <= (-1.05d+14)) .or. (.not. (y <= 6.4d+30))) then
        tmp = x + ((z / y) - (a / (y / x)))
    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 <= -1.05e+14) || !(y <= 6.4e+30)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.05e+14) or not (y <= 6.4e+30):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = t / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.05e+14) || !(y <= 6.4e+30))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	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 <= -1.05e+14) || ~((y <= 6.4e+30)))
		tmp = x + ((z / y) - (a / (y / x)));
	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, -1.05e+14], N[Not[LessEqual[y, 6.4e+30]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e14 or 6.39999999999999945e30 < y

   1. Initial program 6.4%

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

   3. Taylor expanded in y around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-/l* 69.2%

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

   5. Simplified 69.2%

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

   if -1.05e14 < y < 6.39999999999999945e30

   1. Initial program 97.4%

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

   3. Taylor expanded in x around 0 89.7%

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

   4. Taylor expanded in y around 0 76.0%

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

      1. *-commutative 76.0%

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

   6. Simplified 76.0%

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

   7. Taylor expanded in t around inf 68.0%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+14} \lor \neg \left(y \leq 6.4 \cdot 10^{+30}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 62000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.1e+158)
   x
   (if (<= y -1.3e-24) (/ z y) (if (<= y 62000000000.0) (/ 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 <= -3.1e+158) {
		tmp = x;
	} else if (y <= -1.3e-24) {
		tmp = z / y;
	} else if (y <= 62000000000.0) {
		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 <= (-3.1d+158)) then
        tmp = x
    else if (y <= (-1.3d-24)) then
        tmp = z / y
    else if (y <= 62000000000.0d0) 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 <= -3.1e+158) {
		tmp = x;
	} else if (y <= -1.3e-24) {
		tmp = z / y;
	} else if (y <= 62000000000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.1e+158:
		tmp = x
	elif y <= -1.3e-24:
		tmp = z / y
	elif y <= 62000000000.0:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.1e+158)
		tmp = x;
	elseif (y <= -1.3e-24)
		tmp = Float64(z / y);
	elseif (y <= 62000000000.0)
		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 <= -3.1e+158)
		tmp = x;
	elseif (y <= -1.3e-24)
		tmp = z / y;
	elseif (y <= 62000000000.0)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.1e+158], x, If[LessEqual[y, -1.3e-24], N[(z / y), $MachinePrecision], If[LessEqual[y, 62000000000.0], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1000000000000002e158 or 6.2e10 < y

   1. Initial program 4.0%

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

   3. Taylor expanded in y around inf 58.5%

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

   if -3.1000000000000002e158 < y < -1.3e-24

   1. Initial program 38.6%

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

   3. Taylor expanded in x around 0 19.5%

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

   4. Taylor expanded in y around inf 29.0%

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

   if -1.3e-24 < y < 6.2e10

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 63.7%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 62000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 210000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.1e+24) x (if (<= y 210000000000.0) (/ 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 <= -3.1e+24) {
		tmp = x;
	} else if (y <= 210000000000.0) {
		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 <= (-3.1d+24)) then
        tmp = x
    else if (y <= 210000000000.0d0) 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 <= -3.1e+24) {
		tmp = x;
	} else if (y <= 210000000000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.1e+24:
		tmp = x
	elif y <= 210000000000.0:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.1e+24)
		tmp = x;
	elseif (y <= 210000000000.0)
		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 <= -3.1e+24)
		tmp = x;
	elseif (y <= 210000000000.0)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.1e+24], x, If[LessEqual[y, 210000000000.0], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000011e24 or 2.1e11 < y

   1. Initial program 7.1%

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

   3. Taylor expanded in y around inf 51.2%

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

   if -3.10000000000000011e24 < y < 2.1e11

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 59.3%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 210000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 25.1% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 50.1%

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

3. Taylor expanded in y around inf 28.5%

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

4. Final simplification 28.5%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024024 
(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)))