Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.5% → 88.4%

Time: 33.0s

Alternatives: 17

Speedup: 1.3×

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: 56.5% 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: 88.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := {t\_1}^{2}\\ t_3 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ t_4 := y \cdot t\_1\\ t_5 := c + t\_4\\ t_6 := \frac{230661.510616}{t\_5} + \left(\frac{t}{y \cdot t\_5} + y \cdot \left(c \cdot \left(27464.7644705 \cdot \frac{-1}{{y}^{2} \cdot t\_2} - \left(\frac{x}{t\_2} + \frac{z}{y \cdot t\_2}\right)\right) + \left(27464.7644705 \cdot \frac{1}{t\_4} + \frac{z + y \cdot x}{t\_1}\right)\right)\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+148}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+25}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+130}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2 (pow t_1 2.0))
        (t_3 (+ x (- (/ z y) (* a (/ x y)))))
        (t_4 (* y t_1))
        (t_5 (+ c t_4))
        (t_6
         (+
          (/ 230661.510616 t_5)
          (+
           (/ t (* y t_5))
           (*
            y
            (+
             (*
              c
              (-
               (* 27464.7644705 (/ -1.0 (* (pow y 2.0) t_2)))
               (+ (/ x t_2) (/ z (* y t_2)))))
             (+ (* 27464.7644705 (/ 1.0 t_4)) (/ (+ z (* y x)) t_1))))))))
   (if (<= y -2.8e+148)
     t_3
     (if (<= y -3.4e+25)
       t_6
       (if (<= y 3.5e+15)
         (/
          (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 1.6e+130) t_6 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = pow(t_1, 2.0);
	double t_3 = x + ((z / y) - (a * (x / y)));
	double t_4 = y * t_1;
	double t_5 = c + t_4;
	double t_6 = (230661.510616 / t_5) + ((t / (y * t_5)) + (y * ((c * ((27464.7644705 * (-1.0 / (pow(y, 2.0) * t_2))) - ((x / t_2) + (z / (y * t_2))))) + ((27464.7644705 * (1.0 / t_4)) + ((z + (y * x)) / t_1)))));
	double tmp;
	if (y <= -2.8e+148) {
		tmp = t_3;
	} else if (y <= -3.4e+25) {
		tmp = t_6;
	} else if (y <= 3.5e+15) {
		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 <= 1.6e+130) {
		tmp = t_6;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b + Float64(y * Float64(y + a)))
	t_2 = t_1 ^ 2.0
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	t_4 = Float64(y * t_1)
	t_5 = Float64(c + t_4)
	t_6 = Float64(Float64(230661.510616 / t_5) + Float64(Float64(t / Float64(y * t_5)) + Float64(y * Float64(Float64(c * Float64(Float64(27464.7644705 * Float64(-1.0 / Float64((y ^ 2.0) * t_2))) - Float64(Float64(x / t_2) + Float64(z / Float64(y * t_2))))) + Float64(Float64(27464.7644705 * Float64(1.0 / t_4)) + Float64(Float64(z + Float64(y * x)) / t_1))))))
	tmp = 0.0
	if (y <= -2.8e+148)
		tmp = t_3;
	elseif (y <= -3.4e+25)
		tmp = t_6;
	elseif (y <= 3.5e+15)
		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 <= 1.6e+130)
		tmp = t_6;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[t$95$1, 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(c + t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(230661.510616 / t$95$5), $MachinePrecision] + N[(N[(t / N[(y * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(c * N[(N[(27464.7644705 * N[(-1.0 / N[(N[Power[y, 2.0], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x / t$95$2), $MachinePrecision] + N[(z / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+148], t$95$3, If[LessEqual[y, -3.4e+25], t$95$6, If[LessEqual[y, 3.5e+15], 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, 1.6e+130], t$95$6, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999998e148 or 1.6e130 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 84.7%

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

      1. associate--l+ 84.7%

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

      2. associate-/l* 87.9%

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

   5. Simplified 87.9%

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

   if -2.7999999999999998e148 < y < -3.39999999999999984e25 or 3.5e15 < y < 1.6e130

   1. Initial program 9.9%

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

   3. Taylor expanded in i around 0 19.3%

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

   4. Taylor expanded in i around 0 19.7%

      \[\leadsto \color{blue}{230661.510616 \cdot \frac{1}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 19.7%

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

      2. metadata-eval 19.7%

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

      3. associate-/l* 29.3%

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

   6. Simplified 29.3%

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

   7. Taylor expanded in c around 0 72.9%

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

   if -3.39999999999999984e25 < y < 3.5e15

   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. Step-by-step derivation

      1. fma-define 99.0%

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

      2. fma-define 99.0%

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

      3. fma-define 99.0%

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

      4. fma-define 99.1%

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

      5. fma-define 99.1%

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

      6. fma-define 99.1%

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

      7. fma-define 99.1%

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

   3. Simplified 99.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+148}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{230661.510616}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + y \cdot \left(c \cdot \left(27464.7644705 \cdot \frac{-1}{{y}^{2} \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}} - \left(\frac{x}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \frac{z}{y \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}}\right)\right) + \left(27464.7644705 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{z + y \cdot x}{b + y \cdot \left(y + a\right)}\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{230661.510616}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + y \cdot \left(c \cdot \left(27464.7644705 \cdot \frac{-1}{{y}^{2} \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}} - \left(\frac{x}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \frac{z}{y \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}}\right)\right) + \left(27464.7644705 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{z + y \cdot x}{b + y \cdot \left(y + a\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := {t\_1}^{2}\\ t_3 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ t_4 := y \cdot t\_1\\ t_5 := c + t\_4\\ t_6 := y \cdot t\_5\\ t_7 := \frac{230661.510616}{t\_5} + \left(\frac{t}{t\_6} + y \cdot \left(c \cdot \left(27464.7644705 \cdot \frac{-1}{{y}^{2} \cdot t\_2} - \left(\frac{x}{t\_2} + \frac{z}{y \cdot t\_2}\right)\right) + \left(27464.7644705 \cdot \frac{1}{t\_4} + \frac{z + y \cdot x}{t\_1}\right)\right)\right)\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{+148}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{+25}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+20}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \mathsf{fma}\left(y, x, z\right)\right)\right)}{i + t\_6}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+125}:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2 (pow t_1 2.0))
        (t_3 (+ x (- (/ z y) (* a (/ x y)))))
        (t_4 (* y t_1))
        (t_5 (+ c t_4))
        (t_6 (* y t_5))
        (t_7
         (+
          (/ 230661.510616 t_5)
          (+
           (/ t t_6)
           (*
            y
            (+
             (*
              c
              (-
               (* 27464.7644705 (/ -1.0 (* (pow y 2.0) t_2)))
               (+ (/ x t_2) (/ z (* y t_2)))))
             (+ (* 27464.7644705 (/ 1.0 t_4)) (/ (+ z (* y x)) t_1))))))))
   (if (<= y -2.75e+148)
     t_3
     (if (<= y -7.8e+25)
       t_7
       (if (<= y 9e+20)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (fma y x z)))))))
          (+ i t_6))
         (if (<= y 3.4e+125) t_7 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = pow(t_1, 2.0);
	double t_3 = x + ((z / y) - (a * (x / y)));
	double t_4 = y * t_1;
	double t_5 = c + t_4;
	double t_6 = y * t_5;
	double t_7 = (230661.510616 / t_5) + ((t / t_6) + (y * ((c * ((27464.7644705 * (-1.0 / (pow(y, 2.0) * t_2))) - ((x / t_2) + (z / (y * t_2))))) + ((27464.7644705 * (1.0 / t_4)) + ((z + (y * x)) / t_1)))));
	double tmp;
	if (y <= -2.75e+148) {
		tmp = t_3;
	} else if (y <= -7.8e+25) {
		tmp = t_7;
	} else if (y <= 9e+20) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * fma(y, x, z))))))) / (i + t_6);
	} else if (y <= 3.4e+125) {
		tmp = t_7;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b + Float64(y * Float64(y + a)))
	t_2 = t_1 ^ 2.0
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	t_4 = Float64(y * t_1)
	t_5 = Float64(c + t_4)
	t_6 = Float64(y * t_5)
	t_7 = Float64(Float64(230661.510616 / t_5) + Float64(Float64(t / t_6) + Float64(y * Float64(Float64(c * Float64(Float64(27464.7644705 * Float64(-1.0 / Float64((y ^ 2.0) * t_2))) - Float64(Float64(x / t_2) + Float64(z / Float64(y * t_2))))) + Float64(Float64(27464.7644705 * Float64(1.0 / t_4)) + Float64(Float64(z + Float64(y * x)) / t_1))))))
	tmp = 0.0
	if (y <= -2.75e+148)
		tmp = t_3;
	elseif (y <= -7.8e+25)
		tmp = t_7;
	elseif (y <= 9e+20)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * fma(y, x, z))))))) / Float64(i + t_6));
	elseif (y <= 3.4e+125)
		tmp = t_7;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[t$95$1, 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(c + t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(y * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(230661.510616 / t$95$5), $MachinePrecision] + N[(N[(t / t$95$6), $MachinePrecision] + N[(y * N[(N[(c * N[(N[(27464.7644705 * N[(-1.0 / N[(N[Power[y, 2.0], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x / t$95$2), $MachinePrecision] + N[(z / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.75e+148], t$95$3, If[LessEqual[y, -7.8e+25], t$95$7, If[LessEqual[y, 9e+20], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(y * x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+125], t$95$7, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.75e148 or 3.3999999999999999e125 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 84.7%

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

      1. associate--l+ 84.7%

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

      2. associate-/l* 87.9%

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

   5. Simplified 87.9%

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

   if -2.75e148 < y < -7.8000000000000004e25 or 9e20 < y < 3.3999999999999999e125

   1. Initial program 9.9%

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

   3. Taylor expanded in i around 0 19.3%

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

   4. Taylor expanded in i around 0 19.7%

      \[\leadsto \color{blue}{230661.510616 \cdot \frac{1}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 19.7%

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

      2. metadata-eval 19.7%

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

      3. associate-/l* 29.3%

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

   6. Simplified 29.3%

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

   7. Taylor expanded in c around 0 72.9%

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

   if -7.8000000000000004e25 < y < 9e20

   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 99.0%

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

      1. unpow2 99.0%

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

      2. associate-*l* 99.0%

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

      3. *-commutative 99.0%

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

      4. distribute-rgt-out 99.0%

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

      5. *-commutative 99.0%

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

      6. fma-define 99.1%

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

   5. Simplified 99.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+148}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{230661.510616}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + y \cdot \left(c \cdot \left(27464.7644705 \cdot \frac{-1}{{y}^{2} \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}} - \left(\frac{x}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \frac{z}{y \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}}\right)\right) + \left(27464.7644705 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{z + y \cdot x}{b + y \cdot \left(y + a\right)}\right)\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+20}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \mathsf{fma}\left(y, x, z\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+125}:\\ \;\;\;\;\frac{230661.510616}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + y \cdot \left(c \cdot \left(27464.7644705 \cdot \frac{-1}{{y}^{2} \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}} - \left(\frac{x}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \frac{z}{y \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}}\right)\right) + \left(27464.7644705 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{z + y \cdot x}{b + y \cdot \left(y + a\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))
	tmp = 0.0
	if (Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / t_1) <= Inf)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * fma(y, x, z))))))) / t_1);
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return 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]}, If[LessEqual[N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(y * x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 93.5%

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

      1. unpow2 93.5%

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

      2. associate-*l* 93.6%

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

      3. *-commutative 93.6%

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

      4. distribute-rgt-out 93.6%

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

      5. *-commutative 93.6%

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

      6. fma-define 93.6%

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

   5. Simplified 93.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 69.6%

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

      1. associate--l+ 69.6%

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

      2. associate-/l* 71.8%

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

   5. Simplified 71.8%

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

4. Final simplification 84.9%

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

Alternative 4: 84.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 69.6%

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

      1. associate--l+ 69.6%

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

      2. associate-/l* 71.8%

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

   5. Simplified 71.8%

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

4. Final simplification 84.9%

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

Alternative 5: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+41}:\\ \;\;\;\;\left(\frac{\frac{27464.7644705}{a}}{y} + \frac{z}{a}\right) + x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+80}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -2.5e+86)
     t_1
     (if (<= y -2.65e+41)
       (+ (+ (/ (/ 27464.7644705 a) y) (/ z a)) (* x (/ y a)))
       (if (<= y 1.95e+80)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.5e+86) {
		tmp = t_1;
	} else if (y <= -2.65e+41) {
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	} else if (y <= 1.95e+80) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-2.5d+86)) then
        tmp = t_1
    else if (y <= (-2.65d+41)) then
        tmp = (((27464.7644705d0 / a) / y) + (z / a)) + (x * (y / a))
    else if (y <= 1.95d+80) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.5e+86) {
		tmp = t_1;
	} else if (y <= -2.65e+41) {
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	} else if (y <= 1.95e+80) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -2.5e+86:
		tmp = t_1
	elif y <= -2.65e+41:
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a))
	elif y <= 1.95e+80:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -2.5e+86)
		tmp = t_1;
	elseif (y <= -2.65e+41)
		tmp = Float64(Float64(Float64(Float64(27464.7644705 / a) / y) + Float64(z / a)) + Float64(x * Float64(y / a)));
	elseif (y <= 1.95e+80)
		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))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -2.5e+86)
		tmp = t_1;
	elseif (y <= -2.65e+41)
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	elseif (y <= 1.95e+80)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+86], t$95$1, If[LessEqual[y, -2.65e+41], N[(N[(N[(N[(27464.7644705 / a), $MachinePrecision] / y), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+80], 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], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999999e86 or 1.94999999999999999e80 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 75.4%

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

      1. associate--l+ 75.4%

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

      2. associate-/l* 77.8%

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

   5. Simplified 77.8%

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

   if -2.4999999999999999e86 < y < -2.6499999999999998e41

   1. Initial program 1.9%

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

   3. Taylor expanded in i around 0 30.6%

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

   4. Taylor expanded in a around inf 72.2%

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

   5. Taylor expanded in y around inf 71.8%

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

      1. associate-+r+ 71.8%

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

      2. associate-*r/ 71.8%

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

      3. metadata-eval 71.8%

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

      4. associate-/r* 71.8%

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

      5. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

   if -2.6499999999999998e41 < y < 1.94999999999999999e80

   1. Initial program 92.9%

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

   3. Taylor expanded in x around 0 85.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+86}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+41}:\\ \;\;\;\;\left(\frac{\frac{27464.7644705}{a}}{y} + \frac{z}{a}\right) + x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+80}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+35}:\\ \;\;\;\;\left(\frac{\frac{27464.7644705}{a}}{y} + \frac{z}{a}\right) + x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.5e+90)
     t_1
     (if (<= y -2.65e+35)
       (+ (+ (/ (/ 27464.7644705 a) y) (/ z a)) (* x (/ y a)))
       (if (<= y 1.2e+89)
         (/
          (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.5e+90) {
		tmp = t_1;
	} else if (y <= -2.65e+35) {
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.5d+90)) then
        tmp = t_1
    else if (y <= (-2.65d+35)) then
        tmp = (((27464.7644705d0 / a) / y) + (z / a)) + (x * (y / a))
    else if (y <= 1.2d+89) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.5e+90) {
		tmp = t_1;
	} else if (y <= -2.65e+35) {
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.5e+90:
		tmp = t_1
	elif y <= -2.65e+35:
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a))
	elif y <= 1.2e+89:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.5e+90)
		tmp = t_1;
	elseif (y <= -2.65e+35)
		tmp = Float64(Float64(Float64(Float64(27464.7644705 / a) / y) + Float64(z / a)) + Float64(x * Float64(y / a)));
	elseif (y <= 1.2e+89)
		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))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.5e+90)
		tmp = t_1;
	elseif (y <= -2.65e+35)
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	elseif (y <= 1.2e+89)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+90], t$95$1, If[LessEqual[y, -2.65e+35], N[(N[(N[(N[(27464.7644705 / a), $MachinePrecision] / y), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+89], 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], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.49999999999999989e90 or 1.20000000000000002e89 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

   if -1.49999999999999989e90 < y < -2.65000000000000005e35

   1. Initial program 1.9%

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

   3. Taylor expanded in i around 0 30.6%

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

   4. Taylor expanded in a around inf 72.2%

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

   5. Taylor expanded in y around inf 71.8%

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

      1. associate-+r+ 71.8%

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

      2. associate-*r/ 71.8%

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

      3. metadata-eval 71.8%

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

      4. associate-/r* 71.8%

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

      5. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

   if -2.65000000000000005e35 < y < 1.20000000000000002e89

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+90}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+35}:\\ \;\;\;\;\left(\frac{\frac{27464.7644705}{a}}{y} + \frac{z}{a}\right) + x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -350000000:\\ \;\;\;\;\left(\frac{\frac{27464.7644705}{a}}{y} + \frac{z}{a}\right) + x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.6e+87)
     t_1
     (if (<= y -350000000.0)
       (+ (+ (/ (/ 27464.7644705 a) y) (/ z a)) (* x (/ y a)))
       (if (<= y 1.2e+89)
         (/
          (+ t (* y 230661.510616))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.6e+87) {
		tmp = t_1;
	} else if (y <= -350000000.0) {
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.6d+87)) then
        tmp = t_1
    else if (y <= (-350000000.0d0)) then
        tmp = (((27464.7644705d0 / a) / y) + (z / a)) + (x * (y / a))
    else if (y <= 1.2d+89) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.6e+87) {
		tmp = t_1;
	} else if (y <= -350000000.0) {
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.6e+87:
		tmp = t_1
	elif y <= -350000000.0:
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a))
	elif y <= 1.2e+89:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.6e+87)
		tmp = t_1;
	elseif (y <= -350000000.0)
		tmp = Float64(Float64(Float64(Float64(27464.7644705 / a) / y) + Float64(z / a)) + Float64(x * Float64(y / a)));
	elseif (y <= 1.2e+89)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.6e+87)
		tmp = t_1;
	elseif (y <= -350000000.0)
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	elseif (y <= 1.2e+89)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+87], t$95$1, If[LessEqual[y, -350000000.0], N[(N[(N[(N[(27464.7644705 / a), $MachinePrecision] / y), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+89], 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], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6e87 or 1.20000000000000002e89 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

   if -1.6e87 < y < -3.5e8

   1. Initial program 28.6%

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

   3. Taylor expanded in i around 0 55.4%

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

   4. Taylor expanded in a around inf 47.8%

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

   5. Taylor expanded in y around inf 47.0%

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

      1. associate-+r+ 47.0%

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

      2. associate-*r/ 47.0%

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

      3. metadata-eval 47.0%

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

      4. associate-/r* 47.0%

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

      5. associate-/l* 55.6%

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

   7. Simplified 55.6%

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

   if -3.5e8 < y < 1.20000000000000002e89

   1. Initial program 92.7%

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

   3. Taylor expanded in y around 0 78.7%

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

      1. *-commutative 78.7%

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

   5. Simplified 78.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -350000000:\\ \;\;\;\;\left(\frac{\frac{27464.7644705}{a}}{y} + \frac{z}{a}\right) + x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;\frac{z + y \cdot x}{a}\\ \mathbf{elif}\;y \leq -26000 \lor \neg \left(y \leq 1.2 \cdot 10^{+89}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -5.8e+90)
     t_1
     (if (<= y -1.05e+35)
       (/ (+ z (* y x)) a)
       (if (or (<= y -26000.0) (not (<= y 1.2e+89)))
         t_1
         (/ (+ t (* y 230661.510616)) i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.8e+90) {
		tmp = t_1;
	} else if (y <= -1.05e+35) {
		tmp = (z + (y * x)) / a;
	} else if ((y <= -26000.0) || !(y <= 1.2e+89)) {
		tmp = t_1;
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-5.8d+90)) then
        tmp = t_1
    else if (y <= (-1.05d+35)) then
        tmp = (z + (y * x)) / a
    else if ((y <= (-26000.0d0)) .or. (.not. (y <= 1.2d+89))) then
        tmp = t_1
    else
        tmp = (t + (y * 230661.510616d0)) / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.8e+90) {
		tmp = t_1;
	} else if (y <= -1.05e+35) {
		tmp = (z + (y * x)) / a;
	} else if ((y <= -26000.0) || !(y <= 1.2e+89)) {
		tmp = t_1;
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -5.8e+90:
		tmp = t_1
	elif y <= -1.05e+35:
		tmp = (z + (y * x)) / a
	elif (y <= -26000.0) or not (y <= 1.2e+89):
		tmp = t_1
	else:
		tmp = (t + (y * 230661.510616)) / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -5.8e+90)
		tmp = t_1;
	elseif (y <= -1.05e+35)
		tmp = Float64(Float64(z + Float64(y * x)) / a);
	elseif ((y <= -26000.0) || !(y <= 1.2e+89))
		tmp = t_1;
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -5.8e+90)
		tmp = t_1;
	elseif (y <= -1.05e+35)
		tmp = (z + (y * x)) / a;
	elseif ((y <= -26000.0) || ~((y <= 1.2e+89)))
		tmp = t_1;
	else
		tmp = (t + (y * 230661.510616)) / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+90], t$95$1, If[LessEqual[y, -1.05e+35], N[(N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[y, -26000.0], N[Not[LessEqual[y, 1.2e+89]], $MachinePrecision]], t$95$1, N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000003e90 or -1.0499999999999999e35 < y < -26000 or 1.20000000000000002e89 < y

   1. Initial program 5.0%

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

   3. Taylor expanded in y around inf 72.9%

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

      1. associate--l+ 72.9%

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

      2. associate-/l* 75.1%

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

   5. Simplified 75.1%

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

   if -5.8000000000000003e90 < y < -1.0499999999999999e35

   1. Initial program 1.9%

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

   3. Taylor expanded in i around 0 30.6%

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

   4. Taylor expanded in a around inf 72.2%

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

   5. Taylor expanded in y around inf 72.2%

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

   6. Taylor expanded in y around inf 72.2%

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

   if -26000 < y < 1.20000000000000002e89

   1. Initial program 92.6%

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

   3. Taylor expanded in y around 0 79.7%

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

      1. *-commutative 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in i around inf 54.8%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+90}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;\frac{z + y \cdot x}{a}\\ \mathbf{elif}\;y \leq -26000 \lor \neg \left(y \leq 1.2 \cdot 10^{+89}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+33}:\\ \;\;\;\;\frac{z + y \cdot x}{a}\\ \mathbf{elif}\;y \leq -55000:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.1e+85)
     t_1
     (if (<= y -4.3e+33)
       (/ (+ z (* y x)) a)
       (if (<= y -55000.0)
         (- (+ x (/ z y)) (/ (* x a) y))
         (if (<= y 1.2e+89) (/ (+ t (* y 230661.510616)) i) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.1e+85) {
		tmp = t_1;
	} else if (y <= -4.3e+33) {
		tmp = (z + (y * x)) / a;
	} else if (y <= -55000.0) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.1d+85)) then
        tmp = t_1
    else if (y <= (-4.3d+33)) then
        tmp = (z + (y * x)) / a
    else if (y <= (-55000.0d0)) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else if (y <= 1.2d+89) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.1e+85) {
		tmp = t_1;
	} else if (y <= -4.3e+33) {
		tmp = (z + (y * x)) / a;
	} else if (y <= -55000.0) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.1e+85:
		tmp = t_1
	elif y <= -4.3e+33:
		tmp = (z + (y * x)) / a
	elif y <= -55000.0:
		tmp = (x + (z / y)) - ((x * a) / y)
	elif y <= 1.2e+89:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.1e+85)
		tmp = t_1;
	elseif (y <= -4.3e+33)
		tmp = Float64(Float64(z + Float64(y * x)) / a);
	elseif (y <= -55000.0)
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	elseif (y <= 1.2e+89)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.1e+85)
		tmp = t_1;
	elseif (y <= -4.3e+33)
		tmp = (z + (y * x)) / a;
	elseif (y <= -55000.0)
		tmp = (x + (z / y)) - ((x * a) / y);
	elseif (y <= 1.2e+89)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+85], t$95$1, If[LessEqual[y, -4.3e+33], N[(N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -55000.0], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+89], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1000000000000001e85 or 1.20000000000000002e89 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

   if -1.1000000000000001e85 < y < -4.30000000000000028e33

   1. Initial program 1.9%

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

   3. Taylor expanded in i around 0 30.6%

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

   4. Taylor expanded in a around inf 72.2%

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

   5. Taylor expanded in y around inf 72.2%

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

   6. Taylor expanded in y around inf 72.2%

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

   if -4.30000000000000028e33 < y < -55000

   1. Initial program 83.2%

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

   3. Taylor expanded in y around inf 21.3%

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

   if -55000 < y < 1.20000000000000002e89

   1. Initial program 92.6%

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

   3. Taylor expanded in y around 0 79.7%

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

      1. *-commutative 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in i around inf 54.8%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+33}:\\ \;\;\;\;\frac{z + y \cdot x}{a}\\ \mathbf{elif}\;y \leq -55000:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+32}:\\ \;\;\;\;\frac{z + y \cdot x}{a}\\ \mathbf{elif}\;y \leq -12200:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+80}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -3.8e+83)
     t_1
     (if (<= y -1.65e+32)
       (/ (+ z (* y x)) a)
       (if (<= y -12200.0)
         (- (+ x (/ z y)) (/ (* x a) y))
         (if (<= y 1.95e+80)
           (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) i)
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -3.8e+83) {
		tmp = t_1;
	} else if (y <= -1.65e+32) {
		tmp = (z + (y * x)) / a;
	} else if (y <= -12200.0) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 1.95e+80) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-3.8d+83)) then
        tmp = t_1
    else if (y <= (-1.65d+32)) then
        tmp = (z + (y * x)) / a
    else if (y <= (-12200.0d0)) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else if (y <= 1.95d+80) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -3.8e+83) {
		tmp = t_1;
	} else if (y <= -1.65e+32) {
		tmp = (z + (y * x)) / a;
	} else if (y <= -12200.0) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 1.95e+80) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -3.8e+83:
		tmp = t_1
	elif y <= -1.65e+32:
		tmp = (z + (y * x)) / a
	elif y <= -12200.0:
		tmp = (x + (z / y)) - ((x * a) / y)
	elif y <= 1.95e+80:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -3.8e+83)
		tmp = t_1;
	elseif (y <= -1.65e+32)
		tmp = Float64(Float64(z + Float64(y * x)) / a);
	elseif (y <= -12200.0)
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	elseif (y <= 1.95e+80)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -3.8e+83)
		tmp = t_1;
	elseif (y <= -1.65e+32)
		tmp = (z + (y * x)) / a;
	elseif (y <= -12200.0)
		tmp = (x + (z / y)) - ((x * a) / y);
	elseif (y <= 1.95e+80)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+83], t$95$1, If[LessEqual[y, -1.65e+32], N[(N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -12200.0], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+80], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.8000000000000002e83 or 1.94999999999999999e80 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 75.4%

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

      1. associate--l+ 75.4%

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

      2. associate-/l* 77.8%

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

   5. Simplified 77.8%

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

   if -3.8000000000000002e83 < y < -1.6500000000000001e32

   1. Initial program 1.9%

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

   3. Taylor expanded in i around 0 30.6%

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

   4. Taylor expanded in a around inf 72.2%

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

   5. Taylor expanded in y around inf 72.2%

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

   6. Taylor expanded in y around inf 72.2%

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

   if -1.6500000000000001e32 < y < -12200

   1. Initial program 83.2%

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

   3. Taylor expanded in y around inf 21.3%

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

   if -12200 < y < 1.94999999999999999e80

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0 80.8%

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

      1. *-commutative 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in i around inf 55.8%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+83}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+32}:\\ \;\;\;\;\frac{z + y \cdot x}{a}\\ \mathbf{elif}\;y \leq -12200:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+80}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+32}:\\ \;\;\;\;\frac{z + y \cdot x}{a}\\ \mathbf{elif}\;y \leq -55000:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -2.4e+89)
     t_1
     (if (<= y -2e+32)
       (/ (+ z (* y x)) a)
       (if (<= y -55000.0)
         (- (+ x (/ z y)) (/ (* x a) y))
         (if (<= y 1.2e+89)
           (/ (+ t (* y 230661.510616)) (+ i (* y c)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.4e+89) {
		tmp = t_1;
	} else if (y <= -2e+32) {
		tmp = (z + (y * x)) / a;
	} else if (y <= -55000.0) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-2.4d+89)) then
        tmp = t_1
    else if (y <= (-2d+32)) then
        tmp = (z + (y * x)) / a
    else if (y <= (-55000.0d0)) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else if (y <= 1.2d+89) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.4e+89) {
		tmp = t_1;
	} else if (y <= -2e+32) {
		tmp = (z + (y * x)) / a;
	} else if (y <= -55000.0) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -2.4e+89:
		tmp = t_1
	elif y <= -2e+32:
		tmp = (z + (y * x)) / a
	elif y <= -55000.0:
		tmp = (x + (z / y)) - ((x * a) / y)
	elif y <= 1.2e+89:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -2.4e+89)
		tmp = t_1;
	elseif (y <= -2e+32)
		tmp = Float64(Float64(z + Float64(y * x)) / a);
	elseif (y <= -55000.0)
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	elseif (y <= 1.2e+89)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -2.4e+89)
		tmp = t_1;
	elseif (y <= -2e+32)
		tmp = (z + (y * x)) / a;
	elseif (y <= -55000.0)
		tmp = (x + (z / y)) - ((x * a) / y);
	elseif (y <= 1.2e+89)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+89], t$95$1, If[LessEqual[y, -2e+32], N[(N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -55000.0], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+89], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.40000000000000004e89 or 1.20000000000000002e89 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

   if -2.40000000000000004e89 < y < -2.00000000000000011e32

   1. Initial program 1.9%

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

   3. Taylor expanded in i around 0 30.6%

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

   4. Taylor expanded in a around inf 72.2%

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

   5. Taylor expanded in y around inf 72.2%

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

   6. Taylor expanded in y around inf 72.2%

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

   if -2.00000000000000011e32 < y < -55000

   1. Initial program 83.2%

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

   3. Taylor expanded in y around inf 21.3%

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

   if -55000 < y < 1.20000000000000002e89

   1. Initial program 92.6%

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

   3. Taylor expanded in y around 0 79.7%

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

      1. *-commutative 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in y around 0 67.8%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{c \cdot y} + i} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+89}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+32}:\\ \;\;\;\;\frac{z + y \cdot x}{a}\\ \mathbf{elif}\;y \leq -55000:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -11500000000:\\ \;\;\;\;\left(\frac{\frac{27464.7644705}{a}}{y} + \frac{z}{a}\right) + x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.12e+85)
     t_1
     (if (<= y -11500000000.0)
       (+ (+ (/ (/ 27464.7644705 a) y) (/ z a)) (* x (/ y a)))
       (if (<= y 1.2e+89)
         (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.12e+85) {
		tmp = t_1;
	} else if (y <= -11500000000.0) {
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.12d+85)) then
        tmp = t_1
    else if (y <= (-11500000000.0d0)) then
        tmp = (((27464.7644705d0 / a) / y) + (z / a)) + (x * (y / a))
    else if (y <= 1.2d+89) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.12e+85) {
		tmp = t_1;
	} else if (y <= -11500000000.0) {
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.12e+85:
		tmp = t_1
	elif y <= -11500000000.0:
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a))
	elif y <= 1.2e+89:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.12e+85)
		tmp = t_1;
	elseif (y <= -11500000000.0)
		tmp = Float64(Float64(Float64(Float64(27464.7644705 / a) / y) + Float64(z / a)) + Float64(x * Float64(y / a)));
	elseif (y <= 1.2e+89)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.12e+85)
		tmp = t_1;
	elseif (y <= -11500000000.0)
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	elseif (y <= 1.2e+89)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+85], t$95$1, If[LessEqual[y, -11500000000.0], N[(N[(N[(N[(27464.7644705 / a), $MachinePrecision] / y), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+89], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999993e85 or 1.20000000000000002e89 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

   if -1.11999999999999993e85 < y < -1.15e10

   1. Initial program 28.6%

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

   3. Taylor expanded in i around 0 55.4%

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

   4. Taylor expanded in a around inf 47.8%

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

   5. Taylor expanded in y around inf 47.0%

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

      1. associate-+r+ 47.0%

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

      2. associate-*r/ 47.0%

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

      3. metadata-eval 47.0%

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

      4. associate-/r* 47.0%

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

      5. associate-/l* 55.6%

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

   7. Simplified 55.6%

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

   if -1.15e10 < y < 1.20000000000000002e89

   1. Initial program 92.7%

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

   3. Taylor expanded in y around 0 78.7%

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

      1. *-commutative 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in y around 0 74.3%

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

      1. *-commutative 74.3%

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

   8. Simplified 74.3%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+85}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -11500000000:\\ \;\;\;\;\left(\frac{\frac{27464.7644705}{a}}{y} + \frac{z}{a}\right) + x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + y \cdot x}{a}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -18000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.48:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (+ z (* y x)) a)))
   (if (<= y -3.7e+136)
     x
     (if (<= y -18000000000.0)
       t_1
       (if (<= y 0.48)
         (/ (+ t (* y 230661.510616)) i)
         (if (<= y 3.4e+121) t_1 x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z + (y * x)) / a;
	double tmp;
	if (y <= -3.7e+136) {
		tmp = x;
	} else if (y <= -18000000000.0) {
		tmp = t_1;
	} else if (y <= 0.48) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 3.4e+121) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + (y * x)) / a
    if (y <= (-3.7d+136)) then
        tmp = x
    else if (y <= (-18000000000.0d0)) then
        tmp = t_1
    else if (y <= 0.48d0) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 3.4d+121) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z + (y * x)) / a;
	double tmp;
	if (y <= -3.7e+136) {
		tmp = x;
	} else if (y <= -18000000000.0) {
		tmp = t_1;
	} else if (y <= 0.48) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 3.4e+121) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z + (y * x)) / a
	tmp = 0
	if y <= -3.7e+136:
		tmp = x
	elif y <= -18000000000.0:
		tmp = t_1
	elif y <= 0.48:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 3.4e+121:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z + Float64(y * x)) / a)
	tmp = 0.0
	if (y <= -3.7e+136)
		tmp = x;
	elseif (y <= -18000000000.0)
		tmp = t_1;
	elseif (y <= 0.48)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 3.4e+121)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z + (y * x)) / a;
	tmp = 0.0;
	if (y <= -3.7e+136)
		tmp = x;
	elseif (y <= -18000000000.0)
		tmp = t_1;
	elseif (y <= 0.48)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 3.4e+121)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[y, -3.7e+136], x, If[LessEqual[y, -18000000000.0], t$95$1, If[LessEqual[y, 0.48], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 3.4e+121], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7000000000000001e136 or 3.4000000000000001e121 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 68.0%

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

   if -3.7000000000000001e136 < y < -1.8e10 or 0.47999999999999998 < y < 3.4000000000000001e121

   1. Initial program 21.8%

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

   3. Taylor expanded in i around 0 28.5%

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

   4. Taylor expanded in a around inf 32.6%

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

   5. Taylor expanded in y around inf 30.5%

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

   6. Taylor expanded in y around inf 30.3%

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

   if -1.8e10 < y < 0.47999999999999998

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 85.8%

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

      1. *-commutative 85.8%

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

   5. Simplified 85.8%

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

   6. Taylor expanded in i around inf 61.0%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -18000000000:\\ \;\;\;\;\frac{z + y \cdot x}{a}\\ \mathbf{elif}\;y \leq 0.48:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+121}:\\ \;\;\;\;\frac{z + y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 70.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2900000000:\\ \;\;\;\;\left(\frac{\frac{27464.7644705}{a}}{y} + \frac{z}{a}\right) + x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -5.8e+90)
     t_1
     (if (<= y -2900000000.0)
       (+ (+ (/ (/ 27464.7644705 a) y) (/ z a)) (* x (/ y a)))
       (if (<= y 1.2e+89) (/ (+ t (* y 230661.510616)) (+ i (* y c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.8e+90) {
		tmp = t_1;
	} else if (y <= -2900000000.0) {
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-5.8d+90)) then
        tmp = t_1
    else if (y <= (-2900000000.0d0)) then
        tmp = (((27464.7644705d0 / a) / y) + (z / a)) + (x * (y / a))
    else if (y <= 1.2d+89) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.8e+90) {
		tmp = t_1;
	} else if (y <= -2900000000.0) {
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	} else if (y <= 1.2e+89) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -5.8e+90:
		tmp = t_1
	elif y <= -2900000000.0:
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a))
	elif y <= 1.2e+89:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -5.8e+90)
		tmp = t_1;
	elseif (y <= -2900000000.0)
		tmp = Float64(Float64(Float64(Float64(27464.7644705 / a) / y) + Float64(z / a)) + Float64(x * Float64(y / a)));
	elseif (y <= 1.2e+89)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -5.8e+90)
		tmp = t_1;
	elseif (y <= -2900000000.0)
		tmp = (((27464.7644705 / a) / y) + (z / a)) + (x * (y / a));
	elseif (y <= 1.2e+89)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+90], t$95$1, If[LessEqual[y, -2900000000.0], N[(N[(N[(N[(27464.7644705 / a), $MachinePrecision] / y), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+89], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000003e90 or 1.20000000000000002e89 < y

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

   if -5.8000000000000003e90 < y < -2.9e9

   1. Initial program 28.6%

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

   3. Taylor expanded in i around 0 55.4%

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

   4. Taylor expanded in a around inf 47.8%

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

   5. Taylor expanded in y around inf 47.0%

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

      1. associate-+r+ 47.0%

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

      2. associate-*r/ 47.0%

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

      3. metadata-eval 47.0%

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

      4. associate-/r* 47.0%

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

      5. associate-/l* 55.6%

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

   7. Simplified 55.6%

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

   if -2.9e9 < y < 1.20000000000000002e89

   1. Initial program 92.7%

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

   3. Taylor expanded in y around 0 78.7%

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

      1. *-commutative 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in y around 0 67.0%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{c \cdot y} + i} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+90}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2900000000:\\ \;\;\;\;\left(\frac{\frac{27464.7644705}{a}}{y} + \frac{z}{a}\right) + x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -55000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+41}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -55000.0) x (if (<= y 1.35e+41) (/ (+ t (* y 230661.510616)) 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 <= -55000.0) {
		tmp = x;
	} else if (y <= 1.35e+41) {
		tmp = (t + (y * 230661.510616)) / 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 <= (-55000.0d0)) then
        tmp = x
    else if (y <= 1.35d+41) then
        tmp = (t + (y * 230661.510616d0)) / 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 <= -55000.0) {
		tmp = x;
	} else if (y <= 1.35e+41) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -55000.0:
		tmp = x
	elif y <= 1.35e+41:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -55000.0)
		tmp = x;
	elseif (y <= 1.35e+41)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / 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 <= -55000.0)
		tmp = x;
	elseif (y <= 1.35e+41)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -55000.0], x, If[LessEqual[y, 1.35e+41], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -55000 or 1.35e41 < y

   1. Initial program 6.3%

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

   3. Taylor expanded in y around inf 47.5%

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

   if -55000 < y < 1.35e41

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 83.8%

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

      1. *-commutative 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in i around inf 58.6%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -55000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+41}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -560:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -560.0) x (if (<= y 7.2e+89) (/ 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 <= -560.0) {
		tmp = x;
	} else if (y <= 7.2e+89) {
		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 <= (-560.0d0)) then
        tmp = x
    else if (y <= 7.2d+89) 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 <= -560.0) {
		tmp = x;
	} else if (y <= 7.2e+89) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -560.0:
		tmp = x
	elif y <= 7.2e+89:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -560.0)
		tmp = x;
	elseif (y <= 7.2e+89)
		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 <= -560.0)
		tmp = x;
	elseif (y <= 7.2e+89)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -560.0], x, If[LessEqual[y, 7.2e+89], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -560 or 7.2e89 < y

   1. Initial program 4.9%

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

   3. Taylor expanded in y around inf 52.6%

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

   if -560 < y < 7.2e89

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0 48.7%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -560:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.3% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.3%

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

3. Taylor expanded in y around inf 23.5%

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

4. Final simplification 23.5%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024043 
(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)))