Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.4% → 84.3%

Time: 35.7s

Alternatives: 20

Speedup: 1.1×

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: 56.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\frac{y}{x}}\\ t_2 := 27464.7644705 + y \cdot \left(z + y \cdot x\right)\\ t_3 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\\ t_4 := \frac{t}{y \cdot t_3}\\ t_5 := \frac{230661.510616}{t_3}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;x + \left(\frac{z}{y} - t_1\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t_5 + \left(t_4 + \frac{y}{\frac{t_3}{t_2}}\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot t_2\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+51}:\\ \;\;\;\;t_5 + \left(t_4 + \left(\frac{{y}^{2}}{\frac{t_3}{z}} + \frac{y}{\frac{t_3}{27464.7644705 + x \cdot {y}^{2}}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{{y}^{2}}\right)\right) - \left(\left(t_1 + \frac{a}{\frac{{y}^{2}}{z - x \cdot a}}\right) + \frac{b}{\frac{{y}^{2}}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ a (/ y x)))
        (t_2 (+ 27464.7644705 (* y (+ z (* y x)))))
        (t_3 (fma y (fma y (+ y a) b) c))
        (t_4 (/ t (* y t_3)))
        (t_5 (/ 230661.510616 t_3)))
   (if (<= y -1.5e+80)
     (+ x (- (/ z y) t_1))
     (if (<= y -5e+19)
       (+ t_5 (+ t_4 (/ y (/ t_3 t_2))))
       (if (<= y 2.7e-25)
         (/
          (+ t (* y (+ 230661.510616 (* y t_2))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
         (if (<= y 2.8e+51)
           (+
            t_5
            (+
             t_4
             (+
              (/ (pow y 2.0) (/ t_3 z))
              (/ y (/ t_3 (+ 27464.7644705 (* x (pow y 2.0))))))))
           (-
            (+ x (+ (/ z y) (/ 27464.7644705 (pow y 2.0))))
            (+
             (+ t_1 (/ a (/ (pow y 2.0) (- z (* x a)))))
             (/ b (/ (pow y 2.0) x))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a / (y / x);
	double t_2 = 27464.7644705 + (y * (z + (y * x)));
	double t_3 = fma(y, fma(y, (y + a), b), c);
	double t_4 = t / (y * t_3);
	double t_5 = 230661.510616 / t_3;
	double tmp;
	if (y <= -1.5e+80) {
		tmp = x + ((z / y) - t_1);
	} else if (y <= -5e+19) {
		tmp = t_5 + (t_4 + (y / (t_3 / t_2)));
	} else if (y <= 2.7e-25) {
		tmp = (t + (y * (230661.510616 + (y * t_2)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 2.8e+51) {
		tmp = t_5 + (t_4 + ((pow(y, 2.0) / (t_3 / z)) + (y / (t_3 / (27464.7644705 + (x * pow(y, 2.0)))))));
	} else {
		tmp = (x + ((z / y) + (27464.7644705 / pow(y, 2.0)))) - ((t_1 + (a / (pow(y, 2.0) / (z - (x * a))))) + (b / (pow(y, 2.0) / x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a / Float64(y / x))
	t_2 = Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))
	t_3 = fma(y, fma(y, Float64(y + a), b), c)
	t_4 = Float64(t / Float64(y * t_3))
	t_5 = Float64(230661.510616 / t_3)
	tmp = 0.0
	if (y <= -1.5e+80)
		tmp = Float64(x + Float64(Float64(z / y) - t_1));
	elseif (y <= -5e+19)
		tmp = Float64(t_5 + Float64(t_4 + Float64(y / Float64(t_3 / t_2))));
	elseif (y <= 2.7e-25)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * t_2)))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	elseif (y <= 2.8e+51)
		tmp = Float64(t_5 + Float64(t_4 + Float64(Float64((y ^ 2.0) / Float64(t_3 / z)) + Float64(y / Float64(t_3 / Float64(27464.7644705 + Float64(x * (y ^ 2.0))))))));
	else
		tmp = Float64(Float64(x + Float64(Float64(z / y) + Float64(27464.7644705 / (y ^ 2.0)))) - Float64(Float64(t_1 + Float64(a / Float64((y ^ 2.0) / Float64(z - Float64(x * a))))) + Float64(b / Float64((y ^ 2.0) / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$4 = N[(t / N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(230661.510616 / t$95$3), $MachinePrecision]}, If[LessEqual[y, -1.5e+80], N[(x + N[(N[(z / y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e+19], N[(t$95$5 + N[(t$95$4 + N[(y / N[(t$95$3 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-25], N[(N[(t + N[(y * N[(230661.510616 + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+51], N[(t$95$5 + N[(t$95$4 + N[(N[(N[Power[y, 2.0], $MachinePrecision] / N[(t$95$3 / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t$95$3 / N[(27464.7644705 + N[(x * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(z / y), $MachinePrecision] + N[(27464.7644705 / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$1 + N[(a / N[(N[Power[y, 2.0], $MachinePrecision] / N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[Power[y, 2.0], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.49999999999999993e80

   1. Initial program 0.7%

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

   3. Taylor expanded in y around inf 63.3%

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

      1. associate--l+ 63.3%

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

      2. associate-/l* 66.7%

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

   5. Simplified 66.7%

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

   if -1.49999999999999993e80 < y < -5e19

   1. Initial program 26.9%

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

   3. Taylor expanded in i around 0 26.9%

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

   4. Taylor expanded in t around 0 61.1%

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

      1. associate-*r/ 61.1%

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

      2. metadata-eval 61.1%

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

      3. +-commutative 61.1%

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

      4. +-commutative 61.1%

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

      5. +-commutative 61.1%

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

      6. fma-udef 61.1%

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

      7. fma-udef 61.1%

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

   6. Simplified 81.6%

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

   if -5e19 < y < 2.70000000000000016e-25

   1. Initial program 99.8%

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

   if 2.70000000000000016e-25 < y < 2.80000000000000005e51

   1. Initial program 54.5%

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

   3. Taylor expanded in i around 0 54.5%

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

   4. Taylor expanded in z around inf 65.8%

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

      1. associate-*r/ 65.8%

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

      2. metadata-eval 65.8%

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

      3. +-commutative 65.8%

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

      4. +-commutative 65.8%

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

      5. +-commutative 65.8%

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

      6. fma-udef 65.8%

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

      7. fma-udef 65.8%

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

   6. Simplified 82.4%

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

   if 2.80000000000000005e51 < y

   1. Initial program 4.0%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. associate-*r/ 61.8%

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

      3. metadata-eval 61.8%

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

      4. associate-+r+ 61.8%

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

      5. associate-/l* 61.8%

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

      6. associate-/l* 67.3%

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

      7. associate-/l* 72.3%

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

   5. Simplified 72.3%

      \[\leadsto \color{blue}{\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{{y}^{2}}\right)\right) - \left(\left(\frac{a}{\frac{y}{x}} + \frac{a}{\frac{{y}^{2}}{z - a \cdot x}}\right) + \frac{b}{\frac{{y}^{2}}{x}}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{230661.510616}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \left(\frac{t}{y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{27464.7644705 + y \cdot \left(z + y \cdot x\right)}}\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{230661.510616}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \left(\frac{t}{y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \left(\frac{{y}^{2}}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{z}} + \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{27464.7644705 + x \cdot {y}^{2}}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{{y}^{2}}\right)\right) - \left(\left(\frac{a}{\frac{y}{x}} + \frac{a}{\frac{{y}^{2}}{z - x \cdot a}}\right) + \frac{b}{\frac{{y}^{2}}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\frac{y}{x}}\\ t_2 := 27464.7644705 + y \cdot \left(z + y \cdot x\right)\\ t_3 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - t_1\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{230661.510616}{t_3} + \left(\frac{t}{y \cdot t_3} + \frac{y}{\frac{t_3}{t_2}}\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot t_2\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{{y}^{2}}\right)\right) - \left(\left(t_1 + \frac{a}{\frac{{y}^{2}}{z - x \cdot a}}\right) + \frac{b}{\frac{{y}^{2}}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ a (/ y x)))
        (t_2 (+ 27464.7644705 (* y (+ z (* y x)))))
        (t_3 (fma y (fma y (+ y a) b) c)))
   (if (<= y -5.5e+77)
     (+ x (- (/ z y) t_1))
     (if (<= y -4.8e+19)
       (+ (/ 230661.510616 t_3) (+ (/ t (* y t_3)) (/ y (/ t_3 t_2))))
       (if (<= y 6.2e+48)
         (/
          (+ t (* y (+ 230661.510616 (* y t_2))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
         (-
          (+ x (+ (/ z y) (/ 27464.7644705 (pow y 2.0))))
          (+
           (+ t_1 (/ a (/ (pow y 2.0) (- z (* x a)))))
           (/ b (/ (pow y 2.0) x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a / (y / x);
	double t_2 = 27464.7644705 + (y * (z + (y * x)));
	double t_3 = fma(y, fma(y, (y + a), b), c);
	double tmp;
	if (y <= -5.5e+77) {
		tmp = x + ((z / y) - t_1);
	} else if (y <= -4.8e+19) {
		tmp = (230661.510616 / t_3) + ((t / (y * t_3)) + (y / (t_3 / t_2)));
	} else if (y <= 6.2e+48) {
		tmp = (t + (y * (230661.510616 + (y * t_2)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = (x + ((z / y) + (27464.7644705 / pow(y, 2.0)))) - ((t_1 + (a / (pow(y, 2.0) / (z - (x * a))))) + (b / (pow(y, 2.0) / x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a / Float64(y / x))
	t_2 = Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))
	t_3 = fma(y, fma(y, Float64(y + a), b), c)
	tmp = 0.0
	if (y <= -5.5e+77)
		tmp = Float64(x + Float64(Float64(z / y) - t_1));
	elseif (y <= -4.8e+19)
		tmp = Float64(Float64(230661.510616 / t_3) + Float64(Float64(t / Float64(y * t_3)) + Float64(y / Float64(t_3 / t_2))));
	elseif (y <= 6.2e+48)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * t_2)))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = Float64(Float64(x + Float64(Float64(z / y) + Float64(27464.7644705 / (y ^ 2.0)))) - Float64(Float64(t_1 + Float64(a / Float64((y ^ 2.0) / Float64(z - Float64(x * a))))) + Float64(b / Float64((y ^ 2.0) / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision]}, If[LessEqual[y, -5.5e+77], N[(x + N[(N[(z / y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e+19], N[(N[(230661.510616 / t$95$3), $MachinePrecision] + N[(N[(t / N[(y * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t$95$3 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+48], N[(N[(t + N[(y * N[(230661.510616 + N[(y * t$95$2), $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], N[(N[(x + N[(N[(z / y), $MachinePrecision] + N[(27464.7644705 / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$1 + N[(a / N[(N[Power[y, 2.0], $MachinePrecision] / N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[Power[y, 2.0], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.50000000000000036e77

   1. Initial program 0.7%

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

   3. Taylor expanded in y around inf 63.3%

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

      1. associate--l+ 63.3%

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

      2. associate-/l* 66.7%

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

   5. Simplified 66.7%

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

   if -5.50000000000000036e77 < y < -4.8e19

   1. Initial program 26.9%

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

   3. Taylor expanded in i around 0 26.9%

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

   4. Taylor expanded in t around 0 61.1%

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

      1. associate-*r/ 61.1%

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

      2. metadata-eval 61.1%

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

      3. +-commutative 61.1%

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

      4. +-commutative 61.1%

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

      5. +-commutative 61.1%

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

      6. fma-udef 61.1%

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

      7. fma-udef 61.1%

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

   6. Simplified 81.6%

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

   if -4.8e19 < y < 6.20000000000000011e48

   1. Initial program 94.2%

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

   if 6.20000000000000011e48 < y

   1. Initial program 4.0%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. associate-*r/ 61.8%

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

      3. metadata-eval 61.8%

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

      4. associate-+r+ 61.8%

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

      5. associate-/l* 61.8%

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

      6. associate-/l* 67.3%

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

      7. associate-/l* 72.3%

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

   5. Simplified 72.3%

      \[\leadsto \color{blue}{\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{{y}^{2}}\right)\right) - \left(\left(\frac{a}{\frac{y}{x}} + \frac{a}{\frac{{y}^{2}}{z - a \cdot x}}\right) + \frac{b}{\frac{{y}^{2}}{x}}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{230661.510616}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \left(\frac{t}{y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{27464.7644705 + y \cdot \left(z + y \cdot x\right)}}\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{{y}^{2}}\right)\right) - \left(\left(\frac{a}{\frac{y}{x}} + \frac{a}{\frac{{y}^{2}}{z - x \cdot a}}\right) + \frac{b}{\frac{{y}^{2}}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.2% accurate, 0.5× speedup

Math

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

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 (/ y x)))))))

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 / (y / x)));
	}
	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 / (y / x)));
	}
	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 / (y / x)))
	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(y / x))));
	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 / (y / x)));
	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[(y / x), $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 85.2%

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

   if +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 66.0%

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

      1. associate--l+ 66.0%

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

      2. associate-/l* 69.9%

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

   5. Simplified 69.9%

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

4. Final simplification 79.4%

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

Alternative 4: 79.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \frac{1}{\frac{t_1}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}}\\ t_3 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2
         (/
          1.0
          (/
           t_1
           (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))))
        (t_3 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.6e+77)
     t_3
     (if (<= y -2.9e+15)
       t_2
       (if (<= y 9.5e-14)
         (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i (* y t_1)))
         (if (<= y 2.6e+51) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = 1.0 / (t_1 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))));
	double t_3 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.6e+77) {
		tmp = t_3;
	} else if (y <= -2.9e+15) {
		tmp = t_2;
	} else if (y <= 9.5e-14) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 2.6e+51) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (y * (b + (y * (y + a))))
    t_2 = 1.0d0 / (t_1 / (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))
    t_3 = x + ((z / y) - (a / (y / x)))
    if (y <= (-2.6d+77)) then
        tmp = t_3
    else if (y <= (-2.9d+15)) then
        tmp = t_2
    else if (y <= 9.5d-14) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * t_1))
    else if (y <= 2.6d+51) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = 1.0 / (t_1 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))));
	double t_3 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.6e+77) {
		tmp = t_3;
	} else if (y <= -2.9e+15) {
		tmp = t_2;
	} else if (y <= 9.5e-14) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 2.6e+51) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = 1.0 / (t_1 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))
	t_3 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -2.6e+77:
		tmp = t_3
	elif y <= -2.9e+15:
		tmp = t_2
	elif y <= 9.5e-14:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1))
	elif y <= 2.6e+51:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(1.0 / Float64(t_1 / Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))))
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.6e+77)
		tmp = t_3;
	elseif (y <= -2.9e+15)
		tmp = t_2;
	elseif (y <= 9.5e-14)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * t_1)));
	elseif (y <= 2.6e+51)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = 1.0 / (t_1 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))));
	t_3 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.6e+77)
		tmp = t_3;
	elseif (y <= -2.9e+15)
		tmp = t_2;
	elseif (y <= 9.5e-14)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	elseif (y <= 2.6e+51)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[(t$95$1 / N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+77], t$95$3, If[LessEqual[y, -2.9e+15], t$95$2, If[LessEqual[y, 9.5e-14], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+51], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6000000000000002e77 or 2.6000000000000001e51 < y

   1. Initial program 2.5%

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

   3. Taylor expanded in y around inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. associate-/l* 69.6%

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

   5. Simplified 69.6%

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

   if -2.6000000000000002e77 < y < -2.9e15 or 9.4999999999999999e-14 < y < 2.6000000000000001e51

   1. Initial program 42.1%

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

   3. Taylor expanded in i around 0 42.1%

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

   5. Applied egg-rr 42.1%

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

      1. unpow-1 42.1%

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

      2. associate-/l* 57.5%

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

   7. Simplified 57.5%

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

   8. Taylor expanded in t around 0 54.4%

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

   if -2.9e15 < y < 9.4999999999999999e-14

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.4%

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

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{\frac{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{1}{\frac{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ t_3 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1))
        (t_3 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -3.1e+77)
     t_3
     (if (<= y -1.2e-15)
       t_2
       (if (<= y 3.1e-13)
         (/ (+ t (* y 230661.510616)) (+ i (* y t_1)))
         (if (<= y 2.8e+51) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -3.1e+77) {
		tmp = t_3;
	} else if (y <= -1.2e-15) {
		tmp = t_2;
	} else if (y <= 3.1e-13) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 2.8e+51) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (y * (b + (y * (y + a))))
    t_2 = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    t_3 = x + ((z / y) - (a / (y / x)))
    if (y <= (-3.1d+77)) then
        tmp = t_3
    else if (y <= (-1.2d-15)) then
        tmp = t_2
    else if (y <= 3.1d-13) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_1))
    else if (y <= 2.8d+51) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -3.1e+77) {
		tmp = t_3;
	} else if (y <= -1.2e-15) {
		tmp = t_2;
	} else if (y <= 3.1e-13) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 2.8e+51) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	t_3 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -3.1e+77:
		tmp = t_3
	elif y <= -1.2e-15:
		tmp = t_2
	elif y <= 3.1e-13:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1))
	elif y <= 2.8e+51:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1)
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -3.1e+77)
		tmp = t_3;
	elseif (y <= -1.2e-15)
		tmp = t_2;
	elseif (y <= 3.1e-13)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_1)));
	elseif (y <= 2.8e+51)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	t_3 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -3.1e+77)
		tmp = t_3;
	elseif (y <= -1.2e-15)
		tmp = t_2;
	elseif (y <= 3.1e-13)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	elseif (y <= 2.8e+51)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+77], t$95$3, If[LessEqual[y, -1.2e-15], t$95$2, If[LessEqual[y, 3.1e-13], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+51], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.09999999999999999e77 or 2.80000000000000005e51 < y

   1. Initial program 2.5%

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

   3. Taylor expanded in y around inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. associate-/l* 69.6%

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

   5. Simplified 69.6%

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

   if -3.09999999999999999e77 < y < -1.19999999999999997e-15 or 3.0999999999999999e-13 < y < 2.80000000000000005e51

   1. Initial program 52.6%

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

   3. Taylor expanded in i around 0 50.1%

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

   4. Taylor expanded in t around 0 53.3%

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

   if -1.19999999999999997e-15 < y < 3.0999999999999999e-13

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 93.3%

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

      1. *-commutative 93.3%

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

   5. Simplified 93.3%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ t_3 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.15 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1))
        (t_3 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -5.2e+77)
     t_3
     (if (<= y -4.15e+15)
       t_2
       (if (<= y 9.5e-12)
         (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i (* y t_1)))
         (if (<= y 2.75e+51) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -5.2e+77) {
		tmp = t_3;
	} else if (y <= -4.15e+15) {
		tmp = t_2;
	} else if (y <= 9.5e-12) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 2.75e+51) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (y * (b + (y * (y + a))))
    t_2 = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    t_3 = x + ((z / y) - (a / (y / x)))
    if (y <= (-5.2d+77)) then
        tmp = t_3
    else if (y <= (-4.15d+15)) then
        tmp = t_2
    else if (y <= 9.5d-12) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * t_1))
    else if (y <= 2.75d+51) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -5.2e+77) {
		tmp = t_3;
	} else if (y <= -4.15e+15) {
		tmp = t_2;
	} else if (y <= 9.5e-12) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 2.75e+51) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	t_3 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -5.2e+77:
		tmp = t_3
	elif y <= -4.15e+15:
		tmp = t_2
	elif y <= 9.5e-12:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1))
	elif y <= 2.75e+51:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1)
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -5.2e+77)
		tmp = t_3;
	elseif (y <= -4.15e+15)
		tmp = t_2;
	elseif (y <= 9.5e-12)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * t_1)));
	elseif (y <= 2.75e+51)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	t_3 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -5.2e+77)
		tmp = t_3;
	elseif (y <= -4.15e+15)
		tmp = t_2;
	elseif (y <= 9.5e-12)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	elseif (y <= 2.75e+51)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+77], t$95$3, If[LessEqual[y, -4.15e+15], t$95$2, If[LessEqual[y, 9.5e-12], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+51], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000004e77 or 2.75e51 < y

   1. Initial program 2.5%

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

   3. Taylor expanded in y around inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. associate-/l* 69.6%

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

   5. Simplified 69.6%

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

   if -5.2000000000000004e77 < y < -4.15e15 or 9.4999999999999995e-12 < y < 2.75e51

   1. Initial program 42.1%

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

   3. Taylor expanded in i around 0 42.1%

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

   4. Taylor expanded in t around 0 54.3%

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

   if -4.15e15 < y < 9.4999999999999995e-12

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.4%

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

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.15 \cdot 10^{+15}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+51}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{1}{\frac{t_1}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -1.85e+77)
     t_2
     (if (<= y -5e+18)
       (/
        1.0
        (/ t_1 (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
       (if (<= y 2.6e+41)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y t_1)))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1.85e+77) {
		tmp = t_2;
	} else if (y <= -5e+18) {
		tmp = 1.0 / (t_1 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))));
	} else if (y <= 2.6e+41) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (y * (b + (y * (y + a))))
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-1.85d+77)) then
        tmp = t_2
    else if (y <= (-5d+18)) then
        tmp = 1.0d0 / (t_1 / (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))
    else if (y <= 2.6d+41) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1.85e+77) {
		tmp = t_2;
	} else if (y <= -5e+18) {
		tmp = 1.0 / (t_1 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))));
	} else if (y <= 2.6e+41) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -1.85e+77:
		tmp = t_2
	elif y <= -5e+18:
		tmp = 1.0 / (t_1 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))
	elif y <= 2.6e+41:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.85e+77)
		tmp = t_2;
	elseif (y <= -5e+18)
		tmp = Float64(1.0 / Float64(t_1 / Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))));
	elseif (y <= 2.6e+41)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.85e+77)
		tmp = t_2;
	elseif (y <= -5e+18)
		tmp = 1.0 / (t_1 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))));
	elseif (y <= 2.6e+41)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+77], t$95$2, If[LessEqual[y, -5e+18], N[(1.0 / N[(t$95$1 / N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+41], 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 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.84999999999999997e77 or 2.6000000000000001e41 < y

   1. Initial program 2.6%

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

   3. Taylor expanded in y around inf 65.4%

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

      1. associate--l+ 65.4%

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

      2. associate-/l* 69.0%

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

   5. Simplified 69.0%

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

   if -1.84999999999999997e77 < y < -5e18

   1. Initial program 31.7%

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

   3. Taylor expanded in i around 0 31.7%

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

   5. Applied egg-rr 31.8%

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

      1. unpow-1 31.8%

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

      2. associate-/l* 50.7%

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

   7. Simplified 50.7%

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

   8. Taylor expanded in t around 0 57.3%

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

   if -5e18 < y < 2.6000000000000001e41

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 91.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{1}{\frac{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-51}:\\ \;\;\;\;\frac{t}{y \cdot t_2}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-168}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{t}{t_2}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x)))))
        (t_2 (+ c (* y (+ b (* y (+ y a)))))))
   (if (<= y -1.8e+77)
     t_1
     (if (<= y -4.7e+19)
       (/ z a)
       (if (<= y -1.45e-51)
         (/ t (* y t_2))
         (if (<= y 2.8e-168)
           (/ (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))) i)
           (if (<= y 2.8e+26) (/ 1.0 (/ y (/ t t_2))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -1.8e+77) {
		tmp = t_1;
	} else if (y <= -4.7e+19) {
		tmp = z / a;
	} else if (y <= -1.45e-51) {
		tmp = t / (y * t_2);
	} else if (y <= 2.8e-168) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	} else if (y <= 2.8e+26) {
		tmp = 1.0 / (y / (t / t_2));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    t_2 = c + (y * (b + (y * (y + a))))
    if (y <= (-1.8d+77)) then
        tmp = t_1
    else if (y <= (-4.7d+19)) then
        tmp = z / a
    else if (y <= (-1.45d-51)) then
        tmp = t / (y * t_2)
    else if (y <= 2.8d-168) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / i
    else if (y <= 2.8d+26) then
        tmp = 1.0d0 / (y / (t / t_2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -1.8e+77) {
		tmp = t_1;
	} else if (y <= -4.7e+19) {
		tmp = z / a;
	} else if (y <= -1.45e-51) {
		tmp = t / (y * t_2);
	} else if (y <= 2.8e-168) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	} else if (y <= 2.8e+26) {
		tmp = 1.0 / (y / (t / t_2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	t_2 = c + (y * (b + (y * (y + a))))
	tmp = 0
	if y <= -1.8e+77:
		tmp = t_1
	elif y <= -4.7e+19:
		tmp = z / a
	elif y <= -1.45e-51:
		tmp = t / (y * t_2)
	elif y <= 2.8e-168:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i
	elif y <= 2.8e+26:
		tmp = 1.0 / (y / (t / t_2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	t_2 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	tmp = 0.0
	if (y <= -1.8e+77)
		tmp = t_1;
	elseif (y <= -4.7e+19)
		tmp = Float64(z / a);
	elseif (y <= -1.45e-51)
		tmp = Float64(t / Float64(y * t_2));
	elseif (y <= 2.8e-168)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / i);
	elseif (y <= 2.8e+26)
		tmp = Float64(1.0 / Float64(y / Float64(t / t_2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	t_2 = c + (y * (b + (y * (y + a))));
	tmp = 0.0;
	if (y <= -1.8e+77)
		tmp = t_1;
	elseif (y <= -4.7e+19)
		tmp = z / a;
	elseif (y <= -1.45e-51)
		tmp = t / (y * t_2);
	elseif (y <= 2.8e-168)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	elseif (y <= 2.8e+26)
		tmp = 1.0 / (y / (t / t_2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+77], t$95$1, If[LessEqual[y, -4.7e+19], N[(z / a), $MachinePrecision], If[LessEqual[y, -1.45e-51], N[(t / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-168], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 2.8e+26], N[(1.0 / N[(y / N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.7999999999999999e77 or 2.8e26 < y

   1. Initial program 3.6%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. associate-/l* 66.5%

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

   5. Simplified 66.5%

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

   if -1.7999999999999999e77 < y < -4.7e19

   1. Initial program 26.9%

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

   3. Taylor expanded in i around 0 26.9%

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

   4. Taylor expanded in x around 0 26.5%

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

   5. Taylor expanded in a around inf 20.3%

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

   6. Taylor expanded in y around inf 40.5%

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

   if -4.7e19 < y < -1.44999999999999986e-51

   1. Initial program 99.4%

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

   3. Taylor expanded in i around 0 81.3%

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

   4. Taylor expanded in t around inf 28.7%

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

   if -1.44999999999999986e-51 < y < 2.8000000000000002e-168

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. fma-def 99.9%

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

      3. fma-def 99.9%

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

      4. fma-def 99.9%

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

      5. fma-def 99.9%

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

      6. fma-def 99.9%

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

      7. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. fma-udef 99.9%

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

      3. fma-def 99.9%

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

      4. fma-def 99.9%

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

      5. add-cube-cbrt 98.1%

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

      6. pow3 98.2%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{3}}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)} \]

   6. Applied egg-rr 98.2%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{3}}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)} \]

   7. Taylor expanded in x around 0 97.2%

      \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(y, \color{blue}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}, t\right)}\right)}^{3}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)} \]

   8. Taylor expanded in i around inf 77.4%

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

   if 2.8000000000000002e-168 < y < 2.8e26

   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 i around 0 64.6%

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

   5. Applied egg-rr 64.4%

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

      1. unpow-1 64.4%

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

      2. associate-/l* 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around inf 40.8%

      \[\leadsto \frac{1}{\frac{y}{\color{blue}{\frac{t}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-51}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-168}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{t}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -1.8e+77)
     t_1
     (if (<= y -3.3e+19)
       (/ z a)
       (if (<= y -2.4e+19)
         x
         (if (<= y 6.5e+26)
           (/ t (+ 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 / (y / x)));
	double tmp;
	if (y <= -1.8e+77) {
		tmp = t_1;
	} else if (y <= -3.3e+19) {
		tmp = z / a;
	} else if (y <= -2.4e+19) {
		tmp = x;
	} else if (y <= 6.5e+26) {
		tmp = t / (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 / (y / x)))
    if (y <= (-1.8d+77)) then
        tmp = t_1
    else if (y <= (-3.3d+19)) then
        tmp = z / a
    else if (y <= (-2.4d+19)) then
        tmp = x
    else if (y <= 6.5d+26) then
        tmp = t / (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 / (y / x)));
	double tmp;
	if (y <= -1.8e+77) {
		tmp = t_1;
	} else if (y <= -3.3e+19) {
		tmp = z / a;
	} else if (y <= -2.4e+19) {
		tmp = x;
	} else if (y <= 6.5e+26) {
		tmp = t / (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 / (y / x)))
	tmp = 0
	if y <= -1.8e+77:
		tmp = t_1
	elif y <= -3.3e+19:
		tmp = z / a
	elif y <= -2.4e+19:
		tmp = x
	elif y <= 6.5e+26:
		tmp = t / (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(y / x))))
	tmp = 0.0
	if (y <= -1.8e+77)
		tmp = t_1;
	elseif (y <= -3.3e+19)
		tmp = Float64(z / a);
	elseif (y <= -2.4e+19)
		tmp = x;
	elseif (y <= 6.5e+26)
		tmp = Float64(t / 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 / (y / x)));
	tmp = 0.0;
	if (y <= -1.8e+77)
		tmp = t_1;
	elseif (y <= -3.3e+19)
		tmp = z / a;
	elseif (y <= -2.4e+19)
		tmp = x;
	elseif (y <= 6.5e+26)
		tmp = t / (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[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+77], t$95$1, If[LessEqual[y, -3.3e+19], N[(z / a), $MachinePrecision], If[LessEqual[y, -2.4e+19], x, If[LessEqual[y, 6.5e+26], N[(t / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7999999999999999e77 or 6.50000000000000022e26 < y

   1. Initial program 3.6%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. associate-/l* 66.5%

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

   5. Simplified 66.5%

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

   if -1.7999999999999999e77 < y < -3.3e19

   1. Initial program 26.9%

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

   3. Taylor expanded in i around 0 26.9%

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

   4. Taylor expanded in x around 0 26.5%

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

   5. Taylor expanded in a around inf 20.3%

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

   6. Taylor expanded in y around inf 40.5%

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

   if -3.3e19 < y < -2.4e19

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -2.4e19 < y < 6.50000000000000022e26

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 74.4%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-20}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t_1}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i + t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* y (+ c (* y (+ b (* y (+ y a)))))))
        (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -1.8e+77)
     t_2
     (if (<= y -6e+19)
       (/ z a)
       (if (<= y -2.15e-20)
         (/ (+ t (* y 230661.510616)) t_1)
         (if (<= y 2.15e+26) (/ t (+ i t_1)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * (c + (y * (b + (y * (y + a)))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1.8e+77) {
		tmp = t_2;
	} else if (y <= -6e+19) {
		tmp = z / a;
	} else if (y <= -2.15e-20) {
		tmp = (t + (y * 230661.510616)) / t_1;
	} else if (y <= 2.15e+26) {
		tmp = t / (i + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (c + (y * (b + (y * (y + a)))))
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-1.8d+77)) then
        tmp = t_2
    else if (y <= (-6d+19)) then
        tmp = z / a
    else if (y <= (-2.15d-20)) then
        tmp = (t + (y * 230661.510616d0)) / t_1
    else if (y <= 2.15d+26) then
        tmp = t / (i + t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * (c + (y * (b + (y * (y + a)))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1.8e+77) {
		tmp = t_2;
	} else if (y <= -6e+19) {
		tmp = z / a;
	} else if (y <= -2.15e-20) {
		tmp = (t + (y * 230661.510616)) / t_1;
	} else if (y <= 2.15e+26) {
		tmp = t / (i + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = y * (c + (y * (b + (y * (y + a)))))
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -1.8e+77:
		tmp = t_2
	elif y <= -6e+19:
		tmp = z / a
	elif y <= -2.15e-20:
		tmp = (t + (y * 230661.510616)) / t_1
	elif y <= 2.15e+26:
		tmp = t / (i + t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.8e+77)
		tmp = t_2;
	elseif (y <= -6e+19)
		tmp = Float64(z / a);
	elseif (y <= -2.15e-20)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / t_1);
	elseif (y <= 2.15e+26)
		tmp = Float64(t / Float64(i + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = y * (c + (y * (b + (y * (y + a)))));
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.8e+77)
		tmp = t_2;
	elseif (y <= -6e+19)
		tmp = z / a;
	elseif (y <= -2.15e-20)
		tmp = (t + (y * 230661.510616)) / t_1;
	elseif (y <= 2.15e+26)
		tmp = t / (i + t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+77], t$95$2, If[LessEqual[y, -6e+19], N[(z / a), $MachinePrecision], If[LessEqual[y, -2.15e-20], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.15e+26], N[(t / N[(i + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7999999999999999e77 or 2.1499999999999999e26 < y

   1. Initial program 3.6%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. associate-/l* 66.5%

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

   5. Simplified 66.5%

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

   if -1.7999999999999999e77 < y < -6e19

   1. Initial program 26.9%

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

   3. Taylor expanded in i around 0 26.9%

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

   4. Taylor expanded in x around 0 26.5%

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

   5. Taylor expanded in a around inf 20.3%

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

   6. Taylor expanded in y around inf 40.5%

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

   if -6e19 < y < -2.15000000000000006e-20

   1. Initial program 99.2%

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

   3. Taylor expanded in i around 0 89.6%

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

   4. Taylor expanded in y around 0 39.1%

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

   if -2.15000000000000006e-20 < y < 2.1499999999999999e26

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf 77.9%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-20}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t_2}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x)))))
        (t_2 (+ c (* y (+ b (* y (+ y a)))))))
   (if (<= y -1.85e+77)
     t_1
     (if (<= y -4.6e+16)
       (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) t_2)
       (if (<= y 9e+26) (/ (+ t (* y 230661.510616)) (+ i (* y t_2))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -1.85e+77) {
		tmp = t_1;
	} else if (y <= -4.6e+16) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	} else if (y <= 9e+26) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    t_2 = c + (y * (b + (y * (y + a))))
    if (y <= (-1.85d+77)) then
        tmp = t_1
    else if (y <= (-4.6d+16)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))) / t_2
    else if (y <= 9d+26) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -1.85e+77) {
		tmp = t_1;
	} else if (y <= -4.6e+16) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	} else if (y <= 9e+26) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	t_2 = c + (y * (b + (y * (y + a))))
	tmp = 0
	if y <= -1.85e+77:
		tmp = t_1
	elif y <= -4.6e+16:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2
	elif y <= 9e+26:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	t_2 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	tmp = 0.0
	if (y <= -1.85e+77)
		tmp = t_1;
	elseif (y <= -4.6e+16)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / t_2);
	elseif (y <= 9e+26)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	t_2 = c + (y * (b + (y * (y + a))));
	tmp = 0.0;
	if (y <= -1.85e+77)
		tmp = t_1;
	elseif (y <= -4.6e+16)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	elseif (y <= 9e+26)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+77], t$95$1, If[LessEqual[y, -4.6e+16], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 9e+26], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.84999999999999997e77 or 8.99999999999999957e26 < y

   1. Initial program 3.6%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. associate-/l* 66.5%

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

   5. Simplified 66.5%

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

   if -1.84999999999999997e77 < y < -4.6e16

   1. Initial program 35.9%

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

   3. Taylor expanded in i around 0 35.9%

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

   4. Taylor expanded in x around 0 29.9%

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

   5. Taylor expanded in t around 0 41.6%

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

   if -4.6e16 < y < 8.99999999999999957e26

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0 85.7%

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

      1. *-commutative 85.7%

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

   5. Simplified 85.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -5.2e+77)
     t_1
     (if (<= y -4.6e+19)
       (/ z a)
       (if (<= y -1.05e-54)
         (/ t (* y (+ c (* y (+ b (* y (+ y a)))))))
         (if (<= y 2.7e-25)
           (/ (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))) 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 / (y / x)));
	double tmp;
	if (y <= -5.2e+77) {
		tmp = t_1;
	} else if (y <= -4.6e+19) {
		tmp = z / a;
	} else if (y <= -1.05e-54) {
		tmp = t / (y * (c + (y * (b + (y * (y + a))))));
	} else if (y <= 2.7e-25) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / 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 / (y / x)))
    if (y <= (-5.2d+77)) then
        tmp = t_1
    else if (y <= (-4.6d+19)) then
        tmp = z / a
    else if (y <= (-1.05d-54)) then
        tmp = t / (y * (c + (y * (b + (y * (y + a))))))
    else if (y <= 2.7d-25) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / 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 / (y / x)));
	double tmp;
	if (y <= -5.2e+77) {
		tmp = t_1;
	} else if (y <= -4.6e+19) {
		tmp = z / a;
	} else if (y <= -1.05e-54) {
		tmp = t / (y * (c + (y * (b + (y * (y + a))))));
	} else if (y <= 2.7e-25) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -5.2e+77:
		tmp = t_1
	elif y <= -4.6e+19:
		tmp = z / a
	elif y <= -1.05e-54:
		tmp = t / (y * (c + (y * (b + (y * (y + a))))))
	elif y <= 2.7e-25:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / 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(y / x))))
	tmp = 0.0
	if (y <= -5.2e+77)
		tmp = t_1;
	elseif (y <= -4.6e+19)
		tmp = Float64(z / a);
	elseif (y <= -1.05e-54)
		tmp = Float64(t / Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))));
	elseif (y <= 2.7e-25)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / 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 / (y / x)));
	tmp = 0.0;
	if (y <= -5.2e+77)
		tmp = t_1;
	elseif (y <= -4.6e+19)
		tmp = z / a;
	elseif (y <= -1.05e-54)
		tmp = t / (y * (c + (y * (b + (y * (y + a))))));
	elseif (y <= 2.7e-25)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / 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[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+77], t$95$1, If[LessEqual[y, -4.6e+19], N[(z / a), $MachinePrecision], If[LessEqual[y, -1.05e-54], N[(t / N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-25], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.2000000000000004e77 or 2.70000000000000016e-25 < y

   1. Initial program 9.8%

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

   3. Taylor expanded in y around inf 58.4%

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

      1. associate--l+ 58.4%

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

      2. associate-/l* 61.5%

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

   5. Simplified 61.5%

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

   if -5.2000000000000004e77 < y < -4.6e19

   1. Initial program 26.9%

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

   3. Taylor expanded in i around 0 26.9%

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

   4. Taylor expanded in x around 0 26.5%

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

   5. Taylor expanded in a around inf 20.3%

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

   6. Taylor expanded in y around inf 40.5%

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

   if -4.6e19 < y < -1.05e-54

   1. Initial program 99.4%

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

   3. Taylor expanded in i around 0 81.3%

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

   4. Taylor expanded in t around inf 28.7%

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

   if -1.05e-54 < y < 2.70000000000000016e-25

   1. Initial program 99.8%

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

      1. fma-def 99.8%

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

      2. fma-def 99.8%

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

      3. fma-def 99.8%

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

      4. fma-def 99.8%

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

      5. fma-def 99.8%

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

      6. fma-def 99.8%

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

      7. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. fma-udef 99.8%

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

      3. fma-def 99.8%

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

      4. fma-def 99.8%

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

      5. add-cube-cbrt 98.0%

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

      6. pow3 98.0%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}\right)}^{3}}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)} \]

   6. Applied egg-rr 98.0%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right)}\right)}^{3}}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)} \]

   7. Taylor expanded in x around 0 97.3%

      \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(y, \color{blue}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}, t\right)}\right)}^{3}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)} \]

   8. Taylor expanded in i around inf 67.4%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t_2}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i + y \cdot t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x)))))
        (t_2 (+ c (* y (+ b (* y (+ y a)))))))
   (if (<= y -2e+77)
     t_1
     (if (<= y -2.6e-18)
       (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) t_2)
       (if (<= y 7.5e+26) (/ t (+ i (* y t_2))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -2e+77) {
		tmp = t_1;
	} else if (y <= -2.6e-18) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	} else if (y <= 7.5e+26) {
		tmp = t / (i + (y * t_2));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    t_2 = c + (y * (b + (y * (y + a))))
    if (y <= (-2d+77)) then
        tmp = t_1
    else if (y <= (-2.6d-18)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))) / t_2
    else if (y <= 7.5d+26) then
        tmp = t / (i + (y * t_2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -2e+77) {
		tmp = t_1;
	} else if (y <= -2.6e-18) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	} else if (y <= 7.5e+26) {
		tmp = t / (i + (y * t_2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	t_2 = c + (y * (b + (y * (y + a))))
	tmp = 0
	if y <= -2e+77:
		tmp = t_1
	elif y <= -2.6e-18:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2
	elif y <= 7.5e+26:
		tmp = t / (i + (y * t_2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	t_2 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	tmp = 0.0
	if (y <= -2e+77)
		tmp = t_1;
	elseif (y <= -2.6e-18)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / t_2);
	elseif (y <= 7.5e+26)
		tmp = Float64(t / Float64(i + Float64(y * t_2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	t_2 = c + (y * (b + (y * (y + a))));
	tmp = 0.0;
	if (y <= -2e+77)
		tmp = t_1;
	elseif (y <= -2.6e-18)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	elseif (y <= 7.5e+26)
		tmp = t / (i + (y * t_2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+77], t$95$1, If[LessEqual[y, -2.6e-18], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 7.5e+26], N[(t / N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999997e77 or 7.49999999999999941e26 < y

   1. Initial program 3.6%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. associate-/l* 66.5%

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

   5. Simplified 66.5%

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

   if -1.99999999999999997e77 < y < -2.6e-18

   1. Initial program 57.0%

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

   3. Taylor expanded in i around 0 53.0%

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

   4. Taylor expanded in x around 0 41.3%

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

   5. Taylor expanded in t around 0 38.3%

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

   if -2.6e-18 < y < 7.49999999999999941e26

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf 77.9%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.45 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -1.8e+77)
     t_1
     (if (<= y -3.45e+19)
       (/ z a)
       (if (<= y -2.9e-10)
         x
         (if (<= y 2.7e-25) (+ (* 230661.510616 (/ y i)) (/ t 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 / (y / x)));
	double tmp;
	if (y <= -1.8e+77) {
		tmp = t_1;
	} else if (y <= -3.45e+19) {
		tmp = z / a;
	} else if (y <= -2.9e-10) {
		tmp = x;
	} else if (y <= 2.7e-25) {
		tmp = (230661.510616 * (y / i)) + (t / 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 / (y / x)))
    if (y <= (-1.8d+77)) then
        tmp = t_1
    else if (y <= (-3.45d+19)) then
        tmp = z / a
    else if (y <= (-2.9d-10)) then
        tmp = x
    else if (y <= 2.7d-25) then
        tmp = (230661.510616d0 * (y / i)) + (t / 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 / (y / x)));
	double tmp;
	if (y <= -1.8e+77) {
		tmp = t_1;
	} else if (y <= -3.45e+19) {
		tmp = z / a;
	} else if (y <= -2.9e-10) {
		tmp = x;
	} else if (y <= 2.7e-25) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -1.8e+77:
		tmp = t_1
	elif y <= -3.45e+19:
		tmp = z / a
	elif y <= -2.9e-10:
		tmp = x
	elif y <= 2.7e-25:
		tmp = (230661.510616 * (y / i)) + (t / 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(y / x))))
	tmp = 0.0
	if (y <= -1.8e+77)
		tmp = t_1;
	elseif (y <= -3.45e+19)
		tmp = Float64(z / a);
	elseif (y <= -2.9e-10)
		tmp = x;
	elseif (y <= 2.7e-25)
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + Float64(t / 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 / (y / x)));
	tmp = 0.0;
	if (y <= -1.8e+77)
		tmp = t_1;
	elseif (y <= -3.45e+19)
		tmp = z / a;
	elseif (y <= -2.9e-10)
		tmp = x;
	elseif (y <= 2.7e-25)
		tmp = (230661.510616 * (y / i)) + (t / 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[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+77], t$95$1, If[LessEqual[y, -3.45e+19], N[(z / a), $MachinePrecision], If[LessEqual[y, -2.9e-10], x, If[LessEqual[y, 2.7e-25], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7999999999999999e77 or 2.70000000000000016e-25 < y

   1. Initial program 9.8%

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

   3. Taylor expanded in y around inf 58.4%

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

      1. associate--l+ 58.4%

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

      2. associate-/l* 61.5%

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

   5. Simplified 61.5%

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

   if -1.7999999999999999e77 < y < -3.45e19

   1. Initial program 26.9%

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

   3. Taylor expanded in i around 0 26.9%

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

   4. Taylor expanded in x around 0 26.5%

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

   5. Taylor expanded in a around inf 20.3%

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

   6. Taylor expanded in y around inf 40.5%

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

   if -3.45e19 < y < -2.89999999999999981e-10

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 26.4%

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

   if -2.89999999999999981e-10 < y < 2.70000000000000016e-25

   1. Initial program 99.8%

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

   3. Taylor expanded in i around inf 65.2%

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

   4. Taylor expanded in y around 0 62.2%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -3.45 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.4e+77)
     t_1
     (if (<= y -4.6e+19)
       (/ z a)
       (if (<= y -4.5e-55)
         (/ t (* y (+ c (* y (+ b (* y (+ y a)))))))
         (if (<= y 2.7e-25) (+ (* 230661.510616 (/ y i)) (/ t 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 / (y / x)));
	double tmp;
	if (y <= -2.4e+77) {
		tmp = t_1;
	} else if (y <= -4.6e+19) {
		tmp = z / a;
	} else if (y <= -4.5e-55) {
		tmp = t / (y * (c + (y * (b + (y * (y + a))))));
	} else if (y <= 2.7e-25) {
		tmp = (230661.510616 * (y / i)) + (t / 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 / (y / x)))
    if (y <= (-2.4d+77)) then
        tmp = t_1
    else if (y <= (-4.6d+19)) then
        tmp = z / a
    else if (y <= (-4.5d-55)) then
        tmp = t / (y * (c + (y * (b + (y * (y + a))))))
    else if (y <= 2.7d-25) then
        tmp = (230661.510616d0 * (y / i)) + (t / 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 / (y / x)));
	double tmp;
	if (y <= -2.4e+77) {
		tmp = t_1;
	} else if (y <= -4.6e+19) {
		tmp = z / a;
	} else if (y <= -4.5e-55) {
		tmp = t / (y * (c + (y * (b + (y * (y + a))))));
	} else if (y <= 2.7e-25) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -2.4e+77:
		tmp = t_1
	elif y <= -4.6e+19:
		tmp = z / a
	elif y <= -4.5e-55:
		tmp = t / (y * (c + (y * (b + (y * (y + a))))))
	elif y <= 2.7e-25:
		tmp = (230661.510616 * (y / i)) + (t / 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(y / x))))
	tmp = 0.0
	if (y <= -2.4e+77)
		tmp = t_1;
	elseif (y <= -4.6e+19)
		tmp = Float64(z / a);
	elseif (y <= -4.5e-55)
		tmp = Float64(t / Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))));
	elseif (y <= 2.7e-25)
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + Float64(t / 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 / (y / x)));
	tmp = 0.0;
	if (y <= -2.4e+77)
		tmp = t_1;
	elseif (y <= -4.6e+19)
		tmp = z / a;
	elseif (y <= -4.5e-55)
		tmp = t / (y * (c + (y * (b + (y * (y + a))))));
	elseif (y <= 2.7e-25)
		tmp = (230661.510616 * (y / i)) + (t / 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[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+77], t$95$1, If[LessEqual[y, -4.6e+19], N[(z / a), $MachinePrecision], If[LessEqual[y, -4.5e-55], N[(t / N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-25], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.3999999999999999e77 or 2.70000000000000016e-25 < y

   1. Initial program 9.8%

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

   3. Taylor expanded in y around inf 58.4%

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

      1. associate--l+ 58.4%

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

      2. associate-/l* 61.5%

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

   5. Simplified 61.5%

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

   if -2.3999999999999999e77 < y < -4.6e19

   1. Initial program 26.9%

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

   3. Taylor expanded in i around 0 26.9%

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

   4. Taylor expanded in x around 0 26.5%

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

   5. Taylor expanded in a around inf 20.3%

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

   6. Taylor expanded in y around inf 40.5%

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

   if -4.6e19 < y < -4.4999999999999997e-55

   1. Initial program 99.4%

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

   3. Taylor expanded in i around 0 81.3%

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

   4. Taylor expanded in t around inf 28.7%

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

   if -4.4999999999999997e-55 < y < 2.70000000000000016e-25

   1. Initial program 99.8%

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

   3. Taylor expanded in i around inf 68.1%

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

   4. Taylor expanded in y around 0 65.8%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7.2e+80)
   x
   (if (<= y -5e+19)
     (/ z a)
     (if (<= y -2.9e-10)
       x
       (if (<= y 2.7e-25) (+ (* 230661.510616 (/ y i)) (/ 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 <= -7.2e+80) {
		tmp = x;
	} else if (y <= -5e+19) {
		tmp = z / a;
	} else if (y <= -2.9e-10) {
		tmp = x;
	} else if (y <= 2.7e-25) {
		tmp = (230661.510616 * (y / i)) + (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 <= (-7.2d+80)) then
        tmp = x
    else if (y <= (-5d+19)) then
        tmp = z / a
    else if (y <= (-2.9d-10)) then
        tmp = x
    else if (y <= 2.7d-25) then
        tmp = (230661.510616d0 * (y / i)) + (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 <= -7.2e+80) {
		tmp = x;
	} else if (y <= -5e+19) {
		tmp = z / a;
	} else if (y <= -2.9e-10) {
		tmp = x;
	} else if (y <= 2.7e-25) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7.2e+80:
		tmp = x
	elif y <= -5e+19:
		tmp = z / a
	elif y <= -2.9e-10:
		tmp = x
	elif y <= 2.7e-25:
		tmp = (230661.510616 * (y / i)) + (t / i)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7.2e+80)
		tmp = x;
	elseif (y <= -5e+19)
		tmp = Float64(z / a);
	elseif (y <= -2.9e-10)
		tmp = x;
	elseif (y <= 2.7e-25)
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + 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 <= -7.2e+80)
		tmp = x;
	elseif (y <= -5e+19)
		tmp = z / a;
	elseif (y <= -2.9e-10)
		tmp = x;
	elseif (y <= 2.7e-25)
		tmp = (230661.510616 * (y / i)) + (t / i);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7.2e+80], x, If[LessEqual[y, -5e+19], N[(z / a), $MachinePrecision], If[LessEqual[y, -2.9e-10], x, If[LessEqual[y, 2.7e-25], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.1999999999999999e80 or -5e19 < y < -2.89999999999999981e-10 or 2.70000000000000016e-25 < y

   1. Initial program 15.3%

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

   3. Taylor expanded in y around inf 46.3%

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

   if -7.1999999999999999e80 < y < -5e19

   1. Initial program 26.9%

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

   3. Taylor expanded in i around 0 26.9%

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

   4. Taylor expanded in x around 0 26.5%

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

   5. Taylor expanded in a around inf 20.3%

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

   6. Taylor expanded in y around inf 40.5%

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

   if -2.89999999999999981e-10 < y < 2.70000000000000016e-25

   1. Initial program 99.8%

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

   3. Taylor expanded in i around inf 65.2%

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

   4. Taylor expanded in y around 0 62.2%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 54.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+23}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.25e+77)
   x
   (if (<= y -4e+19)
     (/ z a)
     (if (<= y -1.65e-10)
       x
       (if (<= y 2.4e+23) (/ (+ 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 <= -2.25e+77) {
		tmp = x;
	} else if (y <= -4e+19) {
		tmp = z / a;
	} else if (y <= -1.65e-10) {
		tmp = x;
	} else if (y <= 2.4e+23) {
		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 <= (-2.25d+77)) then
        tmp = x
    else if (y <= (-4d+19)) then
        tmp = z / a
    else if (y <= (-1.65d-10)) then
        tmp = x
    else if (y <= 2.4d+23) 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 <= -2.25e+77) {
		tmp = x;
	} else if (y <= -4e+19) {
		tmp = z / a;
	} else if (y <= -1.65e-10) {
		tmp = x;
	} else if (y <= 2.4e+23) {
		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 <= -2.25e+77:
		tmp = x
	elif y <= -4e+19:
		tmp = z / a
	elif y <= -1.65e-10:
		tmp = x
	elif y <= 2.4e+23:
		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 <= -2.25e+77)
		tmp = x;
	elseif (y <= -4e+19)
		tmp = Float64(z / a);
	elseif (y <= -1.65e-10)
		tmp = x;
	elseif (y <= 2.4e+23)
		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 <= -2.25e+77)
		tmp = x;
	elseif (y <= -4e+19)
		tmp = z / a;
	elseif (y <= -1.65e-10)
		tmp = x;
	elseif (y <= 2.4e+23)
		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, -2.25e+77], x, If[LessEqual[y, -4e+19], N[(z / a), $MachinePrecision], If[LessEqual[y, -1.65e-10], x, If[LessEqual[y, 2.4e+23], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25000000000000012e77 or -4e19 < y < -1.65e-10 or 2.4e23 < y

   1. Initial program 10.6%

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

   3. Taylor expanded in y around inf 49.2%

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

   if -2.25000000000000012e77 < y < -4e19

   1. Initial program 26.9%

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

   3. Taylor expanded in i around 0 26.9%

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

   4. Taylor expanded in x around 0 26.5%

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

   5. Taylor expanded in a around inf 20.3%

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

   6. Taylor expanded in y around inf 40.5%

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

   if -1.65e-10 < y < 2.4e23

   1. Initial program 98.9%

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

   3. Taylor expanded in i around inf 61.0%

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

   4. Taylor expanded in y around 0 58.2%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+23}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.45 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.3e+77)
   x
   (if (<= y -3.45e+19)
     (/ z a)
     (if (<= y -1.75e-10) x (if (<= y 1.4e+23) (/ t i) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.3e+77) {
		tmp = x;
	} else if (y <= -3.45e+19) {
		tmp = z / a;
	} else if (y <= -1.75e-10) {
		tmp = x;
	} else if (y <= 1.4e+23) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.3d+77)) then
        tmp = x
    else if (y <= (-3.45d+19)) then
        tmp = z / a
    else if (y <= (-1.75d-10)) then
        tmp = x
    else if (y <= 1.4d+23) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.3e+77) {
		tmp = x;
	} else if (y <= -3.45e+19) {
		tmp = z / a;
	} else if (y <= -1.75e-10) {
		tmp = x;
	} else if (y <= 1.4e+23) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.3e+77:
		tmp = x
	elif y <= -3.45e+19:
		tmp = z / a
	elif y <= -1.75e-10:
		tmp = x
	elif y <= 1.4e+23:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.3e+77)
		tmp = x;
	elseif (y <= -3.45e+19)
		tmp = Float64(z / a);
	elseif (y <= -1.75e-10)
		tmp = x;
	elseif (y <= 1.4e+23)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.3e+77)
		tmp = x;
	elseif (y <= -3.45e+19)
		tmp = z / a;
	elseif (y <= -1.75e-10)
		tmp = x;
	elseif (y <= 1.4e+23)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.3e+77], x, If[LessEqual[y, -3.45e+19], N[(z / a), $MachinePrecision], If[LessEqual[y, -1.75e-10], x, If[LessEqual[y, 1.4e+23], N[(t / i), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.29999999999999995e77 or -3.45e19 < y < -1.7499999999999999e-10 or 1.4e23 < y

   1. Initial program 10.6%

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

   3. Taylor expanded in y around inf 49.2%

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

   if -2.29999999999999995e77 < y < -3.45e19

   1. Initial program 26.9%

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

   3. Taylor expanded in i around 0 26.9%

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

   4. Taylor expanded in x around 0 26.5%

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

   5. Taylor expanded in a around inf 20.3%

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

   6. Taylor expanded in y around inf 40.5%

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

   if -1.7499999999999999e-10 < y < 1.4e23

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 54.0%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.45 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.7e-11) x (if (<= y 9.5e+22) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.7e-11) {
		tmp = x;
	} else if (y <= 9.5e+22) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.7d-11)) then
        tmp = x
    else if (y <= 9.5d+22) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.7e-11) {
		tmp = x;
	} else if (y <= 9.5e+22) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.7e-11:
		tmp = x
	elif y <= 9.5e+22:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.7e-11)
		tmp = x;
	elseif (y <= 9.5e+22)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.7e-11)
		tmp = x;
	elseif (y <= 9.5e+22)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.7e-11], x, If[LessEqual[y, 9.5e+22], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7000000000000001e-11 or 9.49999999999999937e22 < y

   1. Initial program 12.3%

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

   3. Taylor expanded in y around inf 44.6%

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

   if -3.7000000000000001e-11 < y < 9.49999999999999937e22

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 54.0%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.5% 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 52.9%

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

3. Taylor expanded in y around inf 25.3%

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

4. Final simplification 25.3%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(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)))