Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.7% → 84.5%

Time: 20.9s

Alternatives: 19

Speedup: 2.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.7% 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: 84.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := {t\_1}^{2}\\ t_3 := y \cdot t\_1\\ \mathbf{if}\;y \leq -5.3 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + t\_3\right)} + \left(c \cdot \left(27464.7644705 \cdot \frac{-1}{y \cdot t\_2} + \left(230661.510616 \cdot \frac{-1}{t\_2 \cdot {y}^{2}} - \left(\frac{z}{t\_2} + \frac{y \cdot x}{t\_2}\right)\right)\right) + \left(230661.510616 \cdot \frac{1}{t\_3} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{t\_1}\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+43}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot a + \mathsf{fma}\left(-1, z, \mathsf{fma}\left(-1, a \cdot \frac{x \cdot a - z}{y}, b \cdot \frac{x}{y}\right)\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a)))) (t_2 (pow t_1 2.0)) (t_3 (* y t_1)))
   (if (<= y -5.3e+137)
     (+ x (/ z y))
     (if (<= y -1.45e+30)
       (+
        (/ t (+ i (* y (+ c t_3))))
        (+
         (*
          c
          (+
           (* 27464.7644705 (/ -1.0 (* y t_2)))
           (-
            (* 230661.510616 (/ -1.0 (* t_2 (pow y 2.0))))
            (+ (/ z t_2) (/ (* y x) t_2)))))
         (+
          (* 230661.510616 (/ 1.0 t_3))
          (/ (+ 27464.7644705 (* y (+ z (* y x)))) t_1))))
       (if (<= y 5e+43)
         (/
          (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t)
          (fma (fma (fma (+ y a) y b) y c) y i))
         (-
          x
          (/
           (+
            (* x a)
            (fma -1.0 z (fma -1.0 (* a (/ (- (* x a) z) y)) (* b (/ x y)))))
           y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = pow(t_1, 2.0);
	double t_3 = y * t_1;
	double tmp;
	if (y <= -5.3e+137) {
		tmp = x + (z / y);
	} else if (y <= -1.45e+30) {
		tmp = (t / (i + (y * (c + t_3)))) + ((c * ((27464.7644705 * (-1.0 / (y * t_2))) + ((230661.510616 * (-1.0 / (t_2 * pow(y, 2.0)))) - ((z / t_2) + ((y * x) / t_2))))) + ((230661.510616 * (1.0 / t_3)) + ((27464.7644705 + (y * (z + (y * x)))) / t_1)));
	} else if (y <= 5e+43) {
		tmp = fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((y + a), y, b), y, c), y, i);
	} else {
		tmp = x - (((x * a) + fma(-1.0, z, fma(-1.0, (a * (((x * a) - z) / y)), (b * (x / y))))) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b + Float64(y * Float64(y + a)))
	t_2 = t_1 ^ 2.0
	t_3 = Float64(y * t_1)
	tmp = 0.0
	if (y <= -5.3e+137)
		tmp = Float64(x + Float64(z / y));
	elseif (y <= -1.45e+30)
		tmp = Float64(Float64(t / Float64(i + Float64(y * Float64(c + t_3)))) + Float64(Float64(c * Float64(Float64(27464.7644705 * Float64(-1.0 / Float64(y * t_2))) + Float64(Float64(230661.510616 * Float64(-1.0 / Float64(t_2 * (y ^ 2.0)))) - Float64(Float64(z / t_2) + Float64(Float64(y * x) / t_2))))) + Float64(Float64(230661.510616 * Float64(1.0 / t_3)) + Float64(Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))) / t_1))));
	elseif (y <= 5e+43)
		tmp = Float64(fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(y + a), y, b), y, c), y, i));
	else
		tmp = Float64(x - Float64(Float64(Float64(x * a) + fma(-1.0, z, fma(-1.0, Float64(a * Float64(Float64(Float64(x * a) - z) / y)), Float64(b * Float64(x / y))))) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[t$95$1, 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(y * t$95$1), $MachinePrecision]}, If[LessEqual[y, -5.3e+137], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e+30], N[(N[(t / N[(i + N[(y * N[(c + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(27464.7644705 * N[(-1.0 / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(-1.0 / N[(t$95$2 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z / t$95$2), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+43], N[(N[(N[(N[(N[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(x * a), $MachinePrecision] + N[(-1.0 * z + N[(-1.0 * N[(a * N[(N[(N[(x * a), $MachinePrecision] - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.29999999999999968e137

   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 0.0%

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

   4. Taylor expanded in y around inf 89.6%

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

   if -5.29999999999999968e137 < y < -1.4499999999999999e30

   1. Initial program 29.5%

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

   3. Taylor expanded in t around 0 29.5%

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

   4. Taylor expanded in i around 0 46.4%

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

   5. Taylor expanded in c around 0 81.1%

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

   if -1.4499999999999999e30 < y < 5.0000000000000004e43

   1. Initial program 97.6%

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

      1. fma-define 97.7%

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

      2. fma-define 97.7%

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

      3. fma-define 97.7%

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

      4. fma-define 97.7%

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

      5. fma-define 97.7%

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

      6. fma-define 97.7%

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

      7. fma-define 97.7%

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

   3. Simplified 97.7%

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

   if 5.0000000000000004e43 < y

   1. Initial program 4.1%

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

   3. Taylor expanded in y around inf 4.1%

      \[\leadsto \frac{\color{blue}{{y}^{4} \cdot \left(x + \frac{z}{y}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 59.4%

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

      1. mul-1-neg 59.4%

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

   6. Simplified 73.3%

      \[\leadsto \color{blue}{x + \left(-\frac{\mathsf{fma}\left(-1, z, \mathsf{fma}\left(-1, a \cdot \frac{-1 \cdot \left(z - a \cdot x\right)}{y}, b \cdot \frac{x}{y}\right)\right) - \left(-a \cdot x\right)}{y}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(c \cdot \left(27464.7644705 \cdot \frac{-1}{y \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \left(230661.510616 \cdot \frac{-1}{{\left(b + y \cdot \left(y + a\right)\right)}^{2} \cdot {y}^{2}} - \left(\frac{z}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \frac{y \cdot x}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}}\right)\right)\right) + \left(230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)}\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+43}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot a + \mathsf{fma}\left(-1, z, \mathsf{fma}\left(-1, a \cdot \frac{x \cdot a - z}{y}, b \cdot \frac{x}{y}\right)\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := {t\_1}^{2}\\ t_3 := y \cdot t\_1\\ t_4 := i + y \cdot \left(c + t\_3\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{t\_4} + \left(c \cdot \left(27464.7644705 \cdot \frac{-1}{y \cdot t\_2} + \left(230661.510616 \cdot \frac{-1}{t\_2 \cdot {y}^{2}} - \left(\frac{z}{t\_2} + \frac{y \cdot x}{t\_2}\right)\right)\right) + \left(230661.510616 \cdot \frac{1}{t\_3} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{t\_1}\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot \left(y \cdot x\right) + y \cdot z\right)\right)\right)}{t\_4}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot a + \mathsf{fma}\left(-1, z, \mathsf{fma}\left(-1, a \cdot \frac{x \cdot a - z}{y}, b \cdot \frac{x}{y}\right)\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2 (pow t_1 2.0))
        (t_3 (* y t_1))
        (t_4 (+ i (* y (+ c t_3)))))
   (if (<= y -3.2e+137)
     (+ x (/ z y))
     (if (<= y -1.9e+30)
       (+
        (/ t t_4)
        (+
         (*
          c
          (+
           (* 27464.7644705 (/ -1.0 (* y t_2)))
           (-
            (* 230661.510616 (/ -1.0 (* t_2 (pow y 2.0))))
            (+ (/ z t_2) (/ (* y x) t_2)))))
         (+
          (* 230661.510616 (/ 1.0 t_3))
          (/ (+ 27464.7644705 (* y (+ z (* y x)))) t_1))))
       (if (<= y 2.6e+42)
         (/
          (+
           t
           (*
            y
            (+
             230661.510616
             (* y (+ 27464.7644705 (+ (* y (* y x)) (* y z)))))))
          t_4)
         (-
          x
          (/
           (+
            (* x a)
            (fma -1.0 z (fma -1.0 (* a (/ (- (* x a) z) y)) (* b (/ x y)))))
           y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = pow(t_1, 2.0);
	double t_3 = y * t_1;
	double t_4 = i + (y * (c + t_3));
	double tmp;
	if (y <= -3.2e+137) {
		tmp = x + (z / y);
	} else if (y <= -1.9e+30) {
		tmp = (t / t_4) + ((c * ((27464.7644705 * (-1.0 / (y * t_2))) + ((230661.510616 * (-1.0 / (t_2 * pow(y, 2.0)))) - ((z / t_2) + ((y * x) / t_2))))) + ((230661.510616 * (1.0 / t_3)) + ((27464.7644705 + (y * (z + (y * x)))) / t_1)));
	} else if (y <= 2.6e+42) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + ((y * (y * x)) + (y * z))))))) / t_4;
	} else {
		tmp = x - (((x * a) + fma(-1.0, z, fma(-1.0, (a * (((x * a) - z) / y)), (b * (x / y))))) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b + Float64(y * Float64(y + a)))
	t_2 = t_1 ^ 2.0
	t_3 = Float64(y * t_1)
	t_4 = Float64(i + Float64(y * Float64(c + t_3)))
	tmp = 0.0
	if (y <= -3.2e+137)
		tmp = Float64(x + Float64(z / y));
	elseif (y <= -1.9e+30)
		tmp = Float64(Float64(t / t_4) + Float64(Float64(c * Float64(Float64(27464.7644705 * Float64(-1.0 / Float64(y * t_2))) + Float64(Float64(230661.510616 * Float64(-1.0 / Float64(t_2 * (y ^ 2.0)))) - Float64(Float64(z / t_2) + Float64(Float64(y * x) / t_2))))) + Float64(Float64(230661.510616 * Float64(1.0 / t_3)) + Float64(Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))) / t_1))));
	elseif (y <= 2.6e+42)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(Float64(y * Float64(y * x)) + Float64(y * z))))))) / t_4);
	else
		tmp = Float64(x - Float64(Float64(Float64(x * a) + fma(-1.0, z, fma(-1.0, Float64(a * Float64(Float64(Float64(x * a) - z) / y)), Float64(b * Float64(x / y))))) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[t$95$1, 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(y * t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(i + N[(y * N[(c + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+137], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e+30], N[(N[(t / t$95$4), $MachinePrecision] + N[(N[(c * N[(N[(27464.7644705 * N[(-1.0 / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(-1.0 / N[(t$95$2 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z / t$95$2), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+42], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision], N[(x - N[(N[(N[(x * a), $MachinePrecision] + N[(-1.0 * z + N[(-1.0 * N[(a * N[(N[(N[(x * a), $MachinePrecision] - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.20000000000000019e137

   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 0.0%

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

   4. Taylor expanded in y around inf 89.6%

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

   if -3.20000000000000019e137 < y < -1.9000000000000001e30

   1. Initial program 29.5%

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

   3. Taylor expanded in t around 0 29.5%

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

   4. Taylor expanded in i around 0 46.4%

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

   5. Taylor expanded in c around 0 81.1%

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

   if -1.9000000000000001e30 < y < 2.5999999999999999e42

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. distribute-rgt-in 97.7%

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

   4. Applied egg-rr 97.7%

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

   if 2.5999999999999999e42 < y

   1. Initial program 4.1%

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

   3. Taylor expanded in y around inf 4.1%

      \[\leadsto \frac{\color{blue}{{y}^{4} \cdot \left(x + \frac{z}{y}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 59.4%

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

      1. mul-1-neg 59.4%

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

   6. Simplified 73.3%

      \[\leadsto \color{blue}{x + \left(-\frac{\mathsf{fma}\left(-1, z, \mathsf{fma}\left(-1, a \cdot \frac{-1 \cdot \left(z - a \cdot x\right)}{y}, b \cdot \frac{x}{y}\right)\right) - \left(-a \cdot x\right)}{y}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+137}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(c \cdot \left(27464.7644705 \cdot \frac{-1}{y \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \left(230661.510616 \cdot \frac{-1}{{\left(b + y \cdot \left(y + a\right)\right)}^{2} \cdot {y}^{2}} - \left(\frac{z}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \frac{y \cdot x}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}}\right)\right)\right) + \left(230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)}\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot \left(y \cdot x\right) + y \cdot z\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot a + \mathsf{fma}\left(-1, z, \mathsf{fma}\left(-1, a \cdot \frac{x \cdot a - z}{y}, b \cdot \frac{x}{y}\right)\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot \left(y \cdot x\right) + y \cdot z\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot a + \mathsf{fma}\left(-1, z, \mathsf{fma}\left(-1, a \cdot \frac{x \cdot a - z}{y}, b \cdot \frac{x}{y}\right)\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3e+58)
   (+ x (/ z y))
   (if (<= y 5e+43)
     (/
      (+
       t
       (*
        y
        (+ 230661.510616 (* y (+ 27464.7644705 (+ (* y (* y x)) (* y z)))))))
      (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
     (-
      x
      (/
       (+
        (* x a)
        (fma -1.0 z (fma -1.0 (* a (/ (- (* x a) z) y)) (* b (/ x y)))))
       y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3e+58) {
		tmp = x + (z / y);
	} else if (y <= 5e+43) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + ((y * (y * x)) + (y * z))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = x - (((x * a) + fma(-1.0, z, fma(-1.0, (a * (((x * a) - z) / y)), (b * (x / y))))) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3e+58)
		tmp = Float64(x + Float64(z / y));
	elseif (y <= 5e+43)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(Float64(y * Float64(y * x)) + Float64(y * z))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = Float64(x - Float64(Float64(Float64(x * a) + fma(-1.0, z, fma(-1.0, Float64(a * Float64(Float64(Float64(x * a) - z) / y)), Float64(b * Float64(x / y))))) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3e+58], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+43], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision] + N[(y * z), $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], N[(x - N[(N[(N[(x * a), $MachinePrecision] + N[(-1.0 * z + N[(-1.0 * N[(a * N[(N[(N[(x * a), $MachinePrecision] - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000002e58

   1. Initial program 2.1%

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

   3. Taylor expanded in y around inf 2.1%

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

   4. Taylor expanded in y around inf 85.0%

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

   if -3.0000000000000002e58 < y < 5.0000000000000004e43

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. distribute-rgt-in 93.9%

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

   4. Applied egg-rr 93.9%

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

   if 5.0000000000000004e43 < y

   1. Initial program 4.1%

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

   3. Taylor expanded in y around inf 4.1%

      \[\leadsto \frac{\color{blue}{{y}^{4} \cdot \left(x + \frac{z}{y}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 59.4%

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

      1. mul-1-neg 59.4%

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

   6. Simplified 73.3%

      \[\leadsto \color{blue}{x + \left(-\frac{\mathsf{fma}\left(-1, z, \mathsf{fma}\left(-1, a \cdot \frac{-1 \cdot \left(z - a \cdot x\right)}{y}, b \cdot \frac{x}{y}\right)\right) - \left(-a \cdot x\right)}{y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot \left(y \cdot x\right) + y \cdot z\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot a + \mathsf{fma}\left(-1, z, \mathsf{fma}\left(-1, a \cdot \frac{x \cdot a - z}{y}, b \cdot \frac{x}{y}\right)\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+57} \lor \neg \left(y \leq 5 \cdot 10^{+43}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot \left(y \cdot x\right) + y \cdot z\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.4e+57) (not (<= y 5e+43)))
   (+ x (/ z y))
   (/
    (+
     t
     (* y (+ 230661.510616 (* y (+ 27464.7644705 (+ (* y (* y x)) (* y z)))))))
    (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.4e+57) || !(y <= 5e+43)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + ((y * (y * x)) + (y * z))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-5.4d+57)) .or. (.not. (y <= 5d+43))) then
        tmp = x + (z / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + ((y * (y * x)) + (y * z))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.4e+57) || !(y <= 5e+43)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + ((y * (y * x)) + (y * z))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5.4e+57) or not (y <= 5e+43):
		tmp = x + (z / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + ((y * (y * x)) + (y * z))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5.4e+57) || !(y <= 5e+43))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(Float64(y * Float64(y * x)) + Float64(y * z))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5.4e+57) || ~((y <= 5e+43)))
		tmp = x + (z / y);
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + ((y * (y * x)) + (y * z))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5.4e+57], N[Not[LessEqual[y, 5e+43]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision] + N[(y * z), $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]]

Derivation

1. Split input into 2 regimes

2. if y < -5.3999999999999997e57 or 5.0000000000000004e43 < y

   1. Initial program 3.1%

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

   3. Taylor expanded in y around inf 3.1%

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

   4. Taylor expanded in y around inf 79.1%

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

   if -5.3999999999999997e57 < y < 5.0000000000000004e43

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. distribute-rgt-in 93.9%

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

   4. Applied egg-rr 93.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+57} \lor \neg \left(y \leq 5 \cdot 10^{+43}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot \left(y \cdot x\right) + y \cdot z\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+58} \lor \neg \left(y \leq 5 \cdot 10^{+43}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.85e+58) (not (<= y 5e+43)))
   (+ x (/ z y))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
    (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.85e+58) || !(y <= 5e+43)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.85d+58)) .or. (.not. (y <= 5d+43))) then
        tmp = x + (z / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.85e+58) || !(y <= 5e+43)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.85e+58) or not (y <= 5e+43):
		tmp = x + (z / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.85e+58) || !(y <= 5e+43))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.85e+58) || ~((y <= 5e+43)))
		tmp = x + (z / y);
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.85e+58], N[Not[LessEqual[y, 5e+43]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8500000000000001e58 or 5.0000000000000004e43 < y

   1. Initial program 3.1%

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

   3. Taylor expanded in y around inf 3.1%

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

   4. Taylor expanded in y around inf 79.1%

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

   if -1.8500000000000001e58 < y < 5.0000000000000004e43

   1. Initial program 93.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+58} \lor \neg \left(y \leq 5 \cdot 10^{+43}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+58} \lor \neg \left(y \leq 8.2 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.6e+58) (not (<= y 8.2e+32)))
   (+ x (/ z y))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.6e+58) || !(y <= 8.2e+32)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.6d+58)) .or. (.not. (y <= 8.2d+32))) then
        tmp = x + (z / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.6e+58) || !(y <= 8.2e+32)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.6e+58) or not (y <= 8.2e+32):
		tmp = x + (z / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.6e+58) || !(y <= 8.2e+32))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.6e+58) || ~((y <= 8.2e+32)))
		tmp = x + (z / y);
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.6e+58], N[Not[LessEqual[y, 8.2e+32]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.59999999999999996e58 or 8.19999999999999961e32 < 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 4.0%

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

   4. Taylor expanded in y around inf 78.4%

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

   if -3.59999999999999996e58 < y < 8.19999999999999961e32

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0 91.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+58} \lor \neg \left(y \leq 8.2 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -3.5e+58)
     t_1
     (if (<= y -1.5e+27)
       (* y (+ (/ x a) (/ (+ (* 27464.7644705 (/ 1.0 (* y a))) (/ z a)) y)))
       (if (<= y 4.3e+32)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -3.5e+58) {
		tmp = t_1;
	} else if (y <= -1.5e+27) {
		tmp = y * ((x / a) + (((27464.7644705 * (1.0 / (y * a))) + (z / a)) / y));
	} else if (y <= 4.3e+32) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-3.5d+58)) then
        tmp = t_1
    else if (y <= (-1.5d+27)) then
        tmp = y * ((x / a) + (((27464.7644705d0 * (1.0d0 / (y * a))) + (z / a)) / y))
    else if (y <= 4.3d+32) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -3.5e+58) {
		tmp = t_1;
	} else if (y <= -1.5e+27) {
		tmp = y * ((x / a) + (((27464.7644705 * (1.0 / (y * a))) + (z / a)) / y));
	} else if (y <= 4.3e+32) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -3.5e+58:
		tmp = t_1
	elif y <= -1.5e+27:
		tmp = y * ((x / a) + (((27464.7644705 * (1.0 / (y * a))) + (z / a)) / y))
	elif y <= 4.3e+32:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -3.5e+58)
		tmp = t_1;
	elseif (y <= -1.5e+27)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * a))) + Float64(z / a)) / y)));
	elseif (y <= 4.3e+32)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -3.5e+58)
		tmp = t_1;
	elseif (y <= -1.5e+27)
		tmp = y * ((x / a) + (((27464.7644705 * (1.0 / (y * a))) + (z / a)) / y));
	elseif (y <= 4.3e+32)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+58], t$95$1, If[LessEqual[y, -1.5e+27], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(N[(27464.7644705 * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+32], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4999999999999997e58 or 4.2999999999999997e32 < 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 4.0%

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

   4. Taylor expanded in y around inf 78.4%

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

   if -3.4999999999999997e58 < y < -1.49999999999999988e27

   1. Initial program 40.5%

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

   3. Taylor expanded in a around inf 10.5%

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

   4. Taylor expanded in y around -inf 54.1%

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

   if -1.49999999999999988e27 < y < 4.2999999999999997e32

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 97.6%

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

   4. Taylor expanded in y around 0 94.1%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{27464.7644705 \cdot \frac{1}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -5.8e+57)
     t_1
     (if (<= y -1.35e+27)
       (* y (+ (/ x a) (/ z (* y a))))
       (if (<= y -1.15e-127)
         (/ (+ t (* y (+ 230661.510616 (* y (* y z))))) (* y c))
         (if (<= y 2.8e+17)
           (/ (+ 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);
	double tmp;
	if (y <= -5.8e+57) {
		tmp = t_1;
	} else if (y <= -1.35e+27) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else if (y <= -1.15e-127) {
		tmp = (t + (y * (230661.510616 + (y * (y * z))))) / (y * c);
	} else if (y <= 2.8e+17) {
		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)
    if (y <= (-5.8d+57)) then
        tmp = t_1
    else if (y <= (-1.35d+27)) then
        tmp = y * ((x / a) + (z / (y * a)))
    else if (y <= (-1.15d-127)) then
        tmp = (t + (y * (230661.510616d0 + (y * (y * z))))) / (y * c)
    else if (y <= 2.8d+17) 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);
	double tmp;
	if (y <= -5.8e+57) {
		tmp = t_1;
	} else if (y <= -1.35e+27) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else if (y <= -1.15e-127) {
		tmp = (t + (y * (230661.510616 + (y * (y * z))))) / (y * c);
	} else if (y <= 2.8e+17) {
		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)
	tmp = 0
	if y <= -5.8e+57:
		tmp = t_1
	elif y <= -1.35e+27:
		tmp = y * ((x / a) + (z / (y * a)))
	elif y <= -1.15e-127:
		tmp = (t + (y * (230661.510616 + (y * (y * z))))) / (y * c)
	elif y <= 2.8e+17:
		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(z / y))
	tmp = 0.0
	if (y <= -5.8e+57)
		tmp = t_1;
	elseif (y <= -1.35e+27)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(z / Float64(y * a))));
	elseif (y <= -1.15e-127)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(y * z))))) / Float64(y * c));
	elseif (y <= 2.8e+17)
		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);
	tmp = 0.0;
	if (y <= -5.8e+57)
		tmp = t_1;
	elseif (y <= -1.35e+27)
		tmp = y * ((x / a) + (z / (y * a)));
	elseif (y <= -1.15e-127)
		tmp = (t + (y * (230661.510616 + (y * (y * z))))) / (y * c);
	elseif (y <= 2.8e+17)
		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[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+57], t$95$1, If[LessEqual[y, -1.35e+27], N[(y * N[(N[(x / a), $MachinePrecision] + N[(z / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-127], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+17], 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 < -5.8000000000000003e57 or 2.8e17 < y

   1. Initial program 5.7%

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

   3. Taylor expanded in y around inf 5.7%

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

   4. Taylor expanded in y around inf 77.0%

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

   if -5.8000000000000003e57 < y < -1.3499999999999999e27

   1. Initial program 40.5%

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

   3. Taylor expanded in a around inf 10.5%

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

   4. Taylor expanded in y around inf 47.1%

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

   if -1.3499999999999999e27 < y < -1.15000000000000009e-127

   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 x around 0 91.9%

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

   4. Taylor expanded in c around inf 47.8%

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

   5. Taylor expanded in y around inf 47.9%

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

   if -1.15000000000000009e-127 < y < 2.8e17

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 98.9%

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

   4. Taylor expanded in i around inf 79.9%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+57} \lor \neg \left(y \leq 1.22 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.2e+57) (not (<= y 1.22e+32)))
   (+ x (/ z y))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.2e+57) || !(y <= 1.22e+32)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	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 <= (-3.2d+57)) .or. (.not. (y <= 1.22d+32))) then
        tmp = x + (z / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    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 <= -3.2e+57) || !(y <= 1.22e+32)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.2e+57) or not (y <= 1.22e+32):
		tmp = x + (z / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.2e+57) || !(y <= 1.22e+32))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.2e+57) || ~((y <= 1.22e+32)))
		tmp = x + (z / y);
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.2e+57], N[Not[LessEqual[y, 1.22e+32]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000029e57 or 1.22000000000000002e32 < 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 4.0%

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

   4. Taylor expanded in y around inf 78.4%

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

   if -3.20000000000000029e57 < y < 1.22000000000000002e32

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0 91.9%

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

   4. Taylor expanded in y around 0 87.5%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+57} \lor \neg \left(y \leq 1.22 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+57} \lor \neg \left(y \leq 1.3 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.2e+57) (not (<= y 1.3e+32)))
   (+ x (/ z y))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.2e+57) || !(y <= 1.3e+32)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.2d+57)) .or. (.not. (y <= 1.3d+32))) then
        tmp = x + (z / y)
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.2e+57) || !(y <= 1.3e+32)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.2e+57) or not (y <= 1.3e+32):
		tmp = x + (z / y)
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.2e+57) || !(y <= 1.3e+32))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.2e+57) || ~((y <= 1.3e+32)))
		tmp = x + (z / y);
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.2e+57], N[Not[LessEqual[y, 1.3e+32]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000029e57 or 1.3000000000000001e32 < 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 4.0%

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

   4. Taylor expanded in y around inf 78.4%

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

   if -3.20000000000000029e57 < y < 1.3000000000000001e32

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 82.8%

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

      1. *-commutative 82.8%

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

   5. Simplified 82.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+57} \lor \neg \left(y \leq 1.3 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+18}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -8.5e+58)
     t_1
     (if (<= y -1.35e+27)
       (* y (+ (/ x a) (/ z (* y a))))
       (if (<= y -1.15e-127)
         (/ (+ t (* y (+ 230661.510616 (* y (* y z))))) (* y c))
         (if (<= y 2.75e+18) (/ (+ t (* y 230661.510616)) i) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -8.5e+58) {
		tmp = t_1;
	} else if (y <= -1.35e+27) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else if (y <= -1.15e-127) {
		tmp = (t + (y * (230661.510616 + (y * (y * z))))) / (y * c);
	} else if (y <= 2.75e+18) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-8.5d+58)) then
        tmp = t_1
    else if (y <= (-1.35d+27)) then
        tmp = y * ((x / a) + (z / (y * a)))
    else if (y <= (-1.15d-127)) then
        tmp = (t + (y * (230661.510616d0 + (y * (y * z))))) / (y * c)
    else if (y <= 2.75d+18) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -8.5e+58) {
		tmp = t_1;
	} else if (y <= -1.35e+27) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else if (y <= -1.15e-127) {
		tmp = (t + (y * (230661.510616 + (y * (y * z))))) / (y * c);
	} else if (y <= 2.75e+18) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -8.5e+58:
		tmp = t_1
	elif y <= -1.35e+27:
		tmp = y * ((x / a) + (z / (y * a)))
	elif y <= -1.15e-127:
		tmp = (t + (y * (230661.510616 + (y * (y * z))))) / (y * c)
	elif y <= 2.75e+18:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -8.5e+58)
		tmp = t_1;
	elseif (y <= -1.35e+27)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(z / Float64(y * a))));
	elseif (y <= -1.15e-127)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(y * z))))) / Float64(y * c));
	elseif (y <= 2.75e+18)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -8.5e+58)
		tmp = t_1;
	elseif (y <= -1.35e+27)
		tmp = y * ((x / a) + (z / (y * a)));
	elseif (y <= -1.15e-127)
		tmp = (t + (y * (230661.510616 + (y * (y * z))))) / (y * c);
	elseif (y <= 2.75e+18)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+58], t$95$1, If[LessEqual[y, -1.35e+27], N[(y * N[(N[(x / a), $MachinePrecision] + N[(z / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-127], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+18], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.50000000000000015e58 or 2.75e18 < y

   1. Initial program 5.7%

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

   3. Taylor expanded in y around inf 5.7%

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

   4. Taylor expanded in y around inf 77.0%

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

   if -8.50000000000000015e58 < y < -1.3499999999999999e27

   1. Initial program 40.5%

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

   3. Taylor expanded in a around inf 10.5%

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

   4. Taylor expanded in y around inf 47.1%

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

   if -1.3499999999999999e27 < y < -1.15000000000000009e-127

   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 x around 0 91.9%

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

   4. Taylor expanded in c around inf 47.8%

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

   5. Taylor expanded in y around inf 47.9%

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

   if -1.15000000000000009e-127 < y < 2.75e18

   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 79.9%

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

   4. Taylor expanded in y around 0 77.1%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z\right)\right)}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+18}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+57} \lor \neg \left(y \leq 3.7 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.4e+57) (not (<= y 3.7e+32)))
   (+ x (/ z y))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ b (* y y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.4e+57) || !(y <= 3.7e+32)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * y))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.4d+57)) .or. (.not. (y <= 3.7d+32))) then
        tmp = x + (z / y)
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * y))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.4e+57) || !(y <= 3.7e+32)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * y))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.4e+57) or not (y <= 3.7e+32):
		tmp = x + (z / y)
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * y))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.4e+57) || !(y <= 3.7e+32))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * y)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.4e+57) || ~((y <= 3.7e+32)))
		tmp = x + (z / y);
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * y))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.4e+57], N[Not[LessEqual[y, 3.7e+32]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999992e57 or 3.7e32 < 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 4.0%

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

   4. Taylor expanded in y around inf 78.4%

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

   if -3.39999999999999992e57 < y < 3.7e32

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 91.3%

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

   4. Taylor expanded in y around 0 81.2%

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

      1. *-commutative 82.8%

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

   6. Simplified 81.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+57} \lor \neg \left(y \leq 3.7 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ t_2 := t + y \cdot 230661.510616\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;\frac{t\_2}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{t\_2}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))) (t_2 (+ t (* y 230661.510616))))
   (if (<= y -2.8e+58)
     t_1
     (if (<= y -1.65e+27)
       (* y (+ (/ x a) (/ z (* y a))))
       (if (<= y -1.15e-127)
         (/ t_2 (* y c))
         (if (<= y 1.4e+19) (/ t_2 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);
	double t_2 = t + (y * 230661.510616);
	double tmp;
	if (y <= -2.8e+58) {
		tmp = t_1;
	} else if (y <= -1.65e+27) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else if (y <= -1.15e-127) {
		tmp = t_2 / (y * c);
	} else if (y <= 1.4e+19) {
		tmp = t_2 / 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) :: t_2
    real(8) :: tmp
    t_1 = x + (z / y)
    t_2 = t + (y * 230661.510616d0)
    if (y <= (-2.8d+58)) then
        tmp = t_1
    else if (y <= (-1.65d+27)) then
        tmp = y * ((x / a) + (z / (y * a)))
    else if (y <= (-1.15d-127)) then
        tmp = t_2 / (y * c)
    else if (y <= 1.4d+19) then
        tmp = t_2 / 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);
	double t_2 = t + (y * 230661.510616);
	double tmp;
	if (y <= -2.8e+58) {
		tmp = t_1;
	} else if (y <= -1.65e+27) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else if (y <= -1.15e-127) {
		tmp = t_2 / (y * c);
	} else if (y <= 1.4e+19) {
		tmp = t_2 / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	t_2 = t + (y * 230661.510616)
	tmp = 0
	if y <= -2.8e+58:
		tmp = t_1
	elif y <= -1.65e+27:
		tmp = y * ((x / a) + (z / (y * a)))
	elif y <= -1.15e-127:
		tmp = t_2 / (y * c)
	elif y <= 1.4e+19:
		tmp = t_2 / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	t_2 = Float64(t + Float64(y * 230661.510616))
	tmp = 0.0
	if (y <= -2.8e+58)
		tmp = t_1;
	elseif (y <= -1.65e+27)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(z / Float64(y * a))));
	elseif (y <= -1.15e-127)
		tmp = Float64(t_2 / Float64(y * c));
	elseif (y <= 1.4e+19)
		tmp = Float64(t_2 / 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);
	t_2 = t + (y * 230661.510616);
	tmp = 0.0;
	if (y <= -2.8e+58)
		tmp = t_1;
	elseif (y <= -1.65e+27)
		tmp = y * ((x / a) + (z / (y * a)));
	elseif (y <= -1.15e-127)
		tmp = t_2 / (y * c);
	elseif (y <= 1.4e+19)
		tmp = t_2 / 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[(z / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+58], t$95$1, If[LessEqual[y, -1.65e+27], N[(y * N[(N[(x / a), $MachinePrecision] + N[(z / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-127], N[(t$95$2 / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+19], N[(t$95$2 / i), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7999999999999998e58 or 1.4e19 < y

   1. Initial program 5.7%

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

   3. Taylor expanded in y around inf 5.7%

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

   4. Taylor expanded in y around inf 77.0%

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

   if -2.7999999999999998e58 < y < -1.6499999999999999e27

   1. Initial program 40.5%

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

   3. Taylor expanded in a around inf 10.5%

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

   4. Taylor expanded in y around inf 47.1%

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

   if -1.6499999999999999e27 < y < -1.15000000000000009e-127

   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 x around 0 91.9%

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

   4. Taylor expanded in c around inf 47.8%

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

   5. Taylor expanded in y around 0 41.1%

      \[\leadsto \frac{t + \color{blue}{230661.510616 \cdot y}}{c \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 41.1%

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

   7. Simplified 41.1%

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

   if -1.15000000000000009e-127 < y < 1.4e19

   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 79.9%

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

   4. Taylor expanded in y around 0 77.1%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+57} \lor \neg \left(y \leq 4.7 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.2e+57) (not (<= y 4.7e+31)))
   (+ x (/ z y))
   (/ t (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.2e+57) || !(y <= 4.7e+31)) {
		tmp = x + (z / y);
	} else {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.2d+57)) .or. (.not. (y <= 4.7d+31))) then
        tmp = x + (z / y)
    else
        tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.2e+57) || !(y <= 4.7e+31)) {
		tmp = x + (z / y);
	} else {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.2e+57) or not (y <= 4.7e+31):
		tmp = x + (z / y)
	else:
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.2e+57) || !(y <= 4.7e+31))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.2e+57) || ~((y <= 4.7e+31)))
		tmp = x + (z / y);
	else
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.2e+57], N[Not[LessEqual[y, 4.7e+31]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000029e57 or 4.7000000000000002e31 < 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 4.0%

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

   4. Taylor expanded in y around inf 78.4%

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

   if -3.20000000000000029e57 < y < 4.7000000000000002e31

   1. Initial program 94.5%

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

   3. Taylor expanded in t around inf 68.1%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+57} \lor \neg \left(y \leq 4.7 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;\frac{t\_1}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{t\_1}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616))) (t_2 (+ x (/ z y))))
   (if (<= y -2.9e+27)
     t_2
     (if (<= y -1.15e-127)
       (/ t_1 (* y c))
       (if (<= y 1.8e+19) (/ t_1 i) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -2.9e+27) {
		tmp = t_2;
	} else if (y <= -1.15e-127) {
		tmp = t_1 / (y * c);
	} else if (y <= 1.8e+19) {
		tmp = t_1 / i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    t_2 = x + (z / y)
    if (y <= (-2.9d+27)) then
        tmp = t_2
    else if (y <= (-1.15d-127)) then
        tmp = t_1 / (y * c)
    else if (y <= 1.8d+19) then
        tmp = t_1 / i
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -2.9e+27) {
		tmp = t_2;
	} else if (y <= -1.15e-127) {
		tmp = t_1 / (y * c);
	} else if (y <= 1.8e+19) {
		tmp = t_1 / i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	t_2 = x + (z / y)
	tmp = 0
	if y <= -2.9e+27:
		tmp = t_2
	elif y <= -1.15e-127:
		tmp = t_1 / (y * c)
	elif y <= 1.8e+19:
		tmp = t_1 / i
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	t_2 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2.9e+27)
		tmp = t_2;
	elseif (y <= -1.15e-127)
		tmp = Float64(t_1 / Float64(y * c));
	elseif (y <= 1.8e+19)
		tmp = Float64(t_1 / i);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	t_2 = x + (z / y);
	tmp = 0.0;
	if (y <= -2.9e+27)
		tmp = t_2;
	elseif (y <= -1.15e-127)
		tmp = t_1 / (y * c);
	elseif (y <= 1.8e+19)
		tmp = t_1 / i;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+27], t$95$2, If[LessEqual[y, -1.15e-127], N[(t$95$1 / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+19], N[(t$95$1 / i), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9000000000000001e27 or 1.8e19 < y

   1. Initial program 9.4%

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

   3. Taylor expanded in y around inf 8.6%

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

   4. Taylor expanded in y around inf 69.9%

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

   if -2.9000000000000001e27 < y < -1.15000000000000009e-127

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 88.7%

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

   4. Taylor expanded in c around inf 46.0%

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

   5. Taylor expanded in y around 0 39.9%

      \[\leadsto \frac{t + \color{blue}{230661.510616 \cdot y}}{c \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 39.9%

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

   7. Simplified 39.9%

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

   if -1.15000000000000009e-127 < y < 1.8e19

   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 79.9%

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

   4. Taylor expanded in y around 0 77.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 61.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-12} \lor \neg \left(y \leq 2.7 \cdot 10^{+17}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8.6e-12) (not (<= y 2.7e+17)))
   (+ x (/ z y))
   (/ (+ t (* y 230661.510616)) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.6e-12) || !(y <= 2.7e+17)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-8.6d-12)) .or. (.not. (y <= 2.7d+17))) then
        tmp = x + (z / y)
    else
        tmp = (t + (y * 230661.510616d0)) / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.6e-12) || !(y <= 2.7e+17)) {
		tmp = x + (z / y);
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -8.6e-12) or not (y <= 2.7e+17):
		tmp = x + (z / y)
	else:
		tmp = (t + (y * 230661.510616)) / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -8.6e-12) || !(y <= 2.7e+17))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -8.6e-12) || ~((y <= 2.7e+17)))
		tmp = x + (z / y);
	else
		tmp = (t + (y * 230661.510616)) / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -8.6e-12], N[Not[LessEqual[y, 2.7e+17]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.59999999999999971e-12 or 2.7e17 < y

   1. Initial program 13.6%

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

   3. Taylor expanded in y around inf 12.1%

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

   4. Taylor expanded in y around inf 66.4%

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

   if -8.59999999999999971e-12 < y < 2.7e17

   1. Initial program 99.7%

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

   3. Taylor expanded in i around inf 71.3%

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

   4. Taylor expanded in y around 0 69.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-12} \lor \neg \left(y \leq 2.7 \cdot 10^{+17}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-11} \lor \neg \left(y \leq 2.2 \cdot 10^{+19}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2e-11) (not (<= y 2.2e+19))) (+ x (/ z y)) (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2e-11) || !(y <= 2.2e+19)) {
		tmp = x + (z / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2d-11)) .or. (.not. (y <= 2.2d+19))) then
        tmp = x + (z / y)
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2e-11) || !(y <= 2.2e+19)) {
		tmp = x + (z / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2e-11) or not (y <= 2.2e+19):
		tmp = x + (z / y)
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2e-11) || !(y <= 2.2e+19))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2e-11) || ~((y <= 2.2e+19)))
		tmp = x + (z / y);
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2e-11], N[Not[LessEqual[y, 2.2e+19]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999988e-11 or 2.2e19 < y

   1. Initial program 13.6%

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

   3. Taylor expanded in y around inf 12.1%

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

   4. Taylor expanded in y around inf 66.4%

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

   if -1.99999999999999988e-11 < y < 2.2e19

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 61.4%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-11} \lor \neg \left(y \leq 2.2 \cdot 10^{+19}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7.7e-34) x (if (<= y 3.1e+27) (/ 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 <= -7.7e-34) {
		tmp = x;
	} else if (y <= 3.1e+27) {
		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 <= (-7.7d-34)) then
        tmp = x
    else if (y <= 3.1d+27) 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 <= -7.7e-34) {
		tmp = x;
	} else if (y <= 3.1e+27) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7.7e-34:
		tmp = x
	elif y <= 3.1e+27:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7.7e-34)
		tmp = x;
	elseif (y <= 3.1e+27)
		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 <= -7.7e-34)
		tmp = x;
	elseif (y <= 3.1e+27)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7.7e-34], x, If[LessEqual[y, 3.1e+27], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -7.7e-34 or 3.09999999999999996e27 < y

   1. Initial program 15.5%

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

   3. Taylor expanded in y around inf 50.6%

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

   if -7.7e-34 < y < 3.09999999999999996e27

   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 62.1%

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

Alternative 19: 26.1% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.3%

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

3. Taylor expanded in y around inf 27.8%

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

Reproduce

herbie shell --seed 2024116 
(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)))