Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.6% → 85.9%

Time: 31.4s

Alternatives: 17

Speedup: 1.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\\ t_2 := b + y \cdot \left(y + a\right)\\ t_3 := {t\_2}^{2}\\ t_4 := y \cdot t\_2\\ t_5 := x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ t_6 := c + t\_4\\ t_7 := {t\_6}^{2}\\ t_8 := y \cdot t\_6\\ t_9 := i + t\_8\\ t_10 := y \cdot \left(z + y \cdot x\right)\\ t_11 := 27464.7644705 + t\_10\\ t_12 := {t\_1}^{2}\\ \mathbf{if}\;y \leq -1.18 \cdot 10^{+110}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+43}:\\ \;\;\;\;\left(\frac{t}{t\_8} + \left(\left(230661.510616 \cdot \frac{1}{t\_4} + \frac{t\_11}{t\_2}\right) - c \cdot \left(230661.510616 \cdot \frac{1}{{y}^{2} \cdot t\_3} + \left(27464.7644705 \cdot \frac{1}{y \cdot t\_3} + \left(\frac{z}{t\_3} + \frac{y \cdot x}{t\_3}\right)\right)\right)\right)\right) - i \cdot \left(230661.510616 \cdot \frac{1}{y \cdot t\_7} + \left(27464.7644705 \cdot \frac{1}{t\_7} + \left(\frac{t}{t\_7 \cdot {y}^{2}} + \frac{t\_10}{t\_7}\right)\right)\right)\\ \mathbf{elif}\;y \leq 160:\\ \;\;\;\;\frac{t}{t\_9} + \frac{y \cdot \left(230661.510616 + y \cdot t\_11\right)}{t\_9}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+82}:\\ \;\;\;\;\left(\frac{\frac{t}{y}}{t\_1} + \left(\frac{x}{\frac{t\_1}{{y}^{3}}} + \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{t\_1}\right)\right) - i \cdot \left(\left(\frac{230661.510616}{y \cdot t\_12} + \frac{27464.7644705}{t\_12}\right) + \left(\frac{\frac{t}{{y}^{2}}}{t\_12} + \left(\frac{x}{\frac{t\_12}{{y}^{2}}} + \frac{y}{\frac{t\_12}{z}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y (fma y (+ y a) b) c))
        (t_2 (+ b (* y (+ y a))))
        (t_3 (pow t_2 2.0))
        (t_4 (* y t_2))
        (t_5 (+ x (- (/ z y) (/ x (/ y a)))))
        (t_6 (+ c t_4))
        (t_7 (pow t_6 2.0))
        (t_8 (* y t_6))
        (t_9 (+ i t_8))
        (t_10 (* y (+ z (* y x))))
        (t_11 (+ 27464.7644705 t_10))
        (t_12 (pow t_1 2.0)))
   (if (<= y -1.18e+110)
     t_5
     (if (<= y -5.6e+43)
       (-
        (+
         (/ t t_8)
         (-
          (+ (* 230661.510616 (/ 1.0 t_4)) (/ t_11 t_2))
          (*
           c
           (+
            (* 230661.510616 (/ 1.0 (* (pow y 2.0) t_3)))
            (+
             (* 27464.7644705 (/ 1.0 (* y t_3)))
             (+ (/ z t_3) (/ (* y x) t_3)))))))
        (*
         i
         (+
          (* 230661.510616 (/ 1.0 (* y t_7)))
          (+
           (* 27464.7644705 (/ 1.0 t_7))
           (+ (/ t (* t_7 (pow y 2.0))) (/ t_10 t_7))))))
       (if (<= y 160.0)
         (+ (/ t t_9) (/ (* y (+ 230661.510616 (* y t_11))) t_9))
         (if (<= y 4.8e+82)
           (-
            (+
             (/ (/ t y) t_1)
             (+
              (/ x (/ t_1 (pow y 3.0)))
              (/ (fma y (fma y z 27464.7644705) 230661.510616) t_1)))
            (*
             i
             (+
              (+ (/ 230661.510616 (* y t_12)) (/ 27464.7644705 t_12))
              (+
               (/ (/ t (pow y 2.0)) t_12)
               (+ (/ x (/ t_12 (pow y 2.0))) (/ y (/ t_12 z)))))))
           t_5))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, fma(y, (y + a), b), c);
	double t_2 = b + (y * (y + a));
	double t_3 = pow(t_2, 2.0);
	double t_4 = y * t_2;
	double t_5 = x + ((z / y) - (x / (y / a)));
	double t_6 = c + t_4;
	double t_7 = pow(t_6, 2.0);
	double t_8 = y * t_6;
	double t_9 = i + t_8;
	double t_10 = y * (z + (y * x));
	double t_11 = 27464.7644705 + t_10;
	double t_12 = pow(t_1, 2.0);
	double tmp;
	if (y <= -1.18e+110) {
		tmp = t_5;
	} else if (y <= -5.6e+43) {
		tmp = ((t / t_8) + (((230661.510616 * (1.0 / t_4)) + (t_11 / t_2)) - (c * ((230661.510616 * (1.0 / (pow(y, 2.0) * t_3))) + ((27464.7644705 * (1.0 / (y * t_3))) + ((z / t_3) + ((y * x) / t_3))))))) - (i * ((230661.510616 * (1.0 / (y * t_7))) + ((27464.7644705 * (1.0 / t_7)) + ((t / (t_7 * pow(y, 2.0))) + (t_10 / t_7)))));
	} else if (y <= 160.0) {
		tmp = (t / t_9) + ((y * (230661.510616 + (y * t_11))) / t_9);
	} else if (y <= 4.8e+82) {
		tmp = (((t / y) / t_1) + ((x / (t_1 / pow(y, 3.0))) + (fma(y, fma(y, z, 27464.7644705), 230661.510616) / t_1))) - (i * (((230661.510616 / (y * t_12)) + (27464.7644705 / t_12)) + (((t / pow(y, 2.0)) / t_12) + ((x / (t_12 / pow(y, 2.0))) + (y / (t_12 / z))))));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, fma(y, Float64(y + a), b), c)
	t_2 = Float64(b + Float64(y * Float64(y + a)))
	t_3 = t_2 ^ 2.0
	t_4 = Float64(y * t_2)
	t_5 = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))))
	t_6 = Float64(c + t_4)
	t_7 = t_6 ^ 2.0
	t_8 = Float64(y * t_6)
	t_9 = Float64(i + t_8)
	t_10 = Float64(y * Float64(z + Float64(y * x)))
	t_11 = Float64(27464.7644705 + t_10)
	t_12 = t_1 ^ 2.0
	tmp = 0.0
	if (y <= -1.18e+110)
		tmp = t_5;
	elseif (y <= -5.6e+43)
		tmp = Float64(Float64(Float64(t / t_8) + Float64(Float64(Float64(230661.510616 * Float64(1.0 / t_4)) + Float64(t_11 / t_2)) - Float64(c * Float64(Float64(230661.510616 * Float64(1.0 / Float64((y ^ 2.0) * t_3))) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * t_3))) + Float64(Float64(z / t_3) + Float64(Float64(y * x) / t_3))))))) - Float64(i * Float64(Float64(230661.510616 * Float64(1.0 / Float64(y * t_7))) + Float64(Float64(27464.7644705 * Float64(1.0 / t_7)) + Float64(Float64(t / Float64(t_7 * (y ^ 2.0))) + Float64(t_10 / t_7))))));
	elseif (y <= 160.0)
		tmp = Float64(Float64(t / t_9) + Float64(Float64(y * Float64(230661.510616 + Float64(y * t_11))) / t_9));
	elseif (y <= 4.8e+82)
		tmp = Float64(Float64(Float64(Float64(t / y) / t_1) + Float64(Float64(x / Float64(t_1 / (y ^ 3.0))) + Float64(fma(y, fma(y, z, 27464.7644705), 230661.510616) / t_1))) - Float64(i * Float64(Float64(Float64(230661.510616 / Float64(y * t_12)) + Float64(27464.7644705 / t_12)) + Float64(Float64(Float64(t / (y ^ 2.0)) / t_12) + Float64(Float64(x / Float64(t_12 / (y ^ 2.0))) + Float64(y / Float64(t_12 / z)))))));
	else
		tmp = t_5;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Power[t$95$2, 2.0], $MachinePrecision]}, Block[{t$95$4 = N[(y * t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(c + t$95$4), $MachinePrecision]}, Block[{t$95$7 = N[Power[t$95$6, 2.0], $MachinePrecision]}, Block[{t$95$8 = N[(y * t$95$6), $MachinePrecision]}, Block[{t$95$9 = N[(i + t$95$8), $MachinePrecision]}, Block[{t$95$10 = N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$11 = N[(27464.7644705 + t$95$10), $MachinePrecision]}, Block[{t$95$12 = N[Power[t$95$1, 2.0], $MachinePrecision]}, If[LessEqual[y, -1.18e+110], t$95$5, If[LessEqual[y, -5.6e+43], N[(N[(N[(t / t$95$8), $MachinePrecision] + N[(N[(N[(230661.510616 * N[(1.0 / t$95$4), $MachinePrecision]), $MachinePrecision] + N[(t$95$11 / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(230661.510616 * N[(1.0 / N[(N[Power[y, 2.0], $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t$95$3), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(230661.510616 * N[(1.0 / N[(y * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / t$95$7), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(t$95$7 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$10 / t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 160.0], N[(N[(t / t$95$9), $MachinePrecision] + N[(N[(y * N[(230661.510616 + N[(y * t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$9), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+82], N[(N[(N[(N[(t / y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(x / N[(t$95$1 / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(y * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(N[(230661.510616 / N[(y * t$95$12), $MachinePrecision]), $MachinePrecision] + N[(27464.7644705 / t$95$12), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] / t$95$12), $MachinePrecision] + N[(N[(x / N[(t$95$12 / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t$95$12 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1799999999999999e110 or 4.79999999999999996e82 < y

   1. Initial program 0.1%

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

   3. Taylor expanded in y around inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. *-commutative 68.7%

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

      3. associate-/l* 82.1%

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

   5. Simplified 82.1%

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

   if -1.1799999999999999e110 < y < -5.60000000000000038e43

   1. Initial program 3.3%

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

   3. Taylor expanded in i around 0 41.7%

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

   4. Taylor expanded in c around 0 79.5%

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

   if -5.60000000000000038e43 < y < 160

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0 97.6%

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

   if 160 < y < 4.79999999999999996e82

   1. Initial program 29.4%

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

   3. Taylor expanded in x around 0 29.4%

      \[\leadsto \frac{\color{blue}{\left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in i around 0 49.7%

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

   6. Simplified 80.7%

      \[\leadsto \color{blue}{\left(\frac{\frac{t}{y}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \left(\frac{x}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{{y}^{3}}} + \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}\right)\right) - i \cdot \left(\left(\frac{230661.510616}{y \cdot {\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\right)}^{2}} + \frac{27464.7644705}{{\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\right)}^{2}}\right) + \left(\frac{\frac{t}{{y}^{2}}}{{\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\right)}^{2}} + \left(\frac{x}{\frac{{\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\right)}^{2}}{{y}^{2}}} + \frac{y}{\frac{{\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\right)}^{2}}{z}}\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+110}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+43}:\\ \;\;\;\;\left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(\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) - c \cdot \left(230661.510616 \cdot \frac{1}{{y}^{2} \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \left(27464.7644705 \cdot \frac{1}{y \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{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)\right)\right) - i \cdot \left(230661.510616 \cdot \frac{1}{y \cdot {\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}} + \left(27464.7644705 \cdot \frac{1}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}} + \left(\frac{t}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2} \cdot {y}^{2}} + \frac{y \cdot \left(z + y \cdot x\right)}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}}\right)\right)\right)\\ \mathbf{elif}\;y \leq 160:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+82}:\\ \;\;\;\;\left(\frac{\frac{t}{y}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)} + \left(\frac{x}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}{{y}^{3}}} + \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)}\right)\right) - i \cdot \left(\left(\frac{230661.510616}{y \cdot {\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\right)}^{2}} + \frac{27464.7644705}{{\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\right)}^{2}}\right) + \left(\frac{\frac{t}{{y}^{2}}}{{\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\right)}^{2}} + \left(\frac{x}{\frac{{\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\right)}^{2}}{{y}^{2}}} + \frac{y}{\frac{{\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right)\right)}^{2}}{z}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := {t\_1}^{2}\\ t_3 := y \cdot t\_1\\ t_4 := x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ t_5 := c + t\_3\\ t_6 := {t\_5}^{2}\\ t_7 := y \cdot t\_5\\ t_8 := i + t\_7\\ t_9 := y \cdot \left(z + y \cdot x\right)\\ t_10 := 27464.7644705 + t\_9\\ \mathbf{if}\;y \leq -1.52 \cdot 10^{+109}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+45}:\\ \;\;\;\;\left(\frac{t}{t\_7} + \left(\left(230661.510616 \cdot \frac{1}{t\_3} + \frac{t\_10}{t\_1}\right) - c \cdot \left(230661.510616 \cdot \frac{1}{{y}^{2} \cdot t\_2} + \left(27464.7644705 \cdot \frac{1}{y \cdot t\_2} + \left(\frac{z}{t\_2} + \frac{y \cdot x}{t\_2}\right)\right)\right)\right)\right) - i \cdot \left(230661.510616 \cdot \frac{1}{y \cdot t\_6} + \left(27464.7644705 \cdot \frac{1}{t\_6} + \left(\frac{t}{t\_6 \cdot {y}^{2}} + \frac{t\_9}{t\_6}\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{t\_8} + \frac{y \cdot \left(230661.510616 + y \cdot t\_10\right)}{t\_8}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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 (+ x (- (/ z y) (/ x (/ y a)))))
        (t_5 (+ c t_3))
        (t_6 (pow t_5 2.0))
        (t_7 (* y t_5))
        (t_8 (+ i t_7))
        (t_9 (* y (+ z (* y x))))
        (t_10 (+ 27464.7644705 t_9)))
   (if (<= y -1.52e+109)
     t_4
     (if (<= y -5e+45)
       (-
        (+
         (/ t t_7)
         (-
          (+ (* 230661.510616 (/ 1.0 t_3)) (/ t_10 t_1))
          (*
           c
           (+
            (* 230661.510616 (/ 1.0 (* (pow y 2.0) t_2)))
            (+
             (* 27464.7644705 (/ 1.0 (* y t_2)))
             (+ (/ z t_2) (/ (* y x) t_2)))))))
        (*
         i
         (+
          (* 230661.510616 (/ 1.0 (* y t_6)))
          (+
           (* 27464.7644705 (/ 1.0 t_6))
           (+ (/ t (* t_6 (pow y 2.0))) (/ t_9 t_6))))))
       (if (<= y 6.5e+54)
         (+ (/ t t_8) (/ (* y (+ 230661.510616 (* y t_10))) t_8))
         t_4)))))

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 = x + ((z / y) - (x / (y / a)));
	double t_5 = c + t_3;
	double t_6 = pow(t_5, 2.0);
	double t_7 = y * t_5;
	double t_8 = i + t_7;
	double t_9 = y * (z + (y * x));
	double t_10 = 27464.7644705 + t_9;
	double tmp;
	if (y <= -1.52e+109) {
		tmp = t_4;
	} else if (y <= -5e+45) {
		tmp = ((t / t_7) + (((230661.510616 * (1.0 / t_3)) + (t_10 / t_1)) - (c * ((230661.510616 * (1.0 / (pow(y, 2.0) * t_2))) + ((27464.7644705 * (1.0 / (y * t_2))) + ((z / t_2) + ((y * x) / t_2))))))) - (i * ((230661.510616 * (1.0 / (y * t_6))) + ((27464.7644705 * (1.0 / t_6)) + ((t / (t_6 * pow(y, 2.0))) + (t_9 / t_6)))));
	} else if (y <= 6.5e+54) {
		tmp = (t / t_8) + ((y * (230661.510616 + (y * t_10))) / t_8);
	} else {
		tmp = t_4;
	}
	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_10
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = b + (y * (y + a))
    t_2 = t_1 ** 2.0d0
    t_3 = y * t_1
    t_4 = x + ((z / y) - (x / (y / a)))
    t_5 = c + t_3
    t_6 = t_5 ** 2.0d0
    t_7 = y * t_5
    t_8 = i + t_7
    t_9 = y * (z + (y * x))
    t_10 = 27464.7644705d0 + t_9
    if (y <= (-1.52d+109)) then
        tmp = t_4
    else if (y <= (-5d+45)) then
        tmp = ((t / t_7) + (((230661.510616d0 * (1.0d0 / t_3)) + (t_10 / t_1)) - (c * ((230661.510616d0 * (1.0d0 / ((y ** 2.0d0) * t_2))) + ((27464.7644705d0 * (1.0d0 / (y * t_2))) + ((z / t_2) + ((y * x) / t_2))))))) - (i * ((230661.510616d0 * (1.0d0 / (y * t_6))) + ((27464.7644705d0 * (1.0d0 / t_6)) + ((t / (t_6 * (y ** 2.0d0))) + (t_9 / t_6)))))
    else if (y <= 6.5d+54) then
        tmp = (t / t_8) + ((y * (230661.510616d0 + (y * t_10))) / t_8)
    else
        tmp = t_4
    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 = b + (y * (y + a));
	double t_2 = Math.pow(t_1, 2.0);
	double t_3 = y * t_1;
	double t_4 = x + ((z / y) - (x / (y / a)));
	double t_5 = c + t_3;
	double t_6 = Math.pow(t_5, 2.0);
	double t_7 = y * t_5;
	double t_8 = i + t_7;
	double t_9 = y * (z + (y * x));
	double t_10 = 27464.7644705 + t_9;
	double tmp;
	if (y <= -1.52e+109) {
		tmp = t_4;
	} else if (y <= -5e+45) {
		tmp = ((t / t_7) + (((230661.510616 * (1.0 / t_3)) + (t_10 / t_1)) - (c * ((230661.510616 * (1.0 / (Math.pow(y, 2.0) * t_2))) + ((27464.7644705 * (1.0 / (y * t_2))) + ((z / t_2) + ((y * x) / t_2))))))) - (i * ((230661.510616 * (1.0 / (y * t_6))) + ((27464.7644705 * (1.0 / t_6)) + ((t / (t_6 * Math.pow(y, 2.0))) + (t_9 / t_6)))));
	} else if (y <= 6.5e+54) {
		tmp = (t / t_8) + ((y * (230661.510616 + (y * t_10))) / t_8);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b + (y * (y + a))
	t_2 = math.pow(t_1, 2.0)
	t_3 = y * t_1
	t_4 = x + ((z / y) - (x / (y / a)))
	t_5 = c + t_3
	t_6 = math.pow(t_5, 2.0)
	t_7 = y * t_5
	t_8 = i + t_7
	t_9 = y * (z + (y * x))
	t_10 = 27464.7644705 + t_9
	tmp = 0
	if y <= -1.52e+109:
		tmp = t_4
	elif y <= -5e+45:
		tmp = ((t / t_7) + (((230661.510616 * (1.0 / t_3)) + (t_10 / t_1)) - (c * ((230661.510616 * (1.0 / (math.pow(y, 2.0) * t_2))) + ((27464.7644705 * (1.0 / (y * t_2))) + ((z / t_2) + ((y * x) / t_2))))))) - (i * ((230661.510616 * (1.0 / (y * t_6))) + ((27464.7644705 * (1.0 / t_6)) + ((t / (t_6 * math.pow(y, 2.0))) + (t_9 / t_6)))))
	elif y <= 6.5e+54:
		tmp = (t / t_8) + ((y * (230661.510616 + (y * t_10))) / t_8)
	else:
		tmp = t_4
	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(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))))
	t_5 = Float64(c + t_3)
	t_6 = t_5 ^ 2.0
	t_7 = Float64(y * t_5)
	t_8 = Float64(i + t_7)
	t_9 = Float64(y * Float64(z + Float64(y * x)))
	t_10 = Float64(27464.7644705 + t_9)
	tmp = 0.0
	if (y <= -1.52e+109)
		tmp = t_4;
	elseif (y <= -5e+45)
		tmp = Float64(Float64(Float64(t / t_7) + Float64(Float64(Float64(230661.510616 * Float64(1.0 / t_3)) + Float64(t_10 / t_1)) - Float64(c * Float64(Float64(230661.510616 * Float64(1.0 / Float64((y ^ 2.0) * t_2))) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * t_2))) + Float64(Float64(z / t_2) + Float64(Float64(y * x) / t_2))))))) - Float64(i * Float64(Float64(230661.510616 * Float64(1.0 / Float64(y * t_6))) + Float64(Float64(27464.7644705 * Float64(1.0 / t_6)) + Float64(Float64(t / Float64(t_6 * (y ^ 2.0))) + Float64(t_9 / t_6))))));
	elseif (y <= 6.5e+54)
		tmp = Float64(Float64(t / t_8) + Float64(Float64(y * Float64(230661.510616 + Float64(y * t_10))) / t_8));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b + (y * (y + a));
	t_2 = t_1 ^ 2.0;
	t_3 = y * t_1;
	t_4 = x + ((z / y) - (x / (y / a)));
	t_5 = c + t_3;
	t_6 = t_5 ^ 2.0;
	t_7 = y * t_5;
	t_8 = i + t_7;
	t_9 = y * (z + (y * x));
	t_10 = 27464.7644705 + t_9;
	tmp = 0.0;
	if (y <= -1.52e+109)
		tmp = t_4;
	elseif (y <= -5e+45)
		tmp = ((t / t_7) + (((230661.510616 * (1.0 / t_3)) + (t_10 / t_1)) - (c * ((230661.510616 * (1.0 / ((y ^ 2.0) * t_2))) + ((27464.7644705 * (1.0 / (y * t_2))) + ((z / t_2) + ((y * x) / t_2))))))) - (i * ((230661.510616 * (1.0 / (y * t_6))) + ((27464.7644705 * (1.0 / t_6)) + ((t / (t_6 * (y ^ 2.0))) + (t_9 / t_6)))));
	elseif (y <= 6.5e+54)
		tmp = (t / t_8) + ((y * (230661.510616 + (y * t_10))) / t_8);
	else
		tmp = t_4;
	end
	tmp_2 = 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[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(c + t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[Power[t$95$5, 2.0], $MachinePrecision]}, Block[{t$95$7 = N[(y * t$95$5), $MachinePrecision]}, Block[{t$95$8 = N[(i + t$95$7), $MachinePrecision]}, Block[{t$95$9 = N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(27464.7644705 + t$95$9), $MachinePrecision]}, If[LessEqual[y, -1.52e+109], t$95$4, If[LessEqual[y, -5e+45], N[(N[(N[(t / t$95$7), $MachinePrecision] + N[(N[(N[(230661.510616 * N[(1.0 / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(t$95$10 / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(230661.510616 * N[(1.0 / N[(N[Power[y, 2.0], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t$95$2), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(230661.510616 * N[(1.0 / N[(y * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / t$95$6), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(t$95$6 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$9 / t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+54], N[(N[(t / t$95$8), $MachinePrecision] + N[(N[(y * N[(230661.510616 + N[(y * t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$8), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.52000000000000003e109 or 6.5e54 < y

   1. Initial program 1.4%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. associate--l+ 66.4%

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

      2. *-commutative 66.4%

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

      3. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

   if -1.52000000000000003e109 < y < -5e45

   1. Initial program 3.3%

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

   3. Taylor expanded in i around 0 41.7%

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

   4. Taylor expanded in c around 0 79.5%

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

   if -5e45 < y < 6.5e54

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 96.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+109}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+45}:\\ \;\;\;\;\left(\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(\left(230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)}\right) - c \cdot \left(230661.510616 \cdot \frac{1}{{y}^{2} \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \left(27464.7644705 \cdot \frac{1}{y \cdot {\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \left(\frac{z}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}} + \frac{y \cdot x}{{\left(b + y \cdot \left(y + a\right)\right)}^{2}}\right)\right)\right)\right)\right) - i \cdot \left(230661.510616 \cdot \frac{1}{y \cdot {\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}} + \left(27464.7644705 \cdot \frac{1}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}} + \left(\frac{t}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2} \cdot {y}^{2}} + \frac{y \cdot \left(z + y \cdot x\right)}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}}\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+47} \lor \neg \left(y \leq 1.26 \cdot 10^{+54}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t\_1} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ b (* y (+ y a)))))))))
   (if (or (<= y -3.2e+47) (not (<= y 1.26e+54)))
     (+ x (- (/ z y) (/ x (/ y a))))
     (+
      (/ t t_1)
      (/
       (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
       t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * (b + (y * (y + a))))));
	double tmp;
	if ((y <= -3.2e+47) || !(y <= 1.26e+54)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} else {
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / 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 = i + (y * (c + (y * (b + (y * (y + a))))))
    if ((y <= (-3.2d+47)) .or. (.not. (y <= 1.26d+54))) then
        tmp = x + ((z / y) - (x / (y / a)))
    else
        tmp = (t / t_1) + ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))) / 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 = i + (y * (c + (y * (b + (y * (y + a))))));
	double tmp;
	if ((y <= -3.2e+47) || !(y <= 1.26e+54)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} else {
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * (b + (y * (y + a))))))
	tmp = 0
	if (y <= -3.2e+47) or not (y <= 1.26e+54):
		tmp = x + ((z / y) - (x / (y / a)))
	else:
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))
	tmp = 0.0
	if ((y <= -3.2e+47) || !(y <= 1.26e+54))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))));
	else
		tmp = Float64(Float64(t / t_1) + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * (b + (y * (y + a))))));
	tmp = 0.0;
	if ((y <= -3.2e+47) || ~((y <= 1.26e+54)))
		tmp = x + ((z / y) - (x / (y / a)));
	else
		tmp = (t / t_1) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -3.2e+47], N[Not[LessEqual[y, 1.26e+54]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e47 or 1.25999999999999995e54 < y

   1. Initial program 1.5%

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

   3. Taylor expanded in y around inf 63.3%

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

      1. associate--l+ 63.3%

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

      2. *-commutative 63.3%

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

      3. associate-/l* 74.3%

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

   5. Simplified 74.3%

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

   if -3.2e47 < y < 1.25999999999999995e54

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 96.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+47} \lor \neg \left(y \leq 1.26 \cdot 10^{+54}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+47} \lor \neg \left(y \leq 1.3 \cdot 10^{+56}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.2e+47) (not (<= y 1.3e+56)))
   (+ x (- (/ z y) (/ x (/ y a))))
   (/
    (+ 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 <= -4.2e+47) || !(y <= 1.3e+56)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} 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 <= (-4.2d+47)) .or. (.not. (y <= 1.3d+56))) then
        tmp = x + ((z / y) - (x / (y / a)))
    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 <= -4.2e+47) || !(y <= 1.3e+56)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} 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 <= -4.2e+47) or not (y <= 1.3e+56):
		tmp = x + ((z / y) - (x / (y / a)))
	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 <= -4.2e+47) || !(y <= 1.3e+56))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))));
	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 <= -4.2e+47) || ~((y <= 1.3e+56)))
		tmp = x + ((z / y) - (x / (y / a)));
	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, -4.2e+47], N[Not[LessEqual[y, 1.3e+56]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $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 < -4.2e47 or 1.30000000000000005e56 < y

   1. Initial program 1.5%

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

   3. Taylor expanded in y around inf 63.3%

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

      1. associate--l+ 63.3%

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

      2. *-commutative 63.3%

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

      3. associate-/l* 74.3%

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

   5. Simplified 74.3%

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

   if -4.2e47 < y < 1.30000000000000005e56

   1. Initial program 96.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+47} \lor \neg \left(y \leq 1.3 \cdot 10^{+56}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+39} \lor \neg \left(y \leq 7.4 \cdot 10^{+27}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.8e+39) (not (<= y 7.4e+27)))
   (+ x (- (/ z y) (/ x (/ y a))))
   (/
    (+ 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 <= -5.8e+39) || !(y <= 7.4e+27)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} 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 <= (-5.8d+39)) .or. (.not. (y <= 7.4d+27))) then
        tmp = x + ((z / y) - (x / (y / a)))
    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 <= -5.8e+39) || !(y <= 7.4e+27)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} 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 <= -5.8e+39) or not (y <= 7.4e+27):
		tmp = x + ((z / y) - (x / (y / a)))
	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 <= -5.8e+39) || !(y <= 7.4e+27))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))));
	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 <= -5.8e+39) || ~((y <= 7.4e+27)))
		tmp = x + ((z / y) - (x / (y / a)));
	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, -5.8e+39], N[Not[LessEqual[y, 7.4e+27]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $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 < -5.80000000000000059e39 or 7.40000000000000004e27 < y

   1. Initial program 3.3%

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

   3. Taylor expanded in y around inf 61.5%

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

      1. associate--l+ 61.5%

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

      2. *-commutative 61.5%

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

      3. associate-/l* 72.1%

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

   5. Simplified 72.1%

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

   if -5.80000000000000059e39 < y < 7.40000000000000004e27

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 91.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+39} \lor \neg \left(y \leq 7.4 \cdot 10^{+27}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1250000:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ x (/ y a))))))
   (if (<= y -1.2e+79)
     t_1
     (if (<= y -1250000.0)
       (/
        (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))
        (+ c (* y (+ b (* y (+ y a))))))
       (if (<= y 4e+27)
         (/
          (+ 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) - (x / (y / a)));
	double tmp;
	if (y <= -1.2e+79) {
		tmp = t_1;
	} else if (y <= -1250000.0) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / (c + (y * (b + (y * (y + a)))));
	} else if (y <= 4e+27) {
		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) - (x / (y / a)))
    if (y <= (-1.2d+79)) then
        tmp = t_1
    else if (y <= (-1250000.0d0)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / (c + (y * (b + (y * (y + a)))))
    else if (y <= 4d+27) 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) - (x / (y / a)));
	double tmp;
	if (y <= -1.2e+79) {
		tmp = t_1;
	} else if (y <= -1250000.0) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / (c + (y * (b + (y * (y + a)))));
	} else if (y <= 4e+27) {
		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) - (x / (y / a)))
	tmp = 0
	if y <= -1.2e+79:
		tmp = t_1
	elif y <= -1250000.0:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / (c + (y * (b + (y * (y + a)))))
	elif y <= 4e+27:
		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(Float64(z / y) - Float64(x / Float64(y / a))))
	tmp = 0.0
	if (y <= -1.2e+79)
		tmp = t_1;
	elseif (y <= -1250000.0)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))));
	elseif (y <= 4e+27)
		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) - (x / (y / a)));
	tmp = 0.0;
	if (y <= -1.2e+79)
		tmp = t_1;
	elseif (y <= -1250000.0)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / (c + (y * (b + (y * (y + a)))));
	elseif (y <= 4e+27)
		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[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+79], t$95$1, If[LessEqual[y, -1250000.0], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+27], 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 < -1.19999999999999993e79 or 4.0000000000000001e27 < y

   1. Initial program 2.4%

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

   3. Taylor expanded in y around inf 64.0%

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

      1. associate--l+ 64.0%

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

      2. *-commutative 64.0%

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

      3. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

   if -1.19999999999999993e79 < y < -1.25e6

   1. Initial program 51.9%

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

   3. Taylor expanded in i around 0 46.6%

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

   4. Taylor expanded in t around 0 59.2%

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

   if -1.25e6 < y < 4.0000000000000001e27

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 94.1%

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

   4. Taylor expanded in y around 0 90.3%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+79}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{elif}\;y \leq -1250000:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-72}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 21:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ x (/ y a))))))
   (if (<= y -6e+35)
     t_1
     (if (<= y 5.6e-72)
       (/ t (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
       (if (<= y 21.0)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          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) - (x / (y / a)));
	double tmp;
	if (y <= -6e+35) {
		tmp = t_1;
	} else if (y <= 5.6e-72) {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 21.0) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / 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) - (x / (y / a)))
    if (y <= (-6d+35)) then
        tmp = t_1
    else if (y <= 5.6d-72) then
        tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else if (y <= 21.0d0) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / 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) - (x / (y / a)));
	double tmp;
	if (y <= -6e+35) {
		tmp = t_1;
	} else if (y <= 5.6e-72) {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 21.0) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (x / (y / a)))
	tmp = 0
	if y <= -6e+35:
		tmp = t_1
	elif y <= 5.6e-72:
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
	elif y <= 21.0:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))))
	tmp = 0.0
	if (y <= -6e+35)
		tmp = t_1;
	elseif (y <= 5.6e-72)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	elseif (y <= 21.0)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / 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) - (x / (y / a)));
	tmp = 0.0;
	if (y <= -6e+35)
		tmp = t_1;
	elseif (y <= 5.6e-72)
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	elseif (y <= 21.0)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+35], t$95$1, If[LessEqual[y, 5.6e-72], 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], If[LessEqual[y, 21.0], 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] / i), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999981e35 or 21 < 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 60.1%

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

      1. associate--l+ 60.1%

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

      2. *-commutative 60.1%

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

      3. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   if -5.99999999999999981e35 < y < 5.5999999999999996e-72

   1. Initial program 97.9%

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

   3. Taylor expanded in t around inf 72.5%

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

   if 5.5999999999999996e-72 < y < 21

   1. Initial program 99.5%

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

   3. Taylor expanded in i around inf 50.1%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+35}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-72}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 21:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+23} \lor \neg \left(y \leq 4.3 \cdot 10^{+26}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.5e+23) (not (<= y 4.3e+26)))
   (+ x (- (/ z y) (/ x (/ y a))))
   (/
    (+ 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 <= -2.5e+23) || !(y <= 4.3e+26)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} 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 <= (-2.5d+23)) .or. (.not. (y <= 4.3d+26))) then
        tmp = x + ((z / y) - (x / (y / a)))
    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 <= -2.5e+23) || !(y <= 4.3e+26)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} 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 <= -2.5e+23) or not (y <= 4.3e+26):
		tmp = x + ((z / y) - (x / (y / a)))
	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 <= -2.5e+23) || !(y <= 4.3e+26))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))));
	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 <= -2.5e+23) || ~((y <= 4.3e+26)))
		tmp = x + ((z / y) - (x / (y / a)));
	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, -2.5e+23], N[Not[LessEqual[y, 4.3e+26]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $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 < -2.5e23 or 4.2999999999999998e26 < y

   1. Initial program 7.9%

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

   3. Taylor expanded in y around inf 59.0%

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

      1. associate--l+ 59.0%

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

      2. *-commutative 59.0%

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

      3. associate-/l* 69.0%

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

   5. Simplified 69.0%

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

   if -2.5e23 < y < 4.2999999999999998e26

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 93.5%

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

   4. Taylor expanded in y around 0 89.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+23} \lor \neg \left(y \leq 4.3 \cdot 10^{+26}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+33} \lor \neg \left(y \leq 1.6 \cdot 10^{+16}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.1e+33) (not (<= y 1.6e+16)))
   (+ x (- (/ z y) (/ x (/ y a))))
   (/ (+ 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 <= -2.1e+33) || !(y <= 1.6e+16)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} 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 <= (-2.1d+33)) .or. (.not. (y <= 1.6d+16))) then
        tmp = x + ((z / y) - (x / (y / a)))
    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 <= -2.1e+33) || !(y <= 1.6e+16)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} 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 <= -2.1e+33) or not (y <= 1.6e+16):
		tmp = x + ((z / y) - (x / (y / a)))
	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 <= -2.1e+33) || !(y <= 1.6e+16))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))));
	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 <= -2.1e+33) || ~((y <= 1.6e+16)))
		tmp = x + ((z / y) - (x / (y / a)));
	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, -2.1e+33], N[Not[LessEqual[y, 1.6e+16]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $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 < -2.1000000000000001e33 or 1.6e16 < y

   1. Initial program 4.9%

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

   3. Taylor expanded in y around inf 60.6%

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

      1. associate--l+ 60.6%

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

      2. *-commutative 60.6%

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

      3. associate-/l* 70.9%

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

   5. Simplified 70.9%

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

   if -2.1000000000000001e33 < y < 1.6e16

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 79.3%

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

      1. *-commutative 79.3%

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

   5. Simplified 79.3%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+33} \lor \neg \left(y \leq 1.6 \cdot 10^{+16}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 160:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ x (/ y a))))))
   (if (<= y -1.55e+49)
     t_1
     (if (<= y 6.8e-73)
       (/ t (+ i (* y (+ c (* y b)))))
       (if (<= y 160.0)
         (/ (+ 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) - (x / (y / a)));
	double tmp;
	if (y <= -1.55e+49) {
		tmp = t_1;
	} else if (y <= 6.8e-73) {
		tmp = t / (i + (y * (c + (y * b))));
	} else if (y <= 160.0) {
		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) - (x / (y / a)))
    if (y <= (-1.55d+49)) then
        tmp = t_1
    else if (y <= 6.8d-73) then
        tmp = t / (i + (y * (c + (y * b))))
    else if (y <= 160.0d0) 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) - (x / (y / a)));
	double tmp;
	if (y <= -1.55e+49) {
		tmp = t_1;
	} else if (y <= 6.8e-73) {
		tmp = t / (i + (y * (c + (y * b))));
	} else if (y <= 160.0) {
		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) - (x / (y / a)))
	tmp = 0
	if y <= -1.55e+49:
		tmp = t_1
	elif y <= 6.8e-73:
		tmp = t / (i + (y * (c + (y * b))))
	elif y <= 160.0:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))))
	tmp = 0.0
	if (y <= -1.55e+49)
		tmp = t_1;
	elseif (y <= 6.8e-73)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 160.0)
		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) - (x / (y / a)));
	tmp = 0.0;
	if (y <= -1.55e+49)
		tmp = t_1;
	elseif (y <= 6.8e-73)
		tmp = t / (i + (y * (c + (y * b))));
	elseif (y <= 160.0)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+49], t$95$1, If[LessEqual[y, 6.8e-73], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 160.0], 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 3 regimes

2. if y < -1.54999999999999996e49 or 160 < 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 62.1%

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

      1. associate--l+ 62.1%

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

      2. *-commutative 62.1%

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

      3. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

   if -1.54999999999999996e49 < y < 6.80000000000000042e-73

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0 90.2%

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

   4. Taylor expanded in y around 0 85.1%

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

   5. Taylor expanded in t around inf 68.4%

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

   if 6.80000000000000042e-73 < y < 160

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 87.5%

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

   4. Taylor expanded in i around inf 42.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+49}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 160:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+23} \lor \neg \left(y \leq 1.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.65e+23) (not (<= y 1.5e+18)))
   (+ x (- (/ z y) (/ x (/ y a))))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ 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 <= -1.65e+23) || !(y <= 1.5e+18)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (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 <= (-1.65d+23)) .or. (.not. (y <= 1.5d+18))) then
        tmp = x + ((z / y) - (x / (y / a)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (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 <= -1.65e+23) || !(y <= 1.5e+18)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.65e+23) or not (y <= 1.5e+18):
		tmp = x + ((z / y) - (x / (y / a)))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.65e+23) || !(y <= 1.5e+18))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / 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 <= -1.65e+23) || ~((y <= 1.5e+18)))
		tmp = x + ((z / y) - (x / (y / a)));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.65e+23], N[Not[LessEqual[y, 1.5e+18]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $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 < -1.65000000000000015e23 or 1.5e18 < y

   1. Initial program 8.7%

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

   3. Taylor expanded in y around inf 58.6%

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

      1. associate--l+ 58.6%

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

      2. *-commutative 58.6%

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

      3. associate-/l* 68.5%

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

   5. Simplified 68.5%

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

   if -1.65000000000000015e23 < y < 1.5e18

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 93.5%

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

   4. Taylor expanded in y around 0 89.8%

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

   5. Taylor expanded in z around 0 80.1%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+23} \lor \neg \left(y \leq 1.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+33} \lor \neg \left(y \leq 1.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6.6e+33) (not (<= y 1.5e+18)))
   (+ x (- (/ z y) (/ x (/ y a))))
   (/ 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 <= -6.6e+33) || !(y <= 1.5e+18)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} 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 <= (-6.6d+33)) .or. (.not. (y <= 1.5d+18))) then
        tmp = x + ((z / y) - (x / (y / a)))
    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 <= -6.6e+33) || !(y <= 1.5e+18)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} 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 <= -6.6e+33) or not (y <= 1.5e+18):
		tmp = x + ((z / y) - (x / (y / a)))
	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 <= -6.6e+33) || !(y <= 1.5e+18))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))));
	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 <= -6.6e+33) || ~((y <= 1.5e+18)))
		tmp = x + ((z / y) - (x / (y / a)));
	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, -6.6e+33], N[Not[LessEqual[y, 1.5e+18]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $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 < -6.59999999999999953e33 or 1.5e18 < y

   1. Initial program 4.9%

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

   3. Taylor expanded in y around inf 60.6%

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

      1. associate--l+ 60.6%

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

      2. *-commutative 60.6%

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

      3. associate-/l* 70.9%

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

   5. Simplified 70.9%

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

   if -6.59999999999999953e33 < y < 1.5e18

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 65.1%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+33} \lor \neg \left(y \leq 1.5 \cdot 10^{+18}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{-28} \lor \neg \left(y \leq 2.35 \cdot 10^{+22}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.82e-28) (not (<= y 2.35e+22)))
   (+ x (- (/ z y) (/ x (/ y a))))
   (/ 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 <= -1.82e-28) || !(y <= 2.35e+22)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} 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 <= (-1.82d-28)) .or. (.not. (y <= 2.35d+22))) then
        tmp = x + ((z / y) - (x / (y / a)))
    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 <= -1.82e-28) || !(y <= 2.35e+22)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.82e-28) or not (y <= 2.35e+22):
		tmp = x + ((z / y) - (x / (y / a)))
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.82e-28) || !(y <= 2.35e+22))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))));
	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 <= -1.82e-28) || ~((y <= 2.35e+22)))
		tmp = x + ((z / y) - (x / (y / a)));
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.82e-28], N[Not[LessEqual[y, 2.35e+22]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.82000000000000004e-28 or 2.3500000000000001e22 < y

   1. Initial program 14.1%

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

   3. Taylor expanded in y around inf 55.5%

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

      1. associate--l+ 55.5%

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

      2. *-commutative 55.5%

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

      3. associate-/l* 64.7%

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

   5. Simplified 64.7%

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

   if -1.82000000000000004e-28 < y < 2.3500000000000001e22

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 45.8%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{-28} \lor \neg \left(y \leq 2.35 \cdot 10^{+22}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+47} \lor \neg \left(y \leq 6 \cdot 10^{+17}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7.5e+47) (not (<= y 6e+17)))
   (+ x (- (/ z y) (/ x (/ y a))))
   (/ t (+ 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 <= -7.5e+47) || !(y <= 6e+17)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} else {
		tmp = t / (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 <= (-7.5d+47)) .or. (.not. (y <= 6d+17))) then
        tmp = x + ((z / y) - (x / (y / a)))
    else
        tmp = t / (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 <= -7.5e+47) || !(y <= 6e+17)) {
		tmp = x + ((z / y) - (x / (y / a)));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -7.5e+47) or not (y <= 6e+17):
		tmp = x + ((z / y) - (x / (y / a)))
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -7.5e+47) || !(y <= 6e+17))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(x / Float64(y / a))));
	else
		tmp = Float64(t / 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 <= -7.5e+47) || ~((y <= 6e+17)))
		tmp = x + ((z / y) - (x / (y / a)));
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -7.5e+47], N[Not[LessEqual[y, 6e+17]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999999e47 or 6e17 < y

   1. Initial program 3.3%

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

   3. Taylor expanded in y around inf 62.6%

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

      1. associate--l+ 62.6%

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

      2. *-commutative 62.6%

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

      3. associate-/l* 73.3%

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

   5. Simplified 73.3%

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

   if -7.4999999999999999e47 < y < 6e17

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0 89.8%

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

   4. Taylor expanded in y around 0 84.3%

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

   5. Taylor expanded in t around inf 60.6%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+47} \lor \neg \left(y \leq 6 \cdot 10^{+17}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{x}{\frac{y}{a}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0145:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -0.0145) x (if (<= y 4.4e-20) (/ t i) (- x (/ a (/ y x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -0.0145) {
		tmp = x;
	} else if (y <= 4.4e-20) {
		tmp = t / i;
	} else {
		tmp = x - (a / (y / 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 <= (-0.0145d0)) then
        tmp = x
    else if (y <= 4.4d-20) then
        tmp = t / i
    else
        tmp = x - (a / (y / 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 <= -0.0145) {
		tmp = x;
	} else if (y <= 4.4e-20) {
		tmp = t / i;
	} else {
		tmp = x - (a / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -0.0145:
		tmp = x
	elif y <= 4.4e-20:
		tmp = t / i
	else:
		tmp = x - (a / (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -0.0145)
		tmp = x;
	elseif (y <= 4.4e-20)
		tmp = Float64(t / i);
	else
		tmp = Float64(x - Float64(a / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -0.0145)
		tmp = x;
	elseif (y <= 4.4e-20)
		tmp = t / i;
	else
		tmp = x - (a / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -0.0145], x, If[LessEqual[y, 4.4e-20], N[(t / i), $MachinePrecision], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0145000000000000007

   1. Initial program 14.9%

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

   3. Taylor expanded in y around inf 47.9%

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

   if -0.0145000000000000007 < y < 4.39999999999999982e-20

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 47.7%

      \[\leadsto \color{blue}{\frac{t}{i}} \]

   if 4.39999999999999982e-20 < y

   1. Initial program 18.6%

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

   3. Taylor expanded in x around inf 14.0%

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

   4. Taylor expanded in y around inf 44.9%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot x}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.9%

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

      2. unsub-neg 44.9%

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

      3. associate-/l* 54.3%

         \[\leadsto x - \color{blue}{\frac{a}{\frac{y}{x}}} \]

   6. Simplified 54.3%

      \[\leadsto \color{blue}{x - \frac{a}{\frac{y}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0145:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.03:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -0.03) x (if (<= y 4.4e-20) (/ 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 <= -0.03) {
		tmp = x;
	} else if (y <= 4.4e-20) {
		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 <= (-0.03d0)) then
        tmp = x
    else if (y <= 4.4d-20) 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 <= -0.03) {
		tmp = x;
	} else if (y <= 4.4e-20) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -0.03:
		tmp = x
	elif y <= 4.4e-20:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -0.03)
		tmp = x;
	elseif (y <= 4.4e-20)
		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 <= -0.03)
		tmp = x;
	elseif (y <= 4.4e-20)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -0.03], x, If[LessEqual[y, 4.4e-20], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -0.029999999999999999 or 4.39999999999999982e-20 < y

   1. Initial program 16.6%

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

   3. Taylor expanded in y around inf 50.2%

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

   if -0.029999999999999999 < y < 4.39999999999999982e-20

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 47.7%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.03:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.0% 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 54.8%

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

3. Taylor expanded in y around inf 28.7%

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

4. Final simplification 28.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024029 
(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)))