Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.3% → 84.8%

Time: 25.2s

Alternatives: 16

Speedup: 2.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\frac{y}{x}}\\ t_2 := y \cdot \left(y + a\right) + b\\ t_3 := t_2 \cdot t_2\\ t_4 := y \cdot t_2\\ t_5 := \frac{t}{y \cdot \left(c + t_4\right) + i}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+125}:\\ \;\;\;\;\frac{z}{y} + \left(x - t_1\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+22}:\\ \;\;\;\;t_5 + \left(\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{t_2} + \left(230661.510616 \cdot \frac{1}{t_4} - c \cdot \left(\frac{z}{t_3} + \left(27464.7644705 \cdot \frac{1}{t_2 \cdot t_4} + \left(230661.510616 \cdot \frac{1}{t_2 \cdot \left(t_2 \cdot {y}^{2}\right)} + \frac{y \cdot x}{t_3}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+58}:\\ \;\;\;\;t_5 + y \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right) \cdot \frac{1}{\mathsf{fma}\left(y, c + y \cdot \mathsf{fma}\left(y + a, y, b\right), i\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{z - x \cdot a}{\frac{y \cdot y}{a}}\right) - \left(t_1 + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ a (/ y x)))
        (t_2 (+ (* y (+ y a)) b))
        (t_3 (* t_2 t_2))
        (t_4 (* y t_2))
        (t_5 (/ t (+ (* y (+ c t_4)) i))))
   (if (<= y -1.6e+125)
     (+ (/ z y) (- x t_1))
     (if (<= y -2.9e+22)
       (+
        t_5
        (+
         (/ (+ 27464.7644705 (* y (+ z (* y x)))) t_2)
         (-
          (* 230661.510616 (/ 1.0 t_4))
          (*
           c
           (+
            (/ z t_3)
            (+
             (* 27464.7644705 (/ 1.0 (* t_2 t_4)))
             (+
              (* 230661.510616 (/ 1.0 (* t_2 (* t_2 (pow y 2.0)))))
              (/ (* y x) t_3))))))))
       (if (<= y 6.2e+58)
         (+
          t_5
          (*
           y
           (*
            (fma (fma (fma y x z) y 27464.7644705) y 230661.510616)
            (/ 1.0 (fma y (+ c (* y (fma (+ y a) y b))) i)))))
         (-
          (-
           (+ x (+ (/ z y) (/ 27464.7644705 (* y y))))
           (/ (- z (* x a)) (/ (* y y) a)))
          (+ t_1 (* (/ b y) (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a / (y / x);
	double t_2 = (y * (y + a)) + b;
	double t_3 = t_2 * t_2;
	double t_4 = y * t_2;
	double t_5 = t / ((y * (c + t_4)) + i);
	double tmp;
	if (y <= -1.6e+125) {
		tmp = (z / y) + (x - t_1);
	} else if (y <= -2.9e+22) {
		tmp = t_5 + (((27464.7644705 + (y * (z + (y * x)))) / t_2) + ((230661.510616 * (1.0 / t_4)) - (c * ((z / t_3) + ((27464.7644705 * (1.0 / (t_2 * t_4))) + ((230661.510616 * (1.0 / (t_2 * (t_2 * pow(y, 2.0))))) + ((y * x) / t_3)))))));
	} else if (y <= 6.2e+58) {
		tmp = t_5 + (y * (fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616) * (1.0 / fma(y, (c + (y * fma((y + a), y, b))), i))));
	} else {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a / Float64(y / x))
	t_2 = Float64(Float64(y * Float64(y + a)) + b)
	t_3 = Float64(t_2 * t_2)
	t_4 = Float64(y * t_2)
	t_5 = Float64(t / Float64(Float64(y * Float64(c + t_4)) + i))
	tmp = 0.0
	if (y <= -1.6e+125)
		tmp = Float64(Float64(z / y) + Float64(x - t_1));
	elseif (y <= -2.9e+22)
		tmp = Float64(t_5 + Float64(Float64(Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))) / t_2) + Float64(Float64(230661.510616 * Float64(1.0 / t_4)) - Float64(c * Float64(Float64(z / t_3) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(t_2 * t_4))) + Float64(Float64(230661.510616 * Float64(1.0 / Float64(t_2 * Float64(t_2 * (y ^ 2.0))))) + Float64(Float64(y * x) / t_3))))))));
	elseif (y <= 6.2e+58)
		tmp = Float64(t_5 + Float64(y * Float64(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616) * Float64(1.0 / fma(y, Float64(c + Float64(y * fma(Float64(y + a), y, b))), i)))));
	else
		tmp = Float64(Float64(Float64(x + Float64(Float64(z / y) + Float64(27464.7644705 / Float64(y * y)))) - Float64(Float64(z - Float64(x * a)) / Float64(Float64(y * y) / a))) - Float64(t_1 + Float64(Float64(b / y) * Float64(x / y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(y * t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(t / N[(N[(y * N[(c + t$95$4), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+125], N[(N[(z / y), $MachinePrecision] + N[(x - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.9e+22], N[(t$95$5 + N[(N[(N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / t$95$4), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(z / t$95$3), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(t$95$2 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / N[(t$95$2 * N[(t$95$2 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+58], N[(t$95$5 + N[(y * N[(N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * N[(1.0 / N[(y * N[(c + N[(y * N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + N[(N[(z / y), $MachinePrecision] + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / N[(N[(y * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 + N[(N[(b / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.59999999999999992e125

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-/l* 82.5%

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

   4. Simplified 82.5%

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

   if -1.59999999999999992e125 < y < -2.9e22

   1. Initial program 11.6%

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

   2. Taylor expanded in t around inf 11.6%

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

   3. Taylor expanded in i around 0 41.8%

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

   4. Taylor expanded in c around 0 60.1%

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

   if -2.9e22 < y < 6.1999999999999998e58

   1. Initial program 91.2%

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

   2. Taylor expanded in t around inf 91.2%

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

      1. div-inv 91.2%

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

      2. *-commutative 91.2%

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

      3. *-commutative 91.2%

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

      4. *-commutative 91.2%

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

      5. +-commutative 91.2%

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

      6. +-commutative 91.2%

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

      7. fma-def 91.2%

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

      8. fma-def 91.2%

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

      9. *-commutative 91.2%

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

      10. fma-def 91.2%

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

      11. fma-def 91.2%

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

   4. Applied egg-rr 91.2%

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

      1. associate-*l* 92.5%

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

   6. Simplified 92.5%

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

   if 6.1999999999999998e58 < y

   1. Initial program 0.7%

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

   2. Taylor expanded in y around inf 55.8%

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

      1. associate--r+ 55.8%

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

      2. associate-+r+ 55.8%

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

      3. associate-*r/ 55.8%

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

      4. metadata-eval 55.8%

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

      5. unpow2 55.8%

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

      6. associate-/l* 57.7%

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

      7. unpow2 57.7%

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

      8. associate-/l* 57.9%

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

      9. unpow2 57.9%

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

      10. times-frac 66.8%

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

   4. Simplified 66.8%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+125}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i} + \left(\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{y \cdot \left(y + a\right) + b} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(y \cdot \left(y + a\right) + b\right)} - c \cdot \left(\frac{z}{\left(y \cdot \left(y + a\right) + b\right) \cdot \left(y \cdot \left(y + a\right) + b\right)} + \left(27464.7644705 \cdot \frac{1}{\left(y \cdot \left(y + a\right) + b\right) \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(230661.510616 \cdot \frac{1}{\left(y \cdot \left(y + a\right) + b\right) \cdot \left(\left(y \cdot \left(y + a\right) + b\right) \cdot {y}^{2}\right)} + \frac{y \cdot x}{\left(y \cdot \left(y + a\right) + b\right) \cdot \left(y \cdot \left(y + a\right) + b\right)}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i} + y \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right) \cdot \frac{1}{\mathsf{fma}\left(y, c + y \cdot \mathsf{fma}\left(y + a, y, b\right), i\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{z - x \cdot a}{\frac{y \cdot y}{a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \]

Alternative 2: 84.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\frac{y}{x}}\\ t_2 := 27464.7644705 + y \cdot \left(z + y \cdot x\right)\\ t_3 := y \cdot \left(y + a\right) + b\\ t_4 := t_3 \cdot t_3\\ t_5 := y \cdot t_3\\ t_6 := y \cdot \left(c + t_5\right) + i\\ t_7 := \frac{t}{t_6}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{z}{y} + \left(x - t_1\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+22}:\\ \;\;\;\;t_7 + \left(\frac{t_2}{t_3} + \left(230661.510616 \cdot \frac{1}{t_5} - c \cdot \left(\frac{z}{t_4} + \left(27464.7644705 \cdot \frac{1}{t_3 \cdot t_5} + \left(230661.510616 \cdot \frac{1}{t_3 \cdot \left(t_3 \cdot {y}^{2}\right)} + \frac{y \cdot x}{t_4}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+60}:\\ \;\;\;\;t_7 + \frac{y \cdot \left(230661.510616 + y \cdot t_2\right)}{t_6}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{z - x \cdot a}{\frac{y \cdot y}{a}}\right) - \left(t_1 + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ a (/ y x)))
        (t_2 (+ 27464.7644705 (* y (+ z (* y x)))))
        (t_3 (+ (* y (+ y a)) b))
        (t_4 (* t_3 t_3))
        (t_5 (* y t_3))
        (t_6 (+ (* y (+ c t_5)) i))
        (t_7 (/ t t_6)))
   (if (<= y -6.2e+125)
     (+ (/ z y) (- x t_1))
     (if (<= y -2.9e+22)
       (+
        t_7
        (+
         (/ t_2 t_3)
         (-
          (* 230661.510616 (/ 1.0 t_5))
          (*
           c
           (+
            (/ z t_4)
            (+
             (* 27464.7644705 (/ 1.0 (* t_3 t_5)))
             (+
              (* 230661.510616 (/ 1.0 (* t_3 (* t_3 (pow y 2.0)))))
              (/ (* y x) t_4))))))))
       (if (<= y 1.9e+60)
         (+ t_7 (/ (* y (+ 230661.510616 (* y t_2))) t_6))
         (-
          (-
           (+ x (+ (/ z y) (/ 27464.7644705 (* y y))))
           (/ (- z (* x a)) (/ (* y y) a)))
          (+ t_1 (* (/ b y) (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a / (y / x);
	double t_2 = 27464.7644705 + (y * (z + (y * x)));
	double t_3 = (y * (y + a)) + b;
	double t_4 = t_3 * t_3;
	double t_5 = y * t_3;
	double t_6 = (y * (c + t_5)) + i;
	double t_7 = t / t_6;
	double tmp;
	if (y <= -6.2e+125) {
		tmp = (z / y) + (x - t_1);
	} else if (y <= -2.9e+22) {
		tmp = t_7 + ((t_2 / t_3) + ((230661.510616 * (1.0 / t_5)) - (c * ((z / t_4) + ((27464.7644705 * (1.0 / (t_3 * t_5))) + ((230661.510616 * (1.0 / (t_3 * (t_3 * pow(y, 2.0))))) + ((y * x) / t_4)))))));
	} else if (y <= 1.9e+60) {
		tmp = t_7 + ((y * (230661.510616 + (y * t_2))) / t_6);
	} else {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    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) :: tmp
    t_1 = a / (y / x)
    t_2 = 27464.7644705d0 + (y * (z + (y * x)))
    t_3 = (y * (y + a)) + b
    t_4 = t_3 * t_3
    t_5 = y * t_3
    t_6 = (y * (c + t_5)) + i
    t_7 = t / t_6
    if (y <= (-6.2d+125)) then
        tmp = (z / y) + (x - t_1)
    else if (y <= (-2.9d+22)) then
        tmp = t_7 + ((t_2 / t_3) + ((230661.510616d0 * (1.0d0 / t_5)) - (c * ((z / t_4) + ((27464.7644705d0 * (1.0d0 / (t_3 * t_5))) + ((230661.510616d0 * (1.0d0 / (t_3 * (t_3 * (y ** 2.0d0))))) + ((y * x) / t_4)))))))
    else if (y <= 1.9d+60) then
        tmp = t_7 + ((y * (230661.510616d0 + (y * t_2))) / t_6)
    else
        tmp = ((x + ((z / y) + (27464.7644705d0 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a / (y / x);
	double t_2 = 27464.7644705 + (y * (z + (y * x)));
	double t_3 = (y * (y + a)) + b;
	double t_4 = t_3 * t_3;
	double t_5 = y * t_3;
	double t_6 = (y * (c + t_5)) + i;
	double t_7 = t / t_6;
	double tmp;
	if (y <= -6.2e+125) {
		tmp = (z / y) + (x - t_1);
	} else if (y <= -2.9e+22) {
		tmp = t_7 + ((t_2 / t_3) + ((230661.510616 * (1.0 / t_5)) - (c * ((z / t_4) + ((27464.7644705 * (1.0 / (t_3 * t_5))) + ((230661.510616 * (1.0 / (t_3 * (t_3 * Math.pow(y, 2.0))))) + ((y * x) / t_4)))))));
	} else if (y <= 1.9e+60) {
		tmp = t_7 + ((y * (230661.510616 + (y * t_2))) / t_6);
	} else {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a / (y / x)
	t_2 = 27464.7644705 + (y * (z + (y * x)))
	t_3 = (y * (y + a)) + b
	t_4 = t_3 * t_3
	t_5 = y * t_3
	t_6 = (y * (c + t_5)) + i
	t_7 = t / t_6
	tmp = 0
	if y <= -6.2e+125:
		tmp = (z / y) + (x - t_1)
	elif y <= -2.9e+22:
		tmp = t_7 + ((t_2 / t_3) + ((230661.510616 * (1.0 / t_5)) - (c * ((z / t_4) + ((27464.7644705 * (1.0 / (t_3 * t_5))) + ((230661.510616 * (1.0 / (t_3 * (t_3 * math.pow(y, 2.0))))) + ((y * x) / t_4)))))))
	elif y <= 1.9e+60:
		tmp = t_7 + ((y * (230661.510616 + (y * t_2))) / t_6)
	else:
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a / Float64(y / x))
	t_2 = Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))
	t_3 = Float64(Float64(y * Float64(y + a)) + b)
	t_4 = Float64(t_3 * t_3)
	t_5 = Float64(y * t_3)
	t_6 = Float64(Float64(y * Float64(c + t_5)) + i)
	t_7 = Float64(t / t_6)
	tmp = 0.0
	if (y <= -6.2e+125)
		tmp = Float64(Float64(z / y) + Float64(x - t_1));
	elseif (y <= -2.9e+22)
		tmp = Float64(t_7 + Float64(Float64(t_2 / t_3) + Float64(Float64(230661.510616 * Float64(1.0 / t_5)) - Float64(c * Float64(Float64(z / t_4) + Float64(Float64(27464.7644705 * Float64(1.0 / Float64(t_3 * t_5))) + Float64(Float64(230661.510616 * Float64(1.0 / Float64(t_3 * Float64(t_3 * (y ^ 2.0))))) + Float64(Float64(y * x) / t_4))))))));
	elseif (y <= 1.9e+60)
		tmp = Float64(t_7 + Float64(Float64(y * Float64(230661.510616 + Float64(y * t_2))) / t_6));
	else
		tmp = Float64(Float64(Float64(x + Float64(Float64(z / y) + Float64(27464.7644705 / Float64(y * y)))) - Float64(Float64(z - Float64(x * a)) / Float64(Float64(y * y) / a))) - Float64(t_1 + Float64(Float64(b / y) * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a / (y / x);
	t_2 = 27464.7644705 + (y * (z + (y * x)));
	t_3 = (y * (y + a)) + b;
	t_4 = t_3 * t_3;
	t_5 = y * t_3;
	t_6 = (y * (c + t_5)) + i;
	t_7 = t / t_6;
	tmp = 0.0;
	if (y <= -6.2e+125)
		tmp = (z / y) + (x - t_1);
	elseif (y <= -2.9e+22)
		tmp = t_7 + ((t_2 / t_3) + ((230661.510616 * (1.0 / t_5)) - (c * ((z / t_4) + ((27464.7644705 * (1.0 / (t_3 * t_5))) + ((230661.510616 * (1.0 / (t_3 * (t_3 * (y ^ 2.0))))) + ((y * x) / t_4)))))));
	elseif (y <= 1.9e+60)
		tmp = t_7 + ((y * (230661.510616 + (y * t_2))) / t_6);
	else
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(y * t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y * N[(c + t$95$5), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$7 = N[(t / t$95$6), $MachinePrecision]}, If[LessEqual[y, -6.2e+125], N[(N[(z / y), $MachinePrecision] + N[(x - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.9e+22], N[(t$95$7 + N[(N[(t$95$2 / t$95$3), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / t$95$5), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(z / t$95$4), $MachinePrecision] + N[(N[(27464.7644705 * N[(1.0 / N[(t$95$3 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / N[(t$95$3 * N[(t$95$3 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+60], N[(t$95$7 + N[(N[(y * N[(230661.510616 + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + N[(N[(z / y), $MachinePrecision] + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / N[(N[(y * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 + N[(N[(b / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.2e125

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-/l* 82.5%

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

   4. Simplified 82.5%

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

   if -6.2e125 < y < -2.9e22

   1. Initial program 11.6%

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

   2. Taylor expanded in t around inf 11.6%

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

   3. Taylor expanded in i around 0 41.8%

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

   4. Taylor expanded in c around 0 60.1%

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

   if -2.9e22 < y < 1.90000000000000005e60

   1. Initial program 91.2%

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

   2. Taylor expanded in t around inf 91.2%

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

   if 1.90000000000000005e60 < y

   1. Initial program 0.7%

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

   2. Taylor expanded in y around inf 55.8%

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

      1. associate--r+ 55.8%

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

      2. associate-+r+ 55.8%

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

      3. associate-*r/ 55.8%

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

      4. metadata-eval 55.8%

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

      5. unpow2 55.8%

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

      6. associate-/l* 57.7%

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

      7. unpow2 57.7%

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

      8. associate-/l* 57.9%

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

      9. unpow2 57.9%

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

      10. times-frac 66.8%

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

   4. Simplified 66.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i} + \left(\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{y \cdot \left(y + a\right) + b} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(y \cdot \left(y + a\right) + b\right)} - c \cdot \left(\frac{z}{\left(y \cdot \left(y + a\right) + b\right) \cdot \left(y \cdot \left(y + a\right) + b\right)} + \left(27464.7644705 \cdot \frac{1}{\left(y \cdot \left(y + a\right) + b\right) \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(230661.510616 \cdot \frac{1}{\left(y \cdot \left(y + a\right) + b\right) \cdot \left(\left(y \cdot \left(y + a\right) + b\right) \cdot {y}^{2}\right)} + \frac{y \cdot x}{\left(y \cdot \left(y + a\right) + b\right) \cdot \left(y \cdot \left(y + a\right) + b\right)}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{z - x \cdot a}{\frac{y \cdot y}{a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \]

Alternative 3: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\frac{y}{x}}\\ t_2 := y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+53}:\\ \;\;\;\;\frac{z}{y} + \left(x - t_1\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{t_2} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{z - x \cdot a}{\frac{y \cdot y}{a}}\right) - \left(t_1 + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ a (/ y x))) (t_2 (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i)))
   (if (<= y -5.2e+53)
     (+ (/ z y) (- x t_1))
     (if (<= y 1.5e+60)
       (+
        (/ t t_2)
        (/
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
         t_2))
       (-
        (-
         (+ x (+ (/ z y) (/ 27464.7644705 (* y y))))
         (/ (- z (* x a)) (/ (* y y) a)))
        (+ t_1 (* (/ b y) (/ x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a / (y / x);
	double t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i;
	double tmp;
	if (y <= -5.2e+53) {
		tmp = (z / y) + (x - t_1);
	} else if (y <= 1.5e+60) {
		tmp = (t / t_2) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_2);
	} else {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a / (y / x)
    t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i
    if (y <= (-5.2d+53)) then
        tmp = (z / y) + (x - t_1)
    else if (y <= 1.5d+60) then
        tmp = (t / t_2) + ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))) / t_2)
    else
        tmp = ((x + ((z / y) + (27464.7644705d0 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a / (y / x);
	double t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i;
	double tmp;
	if (y <= -5.2e+53) {
		tmp = (z / y) + (x - t_1);
	} else if (y <= 1.5e+60) {
		tmp = (t / t_2) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_2);
	} else {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a / (y / x)
	t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i
	tmp = 0
	if y <= -5.2e+53:
		tmp = (z / y) + (x - t_1)
	elif y <= 1.5e+60:
		tmp = (t / t_2) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_2)
	else:
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a / Float64(y / x))
	t_2 = Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i)
	tmp = 0.0
	if (y <= -5.2e+53)
		tmp = Float64(Float64(z / y) + Float64(x - t_1));
	elseif (y <= 1.5e+60)
		tmp = Float64(Float64(t / t_2) + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_2));
	else
		tmp = Float64(Float64(Float64(x + Float64(Float64(z / y) + Float64(27464.7644705 / Float64(y * y)))) - Float64(Float64(z - Float64(x * a)) / Float64(Float64(y * y) / a))) - Float64(t_1 + Float64(Float64(b / y) * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a / (y / x);
	t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i;
	tmp = 0.0;
	if (y <= -5.2e+53)
		tmp = (z / y) + (x - t_1);
	elseif (y <= 1.5e+60)
		tmp = (t / t_2) + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_2);
	else
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -5.2e+53], N[(N[(z / y), $MachinePrecision] + N[(x - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+60], N[(N[(t / t$95$2), $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$2), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + N[(N[(z / y), $MachinePrecision] + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / N[(N[(y * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 + N[(N[(b / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.19999999999999996e53

   1. Initial program 0.6%

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

   2. Taylor expanded in y around inf 52.1%

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

      1. associate--l+ 52.1%

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

      2. associate-/l* 61.8%

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

   4. Simplified 61.8%

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

   if -5.19999999999999996e53 < y < 1.4999999999999999e60

   1. Initial program 87.4%

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

   2. Taylor expanded in t around inf 87.4%

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

   if 1.4999999999999999e60 < y

   1. Initial program 0.7%

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

   2. Taylor expanded in y around inf 55.8%

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

      1. associate--r+ 55.8%

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

      2. associate-+r+ 55.8%

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

      3. associate-*r/ 55.8%

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

      4. metadata-eval 55.8%

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

      5. unpow2 55.8%

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

      6. associate-/l* 57.7%

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

      7. unpow2 57.7%

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

      8. associate-/l* 57.9%

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

      9. unpow2 57.9%

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

      10. times-frac 66.8%

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

   4. Simplified 66.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+53}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{z - x \cdot a}{\frac{y \cdot y}{a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \]

Alternative 4: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{z}{y} + \left(x - t_1\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+60}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{z - x \cdot a}{\frac{y \cdot y}{a}}\right) - \left(t_1 + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ a (/ y x))))
   (if (<= y -6.2e+54)
     (+ (/ z y) (- x t_1))
     (if (<= y 1.7e+60)
       (/
        (+
         t
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
        (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))
       (-
        (-
         (+ x (+ (/ z y) (/ 27464.7644705 (* y y))))
         (/ (- z (* x a)) (/ (* y y) a)))
        (+ t_1 (* (/ b y) (/ x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a / (y / x);
	double tmp;
	if (y <= -6.2e+54) {
		tmp = (z / y) + (x - t_1);
	} else if (y <= 1.7e+60) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (y / x)
    if (y <= (-6.2d+54)) then
        tmp = (z / y) + (x - t_1)
    else if (y <= 1.7d+60) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
    else
        tmp = ((x + ((z / y) + (27464.7644705d0 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a / (y / x);
	double tmp;
	if (y <= -6.2e+54) {
		tmp = (z / y) + (x - t_1);
	} else if (y <= 1.7e+60) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a / (y / x)
	tmp = 0
	if y <= -6.2e+54:
		tmp = (z / y) + (x - t_1)
	elif y <= 1.7e+60:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	else:
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a / Float64(y / x))
	tmp = 0.0
	if (y <= -6.2e+54)
		tmp = Float64(Float64(z / y) + Float64(x - t_1));
	elseif (y <= 1.7e+60)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	else
		tmp = Float64(Float64(Float64(x + Float64(Float64(z / y) + Float64(27464.7644705 / Float64(y * y)))) - Float64(Float64(z - Float64(x * a)) / Float64(Float64(y * y) / a))) - Float64(t_1 + Float64(Float64(b / y) * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a / (y / x);
	tmp = 0.0;
	if (y <= -6.2e+54)
		tmp = (z / y) + (x - t_1);
	elseif (y <= 1.7e+60)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	else
		tmp = ((x + ((z / y) + (27464.7644705 / (y * y)))) - ((z - (x * a)) / ((y * y) / a))) - (t_1 + ((b / y) * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+54], N[(N[(z / y), $MachinePrecision] + N[(x - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+60], 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[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + N[(N[(z / y), $MachinePrecision] + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / N[(N[(y * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 + N[(N[(b / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1999999999999999e54

   1. Initial program 0.6%

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

   2. Taylor expanded in y around inf 52.1%

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

      1. associate--l+ 52.1%

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

      2. associate-/l* 61.8%

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

   4. Simplified 61.8%

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

   if -6.1999999999999999e54 < y < 1.7e60

   1. Initial program 87.4%

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

   if 1.7e60 < y

   1. Initial program 0.7%

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

   2. Taylor expanded in y around inf 55.8%

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

      1. associate--r+ 55.8%

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

      2. associate-+r+ 55.8%

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

      3. associate-*r/ 55.8%

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

      4. metadata-eval 55.8%

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

      5. unpow2 55.8%

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

      6. associate-/l* 57.7%

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

      7. unpow2 57.7%

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

      8. associate-/l* 57.9%

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

      9. unpow2 57.9%

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

      10. times-frac 66.8%

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

   4. Simplified 66.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+60}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + \left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right)\right) - \frac{z - x \cdot a}{\frac{y \cdot y}{a}}\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \]

Alternative 5: 84.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+55} \lor \neg \left(y \leq 6 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.7e+55) (not (<= y 6e+59)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
    (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.7e+55) || !(y <= 6e+59)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + 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 <= (-1.7d+55)) .or. (.not. (y <= 6d+59))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + 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 <= -1.7e+55) || !(y <= 6e+59)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.7e+55) or not (y <= 6e+59):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.7e+55) || !(y <= 6e+59))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.7e+55) || ~((y <= 6e+59)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.7e+55], N[Not[LessEqual[y, 6e+59]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $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[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6999999999999999e55 or 6.0000000000000001e59 < y

   1. Initial program 0.6%

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

   2. Taylor expanded in y around inf 59.2%

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

      1. associate--l+ 59.2%

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

      2. associate-/l* 64.1%

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

   4. Simplified 64.1%

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

   if -1.6999999999999999e55 < y < 6.0000000000000001e59

   1. Initial program 87.4%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+55} \lor \neg \left(y \leq 6 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \end{array} \]

Alternative 6: 81.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+54} \lor \neg \left(y \leq 1.3 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.4e+54) (not (<= y 1.3e+61)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.4e+54) || !(y <= 1.3e+61)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + 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 <= (-2.4d+54)) .or. (.not. (y <= 1.3d+61))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + 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 <= -2.4e+54) || !(y <= 1.3e+61)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.4e+54) or not (y <= 1.3e+61):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.4e+54) || !(y <= 1.3e+61))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.4e+54) || ~((y <= 1.3e+61)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.4e+54], N[Not[LessEqual[y, 1.3e+61]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $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[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999998e54 or 1.29999999999999986e61 < y

   1. Initial program 0.6%

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

   2. Taylor expanded in y around inf 59.8%

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

      1. associate--l+ 59.8%

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

      2. associate-/l* 64.8%

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

   4. Simplified 64.8%

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

   if -2.39999999999999998e54 < y < 1.29999999999999986e61

   1. Initial program 86.9%

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

   2. Taylor expanded in x around 0 83.2%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+54} \lor \neg \left(y \leq 1.3 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \end{array} \]

Alternative 7: 80.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+54} \lor \neg \left(y \leq 2.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.5e+54) (not (<= y 2.4e+60)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* z (* y y)))))
    (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.5e+54) || !(y <= 2.4e+60)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + 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 <= (-3.5d+54)) .or. (.not. (y <= 2.4d+60))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + 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 <= -3.5e+54) || !(y <= 2.4e+60)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.5e+54) or not (y <= 2.4e+60):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.5e+54) || !(y <= 2.4e+60))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.5e+54) || ~((y <= 2.4e+60)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.5e+54], N[Not[LessEqual[y, 2.4e+60]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5000000000000001e54 or 2.4e60 < y

   1. Initial program 0.6%

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

   2. Taylor expanded in y around inf 59.8%

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

      1. associate--l+ 59.8%

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

      2. associate-/l* 64.8%

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

   4. Simplified 64.8%

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

   if -3.5000000000000001e54 < y < 2.4e60

   1. Initial program 86.9%

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

   2. Taylor expanded in z around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. unpow2 81.5%

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

   4. Simplified 81.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+54} \lor \neg \left(y \leq 2.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \end{array} \]

Alternative 8: 77.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+31} \lor \neg \left(y \leq 1.25 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7.2e+31) (not (<= y 1.25e+61)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7.2e+31) || !(y <= 1.25e+61)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + 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 <= (-7.2d+31)) .or. (.not. (y <= 1.25d+61))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + 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 <= -7.2e+31) || !(y <= 1.25e+61)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -7.2e+31) or not (y <= 1.25e+61):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -7.2e+31) || !(y <= 1.25e+61))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -7.2e+31) || ~((y <= 1.25e+61)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -7.2e+31], N[Not[LessEqual[y, 1.25e+61]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.19999999999999992e31 or 1.25000000000000004e61 < y

   1. Initial program 3.5%

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

   2. Taylor expanded in y around inf 56.9%

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

      1. associate--l+ 56.9%

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

      2. associate-/l* 61.5%

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

   4. Simplified 61.5%

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

   if -7.19999999999999992e31 < y < 1.25000000000000004e61

   1. Initial program 88.8%

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

   2. Taylor expanded in y around 0 79.5%

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

      1. *-commutative 75.7%

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

   4. Simplified 79.5%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+31} \lor \neg \left(y \leq 1.25 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \end{array} \]

Alternative 9: 76.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+30} \lor \neg \left(y \leq 2.9 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7.5e+30) (not (<= y 2.9e+60)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))))

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+30) || !(y <= 2.9e+60)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + 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 <= (-7.5d+30)) .or. (.not. (y <= 2.9d+60))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / ((y * (c + (y * ((y * (y + a)) + b)))) + 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 <= -7.5e+30) || !(y <= 2.9e+60)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -7.5e+30) or not (y <= 2.9e+60):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -7.5e+30) || !(y <= 2.9e+60))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -7.5e+30) || ~((y <= 2.9e+60)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -7.5e+30], N[Not[LessEqual[y, 2.9e+60]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999973e30 or 2.9e60 < y

   1. Initial program 3.5%

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

   2. Taylor expanded in y around inf 56.9%

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

      1. associate--l+ 56.9%

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

      2. associate-/l* 61.5%

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

   4. Simplified 61.5%

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

   if -7.49999999999999973e30 < y < 2.9e60

   1. Initial program 88.8%

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

   2. Taylor expanded in y around 0 78.4%

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

      1. *-commutative 75.0%

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

   4. Simplified 78.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+30} \lor \neg \left(y \leq 2.9 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \end{array} \]

Alternative 10: 74.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-9} \lor \neg \left(y \leq 2.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.7e-9) (not (<= y 2.4e+60)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/
    (+ 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 <= -2.7e-9) || !(y <= 2.4e+60)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} 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 <= (-2.7d-9)) .or. (.not. (y <= 2.4d+60))) then
        tmp = (z / y) + (x - (a / (y / x)))
    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 <= -2.7e-9) || !(y <= 2.4e+60)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} 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 <= -2.7e-9) or not (y <= 2.4e+60):
		tmp = (z / y) + (x - (a / (y / x)))
	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 <= -2.7e-9) || !(y <= 2.4e+60))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	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 <= -2.7e-9) || ~((y <= 2.4e+60)))
		tmp = (z / y) + (x - (a / (y / x)));
	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, -2.7e-9], N[Not[LessEqual[y, 2.4e+60]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $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 < -2.7000000000000002e-9 or 2.4e60 < y

   1. Initial program 7.7%

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

   2. Taylor expanded in y around inf 53.1%

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

      1. associate--l+ 53.1%

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

      2. associate-/l* 57.4%

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

   4. Simplified 57.4%

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

   if -2.7000000000000002e-9 < y < 2.4e60

   1. Initial program 91.5%

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

   2. Taylor expanded in y around 0 84.6%

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

   3. Taylor expanded in y around 0 80.9%

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

      1. *-commutative 80.9%

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

   5. Simplified 80.9%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-9} \lor \neg \left(y \leq 2.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 11: 74.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-9} \lor \neg \left(y \leq 2.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.7e-9) (not (<= y 2.4e+60)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ 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 <= -2.7e-9) || !(y <= 2.4e+60)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (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 <= (-2.7d-9)) .or. (.not. (y <= 2.4d+60))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / (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 <= -2.7e-9) || !(y <= 2.4e+60)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.7e-9) or not (y <= 2.4e+60):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.7e-9) || !(y <= 2.4e+60))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / 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 <= -2.7e-9) || ~((y <= 2.4e+60)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.7e-9], N[Not[LessEqual[y, 2.4e+60]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $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 < -2.7000000000000002e-9 or 2.4e60 < y

   1. Initial program 7.7%

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

   2. Taylor expanded in y around inf 53.1%

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

      1. associate--l+ 53.1%

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

      2. associate-/l* 57.4%

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

   4. Simplified 57.4%

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

   if -2.7000000000000002e-9 < y < 2.4e60

   1. Initial program 91.5%

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

   2. Taylor expanded in y around 0 84.6%

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

   3. Taylor expanded in y around 0 80.0%

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

      1. *-commutative 80.0%

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

   5. Simplified 80.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-9} \lor \neg \left(y \leq 2.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 12: 61.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-9} \lor \neg \left(y \leq 1.4 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.7e-9) (not (<= y 1.4e+15)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (+ (* 230661.510616 (/ y i)) (/ 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 <= -2.7e-9) || !(y <= 1.4e+15)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (230661.510616 * (y / i)) + (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 <= (-2.7d-9)) .or. (.not. (y <= 1.4d+15))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (230661.510616d0 * (y / i)) + (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 <= -2.7e-9) || !(y <= 1.4e+15)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (230661.510616 * (y / i)) + (t / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.7e-9) or not (y <= 1.4e+15):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (230661.510616 * (y / i)) + (t / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.7e-9) || !(y <= 1.4e+15))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + 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 <= -2.7e-9) || ~((y <= 1.4e+15)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (230661.510616 * (y / i)) + (t / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.7e-9], N[Not[LessEqual[y, 1.4e+15]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000002e-9 or 1.4e15 < y

   1. Initial program 10.8%

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

   2. Taylor expanded in y around inf 47.7%

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

      1. associate--l+ 47.7%

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

      2. associate-/l* 51.4%

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

   4. Simplified 51.4%

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

   if -2.7000000000000002e-9 < y < 1.4e15

   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. Taylor expanded in c around 0 78.8%

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

   3. Taylor expanded in y around 0 63.2%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-9} \lor \neg \left(y \leq 1.4 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \end{array} \]

Alternative 13: 67.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-9} \lor \neg \left(y \leq 2.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.7e-9) (not (<= y 2.4e+60)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ 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 <= -2.7e-9) || !(y <= 2.4e+60)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} 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 <= (-2.7d-9)) .or. (.not. (y <= 2.4d+60))) then
        tmp = (z / y) + (x - (a / (y / x)))
    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 <= -2.7e-9) || !(y <= 2.4e+60)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} 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 <= -2.7e-9) or not (y <= 2.4e+60):
		tmp = (z / y) + (x - (a / (y / x)))
	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 <= -2.7e-9) || !(y <= 2.4e+60))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	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 <= -2.7e-9) || ~((y <= 2.4e+60)))
		tmp = (z / y) + (x - (a / (y / x)));
	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, -2.7e-9], N[Not[LessEqual[y, 2.4e+60]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $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 < -2.7000000000000002e-9 or 2.4e60 < y

   1. Initial program 7.7%

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

   2. Taylor expanded in y around inf 53.1%

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

      1. associate--l+ 53.1%

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

      2. associate-/l* 57.4%

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

   4. Simplified 57.4%

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

   if -2.7000000000000002e-9 < y < 2.4e60

   1. Initial program 91.5%

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

   2. Taylor expanded in y around 0 84.6%

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

   3. Taylor expanded in t around inf 65.3%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-9} \lor \neg \left(y \leq 2.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 14: 54.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+58}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7.2e-10)
   x
   (if (<= y 4.2e+58) (+ (* 230661.510616 (/ y i)) (/ t i)) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7.2e-10) {
		tmp = x;
	} else if (y <= 4.2e+58) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-7.2d-10)) then
        tmp = x
    else if (y <= 4.2d+58) then
        tmp = (230661.510616d0 * (y / i)) + (t / i)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7.2e-10) {
		tmp = x;
	} else if (y <= 4.2e+58) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7.2e-10:
		tmp = x
	elif y <= 4.2e+58:
		tmp = (230661.510616 * (y / i)) + (t / i)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7.2e-10)
		tmp = x;
	elseif (y <= 4.2e+58)
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + Float64(t / i));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -7.2e-10)
		tmp = x;
	elseif (y <= 4.2e+58)
		tmp = (230661.510616 * (y / i)) + (t / i);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7.2e-10], x, If[LessEqual[y, 4.2e+58], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e-10 or 4.20000000000000024e58 < y

   1. Initial program 7.6%

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

   2. Taylor expanded in y around inf 37.8%

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

   if -7.2e-10 < y < 4.20000000000000024e58

   1. Initial program 92.1%

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

   2. Taylor expanded in c around 0 72.8%

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

   3. Taylor expanded in y around 0 56.8%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+58}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 50.9% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.1e-9) x (if (<= y 4.5e+58) (/ 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 <= -1.1e-9) {
		tmp = x;
	} else if (y <= 4.5e+58) {
		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 <= (-1.1d-9)) then
        tmp = x
    else if (y <= 4.5d+58) 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 <= -1.1e-9) {
		tmp = x;
	} else if (y <= 4.5e+58) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.1e-9:
		tmp = x
	elif y <= 4.5e+58:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.1e-9)
		tmp = x;
	elseif (y <= 4.5e+58)
		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 <= -1.1e-9)
		tmp = x;
	elseif (y <= 4.5e+58)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.1e-9], x, If[LessEqual[y, 4.5e+58], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0999999999999999e-9 or 4.4999999999999998e58 < y

   1. Initial program 7.6%

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

   2. Taylor expanded in y around inf 37.8%

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

   if -1.0999999999999999e-9 < y < 4.4999999999999998e58

   1. Initial program 92.1%

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

   2. Taylor expanded in y around 0 52.6%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 25.7% 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 53.2%

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

2. Taylor expanded in y around inf 19.1%

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

3. Final simplification 19.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023238 
(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)))