Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.5% → 86.3%

Time: 25.1s

Alternatives: 20

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: 56.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \frac{t}{t_1}\\ t_3 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ t_4 := \left(x \cdot x\right) \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+137}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+27}:\\ \;\;\;\;t_2 + \frac{y}{\frac{y}{x} + \left(\left(\frac{a}{x} + \frac{b}{y \cdot x}\right) - \frac{27464.7644705}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+54}:\\ \;\;\;\;t_2 + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+116}:\\ \;\;\;\;t_2 + \frac{y}{\frac{y}{x} + \left(\left(\frac{\frac{c}{y \cdot y}}{x} + \left(\frac{a}{x} + \frac{\frac{b}{x} - \frac{27464.7644705}{x \cdot x}}{y}\right)\right) - \left(\frac{a \cdot 27464.7644705}{t_4} + \frac{230661.510616}{t_4}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2 (/ t t_1))
        (t_3 (+ (/ z y) (- x (/ a (/ y x)))))
        (t_4 (* (* x x) (* y y))))
   (if (<= y -6.5e+137)
     t_3
     (if (<= y -2.7e+27)
       (+
        t_2
        (/
         y
         (+
          (/ y x)
          (- (+ (/ a x) (/ b (* y x))) (/ 27464.7644705 (* y (* x x)))))))
       (if (<= y 4.4e+54)
         (+
          t_2
          (/
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
           t_1))
         (if (<= y 7e+116)
           (+
            t_2
            (/
             y
             (+
              (/ y x)
              (-
               (+
                (/ (/ c (* y y)) x)
                (+ (/ a x) (/ (- (/ b x) (/ 27464.7644705 (* x x))) y)))
               (+ (/ (* a 27464.7644705) t_4) (/ 230661.510616 t_4))))))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = t / t_1;
	double t_3 = (z / y) + (x - (a / (y / x)));
	double t_4 = (x * x) * (y * y);
	double tmp;
	if (y <= -6.5e+137) {
		tmp = t_3;
	} else if (y <= -2.7e+27) {
		tmp = t_2 + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))));
	} else if (y <= 4.4e+54) {
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else if (y <= 7e+116) {
		tmp = t_2 + (y / ((y / x) + ((((c / (y * y)) / x) + ((a / x) + (((b / x) - (27464.7644705 / (x * x))) / y))) - (((a * 27464.7644705) / t_4) + (230661.510616 / t_4)))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
    t_2 = t / t_1
    t_3 = (z / y) + (x - (a / (y / x)))
    t_4 = (x * x) * (y * y)
    if (y <= (-6.5d+137)) then
        tmp = t_3
    else if (y <= (-2.7d+27)) then
        tmp = t_2 + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705d0 / (y * (x * x))))))
    else if (y <= 4.4d+54) then
        tmp = t_2 + ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))) / t_1)
    else if (y <= 7d+116) then
        tmp = t_2 + (y / ((y / x) + ((((c / (y * y)) / x) + ((a / x) + (((b / x) - (27464.7644705d0 / (x * x))) / y))) - (((a * 27464.7644705d0) / t_4) + (230661.510616d0 / t_4)))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = t / t_1;
	double t_3 = (z / y) + (x - (a / (y / x)));
	double t_4 = (x * x) * (y * y);
	double tmp;
	if (y <= -6.5e+137) {
		tmp = t_3;
	} else if (y <= -2.7e+27) {
		tmp = t_2 + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))));
	} else if (y <= 4.4e+54) {
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else if (y <= 7e+116) {
		tmp = t_2 + (y / ((y / x) + ((((c / (y * y)) / x) + ((a / x) + (((b / x) - (27464.7644705 / (x * x))) / y))) - (((a * 27464.7644705) / t_4) + (230661.510616 / t_4)))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
	t_2 = t / t_1
	t_3 = (z / y) + (x - (a / (y / x)))
	t_4 = (x * x) * (y * y)
	tmp = 0
	if y <= -6.5e+137:
		tmp = t_3
	elif y <= -2.7e+27:
		tmp = t_2 + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))))
	elif y <= 4.4e+54:
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1)
	elif y <= 7e+116:
		tmp = t_2 + (y / ((y / x) + ((((c / (y * y)) / x) + ((a / x) + (((b / x) - (27464.7644705 / (x * x))) / y))) - (((a * 27464.7644705) / t_4) + (230661.510616 / t_4)))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	t_2 = Float64(t / t_1)
	t_3 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	t_4 = Float64(Float64(x * x) * Float64(y * y))
	tmp = 0.0
	if (y <= -6.5e+137)
		tmp = t_3;
	elseif (y <= -2.7e+27)
		tmp = Float64(t_2 + Float64(y / Float64(Float64(y / x) + Float64(Float64(Float64(a / x) + Float64(b / Float64(y * x))) - Float64(27464.7644705 / Float64(y * Float64(x * x)))))));
	elseif (y <= 4.4e+54)
		tmp = Float64(t_2 + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_1));
	elseif (y <= 7e+116)
		tmp = Float64(t_2 + Float64(y / Float64(Float64(y / x) + Float64(Float64(Float64(Float64(c / Float64(y * y)) / x) + Float64(Float64(a / x) + Float64(Float64(Float64(b / x) - Float64(27464.7644705 / Float64(x * x))) / y))) - Float64(Float64(Float64(a * 27464.7644705) / t_4) + Float64(230661.510616 / t_4))))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	t_2 = t / t_1;
	t_3 = (z / y) + (x - (a / (y / x)));
	t_4 = (x * x) * (y * y);
	tmp = 0.0;
	if (y <= -6.5e+137)
		tmp = t_3;
	elseif (y <= -2.7e+27)
		tmp = t_2 + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))));
	elseif (y <= 4.4e+54)
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	elseif (y <= 7e+116)
		tmp = t_2 + (y / ((y / x) + ((((c / (y * y)) / x) + ((a / x) + (((b / x) - (27464.7644705 / (x * x))) / y))) - (((a * 27464.7644705) / t_4) + (230661.510616 / t_4)))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * x), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+137], t$95$3, If[LessEqual[y, -2.7e+27], N[(t$95$2 + N[(y / N[(N[(y / x), $MachinePrecision] + N[(N[(N[(a / x), $MachinePrecision] + N[(b / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27464.7644705 / N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+54], N[(t$95$2 + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+116], N[(t$95$2 + N[(y / N[(N[(y / x), $MachinePrecision] + N[(N[(N[(N[(c / N[(y * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(N[(a / x), $MachinePrecision] + N[(N[(N[(b / x), $MachinePrecision] - N[(27464.7644705 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a * 27464.7644705), $MachinePrecision] / t$95$4), $MachinePrecision] + N[(230661.510616 / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.5000000000000002e137 or 6.99999999999999993e116 < y

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 78.6%

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

      1. associate--l+ 78.6%

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

      2. associate-/l* 81.6%

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

   4. Simplified 81.6%

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

   if -6.5000000000000002e137 < y < -2.6999999999999997e27

   1. Initial program 10.3%

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

   2. Taylor expanded in t around inf 10.3%

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

   3. Taylor expanded in z around 0 10.6%

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

      1. *-commutative 10.6%

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

      2. associate-/l* 15.9%

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

      3. fma-def 15.9%

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

      4. +-commutative 15.9%

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

      5. *-commutative 15.9%

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

      6. fma-udef 15.9%

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

      7. fma-def 15.9%

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

      8. *-commutative 15.9%

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

      9. unpow2 15.9%

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

   5. Simplified 15.9%

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

   6. Taylor expanded in y around inf 64.6%

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

      1. associate--l+ 64.6%

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

      2. +-commutative 64.6%

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

      3. associate-*r/ 64.6%

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

      4. metadata-eval 64.6%

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

      5. unpow2 64.6%

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

   8. Simplified 64.6%

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

   if -2.6999999999999997e27 < y < 4.3999999999999998e54

   1. Initial program 96.5%

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

   2. Taylor expanded in t around inf 96.5%

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

   if 4.3999999999999998e54 < y < 6.99999999999999993e116

   1. Initial program 1.5%

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

   2. Taylor expanded in t around inf 1.5%

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

   3. Taylor expanded in z around 0 1.7%

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

      1. *-commutative 1.7%

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

      2. associate-/l* 1.9%

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

      3. fma-def 1.9%

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

      4. +-commutative 1.9%

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

      5. *-commutative 1.9%

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

      6. fma-udef 1.9%

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

      7. fma-def 1.9%

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

      8. *-commutative 1.9%

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

      9. unpow2 1.9%

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

   5. Simplified 1.9%

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

   6. Taylor expanded in y around -inf 71.9%

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

      1. associate--l+ 71.9%

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

   8. Simplified 78.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+137}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{y}{x} + \left(\left(\frac{a}{x} + \frac{b}{y \cdot x}\right) - \frac{27464.7644705}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+116}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{y}{x} + \left(\left(\frac{\frac{c}{y \cdot y}}{x} + \left(\frac{a}{x} + \frac{\frac{b}{x} - \frac{27464.7644705}{x \cdot x}}{y}\right)\right) - \left(\frac{a \cdot 27464.7644705}{\left(x \cdot x\right) \cdot \left(y \cdot y\right)} + \frac{230661.510616}{\left(x \cdot x\right) \cdot \left(y \cdot y\right)}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 2: 84.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. associate-/l* 68.0%

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

   4. Simplified 68.0%

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

4. Final simplification 83.2%

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

Alternative 3: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \frac{t}{t_1}\\ t_3 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+138}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;t_2 + \frac{y}{\frac{y}{x} + \left(\left(\frac{a}{x} + \frac{b}{y \cdot x}\right) - \frac{27464.7644705}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+53}:\\ \;\;\;\;t_2 + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2 (/ t t_1))
        (t_3 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -6.5e+138)
     t_3
     (if (<= y -7.5e+28)
       (+
        t_2
        (/
         y
         (+
          (/ y x)
          (- (+ (/ a x) (/ b (* y x))) (/ 27464.7644705 (* y (* x x)))))))
       (if (<= y 9e+53)
         (+
          t_2
          (/
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
           t_1))
         t_3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = t / t_1;
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -6.5e+138) {
		tmp = t_3;
	} else if (y <= -7.5e+28) {
		tmp = t_2 + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))));
	} else if (y <= 9e+53) {
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
    t_2 = t / t_1
    t_3 = (z / y) + (x - (a / (y / x)))
    if (y <= (-6.5d+138)) then
        tmp = t_3
    else if (y <= (-7.5d+28)) then
        tmp = t_2 + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705d0 / (y * (x * x))))))
    else if (y <= 9d+53) then
        tmp = t_2 + ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))) / t_1)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = t / t_1;
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -6.5e+138) {
		tmp = t_3;
	} else if (y <= -7.5e+28) {
		tmp = t_2 + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))));
	} else if (y <= 9e+53) {
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
	t_2 = t / t_1
	t_3 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -6.5e+138:
		tmp = t_3
	elif y <= -7.5e+28:
		tmp = t_2 + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))))
	elif y <= 9e+53:
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	t_2 = Float64(t / t_1)
	t_3 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -6.5e+138)
		tmp = t_3;
	elseif (y <= -7.5e+28)
		tmp = Float64(t_2 + Float64(y / Float64(Float64(y / x) + Float64(Float64(Float64(a / x) + Float64(b / Float64(y * x))) - Float64(27464.7644705 / Float64(y * Float64(x * x)))))));
	elseif (y <= 9e+53)
		tmp = Float64(t_2 + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_1));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	t_2 = t / t_1;
	t_3 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -6.5e+138)
		tmp = t_3;
	elseif (y <= -7.5e+28)
		tmp = t_2 + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))));
	elseif (y <= 9e+53)
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+138], t$95$3, If[LessEqual[y, -7.5e+28], N[(t$95$2 + N[(y / N[(N[(y / x), $MachinePrecision] + N[(N[(N[(a / x), $MachinePrecision] + N[(b / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27464.7644705 / N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+53], N[(t$95$2 + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.50000000000000054e138 or 9.0000000000000004e53 < y

   1. Initial program 1.5%

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

   2. Taylor expanded in y around inf 71.2%

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

      1. associate--l+ 71.2%

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

      2. associate-/l* 73.7%

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

   4. Simplified 73.7%

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

   if -6.50000000000000054e138 < y < -7.4999999999999998e28

   1. Initial program 10.3%

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

   2. Taylor expanded in t around inf 10.3%

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

   3. Taylor expanded in z around 0 10.6%

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

      1. *-commutative 10.6%

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

      2. associate-/l* 15.9%

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

      3. fma-def 15.9%

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

      4. +-commutative 15.9%

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

      5. *-commutative 15.9%

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

      6. fma-udef 15.9%

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

      7. fma-def 15.9%

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

      8. *-commutative 15.9%

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

      9. unpow2 15.9%

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

   5. Simplified 15.9%

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

   6. Taylor expanded in y around inf 64.6%

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

      1. associate--l+ 64.6%

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

      2. +-commutative 64.6%

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

      3. associate-*r/ 64.6%

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

      4. metadata-eval 64.6%

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

      5. unpow2 64.6%

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

   8. Simplified 64.6%

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

   if -7.4999999999999998e28 < y < 9.0000000000000004e53

   1. Initial program 97.1%

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

   2. Taylor expanded in t around inf 97.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+138}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{y}{x} + \left(\left(\frac{a}{x} + \frac{b}{y \cdot x}\right) - \frac{27464.7644705}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 4: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{t_1} + \frac{y}{\frac{y}{x} + \left(\left(\frac{a}{x} + \frac{b}{y \cdot x}\right) - \frac{27464.7644705}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+53}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -1.9e+138)
     t_2
     (if (<= y -1.6e+28)
       (+
        (/ t t_1)
        (/
         y
         (+
          (/ y x)
          (- (+ (/ a x) (/ b (* y x))) (/ 27464.7644705 (* y (* x x)))))))
       (if (<= y 9e+53)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          t_1)
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.9e+138) {
		tmp = t_2;
	} else if (y <= -1.6e+28) {
		tmp = (t / t_1) + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))));
	} else if (y <= 9e+53) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
    t_2 = (z / y) + (x - (a / (y / x)))
    if (y <= (-1.9d+138)) then
        tmp = t_2
    else if (y <= (-1.6d+28)) then
        tmp = (t / t_1) + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705d0 / (y * (x * x))))))
    else if (y <= 9d+53) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.9e+138) {
		tmp = t_2;
	} else if (y <= -1.6e+28) {
		tmp = (t / t_1) + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))));
	} else if (y <= 9e+53) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
	t_2 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -1.9e+138:
		tmp = t_2
	elif y <= -1.6e+28:
		tmp = (t / t_1) + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))))
	elif y <= 9e+53:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.9e+138)
		tmp = t_2;
	elseif (y <= -1.6e+28)
		tmp = Float64(Float64(t / t_1) + Float64(y / Float64(Float64(y / x) + Float64(Float64(Float64(a / x) + Float64(b / Float64(y * x))) - Float64(27464.7644705 / Float64(y * Float64(x * x)))))));
	elseif (y <= 9e+53)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	t_2 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.9e+138)
		tmp = t_2;
	elseif (y <= -1.6e+28)
		tmp = (t / t_1) + (y / ((y / x) + (((a / x) + (b / (y * x))) - (27464.7644705 / (y * (x * x))))));
	elseif (y <= 9e+53)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+138], t$95$2, If[LessEqual[y, -1.6e+28], N[(N[(t / t$95$1), $MachinePrecision] + N[(y / N[(N[(y / x), $MachinePrecision] + N[(N[(N[(a / x), $MachinePrecision] + N[(b / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27464.7644705 / N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+53], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.90000000000000006e138 or 9.0000000000000004e53 < y

   1. Initial program 1.5%

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

   2. Taylor expanded in y around inf 71.2%

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

      1. associate--l+ 71.2%

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

      2. associate-/l* 73.7%

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

   4. Simplified 73.7%

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

   if -1.90000000000000006e138 < y < -1.6e28

   1. Initial program 10.3%

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

   2. Taylor expanded in t around inf 10.3%

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

   3. Taylor expanded in z around 0 10.6%

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

      1. *-commutative 10.6%

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

      2. associate-/l* 15.9%

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

      3. fma-def 15.9%

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

      4. +-commutative 15.9%

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

      5. *-commutative 15.9%

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

      6. fma-udef 15.9%

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

      7. fma-def 15.9%

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

      8. *-commutative 15.9%

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

      9. unpow2 15.9%

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

   5. Simplified 15.9%

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

   6. Taylor expanded in y around inf 64.6%

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

      1. associate--l+ 64.6%

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

      2. +-commutative 64.6%

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

      3. associate-*r/ 64.6%

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

      4. metadata-eval 64.6%

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

      5. unpow2 64.6%

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

   8. Simplified 64.6%

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

   if -1.6e28 < y < 9.0000000000000004e53

   1. Initial program 97.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+138}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{y}{x} + \left(\left(\frac{a}{x} + \frac{b}{y \cdot x}\right) - \frac{27464.7644705}{y \cdot \left(x \cdot x\right)}\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+53}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 5: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{t_1} + \frac{y}{\frac{y}{x} + \left(\frac{a}{x} + \frac{\frac{b}{x} - \frac{27464.7644705}{x \cdot x}}{y}\right)}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -4.2e+138)
     t_2
     (if (<= y -5.2e+28)
       (+
        (/ t t_1)
        (/
         y
         (+ (/ y x) (+ (/ a x) (/ (- (/ b x) (/ 27464.7644705 (* x x))) y)))))
       (if (<= y 3.6e+53)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          t_1)
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -4.2e+138) {
		tmp = t_2;
	} else if (y <= -5.2e+28) {
		tmp = (t / t_1) + (y / ((y / x) + ((a / x) + (((b / x) - (27464.7644705 / (x * x))) / y))));
	} else if (y <= 3.6e+53) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
    t_2 = (z / y) + (x - (a / (y / x)))
    if (y <= (-4.2d+138)) then
        tmp = t_2
    else if (y <= (-5.2d+28)) then
        tmp = (t / t_1) + (y / ((y / x) + ((a / x) + (((b / x) - (27464.7644705d0 / (x * x))) / y))))
    else if (y <= 3.6d+53) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -4.2e+138) {
		tmp = t_2;
	} else if (y <= -5.2e+28) {
		tmp = (t / t_1) + (y / ((y / x) + ((a / x) + (((b / x) - (27464.7644705 / (x * x))) / y))));
	} else if (y <= 3.6e+53) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
	t_2 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -4.2e+138:
		tmp = t_2
	elif y <= -5.2e+28:
		tmp = (t / t_1) + (y / ((y / x) + ((a / x) + (((b / x) - (27464.7644705 / (x * x))) / y))))
	elif y <= 3.6e+53:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -4.2e+138)
		tmp = t_2;
	elseif (y <= -5.2e+28)
		tmp = Float64(Float64(t / t_1) + Float64(y / Float64(Float64(y / x) + Float64(Float64(a / x) + Float64(Float64(Float64(b / x) - Float64(27464.7644705 / Float64(x * x))) / y)))));
	elseif (y <= 3.6e+53)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	t_2 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -4.2e+138)
		tmp = t_2;
	elseif (y <= -5.2e+28)
		tmp = (t / t_1) + (y / ((y / x) + ((a / x) + (((b / x) - (27464.7644705 / (x * x))) / y))));
	elseif (y <= 3.6e+53)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+138], t$95$2, If[LessEqual[y, -5.2e+28], N[(N[(t / t$95$1), $MachinePrecision] + N[(y / N[(N[(y / x), $MachinePrecision] + N[(N[(a / x), $MachinePrecision] + N[(N[(N[(b / x), $MachinePrecision] - N[(27464.7644705 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+53], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.20000000000000014e138 or 3.6e53 < y

   1. Initial program 1.5%

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

   2. Taylor expanded in y around inf 71.2%

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

      1. associate--l+ 71.2%

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

      2. associate-/l* 73.7%

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

   4. Simplified 73.7%

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

   if -4.20000000000000014e138 < y < -5.2000000000000004e28

   1. Initial program 10.3%

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

   2. Taylor expanded in t around inf 10.3%

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

   3. Taylor expanded in z around 0 10.6%

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

      1. *-commutative 10.6%

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

      2. associate-/l* 15.9%

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

      3. fma-def 15.9%

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

      4. +-commutative 15.9%

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

      5. *-commutative 15.9%

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

      6. fma-udef 15.9%

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

      7. fma-def 15.9%

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

      8. *-commutative 15.9%

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

      9. unpow2 15.9%

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

   5. Simplified 15.9%

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

   6. Taylor expanded in y around -inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

      3. mul-1-neg 64.5%

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

      4. unsub-neg 64.5%

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

      5. associate-*r/ 64.5%

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

      6. metadata-eval 64.5%

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

      7. unpow2 64.5%

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

   8. Simplified 64.5%

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

   if -5.2000000000000004e28 < y < 3.6e53

   1. Initial program 97.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+138}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{y}{x} + \left(\frac{a}{x} + \frac{\frac{b}{x} - \frac{27464.7644705}{x \cdot x}}{y}\right)}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 6: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4400000000:\\ \;\;\;\;\frac{t}{t_1} + \frac{y}{\frac{y}{x} + \frac{a}{x}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+19}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -7e+138)
     t_2
     (if (<= y -4400000000.0)
       (+ (/ t t_1) (/ y (+ (/ y x) (/ a x))))
       (if (<= y 6e+19)
         (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) t_1)
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -7e+138) {
		tmp = t_2;
	} else if (y <= -4400000000.0) {
		tmp = (t / t_1) + (y / ((y / x) + (a / x)));
	} else if (y <= 6e+19) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
    t_2 = (z / y) + (x - (a / (y / x)))
    if (y <= (-7d+138)) then
        tmp = t_2
    else if (y <= (-4400000000.0d0)) then
        tmp = (t / t_1) + (y / ((y / x) + (a / x)))
    else if (y <= 6d+19) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -7e+138) {
		tmp = t_2;
	} else if (y <= -4400000000.0) {
		tmp = (t / t_1) + (y / ((y / x) + (a / x)));
	} else if (y <= 6e+19) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
	t_2 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -7e+138:
		tmp = t_2
	elif y <= -4400000000.0:
		tmp = (t / t_1) + (y / ((y / x) + (a / x)))
	elif y <= 6e+19:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -7e+138)
		tmp = t_2;
	elseif (y <= -4400000000.0)
		tmp = Float64(Float64(t / t_1) + Float64(y / Float64(Float64(y / x) + Float64(a / x))));
	elseif (y <= 6e+19)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	t_2 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -7e+138)
		tmp = t_2;
	elseif (y <= -4400000000.0)
		tmp = (t / t_1) + (y / ((y / x) + (a / x)));
	elseif (y <= 6e+19)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+138], t$95$2, If[LessEqual[y, -4400000000.0], N[(N[(t / t$95$1), $MachinePrecision] + N[(y / N[(N[(y / x), $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+19], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9999999999999996e138 or 6e19 < y

   1. Initial program 8.0%

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

   2. Taylor expanded in y around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-/l* 71.4%

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

   4. Simplified 71.4%

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

   if -6.9999999999999996e138 < y < -4.4e9

   1. Initial program 22.4%

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

   2. Taylor expanded in t around inf 22.4%

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

   3. Taylor expanded in z around 0 22.7%

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

      1. *-commutative 22.7%

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

      2. associate-/l* 27.0%

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

      3. fma-def 27.0%

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

      4. +-commutative 27.0%

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

      5. *-commutative 27.0%

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

      6. fma-udef 27.0%

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

      7. fma-def 27.0%

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

      8. *-commutative 27.0%

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

      9. unpow2 27.0%

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

   5. Simplified 27.0%

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

   6. Taylor expanded in y around inf 47.8%

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

   if -4.4e9 < y < 6e19

   1. Initial program 99.0%

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

   2. Taylor expanded in z around inf 94.9%

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

      1. *-commutative 94.9%

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

      2. unpow2 94.9%

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

   4. Simplified 94.9%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+138}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4400000000:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{y}{x} + \frac{a}{x}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+19}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 7: 80.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{y}{x} + \frac{a}{x}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -6e+137)
     t_1
     (if (<= y -5e+31)
       (+
        (/ t (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (/ y (+ (/ y x) (/ a x))))
       (if (<= y 7.2e+19)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -6e+137) {
		tmp = t_1;
	} else if (y <= -5e+31) {
		tmp = (t / (i + (y * (c + (y * ((y * (y + a)) + b)))))) + (y / ((y / x) + (a / x)));
	} else if (y <= 7.2e+19) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-6d+137)) then
        tmp = t_1
    else if (y <= (-5d+31)) then
        tmp = (t / (i + (y * (c + (y * ((y * (y + a)) + b)))))) + (y / ((y / x) + (a / x)))
    else if (y <= 7.2d+19) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -6e+137) {
		tmp = t_1;
	} else if (y <= -5e+31) {
		tmp = (t / (i + (y * (c + (y * ((y * (y + a)) + b)))))) + (y / ((y / x) + (a / x)));
	} else if (y <= 7.2e+19) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -6e+137:
		tmp = t_1
	elif y <= -5e+31:
		tmp = (t / (i + (y * (c + (y * ((y * (y + a)) + b)))))) + (y / ((y / x) + (a / x)))
	elif y <= 7.2e+19:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -6e+137)
		tmp = t_1;
	elseif (y <= -5e+31)
		tmp = Float64(Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))) + Float64(y / Float64(Float64(y / x) + Float64(a / x))));
	elseif (y <= 7.2e+19)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -6e+137)
		tmp = t_1;
	elseif (y <= -5e+31)
		tmp = (t / (i + (y * (c + (y * ((y * (y + a)) + b)))))) + (y / ((y / x) + (a / x)));
	elseif (y <= 7.2e+19)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+137], t$95$1, If[LessEqual[y, -5e+31], N[(N[(t / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(y / x), $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+19], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.0000000000000002e137 or 7.2e19 < y

   1. Initial program 8.0%

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

   2. Taylor expanded in y around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-/l* 71.4%

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

   4. Simplified 71.4%

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

   if -6.0000000000000002e137 < y < -5.00000000000000027e31

   1. Initial program 5.9%

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

   2. Taylor expanded in t around inf 5.9%

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

   3. Taylor expanded in z around 0 6.2%

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

      1. *-commutative 6.2%

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

      2. associate-/l* 12.4%

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

      3. fma-def 12.4%

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

      4. +-commutative 12.4%

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

      5. *-commutative 12.4%

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

      6. fma-udef 12.4%

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

      7. fma-def 12.4%

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

      8. *-commutative 12.4%

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

      9. unpow2 12.4%

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

   5. Simplified 12.4%

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

   6. Taylor expanded in y around inf 59.7%

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

   if -5.00000000000000027e31 < y < 7.2e19

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 92.5%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+137}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{y}{x} + \frac{a}{x}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 8: 78.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -112000000000:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{y}{x} + \frac{a}{x}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -1.35e+138)
     t_1
     (if (<= y -112000000000.0)
       (+
        (/ t (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (/ y (+ (/ y x) (/ a x))))
       (if (<= y 7.2e+19)
         (/
          (+ t (* y (+ 230661.510616 (* z (* y y)))))
          (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.35e+138) {
		tmp = t_1;
	} else if (y <= -112000000000.0) {
		tmp = (t / (i + (y * (c + (y * ((y * (y + a)) + b)))))) + (y / ((y / x) + (a / x)));
	} else if (y <= 7.2e+19) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-1.35d+138)) then
        tmp = t_1
    else if (y <= (-112000000000.0d0)) then
        tmp = (t / (i + (y * (c + (y * ((y * (y + a)) + b)))))) + (y / ((y / x) + (a / x)))
    else if (y <= 7.2d+19) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.35e+138) {
		tmp = t_1;
	} else if (y <= -112000000000.0) {
		tmp = (t / (i + (y * (c + (y * ((y * (y + a)) + b)))))) + (y / ((y / x) + (a / x)));
	} else if (y <= 7.2e+19) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -1.35e+138:
		tmp = t_1
	elif y <= -112000000000.0:
		tmp = (t / (i + (y * (c + (y * ((y * (y + a)) + b)))))) + (y / ((y / x) + (a / x)))
	elif y <= 7.2e+19:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.35e+138)
		tmp = t_1;
	elseif (y <= -112000000000.0)
		tmp = Float64(Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))) + Float64(y / Float64(Float64(y / x) + Float64(a / x))));
	elseif (y <= 7.2e+19)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.35e+138)
		tmp = t_1;
	elseif (y <= -112000000000.0)
		tmp = (t / (i + (y * (c + (y * ((y * (y + a)) + b)))))) + (y / ((y / x) + (a / x)));
	elseif (y <= 7.2e+19)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+138], t$95$1, If[LessEqual[y, -112000000000.0], N[(N[(t / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(y / x), $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+19], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35000000000000004e138 or 7.2e19 < y

   1. Initial program 8.0%

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

   2. Taylor expanded in y around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-/l* 71.4%

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

   4. Simplified 71.4%

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

   if -1.35000000000000004e138 < y < -1.12e11

   1. Initial program 22.4%

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

   2. Taylor expanded in t around inf 22.4%

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

   3. Taylor expanded in z around 0 22.7%

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

      1. *-commutative 22.7%

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

      2. associate-/l* 27.0%

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

      3. fma-def 27.0%

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

      4. +-commutative 27.0%

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

      5. *-commutative 27.0%

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

      6. fma-udef 27.0%

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

      7. fma-def 27.0%

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

      8. *-commutative 27.0%

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

      9. unpow2 27.0%

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

   5. Simplified 27.0%

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

   6. Taylor expanded in y around inf 47.8%

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

   if -1.12e11 < y < 7.2e19

   1. Initial program 99.0%

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

   2. Taylor expanded in z around inf 94.9%

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

      1. *-commutative 94.9%

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

      2. unpow2 94.9%

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

   4. Simplified 94.9%

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

   5. Taylor expanded in y around 0 92.6%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+138}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -112000000000:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{y}{x} + \frac{a}{x}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 9: 76.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+76} \lor \neg \left(y \leq 7.2 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.45e+76) (not (<= y 7.2e+19)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.45e+76) || !(y <= 7.2e+19)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + 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 <= (-2.45d+76)) .or. (.not. (y <= 7.2d+19))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * ((y * (y + a)) + 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 <= -2.45e+76) || !(y <= 7.2e+19)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.45e+76) or not (y <= 7.2e+19):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.45e+76) || !(y <= 7.2e+19))
		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 * Float64(Float64(y * Float64(y + a)) + b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.45e+76) || ~((y <= 7.2e+19)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.45e+76], N[Not[LessEqual[y, 7.2e+19]], $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 * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.45000000000000013e76 or 7.2e19 < y

   1. Initial program 7.1%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. associate-/l* 67.8%

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

   4. Simplified 67.8%

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

   if -2.45000000000000013e76 < y < 7.2e19

   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 79.8%

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

      1. *-commutative 79.8%

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

   4. Simplified 79.8%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+76} \lor \neg \left(y \leq 7.2 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \]

Alternative 10: 77.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 1.35 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.25e+76) (not (<= y 1.35e+18)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) (+ 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 <= -2.25e+76) || !(y <= 1.35e+18)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (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 <= (-2.25d+76)) .or. (.not. (y <= 1.35d+18))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / (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 <= -2.25e+76) || !(y <= 1.35e+18)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.25e+76) or not (y <= 1.35e+18):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.25e+76) || !(y <= 1.35e+18))
		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(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 <= -2.25e+76) || ~((y <= 1.35e+18)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.25e+76], N[Not[LessEqual[y, 1.35e+18]], $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[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2499999999999999e76 or 1.35e18 < y

   1. Initial program 7.1%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. associate-/l* 67.8%

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

   4. Simplified 67.8%

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

   if -2.2499999999999999e76 < y < 1.35e18

   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 z around inf 85.5%

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

      1. *-commutative 85.5%

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

      2. unpow2 85.5%

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

   4. Simplified 85.5%

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

   5. Taylor expanded in y around 0 83.4%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 1.35 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 11: 74.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 2.3 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.25e+76) (not (<= y 2.3e+19)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ b (* y y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.25e+76) || !(y <= 2.3e+19)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * y))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.25d+76)) .or. (.not. (y <= 2.3d+19))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * y))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.25e+76) || !(y <= 2.3e+19)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * y))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.25e+76) or not (y <= 2.3e+19):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * y))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.25e+76) || !(y <= 2.3e+19))
		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 * Float64(b + Float64(y * y)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.25e+76) || ~((y <= 2.3e+19)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * y))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.25e+76], N[Not[LessEqual[y, 2.3e+19]], $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 * N[(b + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2499999999999999e76 or 2.3e19 < y

   1. Initial program 7.1%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. associate-/l* 67.8%

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

   4. Simplified 67.8%

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

   if -2.2499999999999999e76 < y < 2.3e19

   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 79.8%

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

      1. *-commutative 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in a around 0 77.9%

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

      1. *-commutative 77.9%

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

      2. +-commutative 77.9%

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

      3. unpow2 77.9%

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

   7. Simplified 77.9%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 2.3 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \end{array} \]

Alternative 12: 74.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 6.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.25e+76) (not (<= y 6.5e+19)))
   (+ (/ 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 <= -2.25e+76) || !(y <= 6.5e+19)) {
		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 <= (-2.25d+76)) .or. (.not. (y <= 6.5d+19))) 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 <= -2.25e+76) || !(y <= 6.5e+19)) {
		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 <= -2.25e+76) or not (y <= 6.5e+19):
		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 <= -2.25e+76) || !(y <= 6.5e+19))
		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 <= -2.25e+76) || ~((y <= 6.5e+19)))
		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, -2.25e+76], N[Not[LessEqual[y, 6.5e+19]], $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 < -2.2499999999999999e76 or 6.5e19 < y

   1. Initial program 7.1%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. associate-/l* 67.8%

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

   4. Simplified 67.8%

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

   if -2.2499999999999999e76 < y < 6.5e19

   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 88.4%

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

   3. Taylor expanded in y around 0 78.9%

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

      1. *-commutative 78.9%

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

   5. Simplified 78.9%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 6.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 13: 72.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 4 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.25e+76) (not (<= y 4e+19)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* a (* y y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.25e+76) || !(y <= 4e+19)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (a * (y * y)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.25d+76)) .or. (.not. (y <= 4d+19))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (a * (y * y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.25e+76) || !(y <= 4e+19)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (a * (y * y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.25e+76) or not (y <= 4e+19):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (a * (y * y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.25e+76) || !(y <= 4e+19))
		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(a * Float64(y * y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.25e+76) || ~((y <= 4e+19)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (a * (y * y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.25e+76], N[Not[LessEqual[y, 4e+19]], $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[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2499999999999999e76 or 4e19 < y

   1. Initial program 7.1%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. associate-/l* 67.8%

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

   4. Simplified 67.8%

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

   if -2.2499999999999999e76 < y < 4e19

   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 79.8%

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

      1. *-commutative 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in a around inf 73.1%

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

      1. *-commutative 73.1%

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

      2. unpow2 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 4 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]

Alternative 14: 59.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 10^{-128}:\\ \;\;\;\;\frac{t_1}{i}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{t_1}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616))) (t_2 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -3.6e+27)
     t_2
     (if (<= y 1e-128) (/ t_1 i) (if (<= y 2.1e+18) (/ t_1 (* y c)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -3.6e+27) {
		tmp = t_2;
	} else if (y <= 1e-128) {
		tmp = t_1 / i;
	} else if (y <= 2.1e+18) {
		tmp = t_1 / (y * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    t_2 = (z / y) + (x - (a / (y / x)))
    if (y <= (-3.6d+27)) then
        tmp = t_2
    else if (y <= 1d-128) then
        tmp = t_1 / i
    else if (y <= 2.1d+18) then
        tmp = t_1 / (y * c)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -3.6e+27) {
		tmp = t_2;
	} else if (y <= 1e-128) {
		tmp = t_1 / i;
	} else if (y <= 2.1e+18) {
		tmp = t_1 / (y * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	t_2 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -3.6e+27:
		tmp = t_2
	elif y <= 1e-128:
		tmp = t_1 / i
	elif y <= 2.1e+18:
		tmp = t_1 / (y * c)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -3.6e+27)
		tmp = t_2;
	elseif (y <= 1e-128)
		tmp = Float64(t_1 / i);
	elseif (y <= 2.1e+18)
		tmp = Float64(t_1 / Float64(y * c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	t_2 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -3.6e+27)
		tmp = t_2;
	elseif (y <= 1e-128)
		tmp = t_1 / i;
	elseif (y <= 2.1e+18)
		tmp = t_1 / (y * c);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+27], t$95$2, If[LessEqual[y, 1e-128], N[(t$95$1 / i), $MachinePrecision], If[LessEqual[y, 2.1e+18], N[(t$95$1 / N[(y * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.59999999999999983e27 or 2.1e18 < y

   1. Initial program 8.4%

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

   2. Taylor expanded in 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* 61.6%

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

   4. Simplified 61.6%

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

   if -3.59999999999999983e27 < y < 1.00000000000000005e-128

   1. Initial program 97.0%

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

   2. Taylor expanded in y around 0 89.6%

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

      1. *-commutative 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in i around inf 66.1%

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

   if 1.00000000000000005e-128 < y < 2.1e18

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 72.2%

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

      1. *-commutative 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in c around inf 36.6%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 10^{-128}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 15: 52.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-128}:\\ \;\;\;\;\frac{t_1}{i}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+18}:\\ \;\;\;\;\frac{t_1}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616))))
   (if (<= y -6.8e+27)
     x
     (if (<= y 1.55e-128) (/ t_1 i) (if (<= y 1.06e+18) (/ t_1 (* y c)) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double tmp;
	if (y <= -6.8e+27) {
		tmp = x;
	} else if (y <= 1.55e-128) {
		tmp = t_1 / i;
	} else if (y <= 1.06e+18) {
		tmp = t_1 / (y * c);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    if (y <= (-6.8d+27)) then
        tmp = x
    else if (y <= 1.55d-128) then
        tmp = t_1 / i
    else if (y <= 1.06d+18) then
        tmp = t_1 / (y * c)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double tmp;
	if (y <= -6.8e+27) {
		tmp = x;
	} else if (y <= 1.55e-128) {
		tmp = t_1 / i;
	} else if (y <= 1.06e+18) {
		tmp = t_1 / (y * c);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	tmp = 0
	if y <= -6.8e+27:
		tmp = x
	elif y <= 1.55e-128:
		tmp = t_1 / i
	elif y <= 1.06e+18:
		tmp = t_1 / (y * c)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	tmp = 0.0
	if (y <= -6.8e+27)
		tmp = x;
	elseif (y <= 1.55e-128)
		tmp = Float64(t_1 / i);
	elseif (y <= 1.06e+18)
		tmp = Float64(t_1 / Float64(y * c));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	tmp = 0.0;
	if (y <= -6.8e+27)
		tmp = x;
	elseif (y <= 1.55e-128)
		tmp = t_1 / i;
	elseif (y <= 1.06e+18)
		tmp = t_1 / (y * c);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+27], x, If[LessEqual[y, 1.55e-128], N[(t$95$1 / i), $MachinePrecision], If[LessEqual[y, 1.06e+18], N[(t$95$1 / N[(y * c), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.8e27 or 1.06e18 < y

   1. Initial program 8.4%

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

   2. Taylor expanded in y around inf 50.4%

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

   if -6.8e27 < y < 1.55000000000000001e-128

   1. Initial program 97.0%

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

   2. Taylor expanded in y around 0 89.6%

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

      1. *-commutative 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in i around inf 66.1%

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

   if 1.55000000000000001e-128 < y < 1.06e18

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 72.2%

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

      1. *-commutative 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in c around inf 36.6%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-128}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+18}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 67.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 10^{+19}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.25e+76) (not (<= y 1e+19)))
   (+ (/ 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 <= -2.25e+76) || !(y <= 1e+19)) {
		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 <= (-2.25d+76)) .or. (.not. (y <= 1d+19))) 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 <= -2.25e+76) || !(y <= 1e+19)) {
		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 <= -2.25e+76) or not (y <= 1e+19):
		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 <= -2.25e+76) || !(y <= 1e+19))
		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 <= -2.25e+76) || ~((y <= 1e+19)))
		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, -2.25e+76], N[Not[LessEqual[y, 1e+19]], $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 < -2.2499999999999999e76 or 1e19 < y

   1. Initial program 7.1%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. associate-/l* 67.8%

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

   4. Simplified 67.8%

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

   if -2.2499999999999999e76 < y < 1e19

   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 88.4%

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

   3. Taylor expanded in t around inf 65.5%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 10^{+19}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 17: 70.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 5.8 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.25e+76) (not (<= y 5.8e+15)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ i (* y c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.25e+76) || !(y <= 5.8e+15)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.25d+76)) .or. (.not. (y <= 5.8d+15))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.25e+76) || !(y <= 5.8e+15)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.25e+76) or not (y <= 5.8e+15):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.25e+76) || !(y <= 5.8e+15))
		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 * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.25e+76) || ~((y <= 5.8e+15)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.25e+76], N[Not[LessEqual[y, 5.8e+15]], $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 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2499999999999999e76 or 5.8e15 < y

   1. Initial program 7.1%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. associate-/l* 67.8%

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

   4. Simplified 67.8%

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

   if -2.2499999999999999e76 < y < 5.8e15

   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 79.8%

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

      1. *-commutative 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in y around 0 71.2%

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

      1. *-commutative 71.2%

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

   7. Simplified 71.2%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+76} \lor \neg \left(y \leq 5.8 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \end{array} \]

Alternative 18: 54.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.55e+25) x (if (<= y 5.5e-20) (/ (+ t (* y 230661.510616)) i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.55e+25) {
		tmp = x;
	} else if (y <= 5.5e-20) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.55d+25)) then
        tmp = x
    else if (y <= 5.5d-20) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.55e+25) {
		tmp = x;
	} else if (y <= 5.5e-20) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.55e+25:
		tmp = x
	elif y <= 5.5e-20:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.55e+25)
		tmp = x;
	elseif (y <= 5.5e-20)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.55e+25)
		tmp = x;
	elseif (y <= 5.5e-20)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.55e+25], x, If[LessEqual[y, 5.5e-20], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5500000000000001e25 or 5.4999999999999996e-20 < y

   1. Initial program 17.2%

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

   2. Taylor expanded in y around inf 45.9%

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

   if -3.5500000000000001e25 < y < 5.4999999999999996e-20

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 87.1%

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

      1. *-commutative 87.1%

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

   4. Simplified 87.1%

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

   5. Taylor expanded in i around inf 57.7%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 50.9% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.8e+22) x (if (<= y 5.5e-20) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.8e+22) {
		tmp = x;
	} else if (y <= 5.5e-20) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.8d+22)) then
        tmp = x
    else if (y <= 5.5d-20) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.8e+22) {
		tmp = x;
	} else if (y <= 5.5e-20) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.8e+22:
		tmp = x
	elif y <= 5.5e-20:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.8e+22)
		tmp = x;
	elseif (y <= 5.5e-20)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.8e+22)
		tmp = x;
	elseif (y <= 5.5e-20)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.8e+22], x, If[LessEqual[y, 5.5e-20], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000004e22 or 5.4999999999999996e-20 < y

   1. Initial program 17.8%

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

   2. Taylor expanded in y around inf 45.6%

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

   if -3.8000000000000004e22 < y < 5.4999999999999996e-20

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 52.2%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 25.5% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.2%

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

2. Taylor expanded in y around inf 24.0%

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

3. Final simplification 24.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023196 
(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)))