Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.8% → 83.3%

Time: 19.1s

Alternatives: 16

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.8% 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: 83.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ t_2 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(\frac{y}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \left(\frac{\frac{230661.510616}{a}}{{y}^{2}} + \left(\frac{t}{a \cdot {y}^{3}} + \frac{z}{a}\right)\right)}{x}\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{t\_1} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
        (t_2 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -3.6e+153)
     t_2
     (if (<= y -4e+42)
       (*
        x
        (+
         (/ y a)
         (/
          (+
           (/ 27464.7644705 (* y a))
           (+
            (/ (/ 230661.510616 a) (pow y 2.0))
            (+ (/ t (* a (pow y 3.0))) (/ z a))))
          x)))
       (if (<= y 1.7e+56)
         (+
          (/ t t_1)
          (/
           (* 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 * (b + (y * (y + a))))));
	double t_2 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_2;
	} else if (y <= -4e+42) {
		tmp = x * ((y / a) + (((27464.7644705 / (y * a)) + (((230661.510616 / a) / pow(y, 2.0)) + ((t / (a * pow(y, 3.0))) + (z / a)))) / x));
	} else if (y <= 1.7e+56) {
		tmp = (t / t_1) + ((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 * (b + (y * (y + a))))))
    t_2 = (x + (z / y)) - (a * (x / y))
    if (y <= (-3.6d+153)) then
        tmp = t_2
    else if (y <= (-4d+42)) then
        tmp = x * ((y / a) + (((27464.7644705d0 / (y * a)) + (((230661.510616d0 / a) / (y ** 2.0d0)) + ((t / (a * (y ** 3.0d0))) + (z / a)))) / x))
    else if (y <= 1.7d+56) then
        tmp = (t / t_1) + ((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 * (b + (y * (y + a))))));
	double t_2 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_2;
	} else if (y <= -4e+42) {
		tmp = x * ((y / a) + (((27464.7644705 / (y * a)) + (((230661.510616 / a) / Math.pow(y, 2.0)) + ((t / (a * Math.pow(y, 3.0))) + (z / a)))) / x));
	} else if (y <= 1.7e+56) {
		tmp = (t / t_1) + ((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 * (b + (y * (y + a))))))
	t_2 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -3.6e+153:
		tmp = t_2
	elif y <= -4e+42:
		tmp = x * ((y / a) + (((27464.7644705 / (y * a)) + (((230661.510616 / a) / math.pow(y, 2.0)) + ((t / (a * math.pow(y, 3.0))) + (z / a)))) / x))
	elif y <= 1.7e+56:
		tmp = (t / t_1) + ((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(b + Float64(y * Float64(y + a)))))))
	t_2 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -3.6e+153)
		tmp = t_2;
	elseif (y <= -4e+42)
		tmp = Float64(x * Float64(Float64(y / a) + Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(Float64(230661.510616 / a) / (y ^ 2.0)) + Float64(Float64(t / Float64(a * (y ^ 3.0))) + Float64(z / a)))) / x)));
	elseif (y <= 1.7e+56)
		tmp = Float64(Float64(t / t_1) + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_1));
	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 * (b + (y * (y + a))))));
	t_2 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -3.6e+153)
		tmp = t_2;
	elseif (y <= -4e+42)
		tmp = x * ((y / a) + (((27464.7644705 / (y * a)) + (((230661.510616 / a) / (y ^ 2.0)) + ((t / (a * (y ^ 3.0))) + (z / a)))) / x));
	elseif (y <= 1.7e+56)
		tmp = (t / t_1) + ((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[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+153], t$95$2, If[LessEqual[y, -4e+42], N[(x * N[(N[(y / a), $MachinePrecision] + N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(230661.510616 / a), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(a * N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+56], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e153 or 1.7e56 < y

   1. Initial program 1.5%

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

   3. Taylor expanded in y around inf 74.4%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -3.6000000000000001e153 < y < -4.00000000000000018e42

   1. Initial program 4.8%

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

   3. Taylor expanded in a around inf 4.7%

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

   4. Taylor expanded in x around -inf 53.0%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y}{a} + -1 \cdot \frac{27464.7644705 \cdot \frac{1}{a \cdot y} + \left(230661.510616 \cdot \frac{1}{a \cdot {y}^{2}} + \left(\frac{t}{a \cdot {y}^{3}} + \frac{z}{a}\right)\right)}{x}\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 53.0%

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

      2. mul-1-neg 53.0%

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

      3. distribute-lft-out 53.0%

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

   6. Simplified 53.0%

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

   if -4.00000000000000018e42 < y < 1.7e56

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0 94.9%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(\frac{y}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \left(\frac{\frac{230661.510616}{a}}{{y}^{2}} + \left(\frac{t}{a \cdot {y}^{3}} + \frac{z}{a}\right)\right)}{x}\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ t_2 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{t\_1} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
        (t_2 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -3.6e+153)
     t_2
     (if (<= y -1.5e+43)
       (* y (+ (/ x a) (/ (+ (/ 27464.7644705 (* y a)) (/ z a)) y)))
       (if (<= y 1.86e+56)
         (+
          (/ t t_1)
          (/
           (* 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 * (b + (y * (y + a))))));
	double t_2 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_2;
	} else if (y <= -1.5e+43) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 1.86e+56) {
		tmp = (t / t_1) + ((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 * (b + (y * (y + a))))))
    t_2 = (x + (z / y)) - (a * (x / y))
    if (y <= (-3.6d+153)) then
        tmp = t_2
    else if (y <= (-1.5d+43)) then
        tmp = y * ((x / a) + (((27464.7644705d0 / (y * a)) + (z / a)) / y))
    else if (y <= 1.86d+56) then
        tmp = (t / t_1) + ((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 * (b + (y * (y + a))))));
	double t_2 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_2;
	} else if (y <= -1.5e+43) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 1.86e+56) {
		tmp = (t / t_1) + ((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 * (b + (y * (y + a))))))
	t_2 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -3.6e+153:
		tmp = t_2
	elif y <= -1.5e+43:
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y))
	elif y <= 1.86e+56:
		tmp = (t / t_1) + ((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(b + Float64(y * Float64(y + a)))))))
	t_2 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -3.6e+153)
		tmp = t_2;
	elseif (y <= -1.5e+43)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) / y)));
	elseif (y <= 1.86e+56)
		tmp = Float64(Float64(t / t_1) + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_1));
	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 * (b + (y * (y + a))))));
	t_2 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -3.6e+153)
		tmp = t_2;
	elseif (y <= -1.5e+43)
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	elseif (y <= 1.86e+56)
		tmp = (t / t_1) + ((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[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+153], t$95$2, If[LessEqual[y, -1.5e+43], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.86e+56], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e153 or 1.86000000000000007e56 < y

   1. Initial program 1.5%

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

   3. Taylor expanded in y around inf 74.4%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -3.6000000000000001e153 < y < -1.50000000000000008e43

   1. Initial program 4.8%

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

   3. Taylor expanded in a around inf 4.7%

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

   4. Taylor expanded in y around -inf 49.5%

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

      1. associate-*r* 49.5%

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

      2. mul-1-neg 49.5%

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

      3. distribute-lft-out 49.5%

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

      4. associate-*r/ 49.5%

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

      5. metadata-eval 49.5%

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

   6. Simplified 49.5%

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

   if -1.50000000000000008e43 < y < 1.86000000000000007e56

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0 94.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -3.6e+153)
     t_1
     (if (<= y -6.8e+43)
       (* y (+ (/ x a) (/ (+ (/ 27464.7644705 (* y a)) (/ z a)) y)))
       (if (<= y 4.7e+55)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -6.8e+43) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 4.7e+55) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - (a * (x / y))
    if (y <= (-3.6d+153)) then
        tmp = t_1
    else if (y <= (-6.8d+43)) then
        tmp = y * ((x / a) + (((27464.7644705d0 / (y * a)) + (z / a)) / y))
    else if (y <= 4.7d+55) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -6.8e+43) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 4.7e+55) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -3.6e+153:
		tmp = t_1
	elif y <= -6.8e+43:
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y))
	elif y <= 4.7e+55:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -6.8e+43)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) / y)));
	elseif (y <= 4.7e+55)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -6.8e+43)
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	elseif (y <= 4.7e+55)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+153], t$95$1, If[LessEqual[y, -6.8e+43], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+55], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e153 or 4.7000000000000001e55 < y

   1. Initial program 1.5%

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

   3. Taylor expanded in y around inf 74.4%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -3.6000000000000001e153 < y < -6.80000000000000024e43

   1. Initial program 4.8%

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

   3. Taylor expanded in a around inf 4.7%

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

   4. Taylor expanded in y around -inf 49.5%

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

      1. associate-*r* 49.5%

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

      2. mul-1-neg 49.5%

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

      3. distribute-lft-out 49.5%

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

      4. associate-*r/ 49.5%

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

      5. metadata-eval 49.5%

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

   6. Simplified 49.5%

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

   if -6.80000000000000024e43 < y < 4.7000000000000001e55

   1. Initial program 94.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot a + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -3.6e+153)
     t_1
     (if (<= y -1.6e+42)
       (* y (+ (/ x a) (/ (+ (/ 27464.7644705 (* y a)) (/ z a)) y)))
       (if (<= y 2.7e+55)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ i (* y (+ c (* y (+ (* y a) b))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -1.6e+42) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 2.7e+55) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * ((y * a) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - (a * (x / y))
    if (y <= (-3.6d+153)) then
        tmp = t_1
    else if (y <= (-1.6d+42)) then
        tmp = y * ((x / a) + (((27464.7644705d0 / (y * a)) + (z / a)) / y))
    else if (y <= 2.7d+55) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * ((y * a) + b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -1.6e+42) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 2.7e+55) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * ((y * a) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -3.6e+153:
		tmp = t_1
	elif y <= -1.6e+42:
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y))
	elif y <= 2.7e+55:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * ((y * a) + b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -1.6e+42)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) / y)));
	elseif (y <= 2.7e+55)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * a) + b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -1.6e+42)
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	elseif (y <= 2.7e+55)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * ((y * a) + 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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+153], t$95$1, If[LessEqual[y, -1.6e+42], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+55], 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 * a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e153 or 2.69999999999999977e55 < y

   1. Initial program 1.5%

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

   3. Taylor expanded in y around inf 74.4%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -3.6000000000000001e153 < y < -1.60000000000000001e42

   1. Initial program 4.8%

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

   3. Taylor expanded in a around inf 4.7%

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

   4. Taylor expanded in y around -inf 49.5%

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

      1. associate-*r* 49.5%

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

      2. mul-1-neg 49.5%

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

      3. distribute-lft-out 49.5%

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

      4. associate-*r/ 49.5%

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

      5. metadata-eval 49.5%

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

   6. Simplified 49.5%

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

   if -1.60000000000000001e42 < y < 2.69999999999999977e55

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 94.8%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot a + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -9.8e+154)
     t_1
     (if (<= y -6.2e+29)
       (* y (+ (/ x a) (/ (+ (/ 27464.7644705 (* y a)) (/ z a)) y)))
       (if (<= y 3.5e+55)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -9.8e+154) {
		tmp = t_1;
	} else if (y <= -6.2e+29) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 3.5e+55) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - (a * (x / y))
    if (y <= (-9.8d+154)) then
        tmp = t_1
    else if (y <= (-6.2d+29)) then
        tmp = y * ((x / a) + (((27464.7644705d0 / (y * a)) + (z / a)) / y))
    else if (y <= 3.5d+55) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -9.8e+154) {
		tmp = t_1;
	} else if (y <= -6.2e+29) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 3.5e+55) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -9.8e+154:
		tmp = t_1
	elif y <= -6.2e+29:
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y))
	elif y <= 3.5e+55:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -9.8e+154)
		tmp = t_1;
	elseif (y <= -6.2e+29)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) / y)));
	elseif (y <= 3.5e+55)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -9.8e+154)
		tmp = t_1;
	elseif (y <= -6.2e+29)
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	elseif (y <= 3.5e+55)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.8e+154], t$95$1, If[LessEqual[y, -6.2e+29], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+55], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.8000000000000003e154 or 3.5000000000000001e55 < y

   1. Initial program 1.5%

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

   3. Taylor expanded in y around inf 74.4%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -9.8000000000000003e154 < y < -6.1999999999999998e29

   1. Initial program 11.8%

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

   3. Taylor expanded in a around inf 8.1%

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

   4. Taylor expanded in y around -inf 49.6%

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

      1. associate-*r* 49.6%

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

      2. mul-1-neg 49.6%

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

      3. distribute-lft-out 49.6%

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

      4. associate-*r/ 49.6%

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

      5. metadata-eval 49.6%

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

   6. Simplified 49.6%

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

   if -6.1999999999999998e29 < y < 3.5000000000000001e55

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 89.7%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+154}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot a + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -3.6e+153)
     t_1
     (if (<= y -8.8e+29)
       (* y (+ (/ x a) (/ (+ (/ 27464.7644705 (* y a)) (/ z a)) y)))
       (if (<= y 1.15e+55)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y (+ c (* y (+ (* y a) b))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -8.8e+29) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 1.15e+55) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * ((y * a) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - (a * (x / y))
    if (y <= (-3.6d+153)) then
        tmp = t_1
    else if (y <= (-8.8d+29)) then
        tmp = y * ((x / a) + (((27464.7644705d0 / (y * a)) + (z / a)) / y))
    else if (y <= 1.15d+55) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * ((y * a) + b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -8.8e+29) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 1.15e+55) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * ((y * a) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -3.6e+153:
		tmp = t_1
	elif y <= -8.8e+29:
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y))
	elif y <= 1.15e+55:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * ((y * a) + b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -8.8e+29)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) / y)));
	elseif (y <= 1.15e+55)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * a) + b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -8.8e+29)
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	elseif (y <= 1.15e+55)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * ((y * a) + 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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+153], t$95$1, If[LessEqual[y, -8.8e+29], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+55], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e153 or 1.14999999999999994e55 < y

   1. Initial program 1.5%

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

   3. Taylor expanded in y around inf 74.4%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -3.6000000000000001e153 < y < -8.8000000000000005e29

   1. Initial program 11.8%

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

   3. Taylor expanded in a around inf 8.1%

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

   4. Taylor expanded in y around -inf 49.6%

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

      1. associate-*r* 49.6%

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

      2. mul-1-neg 49.6%

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

      3. distribute-lft-out 49.6%

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

      4. associate-*r/ 49.6%

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

      5. metadata-eval 49.6%

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

   6. Simplified 49.6%

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

   if -8.8000000000000005e29 < y < 1.14999999999999994e55

   1. Initial program 94.8%

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

   3. Taylor expanded in y around 0 94.7%

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

   4. Taylor expanded in x around 0 89.6%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot a + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 4.85 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -3.6e+153)
     t_1
     (if (<= y -1e+42)
       (* y (+ (/ x a) (/ (+ (/ 27464.7644705 (* y a)) (/ z a)) y)))
       (if (<= y 4.85e+55)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -1e+42) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 4.85e+55) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - (a * (x / y))
    if (y <= (-3.6d+153)) then
        tmp = t_1
    else if (y <= (-1d+42)) then
        tmp = y * ((x / a) + (((27464.7644705d0 / (y * a)) + (z / a)) / y))
    else if (y <= 4.85d+55) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -1e+42) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 4.85e+55) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -3.6e+153:
		tmp = t_1
	elif y <= -1e+42:
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y))
	elif y <= 4.85e+55:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -1e+42)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) / y)));
	elseif (y <= 4.85e+55)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -1e+42)
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	elseif (y <= 4.85e+55)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+153], t$95$1, If[LessEqual[y, -1e+42], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.85e+55], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e153 or 4.8500000000000003e55 < y

   1. Initial program 1.5%

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

   3. Taylor expanded in y around inf 74.4%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -3.6000000000000001e153 < y < -1.00000000000000004e42

   1. Initial program 4.8%

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

   3. Taylor expanded in a around inf 4.7%

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

   4. Taylor expanded in y around -inf 49.5%

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

      1. associate-*r* 49.5%

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

      2. mul-1-neg 49.5%

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

      3. distribute-lft-out 49.5%

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

      4. associate-*r/ 49.5%

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

      5. metadata-eval 49.5%

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

   6. Simplified 49.5%

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

   if -1.00000000000000004e42 < y < 4.8500000000000003e55

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 94.8%

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

   4. Taylor expanded in x around 0 89.1%

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

   5. Taylor expanded in a around 0 83.8%

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

      1. *-commutative 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 4.85 \cdot 10^{+55}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot a + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -3.6e+153)
     t_1
     (if (<= y -1.15e+29)
       (* y (+ (/ x a) (/ (+ (/ 27464.7644705 (* y a)) (/ z a)) y)))
       (if (<= y 2.2e+15)
         (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ (* y a) b))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -1.15e+29) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 2.2e+15) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * a) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - (a * (x / y))
    if (y <= (-3.6d+153)) then
        tmp = t_1
    else if (y <= (-1.15d+29)) then
        tmp = y * ((x / a) + (((27464.7644705d0 / (y * a)) + (z / a)) / y))
    else if (y <= 2.2d+15) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * ((y * a) + b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -1.15e+29) {
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	} else if (y <= 2.2e+15) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * a) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -3.6e+153:
		tmp = t_1
	elif y <= -1.15e+29:
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y))
	elif y <= 2.2e+15:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * a) + b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -1.15e+29)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) / y)));
	elseif (y <= 2.2e+15)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * a) + b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -1.15e+29)
		tmp = y * ((x / a) + (((27464.7644705 / (y * a)) + (z / a)) / y));
	elseif (y <= 2.2e+15)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * a) + 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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+153], t$95$1, If[LessEqual[y, -1.15e+29], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+15], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e153 or 2.2e15 < y

   1. Initial program 4.5%

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

   3. Taylor expanded in y around inf 69.7%

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

      1. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

   if -3.6000000000000001e153 < y < -1.1500000000000001e29

   1. Initial program 11.8%

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

   3. Taylor expanded in a around inf 8.1%

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

   4. Taylor expanded in y around -inf 49.6%

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

      1. associate-*r* 49.6%

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

      2. mul-1-neg 49.6%

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

      3. distribute-lft-out 49.6%

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

      4. associate-*r/ 49.6%

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

      5. metadata-eval 49.6%

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

   6. Simplified 49.6%

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

   if -1.1500000000000001e29 < y < 2.2e15

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 98.2%

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

   4. Taylor expanded in y around 0 85.5%

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

      1. *-commutative 85.5%

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

   6. Simplified 85.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{27464.7644705}{y \cdot a} + \frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot a + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot a + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -3.6e+153)
     t_1
     (if (<= y -1.7e+29)
       (* x (/ y a))
       (if (<= y 2.6e+15)
         (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ (* y a) b))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -1.7e+29) {
		tmp = x * (y / a);
	} else if (y <= 2.6e+15) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * a) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - (a * (x / y))
    if (y <= (-3.6d+153)) then
        tmp = t_1
    else if (y <= (-1.7d+29)) then
        tmp = x * (y / a)
    else if (y <= 2.6d+15) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * ((y * a) + b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -1.7e+29) {
		tmp = x * (y / a);
	} else if (y <= 2.6e+15) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * a) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -3.6e+153:
		tmp = t_1
	elif y <= -1.7e+29:
		tmp = x * (y / a)
	elif y <= 2.6e+15:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * a) + b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -1.7e+29)
		tmp = Float64(x * Float64(y / a));
	elseif (y <= 2.6e+15)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * a) + b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -1.7e+29)
		tmp = x * (y / a);
	elseif (y <= 2.6e+15)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * a) + 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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+153], t$95$1, If[LessEqual[y, -1.7e+29], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+15], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e153 or 2.6e15 < y

   1. Initial program 4.5%

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

   3. Taylor expanded in y around inf 69.7%

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

      1. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

   if -3.6000000000000001e153 < y < -1.69999999999999991e29

   1. Initial program 11.8%

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

   3. Taylor expanded in a around inf 8.1%

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

   4. Taylor expanded in y around inf 39.1%

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

      1. associate-/l* 42.8%

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

   6. Simplified 42.8%

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

   if -1.69999999999999991e29 < y < 2.6e15

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 98.2%

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

   4. Taylor expanded in y around 0 85.5%

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

      1. *-commutative 85.5%

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

   6. Simplified 85.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot a + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot a + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -3.6e+153)
     t_1
     (if (<= y -1.6e+29)
       (* x (/ y a))
       (if (<= y 2e+15) (/ t (+ i (* y (+ c (* y (+ (* y a) b)))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -1.6e+29) {
		tmp = x * (y / a);
	} else if (y <= 2e+15) {
		tmp = t / (i + (y * (c + (y * ((y * a) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - (a * (x / y))
    if (y <= (-3.6d+153)) then
        tmp = t_1
    else if (y <= (-1.6d+29)) then
        tmp = x * (y / a)
    else if (y <= 2d+15) then
        tmp = t / (i + (y * (c + (y * ((y * a) + b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -1.6e+29) {
		tmp = x * (y / a);
	} else if (y <= 2e+15) {
		tmp = t / (i + (y * (c + (y * ((y * a) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -3.6e+153:
		tmp = t_1
	elif y <= -1.6e+29:
		tmp = x * (y / a)
	elif y <= 2e+15:
		tmp = t / (i + (y * (c + (y * ((y * a) + b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -1.6e+29)
		tmp = Float64(x * Float64(y / a));
	elseif (y <= 2e+15)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * a) + b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -1.6e+29)
		tmp = x * (y / a);
	elseif (y <= 2e+15)
		tmp = t / (i + (y * (c + (y * ((y * a) + 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[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+153], t$95$1, If[LessEqual[y, -1.6e+29], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+15], N[(t / N[(i + N[(y * N[(c + N[(y * N[(N[(y * a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e153 or 2e15 < y

   1. Initial program 4.5%

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

   3. Taylor expanded in y around inf 69.7%

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

      1. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

   if -3.6000000000000001e153 < y < -1.59999999999999993e29

   1. Initial program 11.8%

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

   3. Taylor expanded in a around inf 8.1%

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

   4. Taylor expanded in y around inf 39.1%

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

      1. associate-/l* 42.8%

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

   6. Simplified 42.8%

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

   if -1.59999999999999993e29 < y < 2e15

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 98.2%

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

   4. Taylor expanded in t around inf 69.9%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot a + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{elif}\;y \leq 1.5:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -3.6e+153)
     t_1
     (if (<= y -2.45e-23)
       (* y (+ (/ x a) (/ z (* y a))))
       (if (<= y 1.5) (/ (+ t (* y 230661.510616)) i) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -2.45e-23) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else if (y <= 1.5) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - (a * (x / y))
    if (y <= (-3.6d+153)) then
        tmp = t_1
    else if (y <= (-2.45d-23)) then
        tmp = y * ((x / a) + (z / (y * a)))
    else if (y <= 1.5d0) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -3.6e+153) {
		tmp = t_1;
	} else if (y <= -2.45e-23) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else if (y <= 1.5) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -3.6e+153:
		tmp = t_1
	elif y <= -2.45e-23:
		tmp = y * ((x / a) + (z / (y * a)))
	elif y <= 1.5:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -2.45e-23)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(z / Float64(y * a))));
	elseif (y <= 1.5)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -3.6e+153)
		tmp = t_1;
	elseif (y <= -2.45e-23)
		tmp = y * ((x / a) + (z / (y * a)));
	elseif (y <= 1.5)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+153], t$95$1, If[LessEqual[y, -2.45e-23], N[(y * N[(N[(x / a), $MachinePrecision] + N[(z / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e153 or 1.5 < y

   1. Initial program 6.4%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. associate-/l* 74.0%

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

   5. Simplified 74.0%

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

   if -3.6000000000000001e153 < y < -2.4499999999999999e-23

   1. Initial program 30.5%

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

   3. Taylor expanded in a around inf 12.1%

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

   4. Taylor expanded in y around inf 34.5%

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

   if -2.4499999999999999e-23 < y < 1.5

   1. Initial program 99.7%

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

   3. Taylor expanded in i around inf 65.6%

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

   4. Taylor expanded in x around 0 64.8%

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

   5. Taylor expanded in y around 0 63.2%

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

      1. *-commutative 63.2%

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

   7. Simplified 63.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+153}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{elif}\;y \leq 1.5:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+164}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-8}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.4e+164)
   x
   (if (<= y -2.3e-22)
     (* y (+ (/ x a) (/ z (* y a))))
     (if (<= y 4.3e-8)
       (/ (+ t (* y 230661.510616)) i)
       (if (<= y 1.25e+130) (* x (/ y a)) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.4e+164) {
		tmp = x;
	} else if (y <= -2.3e-22) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else if (y <= 4.3e-8) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 1.25e+130) {
		tmp = x * (y / a);
	} 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 <= (-4.4d+164)) then
        tmp = x
    else if (y <= (-2.3d-22)) then
        tmp = y * ((x / a) + (z / (y * a)))
    else if (y <= 4.3d-8) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 1.25d+130) then
        tmp = x * (y / a)
    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 <= -4.4e+164) {
		tmp = x;
	} else if (y <= -2.3e-22) {
		tmp = y * ((x / a) + (z / (y * a)));
	} else if (y <= 4.3e-8) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 1.25e+130) {
		tmp = x * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.4e+164:
		tmp = x
	elif y <= -2.3e-22:
		tmp = y * ((x / a) + (z / (y * a)))
	elif y <= 4.3e-8:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 1.25e+130:
		tmp = x * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.4e+164)
		tmp = x;
	elseif (y <= -2.3e-22)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(z / Float64(y * a))));
	elseif (y <= 4.3e-8)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 1.25e+130)
		tmp = Float64(x * Float64(y / a));
	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 <= -4.4e+164)
		tmp = x;
	elseif (y <= -2.3e-22)
		tmp = y * ((x / a) + (z / (y * a)));
	elseif (y <= 4.3e-8)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 1.25e+130)
		tmp = x * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.4e+164], x, If[LessEqual[y, -2.3e-22], N[(y * N[(N[(x / a), $MachinePrecision] + N[(z / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e-8], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 1.25e+130], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.40000000000000011e164 or 1.2499999999999999e130 < y

   1. Initial program 0.1%

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

   3. Taylor expanded in y around inf 65.6%

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

   if -4.40000000000000011e164 < y < -2.2999999999999998e-22

   1. Initial program 29.7%

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

   3. Taylor expanded in a around inf 11.7%

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

   4. Taylor expanded in y around inf 33.7%

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

   if -2.2999999999999998e-22 < y < 4.3000000000000001e-8

   1. Initial program 99.7%

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

   3. Taylor expanded in i around inf 66.1%

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

   4. Taylor expanded in x around 0 65.3%

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

   5. Taylor expanded in y around 0 63.8%

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

      1. *-commutative 63.8%

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

   7. Simplified 63.8%

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

   if 4.3000000000000001e-8 < y < 1.2499999999999999e130

   1. Initial program 28.7%

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

   3. Taylor expanded in a around inf 13.5%

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

   4. Taylor expanded in y around inf 26.2%

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

      1. associate-/l* 36.9%

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

   6. Simplified 36.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+164}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{y \cdot a}\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-8}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+168}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (/ y a))))
   (if (<= y -2.6e+168)
     x
     (if (<= y -4.7e-35)
       t_1
       (if (<= y 5e-8)
         (/ (+ t (* y 230661.510616)) i)
         (if (<= y 2.05e+130) t_1 x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * (y / a);
	double tmp;
	if (y <= -2.6e+168) {
		tmp = x;
	} else if (y <= -4.7e-35) {
		tmp = t_1;
	} else if (y <= 5e-8) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 2.05e+130) {
		tmp = t_1;
	} 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 = x * (y / a)
    if (y <= (-2.6d+168)) then
        tmp = x
    else if (y <= (-4.7d-35)) then
        tmp = t_1
    else if (y <= 5d-8) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 2.05d+130) then
        tmp = t_1
    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 = x * (y / a);
	double tmp;
	if (y <= -2.6e+168) {
		tmp = x;
	} else if (y <= -4.7e-35) {
		tmp = t_1;
	} else if (y <= 5e-8) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 2.05e+130) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * (y / a)
	tmp = 0
	if y <= -2.6e+168:
		tmp = x
	elif y <= -4.7e-35:
		tmp = t_1
	elif y <= 5e-8:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 2.05e+130:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * Float64(y / a))
	tmp = 0.0
	if (y <= -2.6e+168)
		tmp = x;
	elseif (y <= -4.7e-35)
		tmp = t_1;
	elseif (y <= 5e-8)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 2.05e+130)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * (y / a);
	tmp = 0.0;
	if (y <= -2.6e+168)
		tmp = x;
	elseif (y <= -4.7e-35)
		tmp = t_1;
	elseif (y <= 5e-8)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 2.05e+130)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+168], x, If[LessEqual[y, -4.7e-35], t$95$1, If[LessEqual[y, 5e-8], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 2.05e+130], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e168 or 2.04999999999999989e130 < y

   1. Initial program 0.1%

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

   3. Taylor expanded in y around inf 66.5%

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

   if -2.6e168 < y < -4.7e-35 or 4.9999999999999998e-8 < y < 2.04999999999999989e130

   1. Initial program 31.9%

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

   3. Taylor expanded in a around inf 11.8%

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

   4. Taylor expanded in y around inf 26.3%

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

      1. associate-/l* 31.9%

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

   6. Simplified 31.9%

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

   if -4.7e-35 < y < 4.9999999999999998e-8

   1. Initial program 99.7%

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

   3. Taylor expanded in i around inf 66.1%

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

   4. Taylor expanded in x around 0 66.1%

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

   5. Taylor expanded in y around 0 65.4%

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

      1. *-commutative 65.4%

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

   7. Simplified 65.4%

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

Alternative 14: 49.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+168}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (/ y a))))
   (if (<= y -2.6e+168)
     x
     (if (<= y -1.14e+24)
       t_1
       (if (<= y 8e-11) (/ t i) (if (<= y 1.75e+130) t_1 x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * (y / a);
	double tmp;
	if (y <= -2.6e+168) {
		tmp = x;
	} else if (y <= -1.14e+24) {
		tmp = t_1;
	} else if (y <= 8e-11) {
		tmp = t / i;
	} else if (y <= 1.75e+130) {
		tmp = t_1;
	} 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 = x * (y / a)
    if (y <= (-2.6d+168)) then
        tmp = x
    else if (y <= (-1.14d+24)) then
        tmp = t_1
    else if (y <= 8d-11) then
        tmp = t / i
    else if (y <= 1.75d+130) then
        tmp = t_1
    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 = x * (y / a);
	double tmp;
	if (y <= -2.6e+168) {
		tmp = x;
	} else if (y <= -1.14e+24) {
		tmp = t_1;
	} else if (y <= 8e-11) {
		tmp = t / i;
	} else if (y <= 1.75e+130) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * (y / a)
	tmp = 0
	if y <= -2.6e+168:
		tmp = x
	elif y <= -1.14e+24:
		tmp = t_1
	elif y <= 8e-11:
		tmp = t / i
	elif y <= 1.75e+130:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * Float64(y / a))
	tmp = 0.0
	if (y <= -2.6e+168)
		tmp = x;
	elseif (y <= -1.14e+24)
		tmp = t_1;
	elseif (y <= 8e-11)
		tmp = Float64(t / i);
	elseif (y <= 1.75e+130)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * (y / a);
	tmp = 0.0;
	if (y <= -2.6e+168)
		tmp = x;
	elseif (y <= -1.14e+24)
		tmp = t_1;
	elseif (y <= 8e-11)
		tmp = t / i;
	elseif (y <= 1.75e+130)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+168], x, If[LessEqual[y, -1.14e+24], t$95$1, If[LessEqual[y, 8e-11], N[(t / i), $MachinePrecision], If[LessEqual[y, 1.75e+130], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e168 or 1.75e130 < y

   1. Initial program 0.1%

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

   3. Taylor expanded in y around inf 66.5%

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

   if -2.6e168 < y < -1.14e24 or 7.99999999999999952e-11 < y < 1.75e130

   1. Initial program 19.1%

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

   3. Taylor expanded in a around inf 10.2%

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

   4. Taylor expanded in y around inf 31.1%

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

      1. associate-/l* 37.9%

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

   6. Simplified 37.9%

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

   if -1.14e24 < y < 7.99999999999999952e-11

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 50.8%

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

Alternative 15: 51.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 115000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.05e+33) x (if (<= y 115000.0) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.05e+33) {
		tmp = x;
	} else if (y <= 115000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.05d+33)) then
        tmp = x
    else if (y <= 115000.0d0) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.05e+33) {
		tmp = x;
	} else if (y <= 115000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.05e+33:
		tmp = x
	elif y <= 115000.0:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.05e+33)
		tmp = x;
	elseif (y <= 115000.0)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.05e+33)
		tmp = x;
	elseif (y <= 115000.0)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.05e+33], x, If[LessEqual[y, 115000.0], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e33 or 115000 < y

   1. Initial program 6.8%

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

   3. Taylor expanded in y around inf 45.1%

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

   if -1.05e33 < y < 115000

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 49.7%

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

Alternative 16: 25.7% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 52.1%

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

3. Taylor expanded in y around inf 24.6%

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

Reproduce

herbie shell --seed 2024180 
(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)))