Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.9% → 83.7%

Time: 22.0s

Alternatives: 20

Speedup: 3.0×

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: 55.9% 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: 83.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+64} \lor \neg \left(y \leq 1.12 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t_1} + \left(\frac{x \cdot {y}^{4}}{t_1} + \frac{y \cdot \left(230661.510616 + y \cdot \left(y \cdot z + 27464.7644705\right)\right)}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i)))
   (if (or (<= y -3.8e+64) (not (<= y 1.12e+34)))
     (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))
     (+
      (/ t t_1)
      (+
       (/ (* x (pow y 4.0)) t_1)
       (/ (* y (+ 230661.510616 (* y (+ (* y z) 27464.7644705)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * (c + (y * (b + (y * (y + a)))))) + i;
	double tmp;
	if ((y <= -3.8e+64) || !(y <= 1.12e+34)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t / t_1) + (((x * pow(y, 4.0)) / t_1) + ((y * (230661.510616 + (y * ((y * z) + 27464.7644705)))) / 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 = (y * (c + (y * (b + (y * (y + a)))))) + i
    if ((y <= (-3.8d+64)) .or. (.not. (y <= 1.12d+34))) then
        tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    else
        tmp = (t / t_1) + (((x * (y ** 4.0d0)) / t_1) + ((y * (230661.510616d0 + (y * ((y * z) + 27464.7644705d0)))) / 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 = (y * (c + (y * (b + (y * (y + a)))))) + i;
	double tmp;
	if ((y <= -3.8e+64) || !(y <= 1.12e+34)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t / t_1) + (((x * Math.pow(y, 4.0)) / t_1) + ((y * (230661.510616 + (y * ((y * z) + 27464.7644705)))) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * (c + (y * (b + (y * (y + a)))))) + i
	tmp = 0
	if (y <= -3.8e+64) or not (y <= 1.12e+34):
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	else:
		tmp = (t / t_1) + (((x * math.pow(y, 4.0)) / t_1) + ((y * (230661.510616 + (y * ((y * z) + 27464.7644705)))) / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i)
	tmp = 0.0
	if ((y <= -3.8e+64) || !(y <= 1.12e+34))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))));
	else
		tmp = Float64(Float64(t / t_1) + Float64(Float64(Float64(x * (y ^ 4.0)) / t_1) + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(Float64(y * z) + 27464.7644705)))) / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * (c + (y * (b + (y * (y + a)))))) + i;
	tmp = 0.0;
	if ((y <= -3.8e+64) || ~((y <= 1.12e+34)))
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	else
		tmp = (t / t_1) + (((x * (y ^ 4.0)) / t_1) + ((y * (230661.510616 + (y * ((y * z) + 27464.7644705)))) / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[Or[LessEqual[y, -3.8e+64], N[Not[LessEqual[y, 1.12e+34]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(N[(x * N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(y * N[(230661.510616 + N[(y * N[(N[(y * z), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000001e64 or 1.12e34 < y

   1. Initial program 3.0%

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

      1. add-cbrt-cube 1.3%

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

      2. rem-cube-cbrt 1.3%

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

      3. add-cbrt-cube 1.3%

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

      4. *-commutative 1.3%

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

      5. *-commutative 1.3%

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

      6. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 1.3%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 58.2%

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

      1. associate--r+ 58.2%

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

      2. +-commutative 58.2%

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

      3. associate-*r/ 58.2%

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

      4. metadata-eval 58.2%

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

      5. unpow2 58.2%

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

      6. *-commutative 58.2%

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

      7. associate-/l* 65.7%

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

      8. unpow2 65.7%

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

      9. *-commutative 65.7%

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

      10. associate-/l* 65.6%

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

      11. associate-/l* 72.4%

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

      12. unpow2 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in y around inf 75.0%

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

   if -3.8000000000000001e64 < y < 1.12e34

   1. Initial program 95.6%

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

   2. Taylor expanded in x around 0 95.7%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+64} \lor \neg \left(y \leq 1.12 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i} + \left(\frac{x \cdot {y}^{4}}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i} + \frac{y \cdot \left(230661.510616 + y \cdot \left(y \cdot z + 27464.7644705\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\right)\\ \end{array} \]

Alternative 2: 83.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+61} \lor \neg \left(y \leq 1.12 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + \left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z + 27464.7644705\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.5e+61) (not (<= y 1.12e+34)))
   (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))
   (/
    (+
     t
     (+
      (* x (pow y 4.0))
      (* y (+ 230661.510616 (* y (+ (* y z) 27464.7644705))))))
    (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.5e+61) || !(y <= 1.12e+34)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + ((x * pow(y, 4.0)) + (y * (230661.510616 + (y * ((y * z) + 27464.7644705)))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-4.5d+61)) .or. (.not. (y <= 1.12d+34))) then
        tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    else
        tmp = (t + ((x * (y ** 4.0d0)) + (y * (230661.510616d0 + (y * ((y * z) + 27464.7644705d0)))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.5e+61) || !(y <= 1.12e+34)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + ((x * Math.pow(y, 4.0)) + (y * (230661.510616 + (y * ((y * z) + 27464.7644705)))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.5e+61) or not (y <= 1.12e+34):
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	else:
		tmp = (t + ((x * math.pow(y, 4.0)) + (y * (230661.510616 + (y * ((y * z) + 27464.7644705)))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.5e+61) || !(y <= 1.12e+34))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))));
	else
		tmp = Float64(Float64(t + Float64(Float64(x * (y ^ 4.0)) + Float64(y * Float64(230661.510616 + Float64(y * Float64(Float64(y * z) + 27464.7644705)))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.5e+61) || ~((y <= 1.12e+34)))
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	else
		tmp = (t + ((x * (y ^ 4.0)) + (y * (230661.510616 + (y * ((y * z) + 27464.7644705)))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.5e+61], N[Not[LessEqual[y, 1.12e+34]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(N[(x * N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] + N[(y * N[(230661.510616 + N[(y * N[(N[(y * z), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e61 or 1.12e34 < y

   1. Initial program 3.0%

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

      1. add-cbrt-cube 1.3%

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

      2. rem-cube-cbrt 1.3%

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

      3. add-cbrt-cube 1.3%

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

      4. *-commutative 1.3%

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

      5. *-commutative 1.3%

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

      6. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 1.3%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 58.2%

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

      1. associate--r+ 58.2%

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

      2. +-commutative 58.2%

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

      3. associate-*r/ 58.2%

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

      4. metadata-eval 58.2%

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

      5. unpow2 58.2%

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

      6. *-commutative 58.2%

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

      7. associate-/l* 65.7%

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

      8. unpow2 65.7%

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

      9. *-commutative 65.7%

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

      10. associate-/l* 65.6%

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

      11. associate-/l* 72.4%

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

      12. unpow2 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in y around inf 75.0%

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

   if -4.5e61 < y < 1.12e34

   1. Initial program 95.6%

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

   2. Taylor expanded in x around 0 95.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+61} \lor \neg \left(y \leq 1.12 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + \left(x \cdot {y}^{4} + y \cdot \left(230661.510616 + y \cdot \left(y \cdot z + 27464.7644705\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]

Alternative 3: 83.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+65} \lor \neg \left(y \leq 1.12 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6.2e+65) (not (<= y 1.12e+34)))
   (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
    (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.2e+65) || !(y <= 1.12e+34)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-6.2d+65)) .or. (.not. (y <= 1.12d+34))) then
        tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.2e+65) || !(y <= 1.12e+34)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6.2e+65) or not (y <= 1.12e+34):
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6.2e+65) || !(y <= 1.12e+34))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -6.2e+65) || ~((y <= 1.12e+34)))
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6.2e+65], N[Not[LessEqual[y, 1.12e+34]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.19999999999999981e65 or 1.12e34 < y

   1. Initial program 3.0%

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

      1. add-cbrt-cube 1.3%

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

      2. rem-cube-cbrt 1.3%

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

      3. add-cbrt-cube 1.3%

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

      4. *-commutative 1.3%

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

      5. *-commutative 1.3%

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

      6. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 1.3%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 58.2%

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

      1. associate--r+ 58.2%

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

      2. +-commutative 58.2%

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

      3. associate-*r/ 58.2%

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

      4. metadata-eval 58.2%

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

      5. unpow2 58.2%

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

      6. *-commutative 58.2%

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

      7. associate-/l* 65.7%

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

      8. unpow2 65.7%

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

      9. *-commutative 65.7%

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

      10. associate-/l* 65.6%

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

      11. associate-/l* 72.4%

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

      12. unpow2 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in y around inf 75.0%

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

   if -6.19999999999999981e65 < y < 1.12e34

   1. Initial program 95.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+65} \lor \neg \left(y \leq 1.12 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]

Alternative 4: 79.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+70} \lor \neg \left(y \leq 1.12 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.3e+70) (not (<= y 1.12e+34)))
   (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* y y)))))))
    (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.3e+70) || !(y <= 1.12e+34)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.3d+70)) .or. (.not. (y <= 1.12d+34))) then
        tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (y * y))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.3e+70) || !(y <= 1.12e+34)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.3e+70) or not (y <= 1.12e+34):
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.3e+70) || !(y <= 1.12e+34))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * Float64(y * y))))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.3e+70) || ~((y <= 1.12e+34)))
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.3e+70], N[Not[LessEqual[y, 1.12e+34]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.30000000000000016e70 or 1.12e34 < y

   1. Initial program 3.1%

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

      1. add-cbrt-cube 1.3%

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

      2. rem-cube-cbrt 1.3%

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

      3. add-cbrt-cube 1.3%

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

      4. *-commutative 1.3%

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

      5. *-commutative 1.3%

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

      6. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 1.3%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 58.7%

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

      1. associate--r+ 58.7%

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

      2. +-commutative 58.7%

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

      3. associate-*r/ 58.7%

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

      4. metadata-eval 58.7%

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

      5. unpow2 58.7%

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

      6. *-commutative 58.7%

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

      7. associate-/l* 66.2%

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

      8. unpow2 66.2%

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

      9. *-commutative 66.2%

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

      10. associate-/l* 66.2%

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

      11. associate-/l* 73.1%

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

      12. unpow2 73.1%

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

   6. Simplified 73.1%

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

   7. Taylor expanded in y around inf 75.6%

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

   if -3.30000000000000016e70 < y < 1.12e34

   1. Initial program 95.0%

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

   2. Taylor expanded in z around 0 92.3%

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

      1. *-commutative 92.3%

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

      2. *-commutative 92.3%

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

      3. unpow2 92.3%

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

   4. Simplified 92.3%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+70} \lor \neg \left(y \leq 1.12 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]

Alternative 5: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+50} \lor \neg \left(y \leq 1.12 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.2e+50) (not (<= y 1.12e+34)))
   (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
    (+ i (* y (+ c (* a (* y y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.2e+50) || !(y <= 1.12e+34)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (a * (y * y)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.2d+50)) .or. (.not. (y <= 1.12d+34))) then
        tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (a * (y * y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.2e+50) || !(y <= 1.12e+34)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (a * (y * y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.2e+50) or not (y <= 1.12e+34):
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (a * (y * y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.2e+50) || !(y <= 1.12e+34))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(a * Float64(y * y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.2e+50) || ~((y <= 1.12e+34)))
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (a * (y * y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.2e+50], N[Not[LessEqual[y, 1.12e+34]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2000000000000001e50 or 1.12e34 < y

   1. Initial program 3.9%

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

      1. add-cbrt-cube 1.4%

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

      2. rem-cube-cbrt 1.4%

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

      3. add-cbrt-cube 1.4%

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

      4. *-commutative 1.4%

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

      5. *-commutative 1.4%

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

      6. fma-def 1.4%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 1.4%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 1.4%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 57.3%

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

      1. associate--r+ 57.3%

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

      2. +-commutative 57.3%

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

      3. associate-*r/ 57.3%

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

      4. metadata-eval 57.3%

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

      5. unpow2 57.3%

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

      6. *-commutative 57.3%

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

      7. associate-/l* 64.6%

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

      8. unpow2 64.6%

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

      9. *-commutative 64.6%

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

      10. associate-/l* 64.6%

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

      11. associate-/l* 71.3%

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

      12. unpow2 71.3%

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

   6. Simplified 71.3%

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

   7. Taylor expanded in y around inf 73.8%

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

   if -1.2000000000000001e50 < y < 1.12e34

   1. Initial program 96.3%

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

   2. Taylor expanded in a around inf 92.4%

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

      1. *-commutative 92.4%

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

      2. unpow2 92.4%

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

   4. Simplified 92.4%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+50} \lor \neg \left(y \leq 1.12 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]

Alternative 6: 80.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+61} \lor \neg \left(y \leq 2.9 \cdot 10^{+39}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.1e+61) (not (<= y 2.9e+39)))
   (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.1e+61) || !(y <= 2.9e+39)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.1d+61)) .or. (.not. (y <= 2.9d+39))) then
        tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.1e+61) || !(y <= 2.9e+39)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.1e+61) or not (y <= 2.9e+39):
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.1e+61) || !(y <= 2.9e+39))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.1e+61) || ~((y <= 2.9e+39)))
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.1e+61], N[Not[LessEqual[y, 2.9e+39]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999999e61 or 2.90000000000000029e39 < y

   1. Initial program 3.1%

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

      1. add-cbrt-cube 1.3%

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

      2. rem-cube-cbrt 1.3%

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

      3. add-cbrt-cube 1.3%

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

      4. *-commutative 1.3%

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

      5. *-commutative 1.3%

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

      6. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 1.3%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 58.7%

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

      1. associate--r+ 58.7%

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

      2. +-commutative 58.7%

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

      3. associate-*r/ 58.7%

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

      4. metadata-eval 58.7%

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

      5. unpow2 58.7%

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

      6. *-commutative 58.7%

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

      7. associate-/l* 66.2%

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

      8. unpow2 66.2%

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

      9. *-commutative 66.2%

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

      10. associate-/l* 66.2%

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

      11. associate-/l* 73.1%

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

      12. unpow2 73.1%

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

   6. Simplified 73.1%

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

   7. Taylor expanded in y around inf 75.6%

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

   if -3.0999999999999999e61 < y < 2.90000000000000029e39

   1. Initial program 95.0%

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

   2. Taylor expanded in y around 0 89.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+61} \lor \neg \left(y \leq 2.9 \cdot 10^{+39}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 7: 75.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+70} \lor \neg \left(y \leq 5 \cdot 10^{+38}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.2e+70) (not (<= y 5e+38)))
   (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.2e+70) || !(y <= 5e+38)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.2d+70)) .or. (.not. (y <= 5d+38))) then
        tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.2e+70) || !(y <= 5e+38)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.2e+70) or not (y <= 5e+38):
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.2e+70) || !(y <= 5e+38))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.2e+70) || ~((y <= 5e+38)))
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.2e+70], N[Not[LessEqual[y, 5e+38]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.19999999999999993e70 or 4.9999999999999997e38 < y

   1. Initial program 3.1%

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

      1. add-cbrt-cube 1.4%

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

      2. rem-cube-cbrt 1.3%

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

      3. add-cbrt-cube 1.3%

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

      4. *-commutative 1.3%

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

      5. *-commutative 1.3%

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

      6. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 1.3%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 59.2%

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

      1. associate--r+ 59.2%

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

      2. +-commutative 59.2%

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

      3. associate-*r/ 59.2%

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

      4. metadata-eval 59.2%

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

      5. unpow2 59.2%

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

      6. *-commutative 59.2%

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

      7. associate-/l* 66.8%

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

      8. unpow2 66.8%

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

      9. *-commutative 66.8%

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

      10. associate-/l* 66.8%

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

      11. associate-/l* 73.7%

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

      12. unpow2 73.7%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in y around inf 76.3%

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

   if -1.19999999999999993e70 < y < 4.9999999999999997e38

   1. Initial program 94.3%

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

   2. Taylor expanded in y around 0 87.9%

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

      1. *-commutative 87.9%

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

   4. Simplified 87.9%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+70} \lor \neg \left(y \leq 5 \cdot 10^{+38}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]

Alternative 8: 72.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+70} \lor \neg \left(y \leq 4.4 \cdot 10^{+35}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + \left(y \cdot y\right) \cdot \left(y + a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.2e+70) (not (<= y 4.4e+35)))
   (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ i (* y (+ c (* (* y y) (+ y a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.2e+70) || !(y <= 4.4e+35)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + ((y * y) * (y + a)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.2d+70)) .or. (.not. (y <= 4.4d+35))) then
        tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + ((y * y) * (y + a)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.2e+70) || !(y <= 4.4e+35)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + ((y * y) * (y + a)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.2e+70) or not (y <= 4.4e+35):
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + ((y * y) * (y + a)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.2e+70) || !(y <= 4.4e+35))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(Float64(y * y) * Float64(y + a))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.2e+70) || ~((y <= 4.4e+35)))
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + ((y * y) * (y + a)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.2e+70], N[Not[LessEqual[y, 4.4e+35]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(N[(y * y), $MachinePrecision] * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.19999999999999993e70 or 4.3999999999999997e35 < y

   1. Initial program 3.1%

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

      1. add-cbrt-cube 1.4%

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

      2. rem-cube-cbrt 1.3%

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

      3. add-cbrt-cube 1.3%

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

      4. *-commutative 1.3%

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

      5. *-commutative 1.3%

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

      6. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 1.3%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 1.3%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 59.2%

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

      1. associate--r+ 59.2%

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

      2. +-commutative 59.2%

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

      3. associate-*r/ 59.2%

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

      4. metadata-eval 59.2%

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

      5. unpow2 59.2%

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

      6. *-commutative 59.2%

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

      7. associate-/l* 66.8%

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

      8. unpow2 66.8%

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

      9. *-commutative 66.8%

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

      10. associate-/l* 66.8%

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

      11. associate-/l* 73.7%

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

      12. unpow2 73.7%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in y around inf 76.3%

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

   if -1.19999999999999993e70 < y < 4.3999999999999997e35

   1. Initial program 94.3%

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

   2. Taylor expanded in y around 0 87.9%

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

      1. *-commutative 87.9%

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

   4. Simplified 87.9%

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

   5. Taylor expanded in y around inf 85.8%

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

      1. cube-mult 85.8%

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

      2. unpow2 85.8%

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

      3. distribute-rgt-in 85.8%

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

      4. *-commutative 85.8%

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

      5. unpow2 85.8%

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

   7. Simplified 85.8%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+70} \lor \neg \left(y \leq 4.4 \cdot 10^{+35}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + \left(y \cdot y\right) \cdot \left(y + a\right)\right)}\\ \end{array} \]

Alternative 9: 67.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-43}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))))
   (if (<= y -7.2e+45)
     t_1
     (if (<= y -3e-43)
       (/
        (+
         t
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
        i)
       (if (<= y 2.1e+36)
         (/ t (+ (* y (+ c (* y (+ b (* y (+ y a)))))) 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 = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	double tmp;
	if (y <= -7.2e+45) {
		tmp = t_1;
	} else if (y <= -3e-43) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / i;
	} else if (y <= 2.1e+36) {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + 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 = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    if (y <= (-7.2d+45)) then
        tmp = t_1
    else if (y <= (-3d-43)) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / i
    else if (y <= 2.1d+36) then
        tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + 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 = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	double tmp;
	if (y <= -7.2e+45) {
		tmp = t_1;
	} else if (y <= -3e-43) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / i;
	} else if (y <= 2.1e+36) {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	tmp = 0
	if y <= -7.2e+45:
		tmp = t_1
	elif y <= -3e-43:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / i
	elif y <= 2.1e+36:
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))))
	tmp = 0.0
	if (y <= -7.2e+45)
		tmp = t_1;
	elseif (y <= -3e-43)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / i);
	elseif (y <= 2.1e+36)
		tmp = Float64(t / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	tmp = 0.0;
	if (y <= -7.2e+45)
		tmp = t_1;
	elseif (y <= -3e-43)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / i;
	elseif (y <= 2.1e+36)
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + 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[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+45], t$95$1, If[LessEqual[y, -3e-43], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 2.1e+36], N[(t / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2e45 or 2.10000000000000004e36 < y

   1. Initial program 4.7%

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

      1. add-cbrt-cube 2.2%

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

      2. rem-cube-cbrt 2.2%

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

      3. add-cbrt-cube 2.2%

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

      4. *-commutative 2.2%

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

      5. *-commutative 2.2%

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

      6. fma-def 2.2%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 2.2%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 2.2%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 57.3%

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

      1. associate--r+ 57.3%

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

      2. +-commutative 57.3%

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

      3. associate-*r/ 57.3%

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

      4. metadata-eval 57.3%

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

      5. unpow2 57.3%

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

      6. *-commutative 57.3%

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

      7. associate-/l* 64.6%

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

      8. unpow2 64.6%

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

      9. *-commutative 64.6%

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

      10. associate-/l* 64.6%

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

      11. associate-/l* 71.3%

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

      12. unpow2 71.3%

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

   6. Simplified 71.3%

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

   7. Taylor expanded in y around inf 73.9%

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

   if -7.2e45 < y < -3.00000000000000003e-43

   1. Initial program 71.5%

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

   2. Taylor expanded in i around inf 53.6%

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

   if -3.00000000000000003e-43 < y < 2.10000000000000004e36

   1. Initial program 98.9%

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

   2. Taylor expanded in t around inf 81.0%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+45}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-43}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \end{array} \]

Alternative 10: 75.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+34} \lor \neg \left(y \leq 1.58 \cdot 10^{+38}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.3e+34) (not (<= y 1.58e+38)))
   (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))
   (/ (+ t (* y 230661.510616)) (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.3e+34) || !(y <= 1.58e+38)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-4.3d+34)) .or. (.not. (y <= 1.58d+38))) then
        tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.3e+34) || !(y <= 1.58e+38)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.3e+34) or not (y <= 1.58e+38):
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	else:
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.3e+34) || !(y <= 1.58e+38))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.3e+34) || ~((y <= 1.58e+38)))
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	else
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.3e+34], N[Not[LessEqual[y, 1.58e+38]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.29999999999999994e34 or 1.58e38 < y

   1. Initial program 6.3%

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

      1. add-cbrt-cube 3.0%

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

      2. rem-cube-cbrt 3.0%

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

      3. add-cbrt-cube 3.0%

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

      4. *-commutative 3.0%

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

      5. *-commutative 3.0%

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

      6. fma-def 3.0%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 3.0%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 3.0%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 56.4%

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

      1. associate--r+ 56.4%

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

      2. +-commutative 56.4%

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

      3. associate-*r/ 56.4%

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

      4. metadata-eval 56.4%

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

      5. unpow2 56.4%

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

      6. *-commutative 56.4%

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

      7. associate-/l* 63.6%

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

      8. unpow2 63.6%

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

      9. *-commutative 63.6%

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

      10. associate-/l* 63.6%

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

      11. associate-/l* 70.2%

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

      12. unpow2 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in y around inf 72.8%

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

   if -4.29999999999999994e34 < y < 1.58e38

   1. Initial program 95.5%

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

   2. Taylor expanded in y around 0 88.7%

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

      1. *-commutative 88.7%

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

   4. Simplified 88.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+34} \lor \neg \left(y \leq 1.58 \cdot 10^{+38}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]

Alternative 11: 68.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+36} \lor \neg \left(y \leq 2.35 \cdot 10^{+36}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7.5e+36) (not (<= y 2.35e+36)))
   (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))
   (/ t (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7.5e+36) || !(y <= 2.35e+36)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-7.5d+36)) .or. (.not. (y <= 2.35d+36))) then
        tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    else
        tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7.5e+36) || !(y <= 2.35e+36)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -7.5e+36) or not (y <= 2.35e+36):
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	else:
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -7.5e+36) || !(y <= 2.35e+36))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))));
	else
		tmp = Float64(t / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -7.5e+36) || ~((y <= 2.35e+36)))
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	else
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -7.5e+36], N[Not[LessEqual[y, 2.35e+36]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000054e36 or 2.34999999999999994e36 < y

   1. Initial program 6.3%

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

      1. add-cbrt-cube 3.0%

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

      2. rem-cube-cbrt 3.0%

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

      3. add-cbrt-cube 3.0%

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

      4. *-commutative 3.0%

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

      5. *-commutative 3.0%

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

      6. fma-def 3.0%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 3.0%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 3.0%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 56.4%

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

      1. associate--r+ 56.4%

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

      2. +-commutative 56.4%

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

      3. associate-*r/ 56.4%

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

      4. metadata-eval 56.4%

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

      5. unpow2 56.4%

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

      6. *-commutative 56.4%

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

      7. associate-/l* 63.6%

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

      8. unpow2 63.6%

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

      9. *-commutative 63.6%

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

      10. associate-/l* 63.6%

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

      11. associate-/l* 70.2%

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

      12. unpow2 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in y around inf 72.8%

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

   if -7.50000000000000054e36 < y < 2.34999999999999994e36

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf 75.2%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+36} \lor \neg \left(y \leq 2.35 \cdot 10^{+36}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]

Alternative 12: 74.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+45} \lor \neg \left(y \leq 2.05 \cdot 10^{+37}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.15e+45) (not (<= y 2.05e+37)))
   (- (+ (/ z y) x) (+ (/ a (/ y x)) (/ b (/ (* y y) x))))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.15e+45) || !(y <= 2.05e+37)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.15d+45)) .or. (.not. (y <= 2.05d+37))) then
        tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.15e+45) || !(y <= 2.05e+37)) {
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.15e+45) or not (y <= 2.05e+37):
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.15e+45) || !(y <= 2.05e+37))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(a / Float64(y / x)) + Float64(b / Float64(Float64(y * y) / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.15e+45) || ~((y <= 2.05e+37)))
		tmp = ((z / y) + x) - ((a / (y / x)) + (b / ((y * y) / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.15e+45], N[Not[LessEqual[y, 2.05e+37]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000006e45 or 2.0499999999999999e37 < y

   1. Initial program 4.7%

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

      1. add-cbrt-cube 2.2%

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

      2. rem-cube-cbrt 2.2%

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

      3. add-cbrt-cube 2.2%

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

      4. *-commutative 2.2%

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

      5. *-commutative 2.2%

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

      6. fma-def 2.2%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. fma-def 2.2%

         \[\leadsto \frac{\left(\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 2.2%

      \[\leadsto \frac{\left(\color{blue}{\sqrt[3]{{\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)\right)}^{3}}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around inf 57.3%

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

      1. associate--r+ 57.3%

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

      2. +-commutative 57.3%

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

      3. associate-*r/ 57.3%

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

      4. metadata-eval 57.3%

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

      5. unpow2 57.3%

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

      6. *-commutative 57.3%

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

      7. associate-/l* 64.6%

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

      8. unpow2 64.6%

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

      9. *-commutative 64.6%

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

      10. associate-/l* 64.6%

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

      11. associate-/l* 71.3%

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

      12. unpow2 71.3%

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

   6. Simplified 71.3%

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

   7. Taylor expanded in y around inf 73.9%

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

   if -1.15000000000000006e45 < y < 2.0499999999999999e37

   1. Initial program 95.5%

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

   2. Taylor expanded in y around 0 89.7%

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

      1. *-commutative 89.7%

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

   4. Simplified 89.7%

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

   5. Taylor expanded in y around 0 85.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+45} \lor \neg \left(y \leq 2.05 \cdot 10^{+37}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(\frac{a}{\frac{y}{x}} + \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 13: 66.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+31} \lor \neg \left(y \leq 2.1 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.7e+31) (not (<= y 2.1e+34)))
   (- (+ (/ z y) x) (/ (* x a) y))
   (/ t (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.7e+31) || !(y <= 2.1e+34)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.7d+31)) .or. (.not. (y <= 2.1d+34))) then
        tmp = ((z / y) + x) - ((x * a) / y)
    else
        tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.7e+31) || !(y <= 2.1e+34)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.7e+31) or not (y <= 2.1e+34):
		tmp = ((z / y) + x) - ((x * a) / y)
	else:
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.7e+31) || !(y <= 2.1e+34))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(t / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.7e+31) || ~((y <= 2.1e+34)))
		tmp = ((z / y) + x) - ((x * a) / y);
	else
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.7e+31], N[Not[LessEqual[y, 2.1e+34]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.69999999999999986e31 or 2.10000000000000017e34 < y

   1. Initial program 6.2%

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

   2. Taylor expanded in y around inf 69.6%

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

   if -2.69999999999999986e31 < y < 2.10000000000000017e34

   1. Initial program 96.2%

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

   2. Taylor expanded in t around inf 75.7%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+31} \lor \neg \left(y \leq 2.1 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \end{array} \]

Alternative 14: 61.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-178}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ (/ z y) x) (/ (* x a) y))))
   (if (<= y -1.15e+45)
     t_1
     (if (<= y -4.2e-178)
       (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) i)
       (if (<= y 3.1e+34) (/ t (+ i (* y c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((z / y) + x) - ((x * a) / y);
	double tmp;
	if (y <= -1.15e+45) {
		tmp = t_1;
	} else if (y <= -4.2e-178) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i;
	} else if (y <= 3.1e+34) {
		tmp = t / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((z / y) + x) - ((x * a) / y)
    if (y <= (-1.15d+45)) then
        tmp = t_1
    else if (y <= (-4.2d-178)) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / i
    else if (y <= 3.1d+34) then
        tmp = t / (i + (y * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((z / y) + x) - ((x * a) / y);
	double tmp;
	if (y <= -1.15e+45) {
		tmp = t_1;
	} else if (y <= -4.2e-178) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i;
	} else if (y <= 3.1e+34) {
		tmp = t / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((z / y) + x) - ((x * a) / y)
	tmp = 0
	if y <= -1.15e+45:
		tmp = t_1
	elif y <= -4.2e-178:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i
	elif y <= 3.1e+34:
		tmp = t / (i + (y * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(z / y) + x) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.15e+45)
		tmp = t_1;
	elseif (y <= -4.2e-178)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / i);
	elseif (y <= 3.1e+34)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((z / y) + x) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.15e+45)
		tmp = t_1;
	elseif (y <= -4.2e-178)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i;
	elseif (y <= 3.1e+34)
		tmp = t / (i + (y * c));
	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[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+45], t$95$1, If[LessEqual[y, -4.2e-178], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 3.1e+34], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000006e45 or 3.09999999999999977e34 < y

   1. Initial program 4.7%

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

   2. Taylor expanded in y around inf 71.2%

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

   if -1.15000000000000006e45 < y < -4.2e-178

   1. Initial program 89.6%

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

   2. Taylor expanded in y around 0 78.1%

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

      1. *-commutative 78.1%

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

   4. Simplified 78.1%

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

   5. Taylor expanded in i around inf 60.2%

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

   if -4.2e-178 < y < 3.09999999999999977e34

   1. Initial program 98.6%

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

   2. Taylor expanded in t around inf 80.7%

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

   3. Taylor expanded in y around 0 78.5%

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

      1. *-commutative 78.5%

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

   5. Simplified 78.5%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+45}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-178}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 15: 63.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+31} \lor \neg \left(y \leq 1.3 \cdot 10^{+37}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.4e+31) (not (<= y 1.3e+37)))
   (- (+ (/ z y) x) (/ (* x a) y))
   (/ t (+ i (* y (+ c (* a (* y y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.4e+31) || !(y <= 1.3e+37)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + (a * (y * y)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.4d+31)) .or. (.not. (y <= 1.3d+37))) then
        tmp = ((z / y) + x) - ((x * a) / y)
    else
        tmp = t / (i + (y * (c + (a * (y * y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.4e+31) || !(y <= 1.3e+37)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + (a * (y * y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.4e+31) or not (y <= 1.3e+37):
		tmp = ((z / y) + x) - ((x * a) / y)
	else:
		tmp = t / (i + (y * (c + (a * (y * y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.4e+31) || !(y <= 1.3e+37))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(a * Float64(y * y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.4e+31) || ~((y <= 1.3e+37)))
		tmp = ((z / y) + x) - ((x * a) / y);
	else
		tmp = t / (i + (y * (c + (a * (y * y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.4e+31], N[Not[LessEqual[y, 1.3e+37]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999982e31 or 1.3e37 < y

   1. Initial program 6.2%

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

   2. Taylor expanded in y around inf 69.6%

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

   if -2.39999999999999982e31 < y < 1.3e37

   1. Initial program 96.2%

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

   2. Taylor expanded in t around inf 75.7%

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

   3. Taylor expanded in a around inf 73.5%

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

      1. *-commutative 73.5%

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

      2. unpow2 73.5%

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

   5. Simplified 73.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+31} \lor \neg \left(y \leq 1.3 \cdot 10^{+37}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \end{array} \]

Alternative 16: 63.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+31} \lor \neg \left(y \leq 5.5 \cdot 10^{+38}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.6e+31) (not (<= y 5.5e+38)))
   (- (+ (/ z y) x) (/ (* x a) y))
   (/ t (+ i (* y (+ c (* y (* y a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.6e+31) || !(y <= 5.5e+38)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + (y * (y * a)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.6d+31)) .or. (.not. (y <= 5.5d+38))) then
        tmp = ((z / y) + x) - ((x * a) / y)
    else
        tmp = t / (i + (y * (c + (y * (y * a)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.6e+31) || !(y <= 5.5e+38)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + (y * (y * a)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.6e+31) or not (y <= 5.5e+38):
		tmp = ((z / y) + x) - ((x * a) / y)
	else:
		tmp = t / (i + (y * (c + (y * (y * a)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.6e+31) || !(y <= 5.5e+38))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(y * a))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.6e+31) || ~((y <= 5.5e+38)))
		tmp = ((z / y) + x) - ((x * a) / y);
	else
		tmp = t / (i + (y * (c + (y * (y * a)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.6e+31], N[Not[LessEqual[y, 5.5e+38]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e31 or 5.5000000000000003e38 < y

   1. Initial program 6.2%

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

   2. Taylor expanded in y around inf 69.6%

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

   if -2.6e31 < y < 5.5000000000000003e38

   1. Initial program 96.2%

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

   2. Taylor expanded in t around inf 75.7%

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

   3. Taylor expanded in a around inf 73.5%

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

      1. *-commutative 73.5%

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

      2. unpow2 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in a around 0 73.5%

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

      1. *-commutative 73.5%

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

      2. unpow2 73.5%

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

      3. associate-*l* 73.5%

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

      4. *-commutative 73.5%

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

      5. *-commutative 73.5%

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

   8. Simplified 73.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+31} \lor \neg \left(y \leq 5.5 \cdot 10^{+38}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot a\right)\right)}\\ \end{array} \]

Alternative 17: 62.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+24} \lor \neg \left(y \leq 1.46 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7e+24) (not (<= y 1.46e+34)))
   (- (+ (/ z y) x) (/ (* x a) y))
   (/ t (+ i (* y c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7e+24) || !(y <= 1.46e+34)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-7d+24)) .or. (.not. (y <= 1.46d+34))) then
        tmp = ((z / y) + x) - ((x * a) / y)
    else
        tmp = t / (i + (y * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7e+24) || !(y <= 1.46e+34)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -7e+24) or not (y <= 1.46e+34):
		tmp = ((z / y) + x) - ((x * a) / y)
	else:
		tmp = t / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -7e+24) || !(y <= 1.46e+34))
		tmp = Float64(Float64(Float64(z / y) + x) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(t / Float64(i + Float64(y * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -7e+24) || ~((y <= 1.46e+34)))
		tmp = ((z / y) + x) - ((x * a) / y);
	else
		tmp = t / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -7e+24], N[Not[LessEqual[y, 1.46e+34]], $MachinePrecision]], N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000004e24 or 1.46e34 < y

   1. Initial program 7.0%

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

   2. Taylor expanded in y around inf 69.0%

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

   if -7.0000000000000004e24 < y < 1.46e34

   1. Initial program 96.2%

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

   2. Taylor expanded in t around inf 75.6%

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

   3. Taylor expanded in y around 0 71.2%

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

      1. *-commutative 71.2%

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

   5. Simplified 71.2%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+24} \lor \neg \left(y \leq 1.46 \cdot 10^{+34}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]

Alternative 18: 57.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.5e+45) x (if (<= y 6.2e+37) (/ t (+ i (* y c))) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.5e+45) {
		tmp = x;
	} else if (y <= 6.2e+37) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.5d+45)) then
        tmp = x
    else if (y <= 6.2d+37) then
        tmp = t / (i + (y * c))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.5e+45) {
		tmp = x;
	} else if (y <= 6.2e+37) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.5e+45:
		tmp = x
	elif y <= 6.2e+37:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.5e+45)
		tmp = x;
	elseif (y <= 6.2e+37)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	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 <= -1.5e+45)
		tmp = x;
	elseif (y <= 6.2e+37)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.5e+45], x, If[LessEqual[y, 6.2e+37], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000005e45 or 6.2000000000000004e37 < y

   1. Initial program 4.7%

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

   2. Taylor expanded in y around inf 57.4%

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

   if -1.50000000000000005e45 < y < 6.2000000000000004e37

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf 74.2%

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

   3. Taylor expanded in y around 0 69.2%

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

      1. *-commutative 69.2%

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

   5. Simplified 69.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 50.1% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+17}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.15e+45) x (if (<= y 2.1e+17) (/ 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 <= -1.15e+45) {
		tmp = x;
	} else if (y <= 2.1e+17) {
		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 <= (-1.15d+45)) then
        tmp = x
    else if (y <= 2.1d+17) 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 <= -1.15e+45) {
		tmp = x;
	} else if (y <= 2.1e+17) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.15e+45:
		tmp = x
	elif y <= 2.1e+17:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.15e+45)
		tmp = x;
	elseif (y <= 2.1e+17)
		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 <= -1.15e+45)
		tmp = x;
	elseif (y <= 2.1e+17)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.15e+45], x, If[LessEqual[y, 2.1e+17], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000006e45 or 2.1e17 < y

   1. Initial program 5.4%

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

   2. Taylor expanded in y around inf 56.5%

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

   if -1.15000000000000006e45 < y < 2.1e17

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 57.0%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+17}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 25.3% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.7%

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

2. Taylor expanded in y around inf 28.4%

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

3. Final simplification 28.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023240 
(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)))