Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.1% → 83.3%

Time: 24.0s

Alternatives: 15

Speedup: 1.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)\\ \mathbf{if}\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{t}{t\_1} + \left(y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + x \cdot {y}^{2}\right)}{t\_1} + \frac{z \cdot {y}^{3}}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y (fma y (fma y (+ y a) b) c) i)))
   (if (<=
        (/
         (+
          (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
          t)
         (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))
        2e+295)
     (+
      (/ t t_1)
      (+
       (*
        y
        (/ (+ 230661.510616 (* y (+ 27464.7644705 (* x (pow y 2.0))))) t_1))
       (/ (* z (pow y 3.0)) t_1)))
     (+ x (- (/ z y) (* a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, fma(y, fma(y, (y + a), b), c), i);
	double tmp;
	if ((((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))) <= 2e+295) {
		tmp = (t / t_1) + ((y * ((230661.510616 + (y * (27464.7644705 + (x * pow(y, 2.0))))) / t_1)) + ((z * pow(y, 3.0)) / t_1));
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, fma(y, fma(y, Float64(y + a), b), c), i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))) + t) / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)))) <= 2e+295)
		tmp = Float64(Float64(t / t_1) + Float64(Float64(y * Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * (y ^ 2.0))))) / t_1)) + Float64(Float64(z * (y ^ 3.0)) / t_1)));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[N[(N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+295], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(y * N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2e295

   1. Initial program 90.9%

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

   3. Taylor expanded in z around 0 90.1%

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

      1. +-commutative 90.1%

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

      2. +-commutative 90.1%

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

      3. +-commutative 90.1%

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

      4. +-commutative 90.1%

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

      5. fma-undefine 90.1%

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

      6. fma-undefine 90.1%

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

      7. fma-undefine 90.1%

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

   5. Simplified 91.4%

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

   if 2e295 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 1.3%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)} + \left(y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + x \cdot {y}^{2}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)} + \frac{z \cdot {y}^{3}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\\ t_2 := y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)\\ \mathbf{if}\;\frac{t\_2 + t}{t\_1} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{t}{t\_1} + \frac{t\_2}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))
        (t_2
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))))
   (if (<= (/ (+ t_2 t) t_1) 2e+295)
     (+ (/ t t_1) (/ t_2 t_1))
     (+ x (- (/ z y) (* a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	double t_2 = y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))));
	double tmp;
	if (((t_2 + t) / t_1) <= 2e+295) {
		tmp = (t / t_1) + (t_2 / t_1);
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c))
    t_2 = y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z)))))
    if (((t_2 + t) / t_1) <= 2d+295) then
        tmp = (t / t_1) + (t_2 / t_1)
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	double t_2 = y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))));
	double tmp;
	if (((t_2 + t) / t_1) <= 2e+295) {
		tmp = (t / t_1) + (t_2 / t_1);
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c))
	t_2 = y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))
	tmp = 0
	if ((t_2 + t) / t_1) <= 2e+295:
		tmp = (t / t_1) + (t_2 / t_1)
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)))
	t_2 = Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))))
	tmp = 0.0
	if (Float64(Float64(t_2 + t) / t_1) <= 2e+295)
		tmp = Float64(Float64(t / t_1) + Float64(t_2 / t_1));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	t_2 = y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))));
	tmp = 0.0;
	if (((t_2 + t) / t_1) <= 2e+295)
		tmp = (t / t_1) + (t_2 / t_1);
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$2 + t), $MachinePrecision] / t$95$1), $MachinePrecision], 2e+295], N[(N[(t / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2e295

   1. Initial program 90.9%

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

   3. Taylor expanded in t around 0 90.9%

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

   if 2e295 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 1.3%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
           t)
          (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))))
   (if (<= t_1 2e+295) t_1 (+ x (- (/ z y) (* a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	double tmp;
	if (t_1 <= 2e+295) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z)))))) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    if (t_1 <= 2d+295) then
        tmp = t_1
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	double tmp;
	if (t_1 <= 2e+295) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	tmp = 0
	if t_1 <= 2e+295:
		tmp = t_1
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))) + t) / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))))
	tmp = 0.0
	if (t_1 <= 2e+295)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	tmp = 0.0;
	if (t_1 <= 2e+295)
		tmp = t_1;
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+295], t$95$1, N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2e295

   1. Initial program 90.9%

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

   if 2e295 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 1.3%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -8.4 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 38000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot t\_1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+95}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ y a)) b)) c))
        (t_2 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -8.4e+30)
     t_2
     (if (<= y 38000000.0)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
        (+ i (* y t_1)))
       (if (<= y 4e+95)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))) t_1)
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -8.4e+30) {
		tmp = t_2;
	} else if (y <= 38000000.0) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1));
	} else if (y <= 4e+95) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((y * (y + a)) + b)) + c
    t_2 = x + ((z / y) - (a * (x / y)))
    if (y <= (-8.4d+30)) then
        tmp = t_2
    else if (y <= 38000000.0d0) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * t_1))
    else if (y <= 4d+95) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -8.4e+30) {
		tmp = t_2;
	} else if (y <= 38000000.0) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1));
	} else if (y <= 4e+95) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * (y + a)) + b)) + c
	t_2 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -8.4e+30:
		tmp = t_2
	elif y <= 38000000.0:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1))
	elif y <= 4e+95:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -8.4e+30)
		tmp = t_2;
	elseif (y <= 38000000.0)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * t_1)));
	elseif (y <= 4e+95)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * (y + a)) + b)) + c;
	t_2 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -8.4e+30)
		tmp = t_2;
	elseif (y <= 38000000.0)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1));
	elseif (y <= 4e+95)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.4e+30], t$95$2, If[LessEqual[y, 38000000.0], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+95], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4000000000000001e30 or 4.00000000000000008e95 < y

   1. Initial program 1.4%

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

   3. Taylor expanded in y around inf 71.2%

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

      1. associate--l+ 71.2%

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

      2. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   if -8.4000000000000001e30 < y < 3.8e7

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 93.8%

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

   if 3.8e7 < y < 4.00000000000000008e95

   1. Initial program 31.7%

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

   3. Taylor expanded in t around 0 27.9%

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

   4. Taylor expanded in i around 0 56.4%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+30}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 38000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+95}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot t\_1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+95}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ y a)) b)) c))
        (t_2 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -6.6e+29)
     t_2
     (if (<= y 2.35e-6)
       (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i (* y t_1)))
       (if (<= y 4e+95)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))) t_1)
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -6.6e+29) {
		tmp = t_2;
	} else if (y <= 2.35e-6) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 4e+95) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((y * (y + a)) + b)) + c
    t_2 = x + ((z / y) - (a * (x / y)))
    if (y <= (-6.6d+29)) then
        tmp = t_2
    else if (y <= 2.35d-6) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * t_1))
    else if (y <= 4d+95) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -6.6e+29) {
		tmp = t_2;
	} else if (y <= 2.35e-6) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 4e+95) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * (y + a)) + b)) + c
	t_2 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -6.6e+29:
		tmp = t_2
	elif y <= 2.35e-6:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1))
	elif y <= 4e+95:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -6.6e+29)
		tmp = t_2;
	elseif (y <= 2.35e-6)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * t_1)));
	elseif (y <= 4e+95)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * (y + a)) + b)) + c;
	t_2 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -6.6e+29)
		tmp = t_2;
	elseif (y <= 2.35e-6)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	elseif (y <= 4e+95)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e+29], t$95$2, If[LessEqual[y, 2.35e-6], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+95], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.59999999999999968e29 or 4.00000000000000008e95 < y

   1. Initial program 1.4%

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

   3. Taylor expanded in y around inf 71.2%

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

      1. associate--l+ 71.2%

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

      2. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   if -6.59999999999999968e29 < y < 2.34999999999999995e-6

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 89.2%

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

      1. *-commutative 89.2%

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

   5. Simplified 89.2%

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

   if 2.34999999999999995e-6 < y < 4.00000000000000008e95

   1. Initial program 47.0%

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

   3. Taylor expanded in t around 0 37.9%

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

   4. Taylor expanded in i around 0 56.9%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+29}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+95}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ t_2 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-9}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t\_2}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+95}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y)))))
        (t_2 (+ (* y (+ (* y (+ y a)) b)) c)))
   (if (<= y -2.8e+26)
     t_1
     (if (<= y 4e-9)
       (/ (+ t (* y 230661.510616)) (+ i (* y t_2)))
       (if (<= y 4e+95)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))) t_2)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double t_2 = (y * ((y * (y + a)) + b)) + c;
	double tmp;
	if (y <= -2.8e+26) {
		tmp = t_1;
	} else if (y <= 4e-9) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 4e+95) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    t_2 = (y * ((y * (y + a)) + b)) + c
    if (y <= (-2.8d+26)) then
        tmp = t_1
    else if (y <= 4d-9) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_2))
    else if (y <= 4d+95) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))) / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double t_2 = (y * ((y * (y + a)) + b)) + c;
	double tmp;
	if (y <= -2.8e+26) {
		tmp = t_1;
	} else if (y <= 4e-9) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 4e+95) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	t_2 = (y * ((y * (y + a)) + b)) + c
	tmp = 0
	if y <= -2.8e+26:
		tmp = t_1
	elif y <= 4e-9:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2))
	elif y <= 4e+95:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	t_2 = Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)
	tmp = 0.0
	if (y <= -2.8e+26)
		tmp = t_1;
	elseif (y <= 4e-9)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_2)));
	elseif (y <= 4e+95)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	t_2 = (y * ((y * (y + a)) + b)) + c;
	tmp = 0.0;
	if (y <= -2.8e+26)
		tmp = t_1;
	elseif (y <= 4e-9)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	elseif (y <= 4e+95)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, If[LessEqual[y, -2.8e+26], t$95$1, If[LessEqual[y, 4e-9], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+95], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8e26 or 4.00000000000000008e95 < y

   1. Initial program 1.4%

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

   3. Taylor expanded in y around inf 71.2%

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

      1. associate--l+ 71.2%

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

      2. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   if -2.8e26 < y < 4.00000000000000025e-9

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 87.7%

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

      1. *-commutative 87.7%

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

   5. Simplified 87.7%

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

   if 4.00000000000000025e-9 < y < 4.00000000000000008e95

   1. Initial program 47.0%

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

   3. Taylor expanded in t around 0 37.9%

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

   4. Taylor expanded in i around 0 56.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+26}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-9}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+95}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\\ t_2 := \frac{t}{t\_1}\\ t_3 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+27}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-138}:\\ \;\;\;\;\frac{y \cdot 230661.510616}{t\_1}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))
        (t_2 (/ t t_1))
        (t_3 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -6.2e+27)
     t_3
     (if (<= y -2e-93)
       t_2
       (if (<= y -4.7e-138)
         (/ (* y 230661.510616) t_1)
         (if (<= y 8.5e+26) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	double t_2 = t / t_1;
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -6.2e+27) {
		tmp = t_3;
	} else if (y <= -2e-93) {
		tmp = t_2;
	} else if (y <= -4.7e-138) {
		tmp = (y * 230661.510616) / t_1;
	} else if (y <= 8.5e+26) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c))
    t_2 = t / t_1
    t_3 = x + ((z / y) - (a * (x / y)))
    if (y <= (-6.2d+27)) then
        tmp = t_3
    else if (y <= (-2d-93)) then
        tmp = t_2
    else if (y <= (-4.7d-138)) then
        tmp = (y * 230661.510616d0) / t_1
    else if (y <= 8.5d+26) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	double t_2 = t / t_1;
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -6.2e+27) {
		tmp = t_3;
	} else if (y <= -2e-93) {
		tmp = t_2;
	} else if (y <= -4.7e-138) {
		tmp = (y * 230661.510616) / t_1;
	} else if (y <= 8.5e+26) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c))
	t_2 = t / t_1
	t_3 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -6.2e+27:
		tmp = t_3
	elif y <= -2e-93:
		tmp = t_2
	elif y <= -4.7e-138:
		tmp = (y * 230661.510616) / t_1
	elif y <= 8.5e+26:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)))
	t_2 = Float64(t / t_1)
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -6.2e+27)
		tmp = t_3;
	elseif (y <= -2e-93)
		tmp = t_2;
	elseif (y <= -4.7e-138)
		tmp = Float64(Float64(y * 230661.510616) / t_1);
	elseif (y <= 8.5e+26)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	t_2 = t / t_1;
	t_3 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -6.2e+27)
		tmp = t_3;
	elseif (y <= -2e-93)
		tmp = t_2;
	elseif (y <= -4.7e-138)
		tmp = (y * 230661.510616) / t_1;
	elseif (y <= 8.5e+26)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+27], t$95$3, If[LessEqual[y, -2e-93], t$95$2, If[LessEqual[y, -4.7e-138], N[(N[(y * 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 8.5e+26], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.19999999999999992e27 or 8.5e26 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 62.1%

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

      1. associate--l+ 62.1%

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

      2. associate-/l* 66.6%

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

   5. Simplified 66.6%

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

   if -6.19999999999999992e27 < y < -1.9999999999999998e-93 or -4.7000000000000001e-138 < y < 8.5e26

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 75.8%

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

   if -1.9999999999999998e-93 < y < -4.7000000000000001e-138

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 99.1%

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

   4. Taylor expanded in z around inf 86.9%

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

   5. Taylor expanded in y around 0 72.2%

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

      1. *-commutative 72.2%

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

   7. Simplified 72.2%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+27}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-93}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-138}:\\ \;\;\;\;\frac{y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\\ t_2 := \frac{t}{t\_1}\\ t_3 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+26}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{-93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{y \cdot 230661.510616}{t\_1}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))
        (t_2 (/ t t_1))
        (t_3 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.65e+26)
     t_3
     (if (<= y -1.76e-93)
       t_2
       (if (<= y -4.8e-138)
         (/ (* y 230661.510616) t_1)
         (if (<= y 2.7e+27) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	double t_2 = t / t_1;
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.65e+26) {
		tmp = t_3;
	} else if (y <= -1.76e-93) {
		tmp = t_2;
	} else if (y <= -4.8e-138) {
		tmp = (y * 230661.510616) / t_1;
	} else if (y <= 2.7e+27) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c))
    t_2 = t / t_1
    t_3 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.65d+26)) then
        tmp = t_3
    else if (y <= (-1.76d-93)) then
        tmp = t_2
    else if (y <= (-4.8d-138)) then
        tmp = (y * 230661.510616d0) / t_1
    else if (y <= 2.7d+27) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	double t_2 = t / t_1;
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.65e+26) {
		tmp = t_3;
	} else if (y <= -1.76e-93) {
		tmp = t_2;
	} else if (y <= -4.8e-138) {
		tmp = (y * 230661.510616) / t_1;
	} else if (y <= 2.7e+27) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c))
	t_2 = t / t_1
	t_3 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.65e+26:
		tmp = t_3
	elif y <= -1.76e-93:
		tmp = t_2
	elif y <= -4.8e-138:
		tmp = (y * 230661.510616) / t_1
	elif y <= 2.7e+27:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)))
	t_2 = Float64(t / t_1)
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.65e+26)
		tmp = t_3;
	elseif (y <= -1.76e-93)
		tmp = t_2;
	elseif (y <= -4.8e-138)
		tmp = Float64(Float64(y * 230661.510616) / t_1);
	elseif (y <= 2.7e+27)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * ((y * ((y * (y + a)) + b)) + c));
	t_2 = t / t_1;
	t_3 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.65e+26)
		tmp = t_3;
	elseif (y <= -1.76e-93)
		tmp = t_2;
	elseif (y <= -4.8e-138)
		tmp = (y * 230661.510616) / t_1;
	elseif (y <= 2.7e+27)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+26], t$95$3, If[LessEqual[y, -1.76e-93], t$95$2, If[LessEqual[y, -4.8e-138], N[(N[(y * 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.7e+27], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.64999999999999997e26 or 2.6999999999999997e27 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 62.1%

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

      1. associate--l+ 62.1%

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

      2. associate-/l* 66.6%

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

   5. Simplified 66.6%

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

   if -1.64999999999999997e26 < y < -1.76000000000000001e-93 or -4.7999999999999998e-138 < y < 2.6999999999999997e27

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 75.8%

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

   if -1.76000000000000001e-93 < y < -4.7999999999999998e-138

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 99.1%

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

   4. Taylor expanded in y around 0 72.2%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+26}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{-93}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-95}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -2.7e-16)
     t_1
     (if (<= y 9.2e-95)
       (/ t i)
       (if (<= y 1.25e+40)
         (*
          y
          (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))) i))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.7e-16) {
		tmp = t_1;
	} else if (y <= 9.2e-95) {
		tmp = t / i;
	} else if (y <= 1.25e+40) {
		tmp = y * ((230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-2.7d-16)) then
        tmp = t_1
    else if (y <= 9.2d-95) then
        tmp = t / i
    else if (y <= 1.25d+40) then
        tmp = y * ((230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))) / i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.7e-16) {
		tmp = t_1;
	} else if (y <= 9.2e-95) {
		tmp = t / i;
	} else if (y <= 1.25e+40) {
		tmp = y * ((230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -2.7e-16:
		tmp = t_1
	elif y <= 9.2e-95:
		tmp = t / i
	elif y <= 1.25e+40:
		tmp = y * ((230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -2.7e-16)
		tmp = t_1;
	elseif (y <= 9.2e-95)
		tmp = Float64(t / i);
	elseif (y <= 1.25e+40)
		tmp = Float64(y * Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))) / i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -2.7e-16)
		tmp = t_1;
	elseif (y <= 9.2e-95)
		tmp = t / i;
	elseif (y <= 1.25e+40)
		tmp = y * ((230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e-16], t$95$1, If[LessEqual[y, 9.2e-95], N[(t / i), $MachinePrecision], If[LessEqual[y, 1.25e+40], N[(y * N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.69999999999999999e-16 or 1.25000000000000001e40 < y

   1. Initial program 11.8%

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

   3. Taylor expanded in y around inf 60.1%

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

      1. associate--l+ 60.1%

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

      2. associate-/l* 64.3%

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

   5. Simplified 64.3%

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

   if -2.69999999999999999e-16 < y < 9.19999999999999997e-95

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 56.9%

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

   if 9.19999999999999997e-95 < y < 1.25000000000000001e40

   1. Initial program 88.3%

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

   3. Taylor expanded in t around 0 51.4%

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

   4. Taylor expanded in i around inf 21.4%

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

      1. associate-/l* 25.1%

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

   6. Simplified 25.1%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-16}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-95}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+28} \lor \neg \left(y \leq 1.3 \cdot 10^{+41}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -9.5e+28) (not (<= y 1.3e+41)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9.5e+28) || !(y <= 1.3e+41)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + 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 <= (-9.5d+28)) .or. (.not. (y <= 1.3d+41))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * ((y * ((y * (y + a)) + b)) + 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 <= -9.5e+28) || !(y <= 1.3e+41)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -9.5e+28) or not (y <= 1.3e+41):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -9.5e+28) || !(y <= 1.3e+41))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -9.5e+28) || ~((y <= 1.3e+41)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -9.5e+28], N[Not[LessEqual[y, 1.3e+41]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.49999999999999927e28 or 1.3e41 < y

   1. Initial program 4.5%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. associate-/l* 69.0%

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

   5. Simplified 69.0%

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

   if -9.49999999999999927e28 < y < 1.3e41

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 81.8%

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

      1. *-commutative 81.8%

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

   5. Simplified 81.8%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+28} \lor \neg \left(y \leq 1.3 \cdot 10^{+41}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.14:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+45}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.25e-14)
     t_1
     (if (<= y 0.14)
       (/ t i)
       (if (<= y 2e+45)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))) 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 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.25e-14) {
		tmp = t_1;
	} else if (y <= 0.14) {
		tmp = t / i;
	} else if (y <= 2e+45) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / 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 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.25d-14)) then
        tmp = t_1
    else if (y <= 0.14d0) then
        tmp = t / i
    else if (y <= 2d+45) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))) / 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 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.25e-14) {
		tmp = t_1;
	} else if (y <= 0.14) {
		tmp = t / i;
	} else if (y <= 2e+45) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.25e-14:
		tmp = t_1
	elif y <= 0.14:
		tmp = t / i
	elif y <= 2e+45:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.25e-14)
		tmp = t_1;
	elseif (y <= 0.14)
		tmp = Float64(t / i);
	elseif (y <= 2e+45)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.25e-14)
		tmp = t_1;
	elseif (y <= 0.14)
		tmp = t / i;
	elseif (y <= 2e+45)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / 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[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e-14], t$95$1, If[LessEqual[y, 0.14], N[(t / i), $MachinePrecision], If[LessEqual[y, 2e+45], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e-14 or 1.9999999999999999e45 < y

   1. Initial program 11.1%

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

   3. Taylor expanded in y around inf 61.1%

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

      1. associate--l+ 61.1%

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

      2. associate-/l* 65.4%

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

   5. Simplified 65.4%

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

   if -1.25e-14 < y < 0.14000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 50.3%

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

   if 0.14000000000000001 < y < 1.9999999999999999e45

   1. Initial program 67.4%

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

   3. Taylor expanded in t around 0 44.0%

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

   4. Taylor expanded in c around inf 42.7%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-14}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 0.14:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+45}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+27} \lor \neg \left(y \leq 1.65 \cdot 10^{+26}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.25e+27) (not (<= y 1.65e+26)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ t (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.25e+27) || !(y <= 1.65e+26)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + 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 <= (-1.25d+27)) .or. (.not. (y <= 1.65d+26))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + 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 <= -1.25e+27) || !(y <= 1.65e+26)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.25e+27) or not (y <= 1.65e+26):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.25e+27) || !(y <= 1.65e+26))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.25e+27) || ~((y <= 1.65e+26)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.25e+27], N[Not[LessEqual[y, 1.65e+26]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999995e27 or 1.64999999999999997e26 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 62.1%

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

      1. associate--l+ 62.1%

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

      2. associate-/l* 66.6%

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

   5. Simplified 66.6%

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

   if -1.24999999999999995e27 < y < 1.64999999999999997e26

   1. Initial program 97.6%

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

   3. Taylor expanded in t around inf 71.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+27} \lor \neg \left(y \leq 1.65 \cdot 10^{+26}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-17} \lor \neg \left(y \leq 1.15 \cdot 10^{+22}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.6e-17) (not (<= y 1.15e+22)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.6e-17) || !(y <= 1.15e+22)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.6d-17)) .or. (.not. (y <= 1.15d+22))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.6e-17) || !(y <= 1.15e+22)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.6e-17) or not (y <= 1.15e+22):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.6e-17) || !(y <= 1.15e+22))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.6e-17) || ~((y <= 1.15e+22)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.6e-17], N[Not[LessEqual[y, 1.15e+22]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6000000000000001e-17 or 1.1500000000000001e22 < y

   1. Initial program 13.1%

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

   3. Taylor expanded in y around inf 58.2%

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

      1. associate--l+ 58.2%

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

      2. associate-/l* 62.3%

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

   5. Simplified 62.3%

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

   if -1.6000000000000001e-17 < y < 1.1500000000000001e22

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 48.2%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-17} \lor \neg \left(y \leq 1.15 \cdot 10^{+22}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 86:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7e+31) x (if (<= y 86.0) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7e+31) {
		tmp = x;
	} else if (y <= 86.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-7d+31)) then
        tmp = x
    else if (y <= 86.0d0) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7e+31) {
		tmp = x;
	} else if (y <= 86.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7e+31:
		tmp = x
	elif y <= 86.0:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7e+31)
		tmp = x;
	elseif (y <= 86.0)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -7e+31)
		tmp = x;
	elseif (y <= 86.0)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7e+31], x, If[LessEqual[y, 86.0], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -7e31 or 86 < y

   1. Initial program 9.4%

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

   3. Taylor expanded in y around inf 45.6%

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

   if -7e31 < y < 86

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 47.0%

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

Alternative 15: 26.1% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.3%

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

3. Taylor expanded in y around inf 22.4%

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

Reproduce

herbie shell --seed 2024103 
(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)))