Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.5% → 85.6%

Time: 23.8s

Alternatives: 20

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.6% accurate, 0.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, fma(y, fma(y, (y + a), b), c), i);
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = (t / t_1) + (y / (t_1 / fma(y, fma(y, fma(y, x, z), 27464.7644705), 230661.510616)));
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	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(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(Float64(t / t_1) + Float64(y / Float64(t_1 / fma(y, fma(y, fma(y, x, z), 27464.7644705), 230661.510616))));
	else
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	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[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(t / t$95$1), $MachinePrecision] + N[(y / N[(t$95$1 / N[(y * N[(y * N[(y * x + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.3%

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

   2. Taylor expanded in t around 0 92.3%

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

      1. +-commutative 92.3%

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

      2. *-commutative 92.3%

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

      3. fma-udef 92.3%

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

      4. fma-udef 92.3%

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

      5. fma-udef 92.3%

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

      6. associate-/l* 93.5%

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

   4. Simplified 93.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. associate--l+ 76.3%

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

      2. associate-/l* 79.8%

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

   4. Simplified 79.8%

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

4. Final simplification 88.7%

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

Alternative 2: 84.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.3%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. associate--l+ 76.3%

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

      2. associate-/l* 79.8%

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

   4. Simplified 79.8%

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

4. Final simplification 88.0%

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

Alternative 3: 81.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+60}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+17}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+60}:\\ \;\;\;\;\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.6e+60)
   (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) (/ b (/ (* y y) x))))
   (if (<= y -1.25e+17)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 1.9e+60)
       (/
        1.0
        (/
         (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)
         (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))))
       (+ (/ z y) (- x (/ a (/ y x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.6e+60) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -1.25e+17) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 1.9e+60) {
		tmp = 1.0 / (((y * ((y * ((y * (y + a)) + b)) + c)) + i) / (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))));
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-4.6d+60)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - (b / ((y * y) / x)))
    else if (y <= (-1.25d+17)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 1.9d+60) then
        tmp = 1.0d0 / (((y * ((y * ((y * (y + a)) + b)) + c)) + i) / (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))))
    else
        tmp = (z / y) + (x - (a / (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.6e+60) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -1.25e+17) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 1.9e+60) {
		tmp = 1.0 / (((y * ((y * ((y * (y + a)) + b)) + c)) + i) / (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))));
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.6e+60:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)))
	elif y <= -1.25e+17:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 1.9e+60:
		tmp = 1.0 / (((y * ((y * ((y * (y + a)) + b)) + c)) + i) / (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))))
	else:
		tmp = (z / y) + (x - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.6e+60)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - Float64(b / Float64(Float64(y * y) / x))));
	elseif (y <= -1.25e+17)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 1.9e+60)
		tmp = Float64(1.0 / Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i) / Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z))))))));
	else
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.6e+60)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	elseif (y <= -1.25e+17)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 1.9e+60)
		tmp = 1.0 / (((y * ((y * ((y * (y + a)) + b)) + c)) + i) / (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))));
	else
		tmp = (z / y) + (x - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.6e+60], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e+17], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+60], N[(1.0 / N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision] / N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.60000000000000034e60

   1. Initial program 2.3%

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

      1. div-inv 2.3%

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

      2. *-commutative 2.3%

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

      3. fma-def 2.3%

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

      4. *-commutative 2.3%

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

      5. fma-def 2.3%

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

      6. *-commutative 2.3%

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

      7. fma-def 2.3%

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

      8. fma-def 2.3%

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

      9. *-commutative 2.3%

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

      10. fma-def 2.3%

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

   3. Applied egg-rr 2.3%

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

   4. Taylor expanded in y around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. associate-*r/ 61.4%

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

      3. metadata-eval 61.4%

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

      4. unpow2 61.4%

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

      5. associate-/l* 68.2%

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

      6. unpow2 68.2%

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

      7. associate-/l* 68.3%

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

      8. unpow2 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in a around 0 71.6%

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

      1. associate--l+ 71.6%

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

      2. associate-*r/ 71.7%

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

      3. metadata-eval 71.7%

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

      4. unpow2 71.7%

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

      5. +-commutative 71.7%

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

      6. associate-/l* 79.7%

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

      7. unpow2 79.7%

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

   9. Simplified 79.7%

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

   if -4.60000000000000034e60 < y < -1.25e17

   1. Initial program 26.9%

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

   2. Taylor expanded in a around inf 15.1%

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

   3. Taylor expanded in y around inf 64.0%

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

      1. associate-+r+ 64.0%

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

      2. +-commutative 64.0%

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

      3. *-commutative 64.0%

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

      4. associate-+r+ 64.0%

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

      5. associate-*r/ 64.0%

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

      6. metadata-eval 64.0%

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

   5. Simplified 64.0%

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

      1. *-un-lft-identity 64.0%

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

      2. associate-/l* 75.8%

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

   7. Applied egg-rr 75.8%

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

   if -1.25e17 < y < 1.90000000000000005e60

   1. Initial program 96.6%

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

      1. clear-num 96.0%

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

      2. inv-pow 96.0%

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

   3. Applied egg-rr 96.0%

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

      1. unpow-1 96.0%

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

      2. fma-udef 96.0%

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

      3. *-commutative 96.0%

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

      4. fma-def 96.0%

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

   5. Simplified 96.0%

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

   6. Taylor expanded in x around 0 90.1%

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

   if 1.90000000000000005e60 < y

   1. Initial program 2.7%

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

   2. Taylor expanded in y around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. associate-/l* 80.6%

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

   4. Simplified 80.6%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+60}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+17}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+60}:\\ \;\;\;\;\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 4: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+57}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.5e+61)
   (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) (/ b (/ (* y y) x))))
   (if (<= y -9.6e+24)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 4.9e+57)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* y y)))))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (+ (/ z y) (- x (/ a (/ y x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.5e+61) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -9.6e+24) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 4.9e+57) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (z / y) + (x - (a / (y / 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 <= (-2.5d+61)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - (b / ((y * y) / x)))
    else if (y <= (-9.6d+24)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 4.9d+57) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = (z / y) + (x - (a / (y / 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 <= -2.5e+61) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -9.6e+24) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 4.9e+57) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.5e+61:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)))
	elif y <= -9.6e+24:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 4.9e+57:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = (z / y) + (x - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.5e+61)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - Float64(b / Float64(Float64(y * y) / x))));
	elseif (y <= -9.6e+24)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 4.9e+57)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * Float64(y * y))))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.5e+61)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	elseif (y <= -9.6e+24)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 4.9e+57)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = (z / y) + (x - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.5e+61], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.6e+24], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+57], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.50000000000000009e61

   1. Initial program 2.3%

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

      1. div-inv 2.3%

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

      2. *-commutative 2.3%

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

      3. fma-def 2.3%

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

      4. *-commutative 2.3%

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

      5. fma-def 2.3%

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

      6. *-commutative 2.3%

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

      7. fma-def 2.3%

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

      8. fma-def 2.3%

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

      9. *-commutative 2.3%

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

      10. fma-def 2.3%

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

   3. Applied egg-rr 2.3%

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

   4. Taylor expanded in y around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. associate-*r/ 61.4%

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

      3. metadata-eval 61.4%

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

      4. unpow2 61.4%

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

      5. associate-/l* 68.2%

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

      6. unpow2 68.2%

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

      7. associate-/l* 68.3%

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

      8. unpow2 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in a around 0 71.6%

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

      1. associate--l+ 71.6%

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

      2. associate-*r/ 71.7%

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

      3. metadata-eval 71.7%

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

      4. unpow2 71.7%

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

      5. +-commutative 71.7%

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

      6. associate-/l* 79.7%

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

      7. unpow2 79.7%

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

   9. Simplified 79.7%

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

   if -2.50000000000000009e61 < y < -9.6000000000000003e24

   1. Initial program 16.5%

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

   2. Taylor expanded in a around inf 16.4%

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

   3. Taylor expanded in y around inf 72.3%

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

      1. associate-+r+ 72.3%

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

      2. +-commutative 72.3%

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

      3. *-commutative 72.3%

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

      4. associate-+r+ 72.3%

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

      5. associate-*r/ 72.3%

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

      6. metadata-eval 72.3%

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

   5. Simplified 72.3%

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

      1. *-un-lft-identity 72.3%

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

      2. associate-/l* 85.9%

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

   7. Applied egg-rr 85.9%

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

   if -9.6000000000000003e24 < y < 4.8999999999999999e57

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 91.7%

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

      1. *-commutative 91.7%

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

      2. unpow2 91.7%

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

   4. Simplified 91.7%

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

   if 4.8999999999999999e57 < y

   1. Initial program 2.7%

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

   2. Taylor expanded in y around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. associate-/l* 80.6%

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

   4. Simplified 80.6%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+57}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 5: 81.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+62}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+35}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7e+62)
   (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) (/ b (/ (* y y) x))))
   (if (<= y -39000000000.0)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 2.85e+35)
       (/
        (+ t (* y (+ 230661.510616 (* z (* y y)))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (+ (/ z y) (- x (/ a (/ y x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7e+62) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 2.85e+35) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (z / y) + (x - (a / (y / 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+62)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - (b / ((y * y) / x)))
    else if (y <= (-39000000000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 2.85d+35) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = (z / y) + (x - (a / (y / 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+62) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 2.85e+35) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7e+62:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)))
	elif y <= -39000000000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 2.85e+35:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = (z / y) + (x - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7e+62)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - Float64(b / Float64(Float64(y * y) / x))));
	elseif (y <= -39000000000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 2.85e+35)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -7e+62)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	elseif (y <= -39000000000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 2.85e+35)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = (z / y) + (x - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7e+62], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -39000000000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.85e+35], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.99999999999999967e62

   1. Initial program 2.3%

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

      1. div-inv 2.3%

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

      2. *-commutative 2.3%

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

      3. fma-def 2.3%

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

      4. *-commutative 2.3%

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

      5. fma-def 2.3%

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

      6. *-commutative 2.3%

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

      7. fma-def 2.3%

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

      8. fma-def 2.3%

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

      9. *-commutative 2.3%

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

      10. fma-def 2.3%

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

   3. Applied egg-rr 2.3%

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

   4. Taylor expanded in y around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. associate-*r/ 61.4%

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

      3. metadata-eval 61.4%

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

      4. unpow2 61.4%

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

      5. associate-/l* 68.2%

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

      6. unpow2 68.2%

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

      7. associate-/l* 68.3%

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

      8. unpow2 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in a around 0 71.6%

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

      1. associate--l+ 71.6%

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

      2. associate-*r/ 71.7%

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

      3. metadata-eval 71.7%

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

      4. unpow2 71.7%

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

      5. +-commutative 71.7%

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

      6. associate-/l* 79.7%

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

      7. unpow2 79.7%

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

   9. Simplified 79.7%

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

   if -6.99999999999999967e62 < y < -3.9e10

   1. Initial program 46.6%

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

   2. Taylor expanded in a around inf 20.2%

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

   3. Taylor expanded in y around inf 55.7%

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

      1. associate-+r+ 55.7%

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

      2. +-commutative 55.7%

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

      3. *-commutative 55.7%

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

      4. associate-+r+ 55.7%

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

      5. associate-*r/ 55.7%

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

      6. metadata-eval 55.7%

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

   5. Simplified 55.7%

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

      1. *-un-lft-identity 55.7%

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

      2. associate-/l* 64.4%

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

   7. Applied egg-rr 64.4%

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

   if -3.9e10 < y < 2.84999999999999997e35

   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. Taylor expanded in z around inf 93.8%

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

      1. *-commutative 93.8%

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

      2. unpow2 93.8%

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

   4. Simplified 93.8%

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

   if 2.84999999999999997e35 < y

   1. Initial program 8.3%

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

   2. Taylor expanded in y around inf 69.8%

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

      1. associate--l+ 69.8%

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

      2. associate-/l* 71.9%

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

   4. Simplified 71.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+62}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+35}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 6: 77.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+16}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+56}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7.5e+63)
   (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) (/ b (/ (* y y) x))))
   (if (<= y -8.8e+16)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 1.55e+56)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (+ (/ z y) (- x (/ a (/ y x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7.5e+63) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -8.8e+16) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 1.55e+56) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-7.5d+63)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - (b / ((y * y) / x)))
    else if (y <= (-8.8d+16)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 1.55d+56) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = (z / y) + (x - (a / (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7.5e+63) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -8.8e+16) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 1.55e+56) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7.5e+63:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)))
	elif y <= -8.8e+16:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 1.55e+56:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = (z / y) + (x - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7.5e+63)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - Float64(b / Float64(Float64(y * y) / x))));
	elseif (y <= -8.8e+16)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 1.55e+56)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -7.5e+63)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	elseif (y <= -8.8e+16)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 1.55e+56)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = (z / y) + (x - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7.5e+63], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.8e+16], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+56], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.5000000000000005e63

   1. Initial program 2.3%

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

      1. div-inv 2.3%

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

      2. *-commutative 2.3%

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

      3. fma-def 2.3%

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

      4. *-commutative 2.3%

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

      5. fma-def 2.3%

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

      6. *-commutative 2.3%

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

      7. fma-def 2.3%

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

      8. fma-def 2.3%

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

      9. *-commutative 2.3%

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

      10. fma-def 2.3%

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

   3. Applied egg-rr 2.3%

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

   4. Taylor expanded in y around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. associate-*r/ 61.4%

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

      3. metadata-eval 61.4%

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

      4. unpow2 61.4%

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

      5. associate-/l* 68.2%

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

      6. unpow2 68.2%

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

      7. associate-/l* 68.3%

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

      8. unpow2 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in a around 0 71.6%

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

      1. associate--l+ 71.6%

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

      2. associate-*r/ 71.7%

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

      3. metadata-eval 71.7%

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

      4. unpow2 71.7%

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

      5. +-commutative 71.7%

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

      6. associate-/l* 79.7%

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

      7. unpow2 79.7%

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

   9. Simplified 79.7%

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

   if -7.5000000000000005e63 < y < -8.8e16

   1. Initial program 26.9%

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

   2. Taylor expanded in a around inf 15.1%

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

   3. Taylor expanded in y around inf 64.0%

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

      1. associate-+r+ 64.0%

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

      2. +-commutative 64.0%

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

      3. *-commutative 64.0%

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

      4. associate-+r+ 64.0%

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

      5. associate-*r/ 64.0%

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

      6. metadata-eval 64.0%

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

   5. Simplified 64.0%

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

      1. *-un-lft-identity 64.0%

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

      2. associate-/l* 75.8%

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

   7. Applied egg-rr 75.8%

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

   if -8.8e16 < y < 1.55000000000000002e56

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 85.8%

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

      1. *-commutative 85.8%

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

   4. Simplified 85.8%

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

   if 1.55000000000000002e56 < y

   1. Initial program 2.7%

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

   2. Taylor expanded in y around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. associate-/l* 80.6%

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

   4. Simplified 80.6%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+16}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+56}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 7: 76.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.38e+69)
   (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) (/ b (/ (* y y) x))))
   (if (<= y -39000000000.0)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 9.5e+59)
       (/
        (+ t (* y 230661.510616))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (+ (/ z y) (- x (/ a (/ y x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.38e+69) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 9.5e+59) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.38d+69)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - (b / ((y * y) / x)))
    else if (y <= (-39000000000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 9.5d+59) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = (z / y) + (x - (a / (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.38e+69) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 9.5e+59) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.38e+69:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)))
	elif y <= -39000000000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 9.5e+59:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = (z / y) + (x - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.38e+69)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - Float64(b / Float64(Float64(y * y) / x))));
	elseif (y <= -39000000000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 9.5e+59)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.38e+69)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	elseif (y <= -39000000000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 9.5e+59)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = (z / y) + (x - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.38e+69], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -39000000000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+59], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.37999999999999999e69

   1. Initial program 2.3%

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

      1. div-inv 2.3%

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

      2. *-commutative 2.3%

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

      3. fma-def 2.3%

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

      4. *-commutative 2.3%

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

      5. fma-def 2.3%

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

      6. *-commutative 2.3%

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

      7. fma-def 2.3%

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

      8. fma-def 2.3%

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

      9. *-commutative 2.3%

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

      10. fma-def 2.3%

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

   3. Applied egg-rr 2.3%

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

   4. Taylor expanded in y around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. associate-*r/ 61.4%

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

      3. metadata-eval 61.4%

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

      4. unpow2 61.4%

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

      5. associate-/l* 68.2%

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

      6. unpow2 68.2%

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

      7. associate-/l* 68.3%

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

      8. unpow2 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in a around 0 71.6%

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

      1. associate--l+ 71.6%

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

      2. associate-*r/ 71.7%

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

      3. metadata-eval 71.7%

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

      4. unpow2 71.7%

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

      5. +-commutative 71.7%

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

      6. associate-/l* 79.7%

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

      7. unpow2 79.7%

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

   9. Simplified 79.7%

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

   if -1.37999999999999999e69 < y < -3.9e10

   1. Initial program 46.6%

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

   2. Taylor expanded in a around inf 20.2%

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

   3. Taylor expanded in y around inf 55.7%

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

      1. associate-+r+ 55.7%

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

      2. +-commutative 55.7%

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

      3. *-commutative 55.7%

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

      4. associate-+r+ 55.7%

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

      5. associate-*r/ 55.7%

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

      6. metadata-eval 55.7%

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

   5. Simplified 55.7%

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

      1. *-un-lft-identity 55.7%

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

      2. associate-/l* 64.4%

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

   7. Applied egg-rr 64.4%

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

   if -3.9e10 < y < 9.50000000000000023e59

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 85.3%

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

      1. *-commutative 85.3%

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

   4. Simplified 85.3%

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

   if 9.50000000000000023e59 < y

   1. Initial program 2.7%

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

   2. Taylor expanded in y around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. associate-/l* 80.6%

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

   4. Simplified 80.6%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 8: 69.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -6.8e+75)
     t_1
     (if (<= y -39000000000.0)
       (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
       (if (<= y 7.2e+29)
         (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -6.8e+75) {
		tmp = t_1;
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 7.2e+29) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-6.8d+75)) then
        tmp = t_1
    else if (y <= (-39000000000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 7.2d+29) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -6.8e+75) {
		tmp = t_1;
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 7.2e+29) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -6.8e+75:
		tmp = t_1
	elif y <= -39000000000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 7.2e+29:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -6.8e+75)
		tmp = t_1;
	elseif (y <= -39000000000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 7.2e+29)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -6.8e+75)
		tmp = t_1;
	elseif (y <= -39000000000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 7.2e+29)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+75], t$95$1, If[LessEqual[y, -39000000000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+29], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.80000000000000022e75 or 7.19999999999999952e29 < y

   1. Initial program 5.3%

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

   2. Taylor expanded in y around inf 72.1%

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

      1. associate--l+ 72.1%

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

      2. associate-/l* 75.2%

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

   4. Simplified 75.2%

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

   if -6.80000000000000022e75 < y < -3.9e10

   1. Initial program 47.5%

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

   2. Taylor expanded in a around inf 17.6%

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

   3. Taylor expanded in y around inf 48.1%

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

      1. associate-+r+ 48.1%

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

      2. +-commutative 48.1%

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

      3. *-commutative 48.1%

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

      4. associate-+r+ 48.1%

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

      5. associate-*r/ 48.1%

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

      6. metadata-eval 48.1%

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

   5. Simplified 48.1%

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

      1. *-un-lft-identity 48.1%

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

      2. associate-/l* 55.5%

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

   7. Applied egg-rr 55.5%

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

   if -3.9e10 < y < 7.19999999999999952e29

   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. Taylor expanded in t around inf 79.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+75}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 9: 70.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.7e+60)
   (+ (/ z y) (- (+ x (/ 27464.7644705 (* y y))) (/ b (/ (* y y) x))))
   (if (<= y -39000000000.0)
     (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
     (if (<= y 2.5e+33)
       (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (+ (/ z y) (- x (/ a (/ y x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.7e+60) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 2.5e+33) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-4.7d+60)) then
        tmp = (z / y) + ((x + (27464.7644705d0 / (y * y))) - (b / ((y * y) / x)))
    else if (y <= (-39000000000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 2.5d+33) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = (z / y) + (x - (a / (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.7e+60) {
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 2.5e+33) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (z / y) + (x - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.7e+60:
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)))
	elif y <= -39000000000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 2.5e+33:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = (z / y) + (x - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.7e+60)
		tmp = Float64(Float64(z / y) + Float64(Float64(x + Float64(27464.7644705 / Float64(y * y))) - Float64(b / Float64(Float64(y * y) / x))));
	elseif (y <= -39000000000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 2.5e+33)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.7e+60)
		tmp = (z / y) + ((x + (27464.7644705 / (y * y))) - (b / ((y * y) / x)));
	elseif (y <= -39000000000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 2.5e+33)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = (z / y) + (x - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.7e+60], N[(N[(z / y), $MachinePrecision] + N[(N[(x + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -39000000000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+33], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.6999999999999998e60

   1. Initial program 2.3%

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

      1. div-inv 2.3%

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

      2. *-commutative 2.3%

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

      3. fma-def 2.3%

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

      4. *-commutative 2.3%

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

      5. fma-def 2.3%

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

      6. *-commutative 2.3%

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

      7. fma-def 2.3%

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

      8. fma-def 2.3%

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

      9. *-commutative 2.3%

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

      10. fma-def 2.3%

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

   3. Applied egg-rr 2.3%

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

   4. Taylor expanded in y around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. associate-*r/ 61.4%

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

      3. metadata-eval 61.4%

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

      4. unpow2 61.4%

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

      5. associate-/l* 68.2%

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

      6. unpow2 68.2%

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

      7. associate-/l* 68.3%

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

      8. unpow2 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in a around 0 71.6%

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

      1. associate--l+ 71.6%

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

      2. associate-*r/ 71.7%

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

      3. metadata-eval 71.7%

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

      4. unpow2 71.7%

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

      5. +-commutative 71.7%

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

      6. associate-/l* 79.7%

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

      7. unpow2 79.7%

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

   9. Simplified 79.7%

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

   if -4.6999999999999998e60 < y < -3.9e10

   1. Initial program 46.6%

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

   2. Taylor expanded in a around inf 20.2%

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

   3. Taylor expanded in y around inf 55.7%

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

      1. associate-+r+ 55.7%

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

      2. +-commutative 55.7%

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

      3. *-commutative 55.7%

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

      4. associate-+r+ 55.7%

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

      5. associate-*r/ 55.7%

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

      6. metadata-eval 55.7%

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

   5. Simplified 55.7%

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

      1. *-un-lft-identity 55.7%

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

      2. associate-/l* 64.4%

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

   7. Applied egg-rr 64.4%

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

   if -3.9e10 < y < 2.49999999999999986e33

   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. Taylor expanded in t around inf 79.2%

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

   if 2.49999999999999986e33 < y

   1. Initial program 10.1%

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

   2. Taylor expanded in y around inf 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-/l* 70.7%

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

   4. Simplified 70.7%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;\frac{z}{y} + \left(\left(x + \frac{27464.7644705}{y \cdot y}\right) - \frac{b}{\frac{y \cdot y}{x}}\right)\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 10: 65.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-109}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -1.8e+76)
     t_1
     (if (<= y -39000000000.0)
       (+ (/ z a) (/ (* x y) a))
       (if (<= y 5.4e-109)
         (/ t (+ i (* y c)))
         (if (<= y 1.05e-5)
           (/ t (+ i (* b (* y y))))
           (if (<= y 1.9e+17) (/ t (* y c)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.8e+76) {
		tmp = t_1;
	} else if (y <= -39000000000.0) {
		tmp = (z / a) + ((x * y) / a);
	} else if (y <= 5.4e-109) {
		tmp = t / (i + (y * c));
	} else if (y <= 1.05e-5) {
		tmp = t / (i + (b * (y * y)));
	} else if (y <= 1.9e+17) {
		tmp = t / (y * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-1.8d+76)) then
        tmp = t_1
    else if (y <= (-39000000000.0d0)) then
        tmp = (z / a) + ((x * y) / a)
    else if (y <= 5.4d-109) then
        tmp = t / (i + (y * c))
    else if (y <= 1.05d-5) then
        tmp = t / (i + (b * (y * y)))
    else if (y <= 1.9d+17) then
        tmp = t / (y * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.8e+76) {
		tmp = t_1;
	} else if (y <= -39000000000.0) {
		tmp = (z / a) + ((x * y) / a);
	} else if (y <= 5.4e-109) {
		tmp = t / (i + (y * c));
	} else if (y <= 1.05e-5) {
		tmp = t / (i + (b * (y * y)));
	} else if (y <= 1.9e+17) {
		tmp = t / (y * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -1.8e+76:
		tmp = t_1
	elif y <= -39000000000.0:
		tmp = (z / a) + ((x * y) / a)
	elif y <= 5.4e-109:
		tmp = t / (i + (y * c))
	elif y <= 1.05e-5:
		tmp = t / (i + (b * (y * y)))
	elif y <= 1.9e+17:
		tmp = t / (y * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.8e+76)
		tmp = t_1;
	elseif (y <= -39000000000.0)
		tmp = Float64(Float64(z / a) + Float64(Float64(x * y) / a));
	elseif (y <= 5.4e-109)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	elseif (y <= 1.05e-5)
		tmp = Float64(t / Float64(i + Float64(b * Float64(y * y))));
	elseif (y <= 1.9e+17)
		tmp = Float64(t / Float64(y * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.8e+76)
		tmp = t_1;
	elseif (y <= -39000000000.0)
		tmp = (z / a) + ((x * y) / a);
	elseif (y <= 5.4e-109)
		tmp = t / (i + (y * c));
	elseif (y <= 1.05e-5)
		tmp = t / (i + (b * (y * y)));
	elseif (y <= 1.9e+17)
		tmp = t / (y * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+76], t$95$1, If[LessEqual[y, -39000000000.0], N[(N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-109], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-5], N[(t / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+17], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.8000000000000001e76 or 1.9e17 < y

   1. Initial program 7.2%

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

   2. Taylor expanded in y around inf 71.0%

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

      1. associate--l+ 71.0%

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

      2. associate-/l* 74.0%

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

   4. Simplified 74.0%

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

   if -1.8000000000000001e76 < y < -3.9e10

   1. Initial program 47.5%

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

   2. Taylor expanded in a around inf 17.6%

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

   3. Taylor expanded in y around inf 47.6%

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

   if -3.9e10 < y < 5.4000000000000001e-109

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 83.6%

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

   3. Taylor expanded in y around 0 78.0%

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

   if 5.4000000000000001e-109 < y < 1.04999999999999994e-5

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 66.8%

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

   3. Taylor expanded in b around inf 57.8%

      \[\leadsto \frac{t}{\color{blue}{{y}^{2} \cdot b} + i} \]
   4. Step-by-step derivation

      1. *-commutative 57.8%

         \[\leadsto \frac{t}{\color{blue}{b \cdot {y}^{2}} + i} \]

      2. unpow2 57.8%

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

   5. Simplified 57.8%

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

   if 1.04999999999999994e-5 < y < 1.9e17

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 52.8%

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

   3. Taylor expanded in c around inf 32.1%

      \[\leadsto \color{blue}{\frac{t}{c \cdot y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-109}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 11: 67.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 55000000000:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -2.4e+76)
     t_1
     (if (<= y -39000000000.0)
       (+ (/ z a) (/ (* x y) a))
       (if (<= y 55000000000.0) (/ t (+ i (* y (+ c (* a (* y y)))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -2.4e+76) {
		tmp = t_1;
	} else if (y <= -39000000000.0) {
		tmp = (z / a) + ((x * y) / a);
	} else if (y <= 55000000000.0) {
		tmp = t / (i + (y * (c + (a * (y * y)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-2.4d+76)) then
        tmp = t_1
    else if (y <= (-39000000000.0d0)) then
        tmp = (z / a) + ((x * y) / a)
    else if (y <= 55000000000.0d0) then
        tmp = t / (i + (y * (c + (a * (y * y)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -2.4e+76) {
		tmp = t_1;
	} else if (y <= -39000000000.0) {
		tmp = (z / a) + ((x * y) / a);
	} else if (y <= 55000000000.0) {
		tmp = t / (i + (y * (c + (a * (y * y)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -2.4e+76:
		tmp = t_1
	elif y <= -39000000000.0:
		tmp = (z / a) + ((x * y) / a)
	elif y <= 55000000000.0:
		tmp = t / (i + (y * (c + (a * (y * y)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.4e+76)
		tmp = t_1;
	elseif (y <= -39000000000.0)
		tmp = Float64(Float64(z / a) + Float64(Float64(x * y) / a));
	elseif (y <= 55000000000.0)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(a * Float64(y * y))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.4e+76)
		tmp = t_1;
	elseif (y <= -39000000000.0)
		tmp = (z / a) + ((x * y) / a);
	elseif (y <= 55000000000.0)
		tmp = t / (i + (y * (c + (a * (y * y)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+76], t$95$1, If[LessEqual[y, -39000000000.0], N[(N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 55000000000.0], N[(t / N[(i + N[(y * N[(c + N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e76 or 5.5e10 < y

   1. Initial program 8.1%

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

   2. Taylor expanded in y around inf 70.4%

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

      1. associate--l+ 70.4%

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

      2. associate-/l* 73.3%

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

   4. Simplified 73.3%

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

   if -2.4e76 < y < -3.9e10

   1. Initial program 47.5%

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

   2. Taylor expanded in a around inf 17.6%

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

   3. Taylor expanded in y around inf 47.6%

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

   if -3.9e10 < y < 5.5e10

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 80.0%

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

   3. Taylor expanded in a around inf 71.6%

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

      1. unpow2 71.6%

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

   5. Simplified 71.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 55000000000:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 12: 67.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{x \cdot y}{a}\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -6.2e+75)
     t_1
     (if (<= y -39000000000.0)
       (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ (* x y) a)))
       (if (<= y 3.3e+15) (/ t (+ i (* y (+ c (* a (* y y)))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -6.2e+75) {
		tmp = t_1;
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + ((x * y) / a));
	} else if (y <= 3.3e+15) {
		tmp = t / (i + (y * (c + (a * (y * y)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-6.2d+75)) then
        tmp = t_1
    else if (y <= (-39000000000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + ((x * y) / a))
    else if (y <= 3.3d+15) then
        tmp = t / (i + (y * (c + (a * (y * y)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -6.2e+75) {
		tmp = t_1;
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + ((x * y) / a));
	} else if (y <= 3.3e+15) {
		tmp = t / (i + (y * (c + (a * (y * y)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -6.2e+75:
		tmp = t_1
	elif y <= -39000000000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + ((x * y) / a))
	elif y <= 3.3e+15:
		tmp = t / (i + (y * (c + (a * (y * y)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -6.2e+75)
		tmp = t_1;
	elseif (y <= -39000000000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(Float64(x * y) / a)));
	elseif (y <= 3.3e+15)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(a * Float64(y * y))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -6.2e+75)
		tmp = t_1;
	elseif (y <= -39000000000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + ((x * y) / a));
	elseif (y <= 3.3e+15)
		tmp = t / (i + (y * (c + (a * (y * y)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+75], t$95$1, If[LessEqual[y, -39000000000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+15], N[(t / N[(i + N[(y * N[(c + N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2000000000000002e75 or 3.3e15 < y

   1. Initial program 8.1%

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

   2. Taylor expanded in y around inf 70.4%

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

      1. associate--l+ 70.4%

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

      2. associate-/l* 73.3%

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

   4. Simplified 73.3%

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

   if -6.2000000000000002e75 < y < -3.9e10

   1. Initial program 47.5%

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

   2. Taylor expanded in a around inf 17.6%

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

   3. Taylor expanded in y around inf 48.1%

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

      1. associate-+r+ 48.1%

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

      2. +-commutative 48.1%

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

      3. *-commutative 48.1%

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

      4. associate-+r+ 48.1%

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

      5. associate-*r/ 48.1%

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

      6. metadata-eval 48.1%

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

   5. Simplified 48.1%

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

   if -3.9e10 < y < 3.3e15

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 80.0%

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

   3. Taylor expanded in a around inf 71.6%

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

      1. unpow2 71.6%

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

   5. Simplified 71.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{x \cdot y}{a}\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 13: 67.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -1.7e+74)
     t_1
     (if (<= y -39000000000.0)
       (+ (/ 27464.7644705 (* y a)) (+ (/ z a) (/ y (/ a x))))
       (if (<= y 2.6e+15) (/ t (+ i (* y (+ c (* a (* y y)))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.7e+74) {
		tmp = t_1;
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 2.6e+15) {
		tmp = t / (i + (y * (c + (a * (y * y)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-1.7d+74)) then
        tmp = t_1
    else if (y <= (-39000000000.0d0)) then
        tmp = (27464.7644705d0 / (y * a)) + ((z / a) + (y / (a / x)))
    else if (y <= 2.6d+15) then
        tmp = t / (i + (y * (c + (a * (y * y)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.7e+74) {
		tmp = t_1;
	} else if (y <= -39000000000.0) {
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	} else if (y <= 2.6e+15) {
		tmp = t / (i + (y * (c + (a * (y * y)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -1.7e+74:
		tmp = t_1
	elif y <= -39000000000.0:
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)))
	elif y <= 2.6e+15:
		tmp = t / (i + (y * (c + (a * (y * y)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.7e+74)
		tmp = t_1;
	elseif (y <= -39000000000.0)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(Float64(z / a) + Float64(y / Float64(a / x))));
	elseif (y <= 2.6e+15)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(a * Float64(y * y))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.7e+74)
		tmp = t_1;
	elseif (y <= -39000000000.0)
		tmp = (27464.7644705 / (y * a)) + ((z / a) + (y / (a / x)));
	elseif (y <= 2.6e+15)
		tmp = t / (i + (y * (c + (a * (y * y)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+74], t$95$1, If[LessEqual[y, -39000000000.0], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+15], N[(t / N[(i + N[(y * N[(c + N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e74 or 2.6e15 < y

   1. Initial program 8.1%

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

   2. Taylor expanded in y around inf 70.4%

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

      1. associate--l+ 70.4%

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

      2. associate-/l* 73.3%

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

   4. Simplified 73.3%

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

   if -1.7e74 < y < -3.9e10

   1. Initial program 47.5%

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

   2. Taylor expanded in a around inf 17.6%

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

   3. Taylor expanded in y around inf 48.1%

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

      1. associate-+r+ 48.1%

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

      2. +-commutative 48.1%

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

      3. *-commutative 48.1%

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

      4. associate-+r+ 48.1%

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

      5. associate-*r/ 48.1%

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

      6. metadata-eval 48.1%

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

   5. Simplified 48.1%

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

      1. *-un-lft-identity 48.1%

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

      2. associate-/l* 55.5%

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

   7. Applied egg-rr 55.5%

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

   if -3.9e10 < y < 2.6e15

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 80.0%

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

   3. Taylor expanded in a around inf 71.6%

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

      1. unpow2 71.6%

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

   5. Simplified 71.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+74}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 14: 59.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.1e+74)
   x
   (if (<= y -39000000000.0)
     (+ (/ z a) (/ (* x y) a))
     (if (<= y 6.2e-109)
       (/ t (+ i (* y c)))
       (if (<= y 2.35e+27) (/ t (+ i (* b (* y y)))) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.1e+74) {
		tmp = x;
	} else if (y <= -39000000000.0) {
		tmp = (z / a) + ((x * y) / a);
	} else if (y <= 6.2e-109) {
		tmp = t / (i + (y * c));
	} else if (y <= 2.35e+27) {
		tmp = t / (i + (b * (y * y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-4.1d+74)) then
        tmp = x
    else if (y <= (-39000000000.0d0)) then
        tmp = (z / a) + ((x * y) / a)
    else if (y <= 6.2d-109) then
        tmp = t / (i + (y * c))
    else if (y <= 2.35d+27) then
        tmp = t / (i + (b * (y * y)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.1e+74) {
		tmp = x;
	} else if (y <= -39000000000.0) {
		tmp = (z / a) + ((x * y) / a);
	} else if (y <= 6.2e-109) {
		tmp = t / (i + (y * c));
	} else if (y <= 2.35e+27) {
		tmp = t / (i + (b * (y * y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.1e+74:
		tmp = x
	elif y <= -39000000000.0:
		tmp = (z / a) + ((x * y) / a)
	elif y <= 6.2e-109:
		tmp = t / (i + (y * c))
	elif y <= 2.35e+27:
		tmp = t / (i + (b * (y * y)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.1e+74)
		tmp = x;
	elseif (y <= -39000000000.0)
		tmp = Float64(Float64(z / a) + Float64(Float64(x * y) / a));
	elseif (y <= 6.2e-109)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	elseif (y <= 2.35e+27)
		tmp = Float64(t / Float64(i + Float64(b * Float64(y * y))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.1e+74)
		tmp = x;
	elseif (y <= -39000000000.0)
		tmp = (z / a) + ((x * y) / a);
	elseif (y <= 6.2e-109)
		tmp = t / (i + (y * c));
	elseif (y <= 2.35e+27)
		tmp = t / (i + (b * (y * y)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.1e+74], x, If[LessEqual[y, -39000000000.0], N[(N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-109], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e+27], N[(t / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.1e74 or 2.34999999999999988e27 < y

   1. Initial program 6.3%

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

   2. Taylor expanded in y around inf 60.2%

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

   if -4.1e74 < y < -3.9e10

   1. Initial program 47.5%

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

   2. Taylor expanded in a around inf 17.6%

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

   3. Taylor expanded in y around inf 47.6%

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

   if -3.9e10 < y < 6.1999999999999999e-109

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 83.6%

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

   3. Taylor expanded in y around 0 78.0%

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

   if 6.1999999999999999e-109 < y < 2.34999999999999988e27

   1. Initial program 97.0%

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

   2. Taylor expanded in t around inf 64.1%

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

   3. Taylor expanded in b around inf 50.9%

      \[\leadsto \frac{t}{\color{blue}{{y}^{2} \cdot b} + i} \]
   4. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto \frac{t}{\color{blue}{b \cdot {y}^{2}} + i} \]

      2. unpow2 50.9%

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

   5. Simplified 50.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 59.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+17}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.9e+73)
   x
   (if (<= y -2.45e+17) (/ z a) (if (<= y 1.2e+18) (/ t (+ i (* y c))) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.9e+73) {
		tmp = x;
	} else if (y <= -2.45e+17) {
		tmp = z / a;
	} else if (y <= 1.2e+18) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.9d+73)) then
        tmp = x
    else if (y <= (-2.45d+17)) then
        tmp = z / a
    else if (y <= 1.2d+18) then
        tmp = t / (i + (y * c))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.9e+73) {
		tmp = x;
	} else if (y <= -2.45e+17) {
		tmp = z / a;
	} else if (y <= 1.2e+18) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.9e+73:
		tmp = x
	elif y <= -2.45e+17:
		tmp = z / a
	elif y <= 1.2e+18:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.9e+73)
		tmp = x;
	elseif (y <= -2.45e+17)
		tmp = Float64(z / a);
	elseif (y <= 1.2e+18)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.9e+73)
		tmp = x;
	elseif (y <= -2.45e+17)
		tmp = z / a;
	elseif (y <= 1.2e+18)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.9e+73], x, If[LessEqual[y, -2.45e+17], N[(z / a), $MachinePrecision], If[LessEqual[y, 1.2e+18], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9000000000000001e73 or 1.2e18 < y

   1. Initial program 7.2%

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

   2. Taylor expanded in y around inf 59.6%

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

   if -3.9000000000000001e73 < y < -2.45e17

   1. Initial program 24.5%

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

   2. Taylor expanded in a around inf 13.5%

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

   3. Taylor expanded in z around inf 57.0%

      \[\leadsto \color{blue}{\frac{z}{a}} \]

   if -2.45e17 < y < 1.2e18

   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. Taylor expanded in t around inf 76.9%

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

   3. Taylor expanded in y around 0 67.3%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+17}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 59.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+18}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.5e+73)
   x
   (if (<= y -1.3e+18)
     (+ (/ 27464.7644705 (* y a)) (/ z a))
     (if (<= y 2e+20) (/ t (+ i (* y c))) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.5e+73) {
		tmp = x;
	} else if (y <= -1.3e+18) {
		tmp = (27464.7644705 / (y * a)) + (z / a);
	} else if (y <= 2e+20) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-4.5d+73)) then
        tmp = x
    else if (y <= (-1.3d+18)) then
        tmp = (27464.7644705d0 / (y * a)) + (z / a)
    else if (y <= 2d+20) then
        tmp = t / (i + (y * c))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.5e+73) {
		tmp = x;
	} else if (y <= -1.3e+18) {
		tmp = (27464.7644705 / (y * a)) + (z / a);
	} else if (y <= 2e+20) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.5e+73:
		tmp = x
	elif y <= -1.3e+18:
		tmp = (27464.7644705 / (y * a)) + (z / a)
	elif y <= 2e+20:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.5e+73)
		tmp = x;
	elseif (y <= -1.3e+18)
		tmp = Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a));
	elseif (y <= 2e+20)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.5e+73)
		tmp = x;
	elseif (y <= -1.3e+18)
		tmp = (27464.7644705 / (y * a)) + (z / a);
	elseif (y <= 2e+20)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.5e+73], x, If[LessEqual[y, -1.3e+18], N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+20], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.49999999999999985e73 or 2e20 < y

   1. Initial program 7.2%

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

   2. Taylor expanded in y around inf 59.6%

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

   if -4.49999999999999985e73 < y < -1.3e18

   1. Initial program 24.5%

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

   2. Taylor expanded in a around inf 13.5%

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

   3. Taylor expanded in y around inf 57.6%

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

      1. associate-+r+ 57.6%

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

      2. +-commutative 57.6%

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

      3. *-commutative 57.6%

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

      4. associate-+r+ 57.6%

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

      5. associate-*r/ 57.6%

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

      6. metadata-eval 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in y around 0 57.7%

      \[\leadsto \color{blue}{\frac{z}{a} + 27464.7644705 \cdot \frac{1}{a \cdot y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 57.7%

         \[\leadsto \frac{z}{a} + \color{blue}{\frac{27464.7644705 \cdot 1}{a \cdot y}} \]

      2. metadata-eval 57.7%

         \[\leadsto \frac{z}{a} + \frac{\color{blue}{27464.7644705}}{a \cdot y} \]

      3. *-commutative 57.7%

         \[\leadsto \frac{z}{a} + \frac{27464.7644705}{\color{blue}{y \cdot a}} \]

   8. Simplified 57.7%

      \[\leadsto \color{blue}{\frac{z}{a} + \frac{27464.7644705}{y \cdot a}} \]

   if -1.3e18 < y < 2e20

   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. Taylor expanded in t around inf 76.9%

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

   3. Taylor expanded in y around 0 67.3%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+18}:\\ \;\;\;\;\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 59.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3e+74)
   x
   (if (<= y -39000000000.0)
     (+ (/ z a) (/ (* x y) a))
     (if (<= y 1.4e+20) (/ t (+ i (* y c))) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3e+74) {
		tmp = x;
	} else if (y <= -39000000000.0) {
		tmp = (z / a) + ((x * y) / a);
	} else if (y <= 1.4e+20) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3d+74)) then
        tmp = x
    else if (y <= (-39000000000.0d0)) then
        tmp = (z / a) + ((x * y) / a)
    else if (y <= 1.4d+20) then
        tmp = t / (i + (y * c))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3e+74) {
		tmp = x;
	} else if (y <= -39000000000.0) {
		tmp = (z / a) + ((x * y) / a);
	} else if (y <= 1.4e+20) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3e+74:
		tmp = x
	elif y <= -39000000000.0:
		tmp = (z / a) + ((x * y) / a)
	elif y <= 1.4e+20:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3e+74)
		tmp = x;
	elseif (y <= -39000000000.0)
		tmp = Float64(Float64(z / a) + Float64(Float64(x * y) / a));
	elseif (y <= 1.4e+20)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3e+74)
		tmp = x;
	elseif (y <= -39000000000.0)
		tmp = (z / a) + ((x * y) / a);
	elseif (y <= 1.4e+20)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3e+74], x, If[LessEqual[y, -39000000000.0], N[(N[(z / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+20], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e74 or 1.4e20 < y

   1. Initial program 7.2%

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

   2. Taylor expanded in y around inf 59.6%

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

   if -3e74 < y < -3.9e10

   1. Initial program 47.5%

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

   2. Taylor expanded in a around inf 17.6%

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

   3. Taylor expanded in y around inf 47.6%

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

   if -3.9e10 < y < 1.4e20

   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. Taylor expanded in t around inf 78.9%

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

   3. Taylor expanded in y around 0 69.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -39000000000:\\ \;\;\;\;\frac{z}{a} + \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 51.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.9e+73)
   x
   (if (<= y -1.25e+19) (/ z a) (if (<= y 1.45e+21) (/ t i) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.9e+73) {
		tmp = x;
	} else if (y <= -1.25e+19) {
		tmp = z / a;
	} else if (y <= 1.45e+21) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.9d+73)) then
        tmp = x
    else if (y <= (-1.25d+19)) then
        tmp = z / a
    else if (y <= 1.45d+21) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.9e+73) {
		tmp = x;
	} else if (y <= -1.25e+19) {
		tmp = z / a;
	} else if (y <= 1.45e+21) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.9e+73:
		tmp = x
	elif y <= -1.25e+19:
		tmp = z / a
	elif y <= 1.45e+21:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.9e+73)
		tmp = x;
	elseif (y <= -1.25e+19)
		tmp = Float64(z / a);
	elseif (y <= 1.45e+21)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.9e+73)
		tmp = x;
	elseif (y <= -1.25e+19)
		tmp = z / a;
	elseif (y <= 1.45e+21)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.9e+73], x, If[LessEqual[y, -1.25e+19], N[(z / a), $MachinePrecision], If[LessEqual[y, 1.45e+21], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9000000000000001e73 or 1.45e21 < y

   1. Initial program 7.2%

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

   2. Taylor expanded in y around inf 59.6%

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

   if -3.9000000000000001e73 < y < -1.25e19

   1. Initial program 24.5%

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

   2. Taylor expanded in a around inf 13.5%

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

   3. Taylor expanded in z around inf 57.0%

      \[\leadsto \color{blue}{\frac{z}{a}} \]

   if -1.25e19 < y < 1.45e21

   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. Taylor expanded in y around 0 54.2%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 51.8% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7e+25) x (if (<= y 2.1e+22) (/ 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+25) {
		tmp = x;
	} else if (y <= 2.1e+22) {
		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+25)) then
        tmp = x
    else if (y <= 2.1d+22) 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+25) {
		tmp = x;
	} else if (y <= 2.1e+22) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7e+25:
		tmp = x
	elif y <= 2.1e+22:
		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+25)
		tmp = x;
	elseif (y <= 2.1e+22)
		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+25)
		tmp = x;
	elseif (y <= 2.1e+22)
		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+25], x, If[LessEqual[y, 2.1e+22], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999999e25 or 2.0999999999999998e22 < y

   1. Initial program 7.8%

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

   2. Taylor expanded in y around inf 55.6%

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

   if -6.99999999999999999e25 < y < 2.0999999999999998e22

   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. Taylor expanded in y around 0 53.9%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 27.1% 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 60.2%

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

2. Taylor expanded in y around inf 25.5%

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

3. Final simplification 25.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023192 
(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)))