Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 57.1% → 85.1%

Time: 27.6s

Alternatives: 18

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: 57.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.1% accurate, 0.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/
    (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t)
    (fma (fma (fma (+ y a) y b) y c) y i))
   (+ x (- (/ z y) (/ 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 * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((y + a), y, b), y, c), y, i);
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, 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(fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(y + a), y, b), y, c), y, i));
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := 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[(N[(N[(N[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / y), $MachinePrecision] - 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 96.2%

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

      1. fma-def 96.2%

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

      2. fma-def 96.2%

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

      3. fma-def 96.2%

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

      4. fma-def 96.2%

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

      5. fma-def 96.2%

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

      6. fma-def 96.2%

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

      7. +-commutative 96.2%

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

      8. fma-def 96.2%

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

      9. +-commutative 96.2%

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

   3. Simplified 96.2%

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

   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 68.4%

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

      1. associate--l+ 68.4%

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

      2. associate-/l* 69.2%

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

   4. Simplified 69.2%

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

4. Final simplification 85.9%

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

Alternative 2: 85.1% accurate, 0.5× speedup

Math

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

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 (+ x (- (/ z y) (/ 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 = x + ((z / y) - (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 = x + ((z / y) - (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 = x + ((z / y) - (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(x + Float64(Float64(z / y) - 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 = x + ((z / y) - (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[(x + N[(N[(z / y), $MachinePrecision] - 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 96.2%

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

   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 68.4%

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

      1. associate--l+ 68.4%

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

      2. associate-/l* 69.2%

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

   4. Simplified 69.2%

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

4. Final simplification 85.9%

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

Alternative 3: 81.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ t_2 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{t_2}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y\right)\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x)))))
        (t_2 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (<= y -4.3e+43)
     t_1
     (if (<= y 5.5e-5)
       (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) t_2)
       (if (<= y 2.4e+66)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (* x y)))))))
          t_2)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -4.3e+43) {
		tmp = t_1;
	} else if (y <= 5.5e-5) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	} else if (y <= 2.4e+66) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (x * y))))))) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    if (y <= (-4.3d+43)) then
        tmp = t_1
    else if (y <= 5.5d-5) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / t_2
    else if (y <= 2.4d+66) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (x * y))))))) / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -4.3e+43) {
		tmp = t_1;
	} else if (y <= 5.5e-5) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	} else if (y <= 2.4e+66) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (x * y))))))) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	tmp = 0
	if y <= -4.3e+43:
		tmp = t_1
	elif y <= 5.5e-5:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2
	elif y <= 2.4e+66:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (x * y))))))) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	t_2 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if (y <= -4.3e+43)
		tmp = t_1;
	elseif (y <= 5.5e-5)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / t_2);
	elseif (y <= 2.4e+66)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(x * y))))))) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	tmp = 0.0;
	if (y <= -4.3e+43)
		tmp = t_1;
	elseif (y <= 5.5e-5)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	elseif (y <= 2.4e+66)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (x * y))))))) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -4.3e+43], t$95$1, If[LessEqual[y, 5.5e-5], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 2.4e+66], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3e43 or 2.4000000000000002e66 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in y around inf 69.1%

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

      1. associate--l+ 69.1%

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

      2. associate-/l* 69.9%

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

   4. Simplified 69.9%

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

   if -4.3e43 < y < 5.5000000000000002e-5

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 94.9%

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

      1. *-commutative 94.9%

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

      2. unpow2 94.9%

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

   4. Simplified 94.9%

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

   if 5.5000000000000002e-5 < y < 2.4000000000000002e66

   1. Initial program 81.1%

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

   2. Taylor expanded in x around inf 81.5%

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

      1. unpow2 81.5%

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

      2. associate-*r* 81.4%

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

      3. *-commutative 81.4%

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

   4. Simplified 81.4%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+43}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 4: 80.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+45} \lor \neg \left(y \leq 1.56 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.75e+45) (not (<= y 1.56e+38)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* z (* y y)))))
    (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.75e+45) || !(y <= 1.56e+38)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.75d+45)) .or. (.not. (y <= 1.56d+38))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.75e+45) || !(y <= 1.56e+38)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.75e+45) or not (y <= 1.56e+38):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.75e+45) || !(y <= 1.56e+38))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		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));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.75e+45) || ~((y <= 1.56e+38)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.75e+45], N[Not[LessEqual[y, 1.56e+38]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75000000000000011e45 or 1.5599999999999999e38 < y

   1. Initial program 5.9%

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

   2. Taylor expanded in y around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-/l* 69.0%

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

   4. Simplified 69.0%

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

   if -1.75000000000000011e45 < y < 1.5599999999999999e38

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 91.3%

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

      1. *-commutative 91.3%

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

      2. unpow2 91.3%

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

   4. Simplified 91.3%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+45} \lor \neg \left(y \leq 1.56 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 5: 77.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+47} \lor \neg \left(y \leq 2.1 \cdot 10^{+36}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.4e+47) (not (<= y 2.1e+36)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.4e+47) || !(y <= 2.1e+36)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.4d+47)) .or. (.not. (y <= 2.1d+36))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.4e+47) || !(y <= 2.1e+36)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.4e+47) or not (y <= 2.1e+36):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.4e+47) || !(y <= 2.1e+36))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		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));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.4e+47) || ~((y <= 2.1e+36)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.4e+47], N[Not[LessEqual[y, 2.1e+36]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999994e47 or 2.10000000000000004e36 < y

   1. Initial program 5.9%

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

   2. Taylor expanded in y around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-/l* 69.0%

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

   4. Simplified 69.0%

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

   if -1.39999999999999994e47 < y < 2.10000000000000004e36

   1. Initial program 97.1%

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

   2. Taylor expanded in y around 0 82.2%

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

      1. *-commutative 82.2%

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

   4. Simplified 82.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+47} \lor \neg \left(y \leq 2.1 \cdot 10^{+36}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 6: 74.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+126}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.4e+38)
     t_1
     (if (<= y 1.7e-6)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
        (+ i (* y (+ c (* a (* y y))))))
       (if (<= y 1.7e+126) (+ (/ z a) (/ x (/ a 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 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.4e+38) {
		tmp = t_1;
	} else if (y <= 1.7e-6) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (a * (y * y)))));
	} else if (y <= 1.7e+126) {
		tmp = (z / a) + (x / (a / 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 = x + ((z / y) - (a / (y / x)))
    if (y <= (-2.4d+38)) then
        tmp = t_1
    else if (y <= 1.7d-6) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (a * (y * y)))))
    else if (y <= 1.7d+126) then
        tmp = (z / a) + (x / (a / 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 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.4e+38) {
		tmp = t_1;
	} else if (y <= 1.7e-6) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (a * (y * y)))));
	} else if (y <= 1.7e+126) {
		tmp = (z / a) + (x / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -2.4e+38:
		tmp = t_1
	elif y <= 1.7e-6:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (a * (y * y)))))
	elif y <= 1.7e+126:
		tmp = (z / a) + (x / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.4e+38)
		tmp = t_1;
	elseif (y <= 1.7e-6)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(a * Float64(y * y))))));
	elseif (y <= 1.7e+126)
		tmp = Float64(Float64(z / a) + Float64(x / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.4e+38)
		tmp = t_1;
	elseif (y <= 1.7e-6)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (a * (y * y)))));
	elseif (y <= 1.7e+126)
		tmp = (z / a) + (x / (a / 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[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+38], t$95$1, If[LessEqual[y, 1.7e-6], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+126], N[(N[(z / a), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000017e38 or 1.69999999999999995e126 < y

   1. Initial program 3.6%

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

   2. Taylor expanded in y around inf 74.4%

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

      1. associate--l+ 74.4%

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

      2. associate-/l* 75.3%

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

   4. Simplified 75.3%

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

   if -2.40000000000000017e38 < y < 1.70000000000000003e-6

   1. Initial program 97.7%

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

      1. *-commutative 97.7%

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

      2. +-commutative 97.7%

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

      3. distribute-rgt-in 97.7%

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

      4. *-commutative 97.7%

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

      5. associate-*l* 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in a around inf 88.8%

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

      1. *-commutative 88.8%

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

      2. unpow2 88.8%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in y around 0 86.2%

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

   if 1.70000000000000003e-6 < y < 1.69999999999999995e126

   1. Initial program 43.9%

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

   2. Taylor expanded in a around inf 12.9%

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

   3. Taylor expanded in y around inf 41.7%

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

      1. associate-/l* 45.6%

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

   5. Simplified 45.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+38}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+126}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 7: 76.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+47} \lor \neg \left(y \leq 3 \cdot 10^{+36}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.15e+47) (not (<= y 3e+36)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.15e+47) || !(y <= 3e+36)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.15d+47)) .or. (.not. (y <= 3d+36))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.15e+47) || !(y <= 3e+36)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.15e+47) or not (y <= 3e+36):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.15e+47) || !(y <= 3e+36))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.15e+47) || ~((y <= 3e+36)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.15e+47], N[Not[LessEqual[y, 3e+36]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1499999999999999e47 or 3e36 < y

   1. Initial program 5.9%

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

   2. Taylor expanded in y around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-/l* 69.0%

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

   4. Simplified 69.0%

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

   if -1.1499999999999999e47 < y < 3e36

   1. Initial program 97.1%

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

   2. Taylor expanded in y around 0 81.9%

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

      1. *-commutative 81.9%

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

   4. Simplified 81.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+47} \lor \neg \left(y \leq 3 \cdot 10^{+36}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 8: 73.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+126}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -3.6e+40)
     t_1
     (if (<= y 1.6e-6)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ i (* y (+ c (* y b)))))
       (if (<= y 1.1e+126) (+ (/ z a) (/ x (/ a 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 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -3.6e+40) {
		tmp = t_1;
	} else if (y <= 1.6e-6) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} else if (y <= 1.1e+126) {
		tmp = (z / a) + (x / (a / 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 = x + ((z / y) - (a / (y / x)))
    if (y <= (-3.6d+40)) then
        tmp = t_1
    else if (y <= 1.6d-6) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * b))))
    else if (y <= 1.1d+126) then
        tmp = (z / a) + (x / (a / 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 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -3.6e+40) {
		tmp = t_1;
	} else if (y <= 1.6e-6) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} else if (y <= 1.1e+126) {
		tmp = (z / a) + (x / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -3.6e+40:
		tmp = t_1
	elif y <= 1.6e-6:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	elif y <= 1.1e+126:
		tmp = (z / a) + (x / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -3.6e+40)
		tmp = t_1;
	elseif (y <= 1.6e-6)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 1.1e+126)
		tmp = Float64(Float64(z / a) + Float64(x / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -3.6e+40)
		tmp = t_1;
	elseif (y <= 1.6e-6)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	elseif (y <= 1.1e+126)
		tmp = (z / a) + (x / (a / 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[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+40], t$95$1, If[LessEqual[y, 1.6e-6], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+126], N[(N[(z / a), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.59999999999999996e40 or 1.09999999999999999e126 < y

   1. Initial program 3.6%

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

   2. Taylor expanded in y around inf 74.4%

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

      1. associate--l+ 74.4%

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

      2. associate-/l* 75.3%

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

   4. Simplified 75.3%

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

   if -3.59999999999999996e40 < y < 1.5999999999999999e-6

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 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%

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

   5. Taylor expanded in y around 0 82.1%

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

      1. *-commutative 82.1%

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

   7. Simplified 82.1%

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

   if 1.5999999999999999e-6 < y < 1.09999999999999999e126

   1. Initial program 43.9%

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

   2. Taylor expanded in a around inf 12.9%

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

   3. Taylor expanded in y around inf 41.7%

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

      1. associate-/l* 45.6%

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

   5. Simplified 45.6%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+40}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+126}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 9: 69.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+43} \lor \neg \left(y \leq 3.2 \cdot 10^{+33}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.02e+43) (not (<= y 3.2e+33)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.02e+43) || !(y <= 3.2e+33)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.02d+43)) .or. (.not. (y <= 3.2d+33))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.02e+43) || !(y <= 3.2e+33)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.02e+43) or not (y <= 3.2e+33):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.02e+43) || !(y <= 3.2e+33))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.02e+43) || ~((y <= 3.2e+33)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.02e+43], N[Not[LessEqual[y, 3.2e+33]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e43 or 3.20000000000000017e33 < y

   1. Initial program 5.9%

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

   2. Taylor expanded in y around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-/l* 69.0%

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

   4. Simplified 69.0%

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

   if -1.02e43 < y < 3.20000000000000017e33

   1. Initial program 97.1%

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

   2. Taylor expanded in t around inf 72.3%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+43} \lor \neg \left(y \leq 3.2 \cdot 10^{+33}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 10: 64.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+128}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -1e+44)
     t_1
     (if (<= y -3.5e-57)
       (/ t (+ i (* b (* y y))))
       (if (<= y 1.7e-11)
         (/ t (+ i (* y c)))
         (if (<= y 4.2e+128) (+ (/ z a) (/ x (/ a 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 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1e+44) {
		tmp = t_1;
	} else if (y <= -3.5e-57) {
		tmp = t / (i + (b * (y * y)));
	} else if (y <= 1.7e-11) {
		tmp = t / (i + (y * c));
	} else if (y <= 4.2e+128) {
		tmp = (z / a) + (x / (a / 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 = x + ((z / y) - (a / (y / x)))
    if (y <= (-1d+44)) then
        tmp = t_1
    else if (y <= (-3.5d-57)) then
        tmp = t / (i + (b * (y * y)))
    else if (y <= 1.7d-11) then
        tmp = t / (i + (y * c))
    else if (y <= 4.2d+128) then
        tmp = (z / a) + (x / (a / 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 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1e+44) {
		tmp = t_1;
	} else if (y <= -3.5e-57) {
		tmp = t / (i + (b * (y * y)));
	} else if (y <= 1.7e-11) {
		tmp = t / (i + (y * c));
	} else if (y <= 4.2e+128) {
		tmp = (z / a) + (x / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -1e+44:
		tmp = t_1
	elif y <= -3.5e-57:
		tmp = t / (i + (b * (y * y)))
	elif y <= 1.7e-11:
		tmp = t / (i + (y * c))
	elif y <= 4.2e+128:
		tmp = (z / a) + (x / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1e+44)
		tmp = t_1;
	elseif (y <= -3.5e-57)
		tmp = Float64(t / Float64(i + Float64(b * Float64(y * y))));
	elseif (y <= 1.7e-11)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	elseif (y <= 4.2e+128)
		tmp = Float64(Float64(z / a) + Float64(x / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1e+44)
		tmp = t_1;
	elseif (y <= -3.5e-57)
		tmp = t / (i + (b * (y * y)));
	elseif (y <= 1.7e-11)
		tmp = t / (i + (y * c));
	elseif (y <= 4.2e+128)
		tmp = (z / a) + (x / (a / 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[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+44], t$95$1, If[LessEqual[y, -3.5e-57], N[(t / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-11], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+128], N[(N[(z / a), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.0000000000000001e44 or 4.1999999999999999e128 < y

   1. Initial program 3.6%

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

   2. Taylor expanded in y around inf 74.4%

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

      1. associate--l+ 74.4%

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

      2. associate-/l* 75.3%

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

   4. Simplified 75.3%

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

   if -1.0000000000000001e44 < y < -3.49999999999999991e-57

   1. Initial program 84.8%

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

   2. Taylor expanded in t around inf 41.2%

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

   3. Taylor expanded in b around inf 36.9%

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

      1. unpow2 36.9%

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

   5. Simplified 36.9%

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

   if -3.49999999999999991e-57 < y < 1.6999999999999999e-11

   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 80.9%

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

   3. Taylor expanded in y around 0 74.0%

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

      1. *-commutative 74.0%

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

   5. Simplified 74.0%

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

   if 1.6999999999999999e-11 < y < 4.1999999999999999e128

   1. Initial program 43.9%

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

   2. Taylor expanded in a around inf 12.9%

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

   3. Taylor expanded in y around inf 41.7%

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

      1. associate-/l* 45.6%

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

   5. Simplified 45.6%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+44}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+128}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 11: 57.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{t}{b}}{y \cdot y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+134}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.7e+57)
   x
   (if (<= y -1.7e-49)
     (/ (/ t b) (* y y))
     (if (<= y 1.5e-14)
       (/ t (+ i (* y c)))
       (if (<= y 3.7e+134) (+ (/ z a) (/ 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+57) {
		tmp = x;
	} else if (y <= -1.7e-49) {
		tmp = (t / b) / (y * y);
	} else if (y <= 1.5e-14) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.7e+134) {
		tmp = (z / a) + (x / (a / 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 <= (-4.7d+57)) then
        tmp = x
    else if (y <= (-1.7d-49)) then
        tmp = (t / b) / (y * y)
    else if (y <= 1.5d-14) then
        tmp = t / (i + (y * c))
    else if (y <= 3.7d+134) then
        tmp = (z / a) + (x / (a / 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 <= -4.7e+57) {
		tmp = x;
	} else if (y <= -1.7e-49) {
		tmp = (t / b) / (y * y);
	} else if (y <= 1.5e-14) {
		tmp = t / (i + (y * c));
	} else if (y <= 3.7e+134) {
		tmp = (z / a) + (x / (a / y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.7e+57:
		tmp = x
	elif y <= -1.7e-49:
		tmp = (t / b) / (y * y)
	elif y <= 1.5e-14:
		tmp = t / (i + (y * c))
	elif y <= 3.7e+134:
		tmp = (z / a) + (x / (a / y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.7e+57)
		tmp = x;
	elseif (y <= -1.7e-49)
		tmp = Float64(Float64(t / b) / Float64(y * y));
	elseif (y <= 1.5e-14)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	elseif (y <= 3.7e+134)
		tmp = Float64(Float64(z / a) + Float64(x / Float64(a / 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 <= -4.7e+57)
		tmp = x;
	elseif (y <= -1.7e-49)
		tmp = (t / b) / (y * y);
	elseif (y <= 1.5e-14)
		tmp = t / (i + (y * c));
	elseif (y <= 3.7e+134)
		tmp = (z / a) + (x / (a / y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.7e+57], x, If[LessEqual[y, -1.7e-49], N[(N[(t / b), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-14], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+134], N[(N[(z / a), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.7000000000000003e57 or 3.70000000000000013e134 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in y around inf 58.7%

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

   if -4.7000000000000003e57 < y < -1.70000000000000002e-49

   1. Initial program 75.9%

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

   2. Taylor expanded in t around inf 33.8%

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

   3. Taylor expanded in b around inf 26.9%

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

      1. associate-/r* 30.7%

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

      2. unpow2 30.7%

         \[\leadsto \frac{\frac{t}{b}}{\color{blue}{y \cdot y}} \]

   5. Simplified 30.7%

      \[\leadsto \color{blue}{\frac{\frac{t}{b}}{y \cdot y}} \]

   if -1.70000000000000002e-49 < y < 1.4999999999999999e-14

   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 80.9%

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

   3. Taylor expanded in y around 0 74.0%

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

      1. *-commutative 74.0%

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

   5. Simplified 74.0%

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

   if 1.4999999999999999e-14 < y < 3.70000000000000013e134

   1. Initial program 40.7%

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

   2. Taylor expanded in a around inf 11.9%

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

   3. Taylor expanded in y around inf 38.9%

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

      1. associate-/l* 42.4%

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

   5. Simplified 42.4%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{t}{b}}{y \cdot y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+134}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 58.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-9}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.28e+39)
   x
   (if (<= y -3.1e-50)
     (/ t (+ i (* b (* y y))))
     (if (<= y 1.7e-9)
       (/ t (+ i (* y c)))
       (if (<= y 5.5e+134) (+ (/ z a) (/ 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 <= -1.28e+39) {
		tmp = x;
	} else if (y <= -3.1e-50) {
		tmp = t / (i + (b * (y * y)));
	} else if (y <= 1.7e-9) {
		tmp = t / (i + (y * c));
	} else if (y <= 5.5e+134) {
		tmp = (z / a) + (x / (a / 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 <= (-1.28d+39)) then
        tmp = x
    else if (y <= (-3.1d-50)) then
        tmp = t / (i + (b * (y * y)))
    else if (y <= 1.7d-9) then
        tmp = t / (i + (y * c))
    else if (y <= 5.5d+134) then
        tmp = (z / a) + (x / (a / 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 <= -1.28e+39) {
		tmp = x;
	} else if (y <= -3.1e-50) {
		tmp = t / (i + (b * (y * y)));
	} else if (y <= 1.7e-9) {
		tmp = t / (i + (y * c));
	} else if (y <= 5.5e+134) {
		tmp = (z / a) + (x / (a / y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.28e+39:
		tmp = x
	elif y <= -3.1e-50:
		tmp = t / (i + (b * (y * y)))
	elif y <= 1.7e-9:
		tmp = t / (i + (y * c))
	elif y <= 5.5e+134:
		tmp = (z / a) + (x / (a / y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.28e+39)
		tmp = x;
	elseif (y <= -3.1e-50)
		tmp = Float64(t / Float64(i + Float64(b * Float64(y * y))));
	elseif (y <= 1.7e-9)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	elseif (y <= 5.5e+134)
		tmp = Float64(Float64(z / a) + Float64(x / Float64(a / 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 <= -1.28e+39)
		tmp = x;
	elseif (y <= -3.1e-50)
		tmp = t / (i + (b * (y * y)));
	elseif (y <= 1.7e-9)
		tmp = t / (i + (y * c));
	elseif (y <= 5.5e+134)
		tmp = (z / a) + (x / (a / y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.28e+39], x, If[LessEqual[y, -3.1e-50], N[(t / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-9], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+134], N[(N[(z / a), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.27999999999999994e39 or 5.4999999999999999e134 < y

   1. Initial program 3.7%

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

   2. Taylor expanded in y around inf 56.7%

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

   if -1.27999999999999994e39 < y < -3.1000000000000002e-50

   1. Initial program 84.8%

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

   2. Taylor expanded in t around inf 41.2%

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

   3. Taylor expanded in b around inf 36.9%

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

      1. unpow2 36.9%

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

   5. Simplified 36.9%

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

   if -3.1000000000000002e-50 < y < 1.6999999999999999e-9

   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 80.9%

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

   3. Taylor expanded in y around 0 74.0%

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

      1. *-commutative 74.0%

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

   5. Simplified 74.0%

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

   if 1.6999999999999999e-9 < y < 5.4999999999999999e134

   1. Initial program 40.7%

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

   2. Taylor expanded in a around inf 11.9%

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

   3. Taylor expanded in y around inf 38.9%

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

      1. associate-/l* 42.4%

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

   5. Simplified 42.4%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-9}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 66.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+125}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -4.6e+38)
     t_1
     (if (<= y 2.6e-11)
       (/ t (+ i (* y (+ c (* y b)))))
       (if (<= y 9.6e+125) (+ (/ z a) (/ x (/ a 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 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -4.6e+38) {
		tmp = t_1;
	} else if (y <= 2.6e-11) {
		tmp = t / (i + (y * (c + (y * b))));
	} else if (y <= 9.6e+125) {
		tmp = (z / a) + (x / (a / 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 = x + ((z / y) - (a / (y / x)))
    if (y <= (-4.6d+38)) then
        tmp = t_1
    else if (y <= 2.6d-11) then
        tmp = t / (i + (y * (c + (y * b))))
    else if (y <= 9.6d+125) then
        tmp = (z / a) + (x / (a / 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 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -4.6e+38) {
		tmp = t_1;
	} else if (y <= 2.6e-11) {
		tmp = t / (i + (y * (c + (y * b))));
	} else if (y <= 9.6e+125) {
		tmp = (z / a) + (x / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -4.6e+38:
		tmp = t_1
	elif y <= 2.6e-11:
		tmp = t / (i + (y * (c + (y * b))))
	elif y <= 9.6e+125:
		tmp = (z / a) + (x / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -4.6e+38)
		tmp = t_1;
	elseif (y <= 2.6e-11)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 9.6e+125)
		tmp = Float64(Float64(z / a) + Float64(x / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -4.6e+38)
		tmp = t_1;
	elseif (y <= 2.6e-11)
		tmp = t / (i + (y * (c + (y * b))));
	elseif (y <= 9.6e+125)
		tmp = (z / a) + (x / (a / 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[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+38], t$95$1, If[LessEqual[y, 2.6e-11], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e+125], N[(N[(z / a), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.6000000000000002e38 or 9.5999999999999999e125 < y

   1. Initial program 3.6%

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

   2. Taylor expanded in y around inf 74.4%

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

      1. associate--l+ 74.4%

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

      2. associate-/l* 75.3%

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

   4. Simplified 75.3%

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

   if -4.6000000000000002e38 < y < 2.6000000000000001e-11

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 75.3%

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

   3. Taylor expanded in y around 0 72.2%

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

      1. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   if 2.6000000000000001e-11 < y < 9.5999999999999999e125

   1. Initial program 43.9%

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

   2. Taylor expanded in a around inf 12.9%

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

   3. Taylor expanded in y around inf 41.7%

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

      1. associate-/l* 45.6%

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

   5. Simplified 45.6%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+125}:\\ \;\;\;\;\frac{z}{a} + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 14: 57.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot b\right)}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.4e+43)
   x
   (if (<= y -3.1e-63)
     (/ t (* y (* y b)))
     (if (<= y 3.1e+23) (/ 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 <= -2.4e+43) {
		tmp = x;
	} else if (y <= -3.1e-63) {
		tmp = t / (y * (y * b));
	} else if (y <= 3.1e+23) {
		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 <= (-2.4d+43)) then
        tmp = x
    else if (y <= (-3.1d-63)) then
        tmp = t / (y * (y * b))
    else if (y <= 3.1d+23) 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 <= -2.4e+43) {
		tmp = x;
	} else if (y <= -3.1e-63) {
		tmp = t / (y * (y * b));
	} else if (y <= 3.1e+23) {
		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 <= -2.4e+43:
		tmp = x
	elif y <= -3.1e-63:
		tmp = t / (y * (y * b))
	elif y <= 3.1e+23:
		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 <= -2.4e+43)
		tmp = x;
	elseif (y <= -3.1e-63)
		tmp = Float64(t / Float64(y * Float64(y * b)));
	elseif (y <= 3.1e+23)
		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 <= -2.4e+43)
		tmp = x;
	elseif (y <= -3.1e-63)
		tmp = t / (y * (y * b));
	elseif (y <= 3.1e+23)
		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, -2.4e+43], x, If[LessEqual[y, -3.1e-63], N[(t / N[(y * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+23], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000023e43 or 3.09999999999999971e23 < y

   1. Initial program 5.9%

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

   2. Taylor expanded in y around inf 52.4%

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

   if -2.40000000000000023e43 < y < -3.09999999999999984e-63

   1. Initial program 85.4%

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

   2. Taylor expanded in t around inf 39.4%

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

   3. Taylor expanded in y around 0 34.7%

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

      1. *-commutative 34.7%

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

   5. Simplified 34.7%

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

   6. Taylor expanded in y around inf 31.2%

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

      1. *-commutative 31.2%

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

      2. unpow2 31.2%

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

      3. associate-*r* 31.2%

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

   8. Simplified 31.2%

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

   if -3.09999999999999984e-63 < y < 3.09999999999999971e23

   1. Initial program 99.0%

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

   2. Taylor expanded in t around inf 77.6%

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

   3. Taylor expanded in y around 0 69.6%

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

      1. *-commutative 69.6%

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

   5. Simplified 69.6%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot b\right)}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 57.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{\frac{t}{b}}{y \cdot y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4e+57)
   x
   (if (<= y -5.8e-53)
     (/ (/ t b) (* y y))
     (if (<= y 5e+25) (/ 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 <= -4e+57) {
		tmp = x;
	} else if (y <= -5.8e-53) {
		tmp = (t / b) / (y * y);
	} else if (y <= 5e+25) {
		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 <= (-4d+57)) then
        tmp = x
    else if (y <= (-5.8d-53)) then
        tmp = (t / b) / (y * y)
    else if (y <= 5d+25) 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 <= -4e+57) {
		tmp = x;
	} else if (y <= -5.8e-53) {
		tmp = (t / b) / (y * y);
	} else if (y <= 5e+25) {
		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 <= -4e+57:
		tmp = x
	elif y <= -5.8e-53:
		tmp = (t / b) / (y * y)
	elif y <= 5e+25:
		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 <= -4e+57)
		tmp = x;
	elseif (y <= -5.8e-53)
		tmp = Float64(Float64(t / b) / Float64(y * y));
	elseif (y <= 5e+25)
		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 <= -4e+57)
		tmp = x;
	elseif (y <= -5.8e-53)
		tmp = (t / b) / (y * y);
	elseif (y <= 5e+25)
		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, -4e+57], x, If[LessEqual[y, -5.8e-53], N[(N[(t / b), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+25], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.00000000000000019e57 or 5.00000000000000024e25 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in y around inf 53.9%

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

   if -4.00000000000000019e57 < y < -5.7999999999999996e-53

   1. Initial program 75.9%

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

   2. Taylor expanded in t around inf 33.8%

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

   3. Taylor expanded in b around inf 26.9%

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

      1. associate-/r* 30.7%

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

      2. unpow2 30.7%

         \[\leadsto \frac{\frac{t}{b}}{\color{blue}{y \cdot y}} \]

   5. Simplified 30.7%

      \[\leadsto \color{blue}{\frac{\frac{t}{b}}{y \cdot y}} \]

   if -5.7999999999999996e-53 < y < 5.00000000000000024e25

   1. Initial program 99.0%

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

   2. Taylor expanded in t around inf 77.0%

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

   3. Taylor expanded in y around 0 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{\frac{t}{b}}{y \cdot y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 49.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-65}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.5e+43)
   x
   (if (<= y -3.1e-63) (/ t (* y (* y b))) (if (<= y 1.4e-65) (/ t i) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.5e+43) {
		tmp = x;
	} else if (y <= -3.1e-63) {
		tmp = t / (y * (y * b));
	} else if (y <= 1.4e-65) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.5d+43)) then
        tmp = x
    else if (y <= (-3.1d-63)) then
        tmp = t / (y * (y * b))
    else if (y <= 1.4d-65) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.5e+43) {
		tmp = x;
	} else if (y <= -3.1e-63) {
		tmp = t / (y * (y * b));
	} else if (y <= 1.4e-65) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.5e+43:
		tmp = x
	elif y <= -3.1e-63:
		tmp = t / (y * (y * b))
	elif y <= 1.4e-65:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.5e+43)
		tmp = x;
	elseif (y <= -3.1e-63)
		tmp = Float64(t / Float64(y * Float64(y * b)));
	elseif (y <= 1.4e-65)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.5e+43)
		tmp = x;
	elseif (y <= -3.1e-63)
		tmp = t / (y * (y * b));
	elseif (y <= 1.4e-65)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.5e+43], x, If[LessEqual[y, -3.1e-63], N[(t / N[(y * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-65], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.50000000000000008e43 or 1.4e-65 < y

   1. Initial program 20.7%

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

   2. Taylor expanded in y around inf 44.3%

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

   if -1.50000000000000008e43 < y < -3.09999999999999984e-63

   1. Initial program 85.4%

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

   2. Taylor expanded in t around inf 39.4%

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

   3. Taylor expanded in y around 0 34.7%

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

      1. *-commutative 34.7%

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

   5. Simplified 34.7%

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

   6. Taylor expanded in y around inf 31.2%

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

      1. *-commutative 31.2%

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

      2. unpow2 31.2%

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

      3. associate-*r* 31.2%

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

   8. Simplified 31.2%

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

   if -3.09999999999999984e-63 < y < 1.4e-65

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 63.7%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-65}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 49.1% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-65}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.5e-30) x (if (<= y 1.4e-65) (/ 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 <= -3.5e-30) {
		tmp = x;
	} else if (y <= 1.4e-65) {
		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 <= (-3.5d-30)) then
        tmp = x
    else if (y <= 1.4d-65) 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 <= -3.5e-30) {
		tmp = x;
	} else if (y <= 1.4e-65) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.5e-30:
		tmp = x
	elif y <= 1.4e-65:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.5e-30)
		tmp = x;
	elseif (y <= 1.4e-65)
		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 <= -3.5e-30)
		tmp = x;
	elseif (y <= 1.4e-65)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.5e-30], x, If[LessEqual[y, 1.4e-65], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5000000000000003e-30 or 1.4e-65 < y

   1. Initial program 28.0%

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

   2. Taylor expanded in y around inf 39.5%

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

   if -3.5000000000000003e-30 < y < 1.4e-65

   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 y around 0 62.4%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-65}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 25.3% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.7%

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

2. Taylor expanded in y around inf 23.5%

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

3. Final simplification 23.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023297 
(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)))