Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.7% → 84.1%

Time: 27.0s

Alternatives: 15

Speedup: 1.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.7% 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: 84.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ (* 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 (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * ((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 * (x / y)));
	}
	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 * (x / y)));
	}
	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 * (x / y)))
	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(x / y))));
	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 * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(y * N[(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[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 91.7%

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

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 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. Add Preprocessing

   3. Taylor expanded in y around inf 69.8%

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

      1. associate--l+ 69.8%

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

      2. associate-/l* 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 87.0%

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

Alternative 2: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+44} \lor \neg \left(y \leq 4 \cdot 10^{+63}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.8e+44) (not (<= y 4e+63)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ (* 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 <= -3.8e+44) || !(y <= 4e+63)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((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 <= (-3.8d+44)) .or. (.not. (y <= 4d+63))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((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 <= -3.8e+44) || !(y <= 4e+63)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((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 <= -3.8e+44) or not (y <= 4e+63):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((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 <= -3.8e+44) || !(y <= 4e+63))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / 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 <= -3.8e+44) || ~((y <= 4e+63)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((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, -3.8e+44], N[Not[LessEqual[y, 4e+63]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000002e44 or 4.00000000000000023e63 < y

   1. Initial program 2.5%

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

   3. Taylor expanded in y around inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. associate-/l* 75.9%

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

   5. Simplified 75.9%

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

   if -3.8000000000000002e44 < y < 4.00000000000000023e63

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0 89.3%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+44} \lor \neg \left(y \leq 4 \cdot 10^{+63}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+15} \lor \neg \left(y \leq 6 \cdot 10^{+37}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.65e+15) (not (<= y 6e+37)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y (+ b (* y a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.65e+15) || !(y <= 6e+37)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.65d+15)) .or. (.not. (y <= 6d+37))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.65e+15) || !(y <= 6e+37)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.65e+15) or not (y <= 6e+37):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.65e+15) || !(y <= 6e+37))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.65e+15) || ~((y <= 6e+37)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.65e+15], N[Not[LessEqual[y, 6e+37]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e15 or 6.00000000000000043e37 < y

   1. Initial program 8.7%

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

   3. Taylor expanded in y around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   if -1.65e15 < y < 6.00000000000000043e37

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 93.0%

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

   4. Taylor expanded in y around 0 92.3%

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

      1. *-commutative 92.3%

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

   6. Simplified 92.3%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+15} \lor \neg \left(y \leq 6 \cdot 10^{+37}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+15} \lor \neg \left(y \leq 2.6 \cdot 10^{+39}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.65e+15) (not (<= y 2.6e+39)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.65e+15) || !(y <= 2.6e+39)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.65d+15)) .or. (.not. (y <= 2.6d+39))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.65e+15) || !(y <= 2.6e+39)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.65e+15) or not (y <= 2.6e+39):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.65e+15) || !(y <= 2.6e+39))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.65e+15) || ~((y <= 2.6e+39)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.65e+15], N[Not[LessEqual[y, 2.6e+39]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e15 or 2.6e39 < y

   1. Initial program 8.7%

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

   3. Taylor expanded in y around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   if -1.65e15 < y < 2.6e39

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 93.0%

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

   4. Taylor expanded in y around 0 88.1%

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

      1. *-commutative 88.1%

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

   6. Simplified 88.1%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+15} \lor \neg \left(y \leq 2.6 \cdot 10^{+39}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-136}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ t (+ i (* y (+ c (* y b))))))
        (t_2 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -8.2e-6)
     t_2
     (if (<= y -1.32e-289)
       t_1
       (if (<= y 2.8e-136)
         (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) i)
         (if (<= y 3.1e+38) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (i + (y * (c + (y * b))));
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -8.2e-6) {
		tmp = t_2;
	} else if (y <= -1.32e-289) {
		tmp = t_1;
	} else if (y <= 2.8e-136) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i;
	} else if (y <= 3.1e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (i + (y * (c + (y * b))))
    t_2 = x + ((z / y) - (a * (x / y)))
    if (y <= (-8.2d-6)) then
        tmp = t_2
    else if (y <= (-1.32d-289)) then
        tmp = t_1
    else if (y <= 2.8d-136) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / i
    else if (y <= 3.1d+38) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (i + (y * (c + (y * b))));
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -8.2e-6) {
		tmp = t_2;
	} else if (y <= -1.32e-289) {
		tmp = t_1;
	} else if (y <= 2.8e-136) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i;
	} else if (y <= 3.1e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t / (i + (y * (c + (y * b))))
	t_2 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -8.2e-6:
		tmp = t_2
	elif y <= -1.32e-289:
		tmp = t_1
	elif y <= 2.8e-136:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i
	elif y <= 3.1e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -8.2e-6)
		tmp = t_2;
	elseif (y <= -1.32e-289)
		tmp = t_1;
	elseif (y <= 2.8e-136)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / i);
	elseif (y <= 3.1e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t / (i + (y * (c + (y * b))));
	t_2 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -8.2e-6)
		tmp = t_2;
	elseif (y <= -1.32e-289)
		tmp = t_1;
	elseif (y <= 2.8e-136)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / i;
	elseif (y <= 3.1e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e-6], t$95$2, If[LessEqual[y, -1.32e-289], t$95$1, If[LessEqual[y, 2.8e-136], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 3.1e+38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.1999999999999994e-6 or 3.10000000000000018e38 < y

   1. Initial program 10.3%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. associate-/l* 71.0%

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

   5. Simplified 71.0%

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

   if -8.1999999999999994e-6 < y < -1.31999999999999994e-289 or 2.8000000000000001e-136 < y < 3.10000000000000018e38

   1. Initial program 97.6%

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

   3. Taylor expanded in x around 0 90.0%

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

   4. Taylor expanded in y around 0 83.1%

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

      1. *-commutative 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in t around inf 55.2%

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

   if -1.31999999999999994e-289 < y < 2.8000000000000001e-136

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in i around inf 95.5%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-6}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-289}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-136}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-6} \lor \neg \left(y \leq 1.6 \cdot 10^{+35}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8.2e-6) (not (<= y 1.6e+35)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ (+ 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 <= -8.2e-6) || !(y <= 1.6e+35)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} 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 <= (-8.2d-6)) .or. (.not. (y <= 1.6d+35))) then
        tmp = x + ((z / y) - (a * (x / y)))
    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 <= -8.2e-6) || !(y <= 1.6e+35)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} 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 <= -8.2e-6) or not (y <= 1.6e+35):
		tmp = x + ((z / y) - (a * (x / y)))
	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 <= -8.2e-6) || !(y <= 1.6e+35))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	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 <= -8.2e-6) || ~((y <= 1.6e+35)))
		tmp = x + ((z / y) - (a * (x / y)));
	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, -8.2e-6], N[Not[LessEqual[y, 1.6e+35]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(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 < -8.1999999999999994e-6 or 1.59999999999999991e35 < y

   1. Initial program 10.3%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. associate-/l* 71.0%

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

   5. Simplified 71.0%

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

   if -8.1999999999999994e-6 < y < 1.59999999999999991e35

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 84.6%

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

      1. *-commutative 84.6%

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

   5. Simplified 84.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-6} \lor \neg \left(y \leq 1.6 \cdot 10^{+35}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2700000000 \lor \neg \left(y \leq 4.1 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2700000000.0) (not (<= y 4.1e+38)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2700000000.0) || !(y <= 4.1e+38)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2700000000.0d0)) .or. (.not. (y <= 4.1d+38))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2700000000.0) || !(y <= 4.1e+38)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2700000000.0) or not (y <= 4.1e+38):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2700000000.0) || !(y <= 4.1e+38))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2700000000.0) || ~((y <= 4.1e+38)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2700000000.0], N[Not[LessEqual[y, 4.1e+38]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e9 or 4.1000000000000003e38 < y

   1. Initial program 8.7%

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

   3. Taylor expanded in y around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   if -2.7e9 < y < 4.1000000000000003e38

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 93.0%

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

   4. Taylor expanded in y around 0 88.1%

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

      1. *-commutative 88.1%

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

   6. Simplified 88.1%

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

   7. Taylor expanded in y around 0 81.5%

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

      1. *-commutative 81.5%

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

   9. Simplified 81.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2700000000 \lor \neg \left(y \leq 4.1 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -60000000000000 \lor \neg \left(y \leq 1.55 \cdot 10^{+35}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -60000000000000.0) (not (<= y 1.55e+35)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -60000000000000.0) || !(y <= 1.55e+35)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-60000000000000.0d0)) .or. (.not. (y <= 1.55d+35))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -60000000000000.0) || !(y <= 1.55e+35)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -60000000000000.0) or not (y <= 1.55e+35):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -60000000000000.0) || !(y <= 1.55e+35))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -60000000000000.0) || ~((y <= 1.55e+35)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -60000000000000.0], N[Not[LessEqual[y, 1.55e+35]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6e13 or 1.54999999999999993e35 < y

   1. Initial program 8.7%

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

   3. Taylor expanded in y around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   if -6e13 < y < 1.54999999999999993e35

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 93.0%

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

   4. Taylor expanded in y around 0 81.6%

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

      1. *-commutative 81.6%

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

   6. Simplified 81.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -60000000000000 \lor \neg \left(y \leq 1.55 \cdot 10^{+35}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+14} \lor \neg \left(y \leq 8 \cdot 10^{+16}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.5e+14) (not (<= y 8e+16)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.5e+14) || !(y <= 8e+16)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / 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 <= (-1.5d+14)) .or. (.not. (y <= 8d+16))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / 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 <= -1.5e+14) || !(y <= 8e+16)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.5e+14) or not (y <= 8e+16):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.5e+14) || !(y <= 8e+16))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.5e+14) || ~((y <= 8e+16)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.5e+14], N[Not[LessEqual[y, 8e+16]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e14 or 8e16 < y

   1. Initial program 12.5%

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

   3. Taylor expanded in y around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. associate-/l* 68.1%

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

   5. Simplified 68.1%

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

   if -1.5e14 < y < 8e16

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 94.7%

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

   4. Taylor expanded in i around inf 67.3%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+14} \lor \neg \left(y \leq 8 \cdot 10^{+16}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-6} \lor \neg \left(y \leq 1.9 \cdot 10^{+35}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6.5e-6) (not (<= y 1.9e+35)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.5e-6) || !(y <= 1.9e+35)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-6.5d-6)) .or. (.not. (y <= 1.9d+35))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.5e-6) || !(y <= 1.9e+35)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6.5e-6) or not (y <= 1.9e+35):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6.5e-6) || !(y <= 1.9e+35))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -6.5e-6) || ~((y <= 1.9e+35)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6.5e-6], N[Not[LessEqual[y, 1.9e+35]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999996e-6 or 1.9e35 < y

   1. Initial program 10.3%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. associate-/l* 71.0%

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

   5. Simplified 71.0%

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

   if -6.4999999999999996e-6 < y < 1.9e35

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 92.9%

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

   4. Taylor expanded in y around 0 87.9%

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

      1. *-commutative 87.9%

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

   6. Simplified 87.9%

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

   7. Taylor expanded in y around 0 81.3%

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

      1. *-commutative 81.3%

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

   9. Simplified 81.3%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-6} \lor \neg \left(y \leq 1.9 \cdot 10^{+35}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-8} \lor \neg \left(y \leq 1.1 \cdot 10^{+31}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3e-8) (not (<= y 1.1e+31)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3e-8) || !(y <= 1.1e+31)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3d-8)) .or. (.not. (y <= 1.1d+31))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3e-8) || !(y <= 1.1e+31)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3e-8) or not (y <= 1.1e+31):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3e-8) || !(y <= 1.1e+31))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3e-8) || ~((y <= 1.1e+31)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3e-8], N[Not[LessEqual[y, 1.1e+31]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999973e-8 or 1.10000000000000005e31 < y

   1. Initial program 11.1%

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

   3. Taylor expanded in y around inf 63.7%

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

      1. associate--l+ 63.7%

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

      2. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   if -2.99999999999999973e-8 < y < 1.10000000000000005e31

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 51.0%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-8} \lor \neg \left(y \leq 1.1 \cdot 10^{+31}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-6} \lor \neg \left(y \leq 1.55 \cdot 10^{+35}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8e-6) (not (<= y 1.55e+35)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ t (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8e-6) || !(y <= 1.55e+35)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-8d-6)) .or. (.not. (y <= 1.55d+35))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = t / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8e-6) || !(y <= 1.55e+35)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -8e-6) or not (y <= 1.55e+35):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -8e-6) || !(y <= 1.55e+35))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -8e-6) || ~((y <= 1.55e+35)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -8e-6], N[Not[LessEqual[y, 1.55e+35]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.99999999999999964e-6 or 1.54999999999999993e35 < y

   1. Initial program 10.3%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. associate-/l* 71.0%

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

   5. Simplified 71.0%

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

   if -7.99999999999999964e-6 < y < 1.54999999999999993e35

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 92.9%

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

   4. Taylor expanded in y around 0 87.9%

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

      1. *-commutative 87.9%

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

   6. Simplified 87.9%

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

   7. Taylor expanded in t around inf 63.0%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-6} \lor \neg \left(y \leq 1.55 \cdot 10^{+35}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-19} \lor \neg \left(y \leq 8.2 \cdot 10^{+26}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.6e-19) (not (<= y 8.2e+26)))
   (+ x (/ (- z (* x a)) y))
   (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.6e-19) || !(y <= 8.2e+26)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.6d-19)) .or. (.not. (y <= 8.2d+26))) then
        tmp = x + ((z - (x * a)) / y)
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.6e-19) || !(y <= 8.2e+26)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.6e-19) or not (y <= 8.2e+26):
		tmp = x + ((z - (x * a)) / y)
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.6e-19) || !(y <= 8.2e+26))
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.6e-19) || ~((y <= 8.2e+26)))
		tmp = x + ((z - (x * a)) / y);
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.6e-19], N[Not[LessEqual[y, 8.2e+26]], $MachinePrecision]], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000013e-19 or 8.19999999999999967e26 < y

   1. Initial program 11.1%

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

   3. Taylor expanded in y around inf 51.2%

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

      1. associate-+r+ 51.2%

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

      2. associate--r+ 51.2%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in y around -inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. distribute-lft-out-- 64.0%

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

   8. Simplified 64.0%

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

   9. Taylor expanded in b around 0 63.7%

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

       1. mul-1-neg 63.7%

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

   11. Simplified 63.7%

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

   if -2.60000000000000013e-19 < y < 8.19999999999999967e26

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 51.0%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-19} \lor \neg \left(y \leq 8.2 \cdot 10^{+26}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -8.2e-24) x (if (<= y 7.2e+21) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -8.2e-24) {
		tmp = x;
	} else if (y <= 7.2e+21) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-8.2d-24)) then
        tmp = x
    else if (y <= 7.2d+21) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -8.2e-24) {
		tmp = x;
	} else if (y <= 7.2e+21) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -8.2e-24:
		tmp = x
	elif y <= 7.2e+21:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -8.2e-24)
		tmp = x;
	elseif (y <= 7.2e+21)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -8.2e-24)
		tmp = x;
	elseif (y <= 7.2e+21)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -8.2e-24], x, If[LessEqual[y, 7.2e+21], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -8.20000000000000029e-24 or 7.2e21 < y

   1. Initial program 11.8%

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

   3. Taylor expanded in y around inf 54.2%

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

   if -8.20000000000000029e-24 < y < 7.2e21

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 51.6%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.8% 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 59.4%

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

3. Taylor expanded in y around inf 26.5%

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

4. Final simplification 26.5%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024078 
(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)))