Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.5% → 84.9%

Time: 26.0s

Alternatives: 20

Speedup: 1.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.9% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0 94.9%

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

   if +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 a around inf 0.0%

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

   4. Taylor expanded in y around inf 69.9%

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

      1. associate--l+ 69.9%

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

      2. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

4. Final simplification 86.3%

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

Alternative 2: 84.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           t
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)))
          (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))))
   (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 = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	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 = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	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 = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	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(t + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616))) / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))))
	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 = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	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[(t + N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, 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 94.9%

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

   if +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 a around inf 0.0%

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

   4. Taylor expanded in y around inf 69.9%

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

      1. associate--l+ 69.9%

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

      2. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

4. Final simplification 86.3%

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

Alternative 3: 81.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -0.0013:\\ \;\;\;\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{t\_1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+64}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* y (+ (* y (+ (* y (+ y a)) b)) c)))
        (t_2 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -4.9e+63)
     t_2
     (if (<= y -0.0013)
       (/
        (+
         t
         (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)))
        t_1)
       (if (<= y 4e+64)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i t_1))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * ((y * ((y * (y + a)) + b)) + c);
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -4.9e+63) {
		tmp = t_2;
	} else if (y <= -0.0013) {
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / t_1;
	} else if (y <= 4e+64) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((y * ((y * (y + a)) + b)) + c)
    t_2 = x + ((z / y) - (a * (x / y)))
    if (y <= (-4.9d+63)) then
        tmp = t_2
    else if (y <= (-0.0013d0)) then
        tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0))) / t_1
    else if (y <= 4d+64) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y * ((y * ((y * (y + a)) + b)) + c);
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -4.9e+63) {
		tmp = t_2;
	} else if (y <= -0.0013) {
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / t_1;
	} else if (y <= 4e+64) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = y * ((y * ((y * (y + a)) + b)) + c)
	t_2 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -4.9e+63:
		tmp = t_2
	elif y <= -0.0013:
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / t_1
	elif y <= 4e+64:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -4.9e+63)
		tmp = t_2;
	elseif (y <= -0.0013)
		tmp = Float64(Float64(t + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616))) / t_1);
	elseif (y <= 4e+64)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = y * ((y * ((y * (y + a)) + b)) + c);
	t_2 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -4.9e+63)
		tmp = t_2;
	elseif (y <= -0.0013)
		tmp = (t + (y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616))) / t_1;
	elseif (y <= 4e+64)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + 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[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $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, -4.9e+63], t$95$2, If[LessEqual[y, -0.0013], N[(N[(t + N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 4e+64], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8999999999999997e63 or 4.00000000000000009e64 < y

   1. Initial program 4.1%

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

   3. Taylor expanded in a around inf 3.1%

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

   4. Taylor expanded in y around inf 70.5%

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

      1. associate--l+ 70.5%

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

      2. associate-/l* 72.4%

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

   6. Simplified 72.4%

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

   if -4.8999999999999997e63 < y < -0.0012999999999999999

   1. Initial program 74.0%

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

   3. Taylor expanded in i around 0 67.7%

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

   if -0.0012999999999999999 < y < 4.00000000000000009e64

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 94.3%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+63}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -0.0013:\\ \;\;\;\;\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+64}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+67} \lor \neg \left(y \leq 1.65 \cdot 10^{+64}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.22e+67) (not (<= y 1.65e+64)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.22e+67) || !(y <= 1.65e+64)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.22d+67)) .or. (.not. (y <= 1.65d+64))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.22e+67) || !(y <= 1.65e+64)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.22e+67) or not (y <= 1.65e+64):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.22e+67) || !(y <= 1.65e+64))
		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(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.22e+67) || ~((y <= 1.65e+64)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.22e+67], N[Not[LessEqual[y, 1.65e+64]], $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[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22000000000000004e67 or 1.64999999999999994e64 < y

   1. Initial program 4.1%

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

   3. Taylor expanded in a around inf 3.1%

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

   4. Taylor expanded in y around inf 70.5%

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

      1. associate--l+ 70.5%

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

      2. associate-/l* 72.4%

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

   6. Simplified 72.4%

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

   if -1.22000000000000004e67 < y < 1.64999999999999994e64

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0 89.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+67} \lor \neg \left(y \leq 1.65 \cdot 10^{+64}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+63} \lor \neg \left(y \leq 3.15 \cdot 10^{+50}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7.5e+63) (not (<= y 3.15e+50)))
   (+ 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 <= -7.5e+63) || !(y <= 3.15e+50)) {
		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 <= (-7.5d+63)) .or. (.not. (y <= 3.15d+50))) 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 <= -7.5e+63) || !(y <= 3.15e+50)) {
		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 <= -7.5e+63) or not (y <= 3.15e+50):
		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 <= -7.5e+63) || !(y <= 3.15e+50))
		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 <= -7.5e+63) || ~((y <= 3.15e+50)))
		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, -7.5e+63], N[Not[LessEqual[y, 3.15e+50]], $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 < -7.5000000000000005e63 or 3.14999999999999993e50 < y

   1. Initial program 4.9%

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

   3. Taylor expanded in a around inf 4.0%

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

   4. Taylor expanded in y around inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. associate-/l* 70.5%

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

   6. Simplified 70.5%

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

   if -7.5000000000000005e63 < y < 3.14999999999999993e50

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 90.4%

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

   4. Taylor expanded in y around 0 89.1%

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

      1. *-commutative 89.1%

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

   6. Simplified 89.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+63} \lor \neg \left(y \leq 3.15 \cdot 10^{+50}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+63} \lor \neg \left(y \leq 6.1 \cdot 10^{+43}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.85e+63) (not (<= y 6.1e+43)))
   (+ 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 <= -1.85e+63) || !(y <= 6.1e+43)) {
		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 <= (-1.85d+63)) .or. (.not. (y <= 6.1d+43))) 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 <= -1.85e+63) || !(y <= 6.1e+43)) {
		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 <= -1.85e+63) or not (y <= 6.1e+43):
		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 <= -1.85e+63) || !(y <= 6.1e+43))
		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 <= -1.85e+63) || ~((y <= 6.1e+43)))
		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, -1.85e+63], N[Not[LessEqual[y, 6.1e+43]], $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 < -1.84999999999999984e63 or 6.0999999999999998e43 < y

   1. Initial program 4.9%

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

   3. Taylor expanded in a around inf 4.0%

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

   4. Taylor expanded in y around inf 68.1%

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

      1. associate--l+ 68.1%

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

      2. associate-/l* 69.9%

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

   6. Simplified 69.9%

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

   if -1.84999999999999984e63 < y < 6.0999999999999998e43

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0 91.0%

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

   4. Taylor expanded in y around 0 85.2%

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

      1. *-commutative 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+63} \lor \neg \left(y \leq 6.1 \cdot 10^{+43}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+28} \lor \neg \left(y \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.15e+28) (not (<= y 5e+45)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.15e+28) || !(y <= 5e+45)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.15d+28)) .or. (.not. (y <= 5d+45))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.15e+28) || !(y <= 5e+45)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.15e+28) or not (y <= 5e+45):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.15e+28) || !(y <= 5e+45))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.15e+28) || ~((y <= 5e+45)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.15e+28], N[Not[LessEqual[y, 5e+45]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.14999999999999992e28 or 5e45 < y

   1. Initial program 10.0%

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

   3. Taylor expanded in a around inf 8.2%

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

   4. Taylor expanded in y around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-/l* 65.9%

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

   6. Simplified 65.9%

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

   if -1.14999999999999992e28 < y < 5e45

   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. Add Preprocessing

   3. Taylor expanded in y around 0 86.6%

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

      1. *-commutative 86.6%

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

   5. Simplified 86.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+28} \lor \neg \left(y \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-77}:\\ \;\;\;\;\frac{27464.7644705 + \left(y \cdot z + 230661.510616 \cdot \frac{1}{y}\right)}{b}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -2.5e+74)
     t_1
     (if (<= y -1.9e-77)
       (/ (+ 27464.7644705 (+ (* y z) (* 230661.510616 (/ 1.0 y)))) b)
       (if (<= y 7.5e+42)
         (+ (* 230661.510616 (/ y i)) (/ t (+ i (* y c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.5e+74) {
		tmp = t_1;
	} else if (y <= -1.9e-77) {
		tmp = (27464.7644705 + ((y * z) + (230661.510616 * (1.0 / y)))) / b;
	} else if (y <= 7.5e+42) {
		tmp = (230661.510616 * (y / i)) + (t / (i + (y * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-2.5d+74)) then
        tmp = t_1
    else if (y <= (-1.9d-77)) then
        tmp = (27464.7644705d0 + ((y * z) + (230661.510616d0 * (1.0d0 / y)))) / b
    else if (y <= 7.5d+42) then
        tmp = (230661.510616d0 * (y / i)) + (t / (i + (y * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.5e+74) {
		tmp = t_1;
	} else if (y <= -1.9e-77) {
		tmp = (27464.7644705 + ((y * z) + (230661.510616 * (1.0 / y)))) / b;
	} else if (y <= 7.5e+42) {
		tmp = (230661.510616 * (y / i)) + (t / (i + (y * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -2.5e+74:
		tmp = t_1
	elif y <= -1.9e-77:
		tmp = (27464.7644705 + ((y * z) + (230661.510616 * (1.0 / y)))) / b
	elif y <= 7.5e+42:
		tmp = (230661.510616 * (y / i)) + (t / (i + (y * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -2.5e+74)
		tmp = t_1;
	elseif (y <= -1.9e-77)
		tmp = Float64(Float64(27464.7644705 + Float64(Float64(y * z) + Float64(230661.510616 * Float64(1.0 / y)))) / b);
	elseif (y <= 7.5e+42)
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + Float64(t / Float64(i + Float64(y * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -2.5e+74)
		tmp = t_1;
	elseif (y <= -1.9e-77)
		tmp = (27464.7644705 + ((y * z) + (230661.510616 * (1.0 / y)))) / b;
	elseif (y <= 7.5e+42)
		tmp = (230661.510616 * (y / i)) + (t / (i + (y * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+74], t$95$1, If[LessEqual[y, -1.9e-77], N[(N[(27464.7644705 + N[(N[(y * z), $MachinePrecision] + N[(230661.510616 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 7.5e+42], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999982e74 or 7.50000000000000041e42 < y

   1. Initial program 4.1%

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

   3. Taylor expanded in a around inf 3.1%

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

   4. Taylor expanded in y around inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. associate-/l* 71.6%

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

   6. Simplified 71.6%

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

   if -2.49999999999999982e74 < y < -1.8999999999999999e-77

   1. Initial program 82.3%

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

   3. Taylor expanded in x around 0 65.3%

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

   4. Taylor expanded in t around inf 62.9%

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

   5. Taylor expanded in b around inf 29.4%

      \[\leadsto \color{blue}{\frac{t \cdot \left(27464.7644705 \cdot \frac{1}{t} + \left(230661.510616 \cdot \frac{1}{t \cdot y} + \left(\frac{1}{{y}^{2}} + \frac{y \cdot z}{t}\right)\right)\right)}{b}} \]

   6. Taylor expanded in t around 0 24.4%

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

   if -1.8999999999999999e-77 < y < 7.50000000000000041e42

   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 t around 0 98.9%

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

   4. Taylor expanded in y around 0 79.0%

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

   5. Taylor expanded in y around 0 73.8%

      \[\leadsto \frac{t}{i + \color{blue}{c \cdot y}} + 230661.510616 \cdot \frac{y}{i} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+74}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-77}:\\ \;\;\;\;\frac{27464.7644705 + \left(y \cdot z + 230661.510616 \cdot \frac{1}{y}\right)}{b}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+27} \lor \neg \left(y \leq 8.2 \cdot 10^{+46}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5e+27) (not (<= y 8.2e+46)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ t (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5e+27) || !(y <= 8.2e+46)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-5d+27)) .or. (.not. (y <= 8.2d+46))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5e+27) || !(y <= 8.2e+46)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5e+27) or not (y <= 8.2e+46):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5e+27) || !(y <= 8.2e+46))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5e+27) || ~((y <= 8.2e+46)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5e+27], N[Not[LessEqual[y, 8.2e+46]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999979e27 or 8.19999999999999999e46 < y

   1. Initial program 10.0%

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

   3. Taylor expanded in a around inf 8.2%

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

   4. Taylor expanded in y around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-/l* 65.9%

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

   6. Simplified 65.9%

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

   if -4.99999999999999979e27 < y < 8.19999999999999999e46

   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. Add Preprocessing

   3. Taylor expanded in t around inf 76.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+27} \lor \neg \left(y \leq 8.2 \cdot 10^{+46}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+28} \lor \neg \left(y \leq 4.9 \cdot 10^{+45}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)} + 230661.510616 \cdot \frac{y}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7e+28) (not (<= y 4.9e+45)))
   (+ x (- (/ z y) (* a (/ x y))))
   (+ (/ t (+ i (* y (+ c (* y b))))) (* 230661.510616 (/ y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7e+28) || !(y <= 4.9e+45)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t / (i + (y * (c + (y * b))))) + (230661.510616 * (y / 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 <= (-7d+28)) .or. (.not. (y <= 4.9d+45))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t / (i + (y * (c + (y * b))))) + (230661.510616d0 * (y / 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 <= -7e+28) || !(y <= 4.9e+45)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t / (i + (y * (c + (y * b))))) + (230661.510616 * (y / i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -7e+28) or not (y <= 4.9e+45):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t / (i + (y * (c + (y * b))))) + (230661.510616 * (y / i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -7e+28) || !(y <= 4.9e+45))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b))))) + Float64(230661.510616 * Float64(y / i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -7e+28) || ~((y <= 4.9e+45)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t / (i + (y * (c + (y * b))))) + (230661.510616 * (y / i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -7e+28], N[Not[LessEqual[y, 4.9e+45]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999999e28 or 4.9000000000000002e45 < y

   1. Initial program 10.0%

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

   3. Taylor expanded in a around inf 8.3%

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

   4. Taylor expanded in y around inf 64.8%

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

      1. associate--l+ 64.8%

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

      2. associate-/l* 66.5%

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

   6. Simplified 66.5%

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

   if -6.9999999999999999e28 < y < 4.9000000000000002e45

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 97.0%

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

   4. Taylor expanded in y around 0 66.4%

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

   5. Taylor expanded in y around 0 65.0%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+28} \lor \neg \left(y \leq 4.9 \cdot 10^{+45}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)} + 230661.510616 \cdot \frac{y}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{t - y \cdot -230661.510616}{y}}{c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+46}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -4e+27)
     t_1
     (if (<= y -2.3e-79)
       (/ (/ (- t (* y -230661.510616)) y) c)
       (if (<= y 3.2e+46) (+ (* 230661.510616 (/ y i)) (/ t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -4e+27) {
		tmp = t_1;
	} else if (y <= -2.3e-79) {
		tmp = ((t - (y * -230661.510616)) / y) / c;
	} else if (y <= 3.2e+46) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-4d+27)) then
        tmp = t_1
    else if (y <= (-2.3d-79)) then
        tmp = ((t - (y * (-230661.510616d0))) / y) / c
    else if (y <= 3.2d+46) then
        tmp = (230661.510616d0 * (y / i)) + (t / i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -4e+27) {
		tmp = t_1;
	} else if (y <= -2.3e-79) {
		tmp = ((t - (y * -230661.510616)) / y) / c;
	} else if (y <= 3.2e+46) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -4e+27:
		tmp = t_1
	elif y <= -2.3e-79:
		tmp = ((t - (y * -230661.510616)) / y) / c
	elif y <= 3.2e+46:
		tmp = (230661.510616 * (y / i)) + (t / i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -4e+27)
		tmp = t_1;
	elseif (y <= -2.3e-79)
		tmp = Float64(Float64(Float64(t - Float64(y * -230661.510616)) / y) / c);
	elseif (y <= 3.2e+46)
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + Float64(t / i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -4e+27)
		tmp = t_1;
	elseif (y <= -2.3e-79)
		tmp = ((t - (y * -230661.510616)) / y) / c;
	elseif (y <= 3.2e+46)
		tmp = (230661.510616 * (y / i)) + (t / i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+27], t$95$1, If[LessEqual[y, -2.3e-79], N[(N[(N[(t - N[(y * -230661.510616), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 3.2e+46], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0000000000000001e27 or 3.1999999999999998e46 < y

   1. Initial program 10.0%

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

   3. Taylor expanded in a around inf 8.2%

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

   4. Taylor expanded in y around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-/l* 65.9%

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

   6. Simplified 65.9%

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

   if -4.0000000000000001e27 < y < -2.30000000000000012e-79

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 84.7%

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

   4. Taylor expanded in t around inf 84.9%

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

   5. Taylor expanded in c around -inf 29.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(-1 \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t} - \frac{1}{y}\right)}{c}} \]
   6. Step-by-step derivation

      1. mul-1-neg 29.1%

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

      2. mul-1-neg 29.1%

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

   7. Simplified 29.1%

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

   8. Taylor expanded in y around 0 23.8%

      \[\leadsto -\frac{\color{blue}{\frac{-230661.510616 \cdot y + -1 \cdot t}{y}}}{c} \]

   if -2.30000000000000012e-79 < y < 3.1999999999999998e46

   1. Initial program 98.1%

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

   3. Taylor expanded in t around 0 98.1%

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

   4. Taylor expanded in y around 0 78.1%

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

   5. Taylor expanded in i around inf 66.8%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+27}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{t - y \cdot -230661.510616}{y}}{c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+46}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-7}:\\ \;\;\;\;\frac{y \cdot z}{b}\\ \mathbf{elif}\;y \leq 0.00085:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.5e+119)
   x
   (if (<= y -3e-7)
     (/ (* y z) b)
     (if (<= y 0.00085) (+ (* 230661.510616 (/ y i)) (/ 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+119) {
		tmp = x;
	} else if (y <= -3e-7) {
		tmp = (y * z) / b;
	} else if (y <= 0.00085) {
		tmp = (230661.510616 * (y / i)) + (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+119)) then
        tmp = x
    else if (y <= (-3d-7)) then
        tmp = (y * z) / b
    else if (y <= 0.00085d0) then
        tmp = (230661.510616d0 * (y / i)) + (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+119) {
		tmp = x;
	} else if (y <= -3e-7) {
		tmp = (y * z) / b;
	} else if (y <= 0.00085) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.5e+119:
		tmp = x
	elif y <= -3e-7:
		tmp = (y * z) / b
	elif y <= 0.00085:
		tmp = (230661.510616 * (y / i)) + (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+119)
		tmp = x;
	elseif (y <= -3e-7)
		tmp = Float64(Float64(y * z) / b);
	elseif (y <= 0.00085)
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + 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+119)
		tmp = x;
	elseif (y <= -3e-7)
		tmp = (y * z) / b;
	elseif (y <= 0.00085)
		tmp = (230661.510616 * (y / i)) + (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+119], x, If[LessEqual[y, -3e-7], N[(N[(y * z), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 0.00085], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000001e119 or 8.49999999999999953e-4 < y

   1. Initial program 10.2%

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

   3. Taylor expanded in y around inf 57.1%

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

   if -3.5000000000000001e119 < y < -2.9999999999999999e-7

   1. Initial program 46.9%

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

   3. Taylor expanded in x around 0 26.3%

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

   4. Taylor expanded in t around inf 22.9%

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

   5. Taylor expanded in b around inf 23.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(27464.7644705 \cdot \frac{1}{t} + \left(230661.510616 \cdot \frac{1}{t \cdot y} + \left(\frac{1}{{y}^{2}} + \frac{y \cdot z}{t}\right)\right)\right)}{b}} \]

   6. Taylor expanded in y around inf 22.1%

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

   if -2.9999999999999999e-7 < y < 8.49999999999999953e-4

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 99.7%

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

   4. Taylor expanded in y around 0 73.5%

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

   5. Taylor expanded in i around inf 61.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-7}:\\ \;\;\;\;\frac{y \cdot z}{b}\\ \mathbf{elif}\;y \leq 0.00085:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+28} \lor \neg \left(y \leq 1.1 \cdot 10^{+43}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6e+28) (not (<= y 1.1e+43)))
   (+ x (- (/ z y) (* a (/ x y))))
   (+ (* 230661.510616 (/ y i)) (/ t (+ i (* y c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6e+28) || !(y <= 1.1e+43)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (230661.510616 * (y / i)) + (t / (i + (y * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-6d+28)) .or. (.not. (y <= 1.1d+43))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (230661.510616d0 * (y / i)) + (t / (i + (y * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6e+28) || !(y <= 1.1e+43)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (230661.510616 * (y / i)) + (t / (i + (y * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6e+28) or not (y <= 1.1e+43):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (230661.510616 * (y / i)) + (t / (i + (y * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6e+28) || !(y <= 1.1e+43))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + Float64(t / Float64(i + Float64(y * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -6e+28) || ~((y <= 1.1e+43)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (230661.510616 * (y / i)) + (t / (i + (y * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6e+28], N[Not[LessEqual[y, 1.1e+43]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.0000000000000002e28 or 1.1e43 < y

   1. Initial program 10.0%

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

   3. Taylor expanded in a around inf 8.2%

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

   4. Taylor expanded in y around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-/l* 65.9%

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

   6. Simplified 65.9%

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

   if -6.0000000000000002e28 < y < 1.1e43

   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. Add Preprocessing

   3. Taylor expanded in t around 0 97.7%

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

   4. Taylor expanded in y around 0 66.9%

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

   5. Taylor expanded in y around 0 61.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+28} \lor \neg \left(y \leq 1.1 \cdot 10^{+43}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i + y \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+27} \lor \neg \left(y \leq 4.9 \cdot 10^{+45}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{230661.510616 + y \cdot 27464.7644705}{i} + \frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8.2e+27) (not (<= y 4.9e+45)))
   (+ x (- (/ z y) (* a (/ x y))))
   (+ (* y (/ (+ 230661.510616 (* y 27464.7644705)) i)) (/ 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 <= -8.2e+27) || !(y <= 4.9e+45)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (y * ((230661.510616 + (y * 27464.7644705)) / i)) + (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 <= (-8.2d+27)) .or. (.not. (y <= 4.9d+45))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (y * ((230661.510616d0 + (y * 27464.7644705d0)) / i)) + (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 <= -8.2e+27) || !(y <= 4.9e+45)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (y * ((230661.510616 + (y * 27464.7644705)) / i)) + (t / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -8.2e+27) or not (y <= 4.9e+45):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (y * ((230661.510616 + (y * 27464.7644705)) / i)) + (t / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -8.2e+27) || !(y <= 4.9e+45))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(y * Float64(Float64(230661.510616 + Float64(y * 27464.7644705)) / i)) + 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 <= -8.2e+27) || ~((y <= 4.9e+45)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (y * ((230661.510616 + (y * 27464.7644705)) / i)) + (t / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -8.2e+27], N[Not[LessEqual[y, 4.9e+45]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000005e27 or 4.9000000000000002e45 < y

   1. Initial program 10.0%

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

   3. Taylor expanded in a around inf 8.2%

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

   4. Taylor expanded in y around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-/l* 65.9%

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

   6. Simplified 65.9%

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

   if -8.2000000000000005e27 < y < 4.9000000000000002e45

   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. Add Preprocessing

   3. Taylor expanded in y around 0 36.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(230661.510616 \cdot \frac{1}{i} + y \cdot \left(27464.7644705 \cdot \frac{1}{i} - \left(\frac{b \cdot t}{{i}^{2}} + \frac{c \cdot \left(230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right)}{i}\right)\right)\right) - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]

   4. Taylor expanded in i around inf 56.0%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+27} \lor \neg \left(y \leq 4.9 \cdot 10^{+45}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{230661.510616 + y \cdot 27464.7644705}{i} + \frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+16} \lor \neg \left(y \leq 1.2 \cdot 10^{+46}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6.8e+16) (not (<= y 1.2e+46)))
   (+ x (- (/ z y) (* a (/ x y))))
   (+ (* 230661.510616 (/ y i)) (/ 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 <= -6.8e+16) || !(y <= 1.2e+46)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (230661.510616 * (y / i)) + (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 <= (-6.8d+16)) .or. (.not. (y <= 1.2d+46))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (230661.510616d0 * (y / i)) + (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 <= -6.8e+16) || !(y <= 1.2e+46)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (230661.510616 * (y / i)) + (t / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6.8e+16) or not (y <= 1.2e+46):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (230661.510616 * (y / i)) + (t / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6.8e+16) || !(y <= 1.2e+46))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + 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 <= -6.8e+16) || ~((y <= 1.2e+46)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (230661.510616 * (y / i)) + (t / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6.8e+16], N[Not[LessEqual[y, 1.2e+46]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e16 or 1.20000000000000004e46 < y

   1. Initial program 10.8%

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

   3. Taylor expanded in a around inf 9.0%

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

   4. Taylor expanded in y around inf 63.7%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   5. 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* 65.3%

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

   6. Simplified 65.3%

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

   if -6.8e16 < y < 1.20000000000000004e46

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0 97.7%

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

   4. Taylor expanded in y around 0 67.3%

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

   5. Taylor expanded in i around inf 56.0%

      \[\leadsto \color{blue}{\frac{t}{i}} + 230661.510616 \cdot \frac{y}{i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+16} \lor \neg \left(y \leq 1.2 \cdot 10^{+46}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+21} \lor \neg \left(y \leq 4.9 \cdot 10^{+45}\right):\\ \;\;\;\;x - \frac{x \cdot a - z}{y}\\ \mathbf{else}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5e+21) (not (<= y 4.9e+45)))
   (- x (/ (- (* x a) z) y))
   (+ (* 230661.510616 (/ y i)) (/ 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 <= -5e+21) || !(y <= 4.9e+45)) {
		tmp = x - (((x * a) - z) / y);
	} else {
		tmp = (230661.510616 * (y / i)) + (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 <= (-5d+21)) .or. (.not. (y <= 4.9d+45))) then
        tmp = x - (((x * a) - z) / y)
    else
        tmp = (230661.510616d0 * (y / i)) + (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 <= -5e+21) || !(y <= 4.9e+45)) {
		tmp = x - (((x * a) - z) / y);
	} else {
		tmp = (230661.510616 * (y / i)) + (t / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5e+21) or not (y <= 4.9e+45):
		tmp = x - (((x * a) - z) / y)
	else:
		tmp = (230661.510616 * (y / i)) + (t / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5e+21) || !(y <= 4.9e+45))
		tmp = Float64(x - Float64(Float64(Float64(x * a) - z) / y));
	else
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + 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 <= -5e+21) || ~((y <= 4.9e+45)))
		tmp = x - (((x * a) - z) / y);
	else
		tmp = (230661.510616 * (y / i)) + (t / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5e+21], N[Not[LessEqual[y, 4.9e+45]], $MachinePrecision]], N[(x - N[(N[(N[(x * a), $MachinePrecision] - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e21 or 4.9000000000000002e45 < y

   1. Initial program 10.8%

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

   3. Taylor expanded in y around inf 9.2%

      \[\leadsto \frac{\color{blue}{{y}^{4} \cdot \left(x + \frac{z}{y}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in y around -inf 63.7%

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

      1. mul-1-neg 63.7%

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

      2. distribute-lft-out-- 63.7%

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

      3. mul-1-neg 63.7%

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

   6. Simplified 63.7%

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

   if -5e21 < y < 4.9000000000000002e45

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0 97.7%

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

   4. Taylor expanded in y around 0 67.3%

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

   5. Taylor expanded in i around inf 56.0%

      \[\leadsto \color{blue}{\frac{t}{i}} + 230661.510616 \cdot \frac{y}{i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+21} \lor \neg \left(y \leq 4.9 \cdot 10^{+45}\right):\\ \;\;\;\;x - \frac{x \cdot a - z}{y}\\ \mathbf{else}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-76}:\\ \;\;\;\;\frac{y \cdot z}{b}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.5e+119)
   x
   (if (<= y -2.6e-76) (/ (* y z) b) (if (<= y 1.5e+14) (/ 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+119) {
		tmp = x;
	} else if (y <= -2.6e-76) {
		tmp = (y * z) / b;
	} else if (y <= 1.5e+14) {
		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+119)) then
        tmp = x
    else if (y <= (-2.6d-76)) then
        tmp = (y * z) / b
    else if (y <= 1.5d+14) 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+119) {
		tmp = x;
	} else if (y <= -2.6e-76) {
		tmp = (y * z) / b;
	} else if (y <= 1.5e+14) {
		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+119:
		tmp = x
	elif y <= -2.6e-76:
		tmp = (y * z) / b
	elif y <= 1.5e+14:
		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+119)
		tmp = x;
	elseif (y <= -2.6e-76)
		tmp = Float64(Float64(y * z) / b);
	elseif (y <= 1.5e+14)
		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+119)
		tmp = x;
	elseif (y <= -2.6e-76)
		tmp = (y * z) / b;
	elseif (y <= 1.5e+14)
		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+119], x, If[LessEqual[y, -2.6e-76], N[(N[(y * z), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 1.5e+14], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000001e119 or 1.5e14 < y

   1. Initial program 6.4%

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

   3. Taylor expanded in y around inf 59.4%

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

   if -3.5000000000000001e119 < y < -2.6e-76

   1. Initial program 68.0%

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

   3. Taylor expanded in x around 0 53.8%

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

   4. Taylor expanded in t around inf 51.8%

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

   5. Taylor expanded in b around inf 25.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(27464.7644705 \cdot \frac{1}{t} + \left(230661.510616 \cdot \frac{1}{t \cdot y} + \left(\frac{1}{{y}^{2}} + \frac{y \cdot z}{t}\right)\right)\right)}{b}} \]

   6. Taylor expanded in y around inf 17.8%

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

   if -2.6e-76 < y < 1.5e14

   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. Add Preprocessing

   3. Taylor expanded in y around 0 63.5%

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

Alternative 18: 48.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{z}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.5e+119)
   x
   (if (<= y -2.6e-76) (* y (/ z b)) (if (<= y 9e+14) (/ 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+119) {
		tmp = x;
	} else if (y <= -2.6e-76) {
		tmp = y * (z / b);
	} else if (y <= 9e+14) {
		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+119)) then
        tmp = x
    else if (y <= (-2.6d-76)) then
        tmp = y * (z / b)
    else if (y <= 9d+14) 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+119) {
		tmp = x;
	} else if (y <= -2.6e-76) {
		tmp = y * (z / b);
	} else if (y <= 9e+14) {
		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+119:
		tmp = x
	elif y <= -2.6e-76:
		tmp = y * (z / b)
	elif y <= 9e+14:
		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+119)
		tmp = x;
	elseif (y <= -2.6e-76)
		tmp = Float64(y * Float64(z / b));
	elseif (y <= 9e+14)
		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+119)
		tmp = x;
	elseif (y <= -2.6e-76)
		tmp = y * (z / b);
	elseif (y <= 9e+14)
		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+119], x, If[LessEqual[y, -2.6e-76], N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+14], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000001e119 or 9e14 < y

   1. Initial program 6.4%

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

   3. Taylor expanded in y around inf 59.4%

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

   if -3.5000000000000001e119 < y < -2.6e-76

   1. Initial program 68.0%

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

   3. Taylor expanded in x around 0 53.8%

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

   4. Taylor expanded in t around inf 51.8%

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

   5. Taylor expanded in b around inf 25.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(27464.7644705 \cdot \frac{1}{t} + \left(230661.510616 \cdot \frac{1}{t \cdot y} + \left(\frac{1}{{y}^{2}} + \frac{y \cdot z}{t}\right)\right)\right)}{b}} \]

   6. Taylor expanded in y around inf 17.8%

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

      1. associate-/l* 17.8%

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

   8. Simplified 17.8%

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

   if -2.6e-76 < y < 9e14

   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. Add Preprocessing

   3. Taylor expanded in y around 0 63.5%

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

Alternative 19: 49.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1000000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4e+73) x (if (<= y 1000000000000.0) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4e+73) {
		tmp = x;
	} else if (y <= 1000000000000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-4d+73)) then
        tmp = x
    else if (y <= 1000000000000.0d0) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4e+73) {
		tmp = x;
	} else if (y <= 1000000000000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4e+73:
		tmp = x
	elif y <= 1000000000000.0:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4e+73)
		tmp = x;
	elseif (y <= 1000000000000.0)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4e+73)
		tmp = x;
	elseif (y <= 1000000000000.0)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4e+73], x, If[LessEqual[y, 1000000000000.0], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999993e73 or 1e12 < y

   1. Initial program 6.8%

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

   3. Taylor expanded in y around inf 55.0%

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

   if -3.99999999999999993e73 < y < 1e12

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0 49.7%

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

Alternative 20: 25.5% 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 59.3%

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

3. Taylor expanded in y around inf 24.6%

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

Reproduce

herbie shell --seed 2024137 
(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)))