Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.3% → 83.8%

Time: 21.1s

Alternatives: 17

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.3%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 63.5%

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

      1. associate--l+ 63.5%

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

      2. associate-/l* 66.0%

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

   4. Simplified 66.0%

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

4. Final simplification 81.6%

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

Alternative 2: 80.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -5.5e+144)
     t_1
     (if (<= y -4.6e+51)
       (/ 1.0 (+ (/ 1.0 x) (/ (- (/ a x) (/ z (* x x))) y)))
       (if (<= y -2.8e+33)
         (/ z y)
         (if (<= y 1.65e+47)
           (/
            (+ t (* y (+ 230661.510616 (* z (* y y)))))
            (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -5.5e+144) {
		tmp = t_1;
	} else if (y <= -4.6e+51) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} else if (y <= -2.8e+33) {
		tmp = z / y;
	} else if (y <= 1.65e+47) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-5.5d+144)) then
        tmp = t_1
    else if (y <= (-4.6d+51)) then
        tmp = 1.0d0 / ((1.0d0 / x) + (((a / x) - (z / (x * x))) / y))
    else if (y <= (-2.8d+33)) then
        tmp = z / y
    else if (y <= 1.65d+47) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -5.5e+144) {
		tmp = t_1;
	} else if (y <= -4.6e+51) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} else if (y <= -2.8e+33) {
		tmp = z / y;
	} else if (y <= 1.65e+47) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -5.5e+144:
		tmp = t_1
	elif y <= -4.6e+51:
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y))
	elif y <= -2.8e+33:
		tmp = z / y
	elif y <= 1.65e+47:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -5.5e+144)
		tmp = t_1;
	elseif (y <= -4.6e+51)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) + Float64(Float64(Float64(a / x) - Float64(z / Float64(x * x))) / y)));
	elseif (y <= -2.8e+33)
		tmp = Float64(z / y);
	elseif (y <= 1.65e+47)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -5.5e+144)
		tmp = t_1;
	elseif (y <= -4.6e+51)
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	elseif (y <= -2.8e+33)
		tmp = z / y;
	elseif (y <= 1.65e+47)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+144], t$95$1, If[LessEqual[y, -4.6e+51], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] + N[(N[(N[(a / x), $MachinePrecision] - N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e+33], N[(z / y), $MachinePrecision], If[LessEqual[y, 1.65e+47], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.50000000000000022e144 or 1.65e47 < y

   1. Initial program 2.2%

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

   2. Taylor expanded in y around inf 70.0%

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

      1. associate--l+ 70.0%

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

      2. associate-/l* 72.9%

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

   4. Simplified 72.9%

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

   if -5.50000000000000022e144 < y < -4.6000000000000001e51

   1. Initial program 5.3%

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

      1. clear-num 5.3%

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

      2. inv-pow 5.3%

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

   3. Applied egg-rr 5.3%

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

      1. unpow-1 5.3%

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

      2. fma-udef 5.3%

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

      3. *-commutative 5.3%

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

      4. fma-def 5.3%

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

   5. Simplified 5.3%

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

   6. Taylor expanded in y around -inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. distribute-lft-out-- 57.1%

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

      3. unpow2 57.1%

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

   8. Simplified 57.1%

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

   if -4.6000000000000001e51 < y < -2.8000000000000001e33

   1. Initial program 34.8%

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

   2. Taylor expanded in z around inf 34.8%

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

      1. associate-/l* 67.3%

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

      2. fma-def 67.3%

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

      3. +-commutative 67.3%

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

      4. *-commutative 67.3%

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

      5. fma-udef 67.3%

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

      6. fma-udef 67.3%

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

   4. Simplified 67.3%

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

   5. Taylor expanded in y around inf 67.0%

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

   if -2.8000000000000001e33 < y < 1.65e47

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 89.1%

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

      1. *-commutative 89.1%

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

      2. unpow2 89.1%

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

   4. Simplified 89.1%

      \[\leadsto \frac{\left(\color{blue}{z \cdot \left(y \cdot y\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 3: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -1.35e+145)
     t_1
     (if (<= y -4.6e+51)
       (/ 1.0 (+ (/ 1.0 x) (/ (- (/ a x) (/ z (* x x))) y)))
       (if (<= y -4.5e+36)
         (/ z y)
         (if (<= y 1.35e+48)
           (/
            (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
            (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.35e+145) {
		tmp = t_1;
	} else if (y <= -4.6e+51) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} else if (y <= -4.5e+36) {
		tmp = z / y;
	} else if (y <= 1.35e+48) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-1.35d+145)) then
        tmp = t_1
    else if (y <= (-4.6d+51)) then
        tmp = 1.0d0 / ((1.0d0 / x) + (((a / x) - (z / (x * x))) / y))
    else if (y <= (-4.5d+36)) then
        tmp = z / y
    else if (y <= 1.35d+48) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.35e+145) {
		tmp = t_1;
	} else if (y <= -4.6e+51) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} else if (y <= -4.5e+36) {
		tmp = z / y;
	} else if (y <= 1.35e+48) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -1.35e+145:
		tmp = t_1
	elif y <= -4.6e+51:
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y))
	elif y <= -4.5e+36:
		tmp = z / y
	elif y <= 1.35e+48:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.35e+145)
		tmp = t_1;
	elseif (y <= -4.6e+51)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) + Float64(Float64(Float64(a / x) - Float64(z / Float64(x * x))) / y)));
	elseif (y <= -4.5e+36)
		tmp = Float64(z / y);
	elseif (y <= 1.35e+48)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.35e+145)
		tmp = t_1;
	elseif (y <= -4.6e+51)
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	elseif (y <= -4.5e+36)
		tmp = z / y;
	elseif (y <= 1.35e+48)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+145], t$95$1, If[LessEqual[y, -4.6e+51], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] + N[(N[(N[(a / x), $MachinePrecision] - N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e+36], N[(z / y), $MachinePrecision], If[LessEqual[y, 1.35e+48], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35000000000000011e145 or 1.35000000000000002e48 < y

   1. Initial program 2.2%

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

   2. Taylor expanded in y around inf 70.0%

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

      1. associate--l+ 70.0%

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

      2. associate-/l* 72.9%

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

   4. Simplified 72.9%

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

   if -1.35000000000000011e145 < y < -4.6000000000000001e51

   1. Initial program 5.3%

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

      1. clear-num 5.3%

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

      2. inv-pow 5.3%

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

   3. Applied egg-rr 5.3%

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

      1. unpow-1 5.3%

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

      2. fma-udef 5.3%

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

      3. *-commutative 5.3%

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

      4. fma-def 5.3%

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

   5. Simplified 5.3%

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

   6. Taylor expanded in y around -inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. distribute-lft-out-- 57.1%

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

      3. unpow2 57.1%

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

   8. Simplified 57.1%

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

   if -4.6000000000000001e51 < y < -4.49999999999999997e36

   1. Initial program 52.2%

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

   2. Taylor expanded in z around inf 52.2%

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

      1. associate-/l* 99.2%

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

      2. fma-def 99.2%

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

      3. +-commutative 99.2%

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

      4. *-commutative 99.2%

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

      5. fma-udef 99.2%

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

      6. fma-udef 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -4.49999999999999997e36 < y < 1.35000000000000002e48

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 83.0%

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

      1. *-commutative 83.0%

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

   4. Simplified 83.0%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+145}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 4: 75.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{+51}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{+35}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -2.1e+145)
     t_1
     (if (<= y -5.7e+51)
       (/ 1.0 (+ (/ 1.0 x) (/ (- (/ a x) (/ z (* x x))) y)))
       (if (<= y -1.62e+35)
         (/ z y)
         (if (<= y 1.48e+47)
           (/
            (+ t (* y 230661.510616))
            (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -2.1e+145) {
		tmp = t_1;
	} else if (y <= -5.7e+51) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} else if (y <= -1.62e+35) {
		tmp = z / y;
	} else if (y <= 1.48e+47) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-2.1d+145)) then
        tmp = t_1
    else if (y <= (-5.7d+51)) then
        tmp = 1.0d0 / ((1.0d0 / x) + (((a / x) - (z / (x * x))) / y))
    else if (y <= (-1.62d+35)) then
        tmp = z / y
    else if (y <= 1.48d+47) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -2.1e+145) {
		tmp = t_1;
	} else if (y <= -5.7e+51) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} else if (y <= -1.62e+35) {
		tmp = z / y;
	} else if (y <= 1.48e+47) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -2.1e+145:
		tmp = t_1
	elif y <= -5.7e+51:
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y))
	elif y <= -1.62e+35:
		tmp = z / y
	elif y <= 1.48e+47:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.1e+145)
		tmp = t_1;
	elseif (y <= -5.7e+51)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) + Float64(Float64(Float64(a / x) - Float64(z / Float64(x * x))) / y)));
	elseif (y <= -1.62e+35)
		tmp = Float64(z / y);
	elseif (y <= 1.48e+47)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.1e+145)
		tmp = t_1;
	elseif (y <= -5.7e+51)
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	elseif (y <= -1.62e+35)
		tmp = z / y;
	elseif (y <= 1.48e+47)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+145], t$95$1, If[LessEqual[y, -5.7e+51], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] + N[(N[(N[(a / x), $MachinePrecision] - N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.62e+35], N[(z / y), $MachinePrecision], If[LessEqual[y, 1.48e+47], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.09999999999999989e145 or 1.47999999999999996e47 < y

   1. Initial program 2.2%

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

   2. Taylor expanded in y around inf 70.0%

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

      1. associate--l+ 70.0%

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

      2. associate-/l* 72.9%

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

   4. Simplified 72.9%

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

   if -2.09999999999999989e145 < y < -5.7000000000000002e51

   1. Initial program 5.3%

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

      1. clear-num 5.3%

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

      2. inv-pow 5.3%

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

   3. Applied egg-rr 5.3%

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

      1. unpow-1 5.3%

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

      2. fma-udef 5.3%

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

      3. *-commutative 5.3%

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

      4. fma-def 5.3%

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

   5. Simplified 5.3%

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

   6. Taylor expanded in y around -inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. distribute-lft-out-- 57.1%

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

      3. unpow2 57.1%

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

   8. Simplified 57.1%

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

   if -5.7000000000000002e51 < y < -1.62e35

   1. Initial program 52.2%

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

   2. Taylor expanded in z around inf 52.2%

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

      1. associate-/l* 99.2%

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

      2. fma-def 99.2%

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

      3. +-commutative 99.2%

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

      4. *-commutative 99.2%

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

      5. fma-udef 99.2%

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

      6. fma-udef 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -1.62e35 < y < 1.47999999999999996e47

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 81.9%

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

      1. *-commutative 81.9%

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

   4. Simplified 81.9%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+145}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{+51}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{+35}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 5: 75.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -5.1 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-14}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{y \cdot c}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -5.1e+144)
     t_1
     (if (<= y -4.6e+51)
       (/ 1.0 (+ (/ 1.0 x) (/ (- (/ a x) (/ z (* x x))) y)))
       (if (<= y -3e-14)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* x y))))))))
          (* y c))
         (if (<= y 6.1e+47)
           (/
            (+ t (* y 230661.510616))
            (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -5.1e+144) {
		tmp = t_1;
	} else if (y <= -4.6e+51) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} else if (y <= -3e-14) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y)))))))) / (y * c);
	} else if (y <= 6.1e+47) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-5.1d+144)) then
        tmp = t_1
    else if (y <= (-4.6d+51)) then
        tmp = 1.0d0 / ((1.0d0 / x) + (((a / x) - (z / (x * x))) / y))
    else if (y <= (-3d-14)) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (x * y)))))))) / (y * c)
    else if (y <= 6.1d+47) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -5.1e+144) {
		tmp = t_1;
	} else if (y <= -4.6e+51) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} else if (y <= -3e-14) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y)))))))) / (y * c);
	} else if (y <= 6.1e+47) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -5.1e+144:
		tmp = t_1
	elif y <= -4.6e+51:
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y))
	elif y <= -3e-14:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y)))))))) / (y * c)
	elif y <= 6.1e+47:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -5.1e+144)
		tmp = t_1;
	elseif (y <= -4.6e+51)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) + Float64(Float64(Float64(a / x) - Float64(z / Float64(x * x))) / y)));
	elseif (y <= -3e-14)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(x * y)))))))) / Float64(y * c));
	elseif (y <= 6.1e+47)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -5.1e+144)
		tmp = t_1;
	elseif (y <= -4.6e+51)
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	elseif (y <= -3e-14)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y)))))))) / (y * c);
	elseif (y <= 6.1e+47)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.1e+144], t$95$1, If[LessEqual[y, -4.6e+51], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] + N[(N[(N[(a / x), $MachinePrecision] - N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-14], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.1e+47], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.0999999999999999e144 or 6.10000000000000019e47 < y

   1. Initial program 2.2%

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

   2. Taylor expanded in y around inf 70.0%

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

      1. associate--l+ 70.0%

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

      2. associate-/l* 72.9%

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

   4. Simplified 72.9%

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

   if -5.0999999999999999e144 < y < -4.6000000000000001e51

   1. Initial program 5.3%

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

      1. clear-num 5.3%

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

      2. inv-pow 5.3%

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

   3. Applied egg-rr 5.3%

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

      1. unpow-1 5.3%

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

      2. fma-udef 5.3%

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

      3. *-commutative 5.3%

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

      4. fma-def 5.3%

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

   5. Simplified 5.3%

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

   6. Taylor expanded in y around -inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. distribute-lft-out-- 57.1%

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

      3. unpow2 57.1%

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

   8. Simplified 57.1%

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

   if -4.6000000000000001e51 < y < -2.9999999999999998e-14

   1. Initial program 75.2%

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

   2. Taylor expanded in c around inf 38.3%

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

   if -2.9999999999999998e-14 < y < 6.10000000000000019e47

   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. Taylor expanded in y around 0 86.6%

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

      1. *-commutative 86.6%

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

   4. 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 4 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+144}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-14}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{y \cdot c}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 6: 68.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+35}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+47}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -1.5e+145)
     t_1
     (if (<= y -4.6e+51)
       (/ 1.0 (+ (/ 1.0 x) (/ (- (/ a x) (/ z (* x x))) y)))
       (if (<= y -9e+35)
         (/ z y)
         (if (<= y 1.55e+47)
           (/ t (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.5e+145) {
		tmp = t_1;
	} else if (y <= -4.6e+51) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} else if (y <= -9e+35) {
		tmp = z / y;
	} else if (y <= 1.55e+47) {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-1.5d+145)) then
        tmp = t_1
    else if (y <= (-4.6d+51)) then
        tmp = 1.0d0 / ((1.0d0 / x) + (((a / x) - (z / (x * x))) / y))
    else if (y <= (-9d+35)) then
        tmp = z / y
    else if (y <= 1.55d+47) then
        tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.5e+145) {
		tmp = t_1;
	} else if (y <= -4.6e+51) {
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	} else if (y <= -9e+35) {
		tmp = z / y;
	} else if (y <= 1.55e+47) {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -1.5e+145:
		tmp = t_1
	elif y <= -4.6e+51:
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y))
	elif y <= -9e+35:
		tmp = z / y
	elif y <= 1.55e+47:
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.5e+145)
		tmp = t_1;
	elseif (y <= -4.6e+51)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) + Float64(Float64(Float64(a / x) - Float64(z / Float64(x * x))) / y)));
	elseif (y <= -9e+35)
		tmp = Float64(z / y);
	elseif (y <= 1.55e+47)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.5e+145)
		tmp = t_1;
	elseif (y <= -4.6e+51)
		tmp = 1.0 / ((1.0 / x) + (((a / x) - (z / (x * x))) / y));
	elseif (y <= -9e+35)
		tmp = z / y;
	elseif (y <= 1.55e+47)
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+145], t$95$1, If[LessEqual[y, -4.6e+51], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] + N[(N[(N[(a / x), $MachinePrecision] - N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e+35], N[(z / y), $MachinePrecision], If[LessEqual[y, 1.55e+47], N[(t / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5000000000000001e145 or 1.55e47 < y

   1. Initial program 2.2%

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

   2. Taylor expanded in y around inf 70.0%

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

      1. associate--l+ 70.0%

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

      2. associate-/l* 72.9%

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

   4. Simplified 72.9%

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

   if -1.5000000000000001e145 < y < -4.6000000000000001e51

   1. Initial program 5.3%

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

      1. clear-num 5.3%

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

      2. inv-pow 5.3%

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

   3. Applied egg-rr 5.3%

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

      1. unpow-1 5.3%

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

      2. fma-udef 5.3%

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

      3. *-commutative 5.3%

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

      4. fma-def 5.3%

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

   5. Simplified 5.3%

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

   6. Taylor expanded in y around -inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. distribute-lft-out-- 57.1%

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

      3. unpow2 57.1%

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

   8. Simplified 57.1%

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

   if -4.6000000000000001e51 < y < -8.9999999999999993e35

   1. Initial program 52.2%

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

   2. Taylor expanded in z around inf 52.2%

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

      1. associate-/l* 99.2%

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

      2. fma-def 99.2%

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

      3. +-commutative 99.2%

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

      4. *-commutative 99.2%

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

      5. fma-udef 99.2%

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

      6. fma-udef 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -8.9999999999999993e35 < y < 1.55e47

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 74.7%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+145}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+35}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+47}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 7: 68.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+35} \lor \neg \left(y \leq 1.72 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.15e+35) (not (<= y 1.72e+47)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ t (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.15e+35) || !(y <= 1.72e+47)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + 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 <= (-1.15d+35)) .or. (.not. (y <= 1.72d+47))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = t / (i + (y * (c + (y * ((y * (y + a)) + 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 <= -1.15e+35) || !(y <= 1.72e+47)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.15e+35) or not (y <= 1.72e+47):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.15e+35) || !(y <= 1.72e+47))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.15e+35) || ~((y <= 1.72e+47)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.15e+35], N[Not[LessEqual[y, 1.72e+47]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1499999999999999e35 or 1.72000000000000002e47 < y

   1. Initial program 3.6%

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

   2. Taylor expanded in y around inf 65.1%

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

      1. associate--l+ 65.1%

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

      2. associate-/l* 67.5%

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

   4. Simplified 67.5%

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

   if -1.1499999999999999e35 < y < 1.72000000000000002e47

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 74.7%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+35} \lor \neg \left(y \leq 1.72 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \]

Alternative 8: 70.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+34} \lor \neg \left(y \leq 7.1 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.4e+34) (not (<= y 7.1e+47)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ 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 <= -2.4e+34) || !(y <= 7.1e+47)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (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 <= (-2.4d+34)) .or. (.not. (y <= 7.1d+47))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (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 <= -2.4e+34) || !(y <= 7.1e+47)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.4e+34) or not (y <= 7.1e+47):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.4e+34) || !(y <= 7.1e+47))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / 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 <= -2.4e+34) || ~((y <= 7.1e+47)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.4e+34], N[Not[LessEqual[y, 7.1e+47]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999987e34 or 7.1000000000000002e47 < y

   1. Initial program 3.6%

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

   2. Taylor expanded in y around inf 65.1%

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

      1. associate--l+ 65.1%

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

      2. associate-/l* 67.5%

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

   4. Simplified 67.5%

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

   if -2.39999999999999987e34 < y < 7.1000000000000002e47

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 83.0%

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

      1. *-commutative 83.0%

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

   4. Simplified 83.0%

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

   5. Taylor expanded in y around 0 72.7%

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

      1. *-commutative 72.7%

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

   7. Simplified 72.7%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+34} \lor \neg \left(y \leq 7.1 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot c}\\ \end{array} \]

Alternative 9: 67.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+35} \lor \neg \left(y \leq 3 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{i + y \cdot \left(c + y \cdot b\right)}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.25e+35) (not (<= y 3e+47)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ 1.0 (/ (+ i (* y (+ c (* y b)))) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.25e+35) || !(y <= 3e+47)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = 1.0 / ((i + (y * (c + (y * b)))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.25d+35)) .or. (.not. (y <= 3d+47))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = 1.0d0 / ((i + (y * (c + (y * b)))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.25e+35) || !(y <= 3e+47)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = 1.0 / ((i + (y * (c + (y * b)))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.25e+35) or not (y <= 3e+47):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = 1.0 / ((i + (y * (c + (y * b)))) / t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.25e+35) || !(y <= 3e+47))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(1.0 / Float64(Float64(i + Float64(y * Float64(c + Float64(y * b)))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.25e+35) || ~((y <= 3e+47)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = 1.0 / ((i + (y * (c + (y * b)))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.25e+35], N[Not[LessEqual[y, 3e+47]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25000000000000005e35 or 3.0000000000000001e47 < y

   1. Initial program 3.6%

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

   2. Taylor expanded in y around inf 65.1%

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

      1. associate--l+ 65.1%

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

      2. associate-/l* 67.5%

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

   4. Simplified 67.5%

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

   if -1.25000000000000005e35 < y < 3.0000000000000001e47

   1. Initial program 94.6%

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

      1. clear-num 93.6%

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

      2. inv-pow 93.6%

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

   3. Applied egg-rr 93.6%

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

      1. unpow-1 93.6%

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

      2. fma-udef 93.6%

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

      3. *-commutative 93.6%

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

      4. fma-def 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in t around inf 73.7%

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

   7. Taylor expanded in y around 0 72.5%

      \[\leadsto \frac{1}{\frac{y \cdot \left(c + \color{blue}{y \cdot b}\right) + i}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+35} \lor \neg \left(y \leq 3 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{i + y \cdot \left(c + y \cdot b\right)}{t}}\\ \end{array} \]

Alternative 10: 50.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{t}{c}}{y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y \cdot y}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.8e+28)
   x
   (if (<= y -3.2e-62)
     (/ (/ t c) y)
     (if (<= y 1.65e-40) (/ t i) (if (<= y 1.6e+48) (* x (/ (* y y) b)) x)))))

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+28) {
		tmp = x;
	} else if (y <= -3.2e-62) {
		tmp = (t / c) / y;
	} else if (y <= 1.65e-40) {
		tmp = t / i;
	} else if (y <= 1.6e+48) {
		tmp = x * ((y * y) / b);
	} 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 <= (-6.8d+28)) then
        tmp = x
    else if (y <= (-3.2d-62)) then
        tmp = (t / c) / y
    else if (y <= 1.65d-40) then
        tmp = t / i
    else if (y <= 1.6d+48) then
        tmp = x * ((y * y) / b)
    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 <= -6.8e+28) {
		tmp = x;
	} else if (y <= -3.2e-62) {
		tmp = (t / c) / y;
	} else if (y <= 1.65e-40) {
		tmp = t / i;
	} else if (y <= 1.6e+48) {
		tmp = x * ((y * y) / b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.8e+28:
		tmp = x
	elif y <= -3.2e-62:
		tmp = (t / c) / y
	elif y <= 1.65e-40:
		tmp = t / i
	elif y <= 1.6e+48:
		tmp = x * ((y * y) / b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.8e+28)
		tmp = x;
	elseif (y <= -3.2e-62)
		tmp = Float64(Float64(t / c) / y);
	elseif (y <= 1.65e-40)
		tmp = Float64(t / i);
	elseif (y <= 1.6e+48)
		tmp = Float64(x * Float64(Float64(y * y) / b));
	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 <= -6.8e+28)
		tmp = x;
	elseif (y <= -3.2e-62)
		tmp = (t / c) / y;
	elseif (y <= 1.65e-40)
		tmp = t / i;
	elseif (y <= 1.6e+48)
		tmp = x * ((y * y) / b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.8e+28], x, If[LessEqual[y, -3.2e-62], N[(N[(t / c), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.65e-40], N[(t / i), $MachinePrecision], If[LessEqual[y, 1.6e+48], N[(x * N[(N[(y * y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.8e28 or 1.6000000000000001e48 < y

   1. Initial program 3.5%

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

   2. Taylor expanded in y around inf 51.9%

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

   if -6.8e28 < y < -3.20000000000000021e-62

   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. Taylor expanded in c around inf 46.1%

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

   3. Taylor expanded in y around 0 35.2%

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

      1. associate-/r* 35.4%

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

   5. Simplified 35.4%

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

   if -3.20000000000000021e-62 < y < 1.64999999999999996e-40

   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. Taylor expanded in y around 0 61.8%

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

   if 1.64999999999999996e-40 < y < 1.6000000000000001e48

   1. Initial program 71.1%

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

   2. Taylor expanded in x around inf 26.0%

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

   3. Taylor expanded in b around inf 16.0%

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

      1. associate-/l* 32.3%

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

      2. unpow2 32.3%

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

   5. Simplified 32.3%

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

      1. associate-/r/ 32.3%

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

   7. Applied egg-rr 32.3%

      \[\leadsto \color{blue}{\frac{y \cdot y}{b} \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{t}{c}}{y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y \cdot y}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 50.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{t}{c}}{y} + \frac{230661.510616}{c}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y \cdot y}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.7e+51)
   x
   (if (<= y -1.14e-63)
     (+ (/ (/ t c) y) (/ 230661.510616 c))
     (if (<= y 2.1e-40) (/ t i) (if (<= y 3.05e+49) (* x (/ (* y y) b)) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5.7e+51) {
		tmp = x;
	} else if (y <= -1.14e-63) {
		tmp = ((t / c) / y) + (230661.510616 / c);
	} else if (y <= 2.1e-40) {
		tmp = t / i;
	} else if (y <= 3.05e+49) {
		tmp = x * ((y * y) / b);
	} 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 <= (-5.7d+51)) then
        tmp = x
    else if (y <= (-1.14d-63)) then
        tmp = ((t / c) / y) + (230661.510616d0 / c)
    else if (y <= 2.1d-40) then
        tmp = t / i
    else if (y <= 3.05d+49) then
        tmp = x * ((y * y) / b)
    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 <= -5.7e+51) {
		tmp = x;
	} else if (y <= -1.14e-63) {
		tmp = ((t / c) / y) + (230661.510616 / c);
	} else if (y <= 2.1e-40) {
		tmp = t / i;
	} else if (y <= 3.05e+49) {
		tmp = x * ((y * y) / b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.7e+51:
		tmp = x
	elif y <= -1.14e-63:
		tmp = ((t / c) / y) + (230661.510616 / c)
	elif y <= 2.1e-40:
		tmp = t / i
	elif y <= 3.05e+49:
		tmp = x * ((y * y) / b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.7e+51)
		tmp = x;
	elseif (y <= -1.14e-63)
		tmp = Float64(Float64(Float64(t / c) / y) + Float64(230661.510616 / c));
	elseif (y <= 2.1e-40)
		tmp = Float64(t / i);
	elseif (y <= 3.05e+49)
		tmp = Float64(x * Float64(Float64(y * y) / b));
	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 <= -5.7e+51)
		tmp = x;
	elseif (y <= -1.14e-63)
		tmp = ((t / c) / y) + (230661.510616 / c);
	elseif (y <= 2.1e-40)
		tmp = t / i;
	elseif (y <= 3.05e+49)
		tmp = x * ((y * y) / b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.7e+51], x, If[LessEqual[y, -1.14e-63], N[(N[(N[(t / c), $MachinePrecision] / y), $MachinePrecision] + N[(230661.510616 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-40], N[(t / i), $MachinePrecision], If[LessEqual[y, 3.05e+49], N[(x * N[(N[(y * y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.7000000000000002e51 or 3.04999999999999982e49 < y

   1. Initial program 2.7%

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

   2. Taylor expanded in y around inf 53.1%

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

   if -5.7000000000000002e51 < y < -1.1400000000000001e-63

   1. Initial program 87.2%

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

   2. Taylor expanded in c around inf 40.7%

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

   3. Taylor expanded in y around 0 31.9%

      \[\leadsto \color{blue}{230661.510616 \cdot \frac{1}{c} + \frac{t}{c \cdot y}} \]
   4. Step-by-step derivation

      1. +-commutative 31.9%

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

      2. associate-/r* 32.0%

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

      3. associate-*r/ 32.0%

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

      4. metadata-eval 32.0%

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

   5. Simplified 32.0%

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

   if -1.1400000000000001e-63 < y < 2.10000000000000018e-40

   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. Taylor expanded in y around 0 61.8%

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

   if 2.10000000000000018e-40 < y < 3.04999999999999982e49

   1. Initial program 71.1%

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

   2. Taylor expanded in x around inf 26.0%

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

   3. Taylor expanded in b around inf 16.0%

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

      1. associate-/l* 32.3%

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

      2. unpow2 32.3%

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

   5. Simplified 32.3%

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

      1. associate-/r/ 32.3%

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

   7. Applied egg-rr 32.3%

      \[\leadsto \color{blue}{\frac{y \cdot y}{b} \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{t}{c}}{y} + \frac{230661.510616}{c}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y \cdot y}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 64.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+33} \lor \neg \left(y \leq 1.48 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{i + y \cdot c}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.8e+33) (not (<= y 1.48e+47)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ 1.0 (/ (+ i (* y c)) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.8e+33) || !(y <= 1.48e+47)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = 1.0 / ((i + (y * c)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-4.8d+33)) .or. (.not. (y <= 1.48d+47))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = 1.0d0 / ((i + (y * c)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.8e+33) || !(y <= 1.48e+47)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = 1.0 / ((i + (y * c)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.8e+33) or not (y <= 1.48e+47):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = 1.0 / ((i + (y * c)) / t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.8e+33) || !(y <= 1.48e+47))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(1.0 / Float64(Float64(i + Float64(y * c)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.8e+33) || ~((y <= 1.48e+47)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = 1.0 / ((i + (y * c)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.8e+33], N[Not[LessEqual[y, 1.48e+47]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e33 or 1.47999999999999996e47 < y

   1. Initial program 3.6%

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

   2. Taylor expanded in y around inf 65.1%

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

      1. associate--l+ 65.1%

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

      2. associate-/l* 67.5%

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

   4. Simplified 67.5%

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

   if -4.8e33 < y < 1.47999999999999996e47

   1. Initial program 94.6%

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

      1. clear-num 93.6%

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

      2. inv-pow 93.6%

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

   3. Applied egg-rr 93.6%

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

      1. unpow-1 93.6%

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

      2. fma-udef 93.6%

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

      3. *-commutative 93.6%

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

      4. fma-def 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in t around inf 73.7%

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

   7. Taylor expanded in y around 0 65.5%

      \[\leadsto \frac{1}{\frac{\color{blue}{c \cdot y} + i}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+33} \lor \neg \left(y \leq 1.48 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{i + y \cdot c}{t}}\\ \end{array} \]

Alternative 13: 57.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{1}{\frac{i + y \cdot c}{t}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.3e+35) x (if (<= y 2.6e+48) (/ 1.0 (/ (+ i (* y c)) t)) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.3e+35) {
		tmp = x;
	} else if (y <= 2.6e+48) {
		tmp = 1.0 / ((i + (y * c)) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.3d+35)) then
        tmp = x
    else if (y <= 2.6d+48) then
        tmp = 1.0d0 / ((i + (y * c)) / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.3e+35) {
		tmp = x;
	} else if (y <= 2.6e+48) {
		tmp = 1.0 / ((i + (y * c)) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.3e+35:
		tmp = x
	elif y <= 2.6e+48:
		tmp = 1.0 / ((i + (y * c)) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.3e+35)
		tmp = x;
	elseif (y <= 2.6e+48)
		tmp = Float64(1.0 / Float64(Float64(i + Float64(y * c)) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.3e+35)
		tmp = x;
	elseif (y <= 2.6e+48)
		tmp = 1.0 / ((i + (y * c)) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.3e+35], x, If[LessEqual[y, 2.6e+48], N[(1.0 / N[(N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999998e35 or 2.59999999999999995e48 < y

   1. Initial program 3.6%

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

   2. Taylor expanded in y around inf 52.3%

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

   if -2.2999999999999998e35 < y < 2.59999999999999995e48

   1. Initial program 94.6%

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

      1. clear-num 93.6%

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

      2. inv-pow 93.6%

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

   3. Applied egg-rr 93.6%

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

      1. unpow-1 93.6%

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

      2. fma-udef 93.6%

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

      3. *-commutative 93.6%

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

      4. fma-def 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in t around inf 73.7%

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

   7. Taylor expanded in y around 0 65.5%

      \[\leadsto \frac{1}{\frac{\color{blue}{c \cdot y} + i}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{1}{\frac{i + y \cdot c}{t}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 50.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 6200000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.5e+28)
   x
   (if (<= y -1.32e-61) (/ t (* y c)) (if (<= y 6200000000.0) (/ 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 <= -2.5e+28) {
		tmp = x;
	} else if (y <= -1.32e-61) {
		tmp = t / (y * c);
	} else if (y <= 6200000000.0) {
		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 <= (-2.5d+28)) then
        tmp = x
    else if (y <= (-1.32d-61)) then
        tmp = t / (y * c)
    else if (y <= 6200000000.0d0) 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 <= -2.5e+28) {
		tmp = x;
	} else if (y <= -1.32e-61) {
		tmp = t / (y * c);
	} else if (y <= 6200000000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.5e+28:
		tmp = x
	elif y <= -1.32e-61:
		tmp = t / (y * c)
	elif y <= 6200000000.0:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.5e+28)
		tmp = x;
	elseif (y <= -1.32e-61)
		tmp = Float64(t / Float64(y * c));
	elseif (y <= 6200000000.0)
		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 <= -2.5e+28)
		tmp = x;
	elseif (y <= -1.32e-61)
		tmp = t / (y * c);
	elseif (y <= 6200000000.0)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.5e+28], x, If[LessEqual[y, -1.32e-61], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6200000000.0], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999979e28 or 6.2e9 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in y around inf 49.3%

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

   if -2.49999999999999979e28 < y < -1.32000000000000002e-61

   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. Taylor expanded in c around inf 46.1%

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

   3. Taylor expanded in y around 0 35.2%

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

   if -1.32000000000000002e-61 < y < 6.2e9

   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. Taylor expanded in y around 0 56.4%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 6200000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 50.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{t}{c}}{y}\\ \mathbf{elif}\;y \leq 12500000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.2e+29)
   x
   (if (<= y -7e-62) (/ (/ t c) y) (if (<= y 12500000000000.0) (/ 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 <= -4.2e+29) {
		tmp = x;
	} else if (y <= -7e-62) {
		tmp = (t / c) / y;
	} else if (y <= 12500000000000.0) {
		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 <= (-4.2d+29)) then
        tmp = x
    else if (y <= (-7d-62)) then
        tmp = (t / c) / y
    else if (y <= 12500000000000.0d0) 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 <= -4.2e+29) {
		tmp = x;
	} else if (y <= -7e-62) {
		tmp = (t / c) / y;
	} else if (y <= 12500000000000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.2e+29:
		tmp = x
	elif y <= -7e-62:
		tmp = (t / c) / y
	elif y <= 12500000000000.0:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.2e+29)
		tmp = x;
	elseif (y <= -7e-62)
		tmp = Float64(Float64(t / c) / y);
	elseif (y <= 12500000000000.0)
		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 <= -4.2e+29)
		tmp = x;
	elseif (y <= -7e-62)
		tmp = (t / c) / y;
	elseif (y <= 12500000000000.0)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.2e+29], x, If[LessEqual[y, -7e-62], N[(N[(t / c), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 12500000000000.0], N[(t / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2000000000000003e29 or 1.25e13 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in y around inf 49.3%

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

   if -4.2000000000000003e29 < y < -7.0000000000000003e-62

   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. Taylor expanded in c around inf 46.1%

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

   3. Taylor expanded in y around 0 35.2%

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

      1. associate-/r* 35.4%

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

   5. Simplified 35.4%

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

   if -7.0000000000000003e-62 < y < 1.25e13

   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. Taylor expanded in y around 0 56.4%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{t}{c}}{y}\\ \mathbf{elif}\;y \leq 12500000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 50.3% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 820000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3e-14) x (if (<= y 820000000.0) (/ 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 <= -3e-14) {
		tmp = x;
	} else if (y <= 820000000.0) {
		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 <= (-3d-14)) then
        tmp = x
    else if (y <= 820000000.0d0) 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 <= -3e-14) {
		tmp = x;
	} else if (y <= 820000000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3e-14:
		tmp = x
	elif y <= 820000000.0:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3e-14)
		tmp = x;
	elseif (y <= 820000000.0)
		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 <= -3e-14)
		tmp = x;
	elseif (y <= 820000000.0)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3e-14], x, If[LessEqual[y, 820000000.0], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9999999999999998e-14 or 8.2e8 < y

   1. Initial program 10.5%

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

   2. Taylor expanded in y around inf 47.0%

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

   if -2.9999999999999998e-14 < y < 8.2e8

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 52.2%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 820000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 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 51.9%

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

2. Taylor expanded in y around inf 26.7%

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

3. Final simplification 26.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023185 
(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)))