Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.0% → 84.3%

Time: 28.1s

Alternatives: 13

Speedup: 2.2×

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: 55.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))
   (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 * ((x * y) + z))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	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 * ((x * y) + z))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	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 * ((x * y) + z))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	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(Float64(x * y) + z))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))))
	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 * ((x * y) + z))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	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[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $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 91.7%

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

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 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. Add Preprocessing

   3. Taylor expanded in y around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. associate--l+ 63.5%

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

      3. associate-/l* 69.3%

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

   5. Simplified 69.3%

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

4. Final simplification 83.7%

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

Alternative 2: 77.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ \mathbf{if}\;y \leq -8.4 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-25}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t_1}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-54}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a)))))))
   (if (<= y -8.4e+86)
     (+ (/ z y) (- x (/ a (/ y x))))
     (if (<= y -6.9e-25)
       (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) t_1)
       (if (<= y -1.6e-54)
         (/ (+ t (* y 230661.510616)) (+ i (* y t_1)))
         (if (<= y 2.95e+66)
           (/
            (+
             t
             (*
              y
              (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))))
            (+ i (* y (+ c (* y b)))))
           (+ x (/ z y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -8.4e+86) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -6.9e-25) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= -1.6e-54) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 2.95e+66) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + (z / y);
	}
	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 = c + (y * (b + (y * (y + a))))
    if (y <= (-8.4d+86)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-6.9d-25)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))) / t_1
    else if (y <= (-1.6d-54)) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_1))
    else if (y <= 2.95d+66) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))))) / (i + (y * (c + (y * b))))
    else
        tmp = x + (z / y)
    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 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -8.4e+86) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -6.9e-25) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= -1.6e-54) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 2.95e+66) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	tmp = 0
	if y <= -8.4e+86:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -6.9e-25:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1
	elif y <= -1.6e-54:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1))
	elif y <= 2.95e+66:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / (i + (y * (c + (y * b))))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	tmp = 0.0
	if (y <= -8.4e+86)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -6.9e-25)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / t_1);
	elseif (y <= -1.6e-54)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_1)));
	elseif (y <= 2.95e+66)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	tmp = 0.0;
	if (y <= -8.4e+86)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -6.9e-25)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	elseif (y <= -1.6e-54)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	elseif (y <= 2.95e+66)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / (i + (y * (c + (y * b))));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.4e+86], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.9e-25], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, -1.6e-54], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e+66], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.3999999999999996e86

   1. Initial program 2.6%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. associate--l+ 68.9%

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

      3. associate-/l* 74.4%

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

   5. Simplified 74.4%

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

   if -8.3999999999999996e86 < y < -6.89999999999999975e-25

   1. Initial program 53.3%

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

   3. Taylor expanded in i around 0 52.8%

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

   4. Taylor expanded in x around 0 42.9%

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

   5. Taylor expanded in t around 0 57.3%

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

   if -6.89999999999999975e-25 < y < -1.59999999999999999e-54

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 90.4%

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

      1. *-commutative 90.4%

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

   5. Simplified 90.4%

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

   if -1.59999999999999999e-54 < y < 2.94999999999999994e66

   1. Initial program 94.1%

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

   3. Taylor expanded in y around 0 91.2%

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

      1. *-commutative 91.2%

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

   5. Simplified 91.2%

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

   if 2.94999999999999994e66 < y

   1. Initial program 2.5%

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

   3. Taylor expanded in y around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. associate--l+ 64.0%

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

      3. associate-/l* 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in a around 0 70.6%

      \[\leadsto \color{blue}{x + \frac{z}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-25}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-54}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+87}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-25}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t_1}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-46}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{+41}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+113}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a)))))))
   (if (<= y -2.4e+87)
     (+ (/ z y) (- x (/ a (/ y x))))
     (if (<= y -6.9e-25)
       (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) t_1)
       (if (<= y 9.2e-46)
         (/ (+ t (* y 230661.510616)) (+ i (* y t_1)))
         (if (<= y 1.56e+41)
           (/
            (+
             t
             (*
              y
              (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))))
            (* y (+ c (* y b))))
           (if (<= y 3.2e+113) (+ x (/ z y)) (/ x (+ 1.0 (/ a y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -2.4e+87) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -6.9e-25) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= 9.2e-46) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 1.56e+41) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / (y * (c + (y * b)));
	} else if (y <= 3.2e+113) {
		tmp = x + (z / y);
	} else {
		tmp = x / (1.0 + (a / y));
	}
	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 = c + (y * (b + (y * (y + a))))
    if (y <= (-2.4d+87)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-6.9d-25)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))) / t_1
    else if (y <= 9.2d-46) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_1))
    else if (y <= 1.56d+41) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))))) / (y * (c + (y * b)))
    else if (y <= 3.2d+113) then
        tmp = x + (z / y)
    else
        tmp = x / (1.0d0 + (a / y))
    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 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -2.4e+87) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -6.9e-25) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= 9.2e-46) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 1.56e+41) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / (y * (c + (y * b)));
	} else if (y <= 3.2e+113) {
		tmp = x + (z / y);
	} else {
		tmp = x / (1.0 + (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	tmp = 0
	if y <= -2.4e+87:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -6.9e-25:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1
	elif y <= 9.2e-46:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1))
	elif y <= 1.56e+41:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / (y * (c + (y * b)))
	elif y <= 3.2e+113:
		tmp = x + (z / y)
	else:
		tmp = x / (1.0 + (a / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	tmp = 0.0
	if (y <= -2.4e+87)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -6.9e-25)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / t_1);
	elseif (y <= 9.2e-46)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_1)));
	elseif (y <= 1.56e+41)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))))) / Float64(y * Float64(c + Float64(y * b))));
	elseif (y <= 3.2e+113)
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(x / Float64(1.0 + Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	tmp = 0.0;
	if (y <= -2.4e+87)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -6.9e-25)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	elseif (y <= 9.2e-46)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	elseif (y <= 1.56e+41)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / (y * (c + (y * b)));
	elseif (y <= 3.2e+113)
		tmp = x + (z / y);
	else
		tmp = x / (1.0 + (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+87], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.9e-25], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 9.2e-46], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.56e+41], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+113], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.39999999999999981e87

   1. Initial program 2.6%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. associate--l+ 68.9%

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

      3. associate-/l* 74.4%

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

   5. Simplified 74.4%

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

   if -2.39999999999999981e87 < y < -6.89999999999999975e-25

   1. Initial program 53.3%

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

   3. Taylor expanded in i around 0 52.8%

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

   4. Taylor expanded in x around 0 42.9%

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

   5. Taylor expanded in t around 0 57.3%

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

   if -6.89999999999999975e-25 < y < 9.1999999999999997e-46

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 95.2%

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

      1. *-commutative 95.2%

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

   5. Simplified 95.2%

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

   if 9.1999999999999997e-46 < y < 1.56e41

   1. Initial program 78.6%

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

   3. Taylor expanded in i around 0 51.8%

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

   4. Taylor expanded in y around 0 44.5%

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

      1. *-commutative 44.5%

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

   6. Simplified 44.5%

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

   if 1.56e41 < y < 3.1999999999999998e113

   1. Initial program 21.0%

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

   3. Taylor expanded in y around inf 21.7%

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

      1. +-commutative 21.7%

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

      2. associate--l+ 21.7%

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

      3. associate-/l* 28.0%

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

   5. Simplified 28.0%

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

   6. Taylor expanded in a around 0 28.2%

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

   if 3.1999999999999998e113 < y

   1. Initial program 2.8%

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

   3. Taylor expanded in i around 0 2.8%

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

   4. Taylor expanded in x around inf 0.0%

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

      1. associate-/l* 0.0%

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

      2. +-commutative 0.0%

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

      3. fma-udef 0.0%

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

      4. +-commutative 0.0%

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

      5. +-commutative 0.0%

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

      6. fma-udef 0.0%

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

   6. Simplified 0.0%

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

   7. Taylor expanded in y around inf 83.9%

      \[\leadsto \frac{x}{\color{blue}{1 + \frac{a}{y}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+87}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-25}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-46}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{+41}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+113}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t_1}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a)))))))
   (if (<= y -7.8e+86)
     (+ (/ z y) (- x (/ a (/ y x))))
     (if (<= y -5.4e-33)
       (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) t_1)
       (if (<= y 6.5e-63)
         (/ t (+ i (* y t_1)))
         (if (<= y 4.2e+50)
           (/
            (+
             t
             (*
              y
              (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))))
            i)
           (+ x (/ z y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -7.8e+86) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -5.4e-33) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= 6.5e-63) {
		tmp = t / (i + (y * t_1));
	} else if (y <= 4.2e+50) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i;
	} else {
		tmp = x + (z / y);
	}
	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 = c + (y * (b + (y * (y + a))))
    if (y <= (-7.8d+86)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-5.4d-33)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))) / t_1
    else if (y <= 6.5d-63) then
        tmp = t / (i + (y * t_1))
    else if (y <= 4.2d+50) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))))) / i
    else
        tmp = x + (z / y)
    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 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -7.8e+86) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -5.4e-33) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= 6.5e-63) {
		tmp = t / (i + (y * t_1));
	} else if (y <= 4.2e+50) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	tmp = 0
	if y <= -7.8e+86:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -5.4e-33:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1
	elif y <= 6.5e-63:
		tmp = t / (i + (y * t_1))
	elif y <= 4.2e+50:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	tmp = 0.0
	if (y <= -7.8e+86)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -5.4e-33)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / t_1);
	elseif (y <= 6.5e-63)
		tmp = Float64(t / Float64(i + Float64(y * t_1)));
	elseif (y <= 4.2e+50)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))))) / i);
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	tmp = 0.0;
	if (y <= -7.8e+86)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -5.4e-33)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	elseif (y <= 6.5e-63)
		tmp = t / (i + (y * t_1));
	elseif (y <= 4.2e+50)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e+86], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.4e-33], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 6.5e-63], N[(t / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+50], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.8000000000000004e86

   1. Initial program 2.6%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. associate--l+ 68.9%

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

      3. associate-/l* 74.4%

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

   5. Simplified 74.4%

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

   if -7.8000000000000004e86 < y < -5.4000000000000002e-33

   1. Initial program 59.6%

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

   3. Taylor expanded in i around 0 54.8%

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

   4. Taylor expanded in x around 0 42.2%

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

   5. Taylor expanded in t around 0 54.5%

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

   if -5.4000000000000002e-33 < y < 6.4999999999999998e-63

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 80.8%

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

   if 6.4999999999999998e-63 < y < 4.1999999999999999e50

   1. Initial program 74.0%

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

   3. Taylor expanded in i around inf 38.5%

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

   if 4.1999999999999999e50 < y

   1. Initial program 4.8%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. associate--l+ 58.8%

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

      3. associate-/l* 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in a around 0 66.9%

      \[\leadsto \color{blue}{x + \frac{z}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-25}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t_1}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-56}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a)))))))
   (if (<= y -7.8e+86)
     (+ (/ z y) (- x (/ a (/ y x))))
     (if (<= y -6.9e-25)
       (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) t_1)
       (if (<= y 5e-56)
         (/ (+ t (* y 230661.510616)) (+ i (* y t_1)))
         (if (<= y 4.2e+50)
           (/
            (+
             t
             (*
              y
              (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))))
            i)
           (+ x (/ z y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -7.8e+86) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -6.9e-25) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= 5e-56) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 4.2e+50) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i;
	} else {
		tmp = x + (z / y);
	}
	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 = c + (y * (b + (y * (y + a))))
    if (y <= (-7.8d+86)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= (-6.9d-25)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))) / t_1
    else if (y <= 5d-56) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_1))
    else if (y <= 4.2d+50) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))))) / i
    else
        tmp = x + (z / y)
    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 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -7.8e+86) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= -6.9e-25) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	} else if (y <= 5e-56) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 4.2e+50) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	tmp = 0
	if y <= -7.8e+86:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= -6.9e-25:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1
	elif y <= 5e-56:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1))
	elif y <= 4.2e+50:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	tmp = 0.0
	if (y <= -7.8e+86)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= -6.9e-25)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / t_1);
	elseif (y <= 5e-56)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_1)));
	elseif (y <= 4.2e+50)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))))) / i);
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	tmp = 0.0;
	if (y <= -7.8e+86)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= -6.9e-25)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_1;
	elseif (y <= 5e-56)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	elseif (y <= 4.2e+50)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e+86], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.9e-25], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 5e-56], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+50], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.8000000000000004e86

   1. Initial program 2.6%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. associate--l+ 68.9%

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

      3. associate-/l* 74.4%

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

   5. Simplified 74.4%

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

   if -7.8000000000000004e86 < y < -6.89999999999999975e-25

   1. Initial program 53.3%

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

   3. Taylor expanded in i around 0 52.8%

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

   4. Taylor expanded in x around 0 42.9%

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

   5. Taylor expanded in t around 0 57.3%

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

   if -6.89999999999999975e-25 < y < 4.99999999999999997e-56

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 95.9%

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

      1. *-commutative 95.9%

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

   5. Simplified 95.9%

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

   if 4.99999999999999997e-56 < y < 4.1999999999999999e50

   1. Initial program 74.0%

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

   3. Taylor expanded in i around inf 38.5%

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

   if 4.1999999999999999e50 < y

   1. Initial program 4.8%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. associate--l+ 58.8%

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

      3. associate-/l* 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in a around 0 66.9%

      \[\leadsto \color{blue}{x + \frac{z}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-25}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-56}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.4e+30)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y 2.6e+52)
     (/
      (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
      (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5.4e+30) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= 2.6e+52) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = x + (z / y);
	}
	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 <= (-5.4d+30)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= 2.6d+52) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else
        tmp = x + (z / y)
    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 <= -5.4e+30) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= 2.6e+52) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.4e+30:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= 2.6e+52:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.4e+30)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= 2.6e+52)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -5.4e+30)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= 2.6e+52)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.4e+30], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+52], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3999999999999997e30

   1. Initial program 7.7%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. associate--l+ 62.5%

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

      3. associate-/l* 67.0%

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

   5. Simplified 67.0%

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

   if -5.3999999999999997e30 < y < 2.6e52

   1. Initial program 95.2%

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

   3. Taylor expanded in x around 0 89.7%

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

   if 2.6e52 < y

   1. Initial program 4.8%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. associate--l+ 58.8%

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

      3. associate-/l* 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in a around 0 66.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.8e+22)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y 9e-58)
     (/ t (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
     (if (<= y 4.2e+50)
       (/
        (+
         t
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))))
        i)
       (+ x (/ z y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.8e+22) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= 9e-58) {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 4.2e+50) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.8d+22)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= 9d-58) then
        tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else if (y <= 4.2d+50) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))))) / i
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.8e+22) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= 9e-58) {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else if (y <= 4.2e+50) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.8e+22:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= 9e-58:
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
	elif y <= 4.2e+50:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.8e+22)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= 9e-58)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	elseif (y <= 4.2e+50)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))))) / i);
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.8e+22)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= 9e-58)
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	elseif (y <= 4.2e+50)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / i;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.8e+22], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-58], N[(t / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+50], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.8000000000000004e22

   1. Initial program 10.7%

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

   3. Taylor expanded in y around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. associate--l+ 59.0%

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

      3. associate-/l* 63.2%

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

   5. Simplified 63.2%

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

   if -3.8000000000000004e22 < y < 9.0000000000000006e-58

   1. Initial program 99.6%

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

   3. Taylor expanded in t around inf 76.8%

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

   if 9.0000000000000006e-58 < y < 4.1999999999999999e50

   1. Initial program 74.0%

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

   3. Taylor expanded in i around inf 38.5%

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

   if 4.1999999999999999e50 < y

   1. Initial program 4.8%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. associate--l+ 58.8%

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

      3. associate-/l* 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in a around 0 66.9%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2700000000:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-129}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2700000000.0)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y 5.8e-129)
     (/ t i)
     (if (<= y 7.5e+28)
       (/ t (* y (+ c (* y (+ b (* y (+ y a)))))))
       (+ x (/ z y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2700000000.0) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= 5.8e-129) {
		tmp = t / i;
	} else if (y <= 7.5e+28) {
		tmp = t / (y * (c + (y * (b + (y * (y + a))))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2700000000.0d0)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= 5.8d-129) then
        tmp = t / i
    else if (y <= 7.5d+28) then
        tmp = t / (y * (c + (y * (b + (y * (y + a))))))
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2700000000.0) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= 5.8e-129) {
		tmp = t / i;
	} else if (y <= 7.5e+28) {
		tmp = t / (y * (c + (y * (b + (y * (y + a))))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2700000000.0:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= 5.8e-129:
		tmp = t / i
	elif y <= 7.5e+28:
		tmp = t / (y * (c + (y * (b + (y * (y + a))))))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2700000000.0)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= 5.8e-129)
		tmp = Float64(t / i);
	elseif (y <= 7.5e+28)
		tmp = Float64(t / Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2700000000.0)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= 5.8e-129)
		tmp = t / i;
	elseif (y <= 7.5e+28)
		tmp = t / (y * (c + (y * (b + (y * (y + a))))));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2700000000.0], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-129], N[(t / i), $MachinePrecision], If[LessEqual[y, 7.5e+28], N[(t / N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7e9

   1. Initial program 10.7%

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

   3. Taylor expanded in y around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. associate--l+ 59.0%

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

      3. associate-/l* 63.2%

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

   5. Simplified 63.2%

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

   if -2.7e9 < y < 5.80000000000000034e-129

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 58.2%

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

   if 5.80000000000000034e-129 < y < 7.4999999999999998e28

   1. Initial program 92.7%

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

   3. Taylor expanded in i around 0 62.3%

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

   4. Taylor expanded in x around 0 55.9%

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

   5. Taylor expanded in t around inf 36.0%

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

   if 7.4999999999999998e28 < y

   1. Initial program 11.5%

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

   3. Taylor expanded in y around inf 53.4%

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

      1. +-commutative 53.4%

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

      2. associate--l+ 53.4%

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

      3. associate-/l* 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in a around 0 60.6%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2700000000:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-129}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+66}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -8.8e+21)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y 2.95e+66)
     (/ t (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -8.8e+21) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= 2.95e+66) {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-8.8d+21)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= 2.95d+66) then
        tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -8.8e+21) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= 2.95e+66) {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -8.8e+21:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= 2.95e+66:
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -8.8e+21)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= 2.95e+66)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -8.8e+21)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= 2.95e+66)
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -8.8e+21], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e+66], N[(t / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.8e21

   1. Initial program 10.7%

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

   3. Taylor expanded in y around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. associate--l+ 59.0%

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

      3. associate-/l* 63.2%

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

   5. Simplified 63.2%

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

   if -8.8e21 < y < 2.94999999999999994e66

   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. Add Preprocessing

   3. Taylor expanded in t around inf 67.9%

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

   if 2.94999999999999994e66 < y

   1. Initial program 2.5%

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

   3. Taylor expanded in y around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. associate--l+ 64.0%

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

      3. associate-/l* 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in a around 0 70.6%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+66}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -8e+21)
   (+ (/ z y) (- x (/ a (/ y x))))
   (if (<= y 4.4e+29) (/ t i) (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -8e+21) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= 4.4e+29) {
		tmp = t / i;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-8d+21)) then
        tmp = (z / y) + (x - (a / (y / x)))
    else if (y <= 4.4d+29) then
        tmp = t / i
    else
        tmp = x + (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -8e+21) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else if (y <= 4.4e+29) {
		tmp = t / i;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -8e+21:
		tmp = (z / y) + (x - (a / (y / x)))
	elif y <= 4.4e+29:
		tmp = t / i
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -8e+21)
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	elseif (y <= 4.4e+29)
		tmp = Float64(t / i);
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -8e+21)
		tmp = (z / y) + (x - (a / (y / x)));
	elseif (y <= 4.4e+29)
		tmp = t / i;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -8e+21], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+29], N[(t / i), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8e21

   1. Initial program 10.7%

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

   3. Taylor expanded in y around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. associate--l+ 59.0%

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

      3. associate-/l* 63.2%

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

   5. Simplified 63.2%

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

   if -8e21 < y < 4.4000000000000003e29

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 48.8%

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

   if 4.4000000000000003e29 < y

   1. Initial program 11.7%

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

   3. Taylor expanded in y around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. associate--l+ 54.4%

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

      3. associate-/l* 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in a around 0 61.6%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.22 \lor \neg \left(y \leq 1.18 \cdot 10^{+30}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -0.22) (not (<= y 1.18e+30))) (+ x (/ z y)) (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -0.22) || !(y <= 1.18e+30)) {
		tmp = x + (z / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-0.22d0)) .or. (.not. (y <= 1.18d+30))) then
        tmp = x + (z / y)
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -0.22) || !(y <= 1.18e+30)) {
		tmp = x + (z / y);
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -0.22) or not (y <= 1.18e+30):
		tmp = x + (z / y)
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -0.22) || !(y <= 1.18e+30))
		tmp = Float64(x + Float64(z / y));
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -0.22) || ~((y <= 1.18e+30)))
		tmp = x + (z / y);
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -0.22], N[Not[LessEqual[y, 1.18e+30]], $MachinePrecision]], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.220000000000000001 or 1.18e30 < y

   1. Initial program 11.9%

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

   3. Taylor expanded in y around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. associate--l+ 56.3%

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

      3. associate-/l* 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in a around 0 61.7%

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

   if -0.220000000000000001 < y < 1.18e30

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 49.1%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.22 \lor \neg \left(y \leq 1.18 \cdot 10^{+30}\right):\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1850:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+50}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1850.0) x (if (<= y 4.5e+50) (/ 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 <= -1850.0) {
		tmp = x;
	} else if (y <= 4.5e+50) {
		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 <= (-1850.0d0)) then
        tmp = x
    else if (y <= 4.5d+50) 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 <= -1850.0) {
		tmp = x;
	} else if (y <= 4.5e+50) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1850.0:
		tmp = x
	elif y <= 4.5e+50:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1850.0)
		tmp = x;
	elseif (y <= 4.5e+50)
		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 <= -1850.0)
		tmp = x;
	elseif (y <= 4.5e+50)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1850.0], x, If[LessEqual[y, 4.5e+50], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1850 or 4.50000000000000014e50 < y

   1. Initial program 8.9%

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

   3. Taylor expanded in y around inf 44.1%

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

   if -1850 < y < 4.50000000000000014e50

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 47.9%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1850:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+50}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.5% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.1%

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

3. Taylor expanded in y around inf 20.7%

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

4. Final simplification 20.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024018 
(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)))