Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 57.0% → 84.7%

Time: 19.6s

Alternatives: 20

Speedup: 1.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 57.0% 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: 84.7% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* x y))))))))
          (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))
   (if (<= t_1 INFINITY) t_1 (+ 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 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y)))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y)))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	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[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.8%

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

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

   1. Initial program 0.0%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 0.0%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 70.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 70.6%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 76.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 76.2%

       \[\leadsto \color{blue}{x + \frac{z}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.8%

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

Alternative 2: 79.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+62}:\\ \;\;\;\;\frac{1}{i + y \cdot \left(c + \left(y + a\right) \cdot \left(y \cdot y\right)\right)} \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2.6e+35)
     t_1
     (if (<= y 1.6e-132)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* y y)))))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (if (<= y 3.6e+62)
         (*
          (/ 1.0 (+ i (* y (+ c (* (+ y a) (* y y))))))
          (+
           t
           (*
            y
            (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* x y)))))))))
         (if (<= y 2.2e+99) (* z (/ y b)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2.6e+35) {
		tmp = t_1;
	} else if (y <= 1.6e-132) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 3.6e+62) {
		tmp = (1.0 / (i + (y * (c + ((y + a) * (y * y)))))) * (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y))))))));
	} else if (y <= 2.2e+99) {
		tmp = z * (y / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-2.6d+35)) then
        tmp = t_1
    else if (y <= 1.6d-132) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= 3.6d+62) then
        tmp = (1.0d0 / (i + (y * (c + ((y + a) * (y * y)))))) * (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (x * y))))))))
    else if (y <= 2.2d+99) then
        tmp = z * (y / b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2.6e+35) {
		tmp = t_1;
	} else if (y <= 1.6e-132) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 3.6e+62) {
		tmp = (1.0 / (i + (y * (c + ((y + a) * (y * y)))))) * (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y))))))));
	} else if (y <= 2.2e+99) {
		tmp = z * (y / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -2.6e+35:
		tmp = t_1
	elif y <= 1.6e-132:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= 3.6e+62:
		tmp = (1.0 / (i + (y * (c + ((y + a) * (y * y)))))) * (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y))))))))
	elif y <= 2.2e+99:
		tmp = z * (y / b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2.6e+35)
		tmp = t_1;
	elseif (y <= 1.6e-132)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * Float64(y * y))))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= 3.6e+62)
		tmp = Float64(Float64(1.0 / Float64(i + Float64(y * Float64(c + Float64(Float64(y + a) * Float64(y * y)))))) * Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(x * y)))))))));
	elseif (y <= 2.2e+99)
		tmp = Float64(z * Float64(y / b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -2.6e+35)
		tmp = t_1;
	elseif (y <= 1.6e-132)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= 3.6e+62)
		tmp = (1.0 / (i + (y * (c + ((y + a) * (y * y)))))) * (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y))))))));
	elseif (y <= 2.2e+99)
		tmp = z * (y / b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+35], t$95$1, If[LessEqual[y, 1.6e-132], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+62], N[(N[(1.0 / N[(i + N[(y * N[(c + N[(N[(y + a), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+99], N[(z * N[(y / b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.60000000000000007e35 or 2.19999999999999978e99 < y

   1. Initial program 5.0%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 5.0%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 72.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 72.5%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 78.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 78.0%

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

   if -2.60000000000000007e35 < y < 1.6000000000000001e-132

   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 x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot {y}^{2}\right)}, \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left({y}^{2}\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(y, a\right)}, y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \color{blue}{a}\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      3. *-lowering-*.f64 96.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \color{blue}{a}\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 96.7%

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

   if 1.6000000000000001e-132 < y < 3.6e62

   1. Initial program 88.1%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in b around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\color{blue}{\left(y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)}, i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right)}, \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \left({y}^{2} \cdot \left(a + y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)}\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(\left({y}^{2}\right), \left(a + y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \color{blue}{\frac{54929528941}{2000000}}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(\left(y \cdot y\right), \left(a + y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(a + y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      6. +-lowering-+.f64 80.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(a, y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

   7. Simplified 80.7%

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

   if 3.6e62 < y < 2.19999999999999978e99

   1. Initial program 0.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 0.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 0.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y \cdot \left(y \cdot y\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{z}\right) \]

   7. Applied egg-rr 3.6%

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

   8. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{b}\right)}, z\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 51.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, b\right), z\right) \]

   10. Simplified 51.6%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+62}:\\ \;\;\;\;\frac{1}{i + y \cdot \left(c + \left(y + a\right) \cdot \left(y \cdot y\right)\right)} \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-134}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+62}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + \left(y + a\right) \cdot \left(y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2.6e+35)
     t_1
     (if (<= y 2e-134)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* y y)))))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (if (<= y 3.6e+62)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* x y))))))))
          (+ i (* y (+ c (* (+ y a) (* y y))))))
         (if (<= y 2.2e+99) (* z (/ y b)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2.6e+35) {
		tmp = t_1;
	} else if (y <= 2e-134) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 3.6e+62) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y)))))))) / (i + (y * (c + ((y + a) * (y * y)))));
	} else if (y <= 2.2e+99) {
		tmp = z * (y / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-2.6d+35)) then
        tmp = t_1
    else if (y <= 2d-134) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= 3.6d+62) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (x * y)))))))) / (i + (y * (c + ((y + a) * (y * y)))))
    else if (y <= 2.2d+99) then
        tmp = z * (y / b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2.6e+35) {
		tmp = t_1;
	} else if (y <= 2e-134) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 3.6e+62) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y)))))))) / (i + (y * (c + ((y + a) * (y * y)))));
	} else if (y <= 2.2e+99) {
		tmp = z * (y / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -2.6e+35:
		tmp = t_1
	elif y <= 2e-134:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= 3.6e+62:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y)))))))) / (i + (y * (c + ((y + a) * (y * y)))))
	elif y <= 2.2e+99:
		tmp = z * (y / b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2.6e+35)
		tmp = t_1;
	elseif (y <= 2e-134)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * Float64(y * y))))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= 3.6e+62)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(x * y)))))))) / Float64(i + Float64(y * Float64(c + Float64(Float64(y + a) * Float64(y * y))))));
	elseif (y <= 2.2e+99)
		tmp = Float64(z * Float64(y / b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -2.6e+35)
		tmp = t_1;
	elseif (y <= 2e-134)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= 3.6e+62)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (x * y)))))))) / (i + (y * (c + ((y + a) * (y * y)))));
	elseif (y <= 2.2e+99)
		tmp = z * (y / b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+35], t$95$1, If[LessEqual[y, 2e-134], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+62], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(N[(y + a), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+99], N[(z * N[(y / b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.60000000000000007e35 or 2.19999999999999978e99 < y

   1. Initial program 5.0%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 5.0%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 72.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 72.5%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 78.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 78.0%

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

   if -2.60000000000000007e35 < y < 2.00000000000000008e-134

   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 x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot {y}^{2}\right)}, \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left({y}^{2}\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(y, a\right)}, y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \color{blue}{a}\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      3. *-lowering-*.f64 96.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \color{blue}{a}\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 96.7%

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

   if 2.00000000000000008e-134 < y < 3.6e62

   1. Initial program 88.1%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right), \color{blue}{\left(i + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \left(y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right), \left(\color{blue}{i} + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right), \left(i + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \left(y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right)\right), \left(i + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right)\right), \left(i + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right)\right)\right), \left(i + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \left(z + x \cdot y\right)\right)\right)\right)\right)\right)\right), \left(i + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \left(x \cdot y\right)\right)\right)\right)\right)\right)\right)\right), \left(i + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \left(y \cdot x\right)\right)\right)\right)\right)\right)\right)\right), \left(i + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right)\right), \left(i + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(i, \color{blue}{\left(y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \color{blue}{\left(c + {y}^{2} \cdot \left(a + y\right)\right)}\right)\right)\right) \]

   5. Simplified 80.5%

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

   if 3.6e62 < y < 2.19999999999999978e99

   1. Initial program 0.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 0.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 0.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y \cdot \left(y \cdot y\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{z}\right) \]

   7. Applied egg-rr 3.6%

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

   8. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{b}\right)}, z\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 51.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, b\right), z\right) \]

   10. Simplified 51.6%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-134}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+62}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + \left(y + a\right) \cdot \left(y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+62}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -1.3e+35)
     t_1
     (if (<= y 3.6e+62)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (if (<= y 2.2e+99) (* z (/ y b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -1.3e+35) {
		tmp = t_1;
	} else if (y <= 3.6e+62) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 2.2e+99) {
		tmp = z * (y / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-1.3d+35)) then
        tmp = t_1
    else if (y <= 3.6d+62) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= 2.2d+99) then
        tmp = z * (y / b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -1.3e+35) {
		tmp = t_1;
	} else if (y <= 3.6e+62) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 2.2e+99) {
		tmp = z * (y / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -1.3e+35:
		tmp = t_1
	elif y <= 3.6e+62:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= 2.2e+99:
		tmp = z * (y / b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -1.3e+35)
		tmp = t_1;
	elseif (y <= 3.6e+62)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= 2.2e+99)
		tmp = Float64(z * Float64(y / b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -1.3e+35)
		tmp = t_1;
	elseif (y <= 3.6e+62)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= 2.2e+99)
		tmp = z * (y / b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+35], t$95$1, If[LessEqual[y, 3.6e+62], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+99], N[(z * N[(y / b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.30000000000000003e35 or 2.19999999999999978e99 < y

   1. Initial program 5.0%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 5.0%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 72.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 72.5%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 78.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 78.0%

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

   if -1.30000000000000003e35 < y < 3.6e62

   1. Initial program 96.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(y \cdot z\right)}, \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 88.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, z\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(y, a\right)}, y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 88.6%

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

   if 3.6e62 < y < 2.19999999999999978e99

   1. Initial program 0.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 0.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 0.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y \cdot \left(y \cdot y\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{z}\right) \]

   7. Applied egg-rr 3.6%

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

   8. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{b}\right)}, z\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 51.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, b\right), z\right) \]

   10. Simplified 51.6%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+62}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2.6e+35)
     t_1
     (if (<= y 3.4e+41)
       (/
        (+ t (* y (+ 230661.510616 (* x (* y (* y y))))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2.6e+35) {
		tmp = t_1;
	} else if (y <= 3.4e+41) {
		tmp = (t + (y * (230661.510616 + (x * (y * (y * y)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-2.6d+35)) then
        tmp = t_1
    else if (y <= 3.4d+41) then
        tmp = (t + (y * (230661.510616d0 + (x * (y * (y * y)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2.6e+35) {
		tmp = t_1;
	} else if (y <= 3.4e+41) {
		tmp = (t + (y * (230661.510616 + (x * (y * (y * y)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -2.6e+35:
		tmp = t_1
	elif y <= 3.4e+41:
		tmp = (t + (y * (230661.510616 + (x * (y * (y * y)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2.6e+35)
		tmp = t_1;
	elseif (y <= 3.4e+41)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(x * Float64(y * Float64(y * y)))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -2.6e+35)
		tmp = t_1;
	elseif (y <= 3.4e+41)
		tmp = (t + (y * (230661.510616 + (x * (y * (y * y)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+35], t$95$1, If[LessEqual[y, 3.4e+41], N[(N[(t + N[(y * N[(230661.510616 + N[(x * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000007e35 or 3.39999999999999998e41 < y

   1. Initial program 6.2%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 6.2%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 66.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 66.1%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 71.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 71.0%

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

   if -2.60000000000000007e35 < y < 3.39999999999999998e41

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot {y}^{3}\right)}, \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left({y}^{3}\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right)}, y\right), c\right), y\right), i\right)\right) \]

      2. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot \left(y \cdot y\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), \color{blue}{b}\right), y\right), c\right), y\right), i\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot {y}^{2}\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), \color{blue}{b}\right), y\right), c\right), y\right), i\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      6. *-lowering-*.f64 88.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 88.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{+41}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -3.9e+34)
     t_1
     (if (<= y 1.38e+41)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* y y)))))))
        (+ i (* y (+ c (* y b)))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -3.9e+34) {
		tmp = t_1;
	} else if (y <= 1.38e+41) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-3.9d+34)) then
        tmp = t_1
    else if (y <= 1.38d+41) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (y * y))))))) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -3.9e+34) {
		tmp = t_1;
	} else if (y <= 1.38e+41) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -3.9e+34:
		tmp = t_1
	elif y <= 1.38e+41:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -3.9e+34)
		tmp = t_1;
	elseif (y <= 1.38e+41)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * Float64(y * y))))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -3.9e+34)
		tmp = t_1;
	elseif (y <= 1.38e+41)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / (i + (y * (c + (y * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+34], t$95$1, If[LessEqual[y, 1.38e+41], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.90000000000000019e34 or 1.3800000000000001e41 < y

   1. Initial program 6.2%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 6.2%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 66.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 66.1%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 71.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 71.0%

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

   if -3.90000000000000019e34 < y < 1.3800000000000001e41

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot {y}^{2}\right)}, \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left({y}^{2}\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(y, a\right)}, y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \color{blue}{a}\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      3. *-lowering-*.f64 89.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \color{blue}{a}\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 89.6%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(b \cdot y\right)}, c\right), y\right), i\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 84.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, y\right), c\right), y\right), i\right)\right) \]

   8. Simplified 84.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{+41}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -5.2e+32)
     t_1
     (if (<= y 1.06e+47)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -5.2e+32) {
		tmp = t_1;
	} else if (y <= 1.06e+47) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-5.2d+32)) then
        tmp = t_1
    else if (y <= 1.06d+47) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -5.2e+32) {
		tmp = t_1;
	} else if (y <= 1.06e+47) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -5.2e+32:
		tmp = t_1
	elif y <= 1.06e+47:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -5.2e+32)
		tmp = t_1;
	elseif (y <= 1.06e+47)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -5.2e+32)
		tmp = t_1;
	elseif (y <= 1.06e+47)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+32], t$95$1, If[LessEqual[y, 1.06e+47], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000004e32 or 1.05999999999999996e47 < y

   1. Initial program 5.4%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 5.4%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 66.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 66.6%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 71.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 71.5%

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

   if -5.2000000000000004e32 < y < 1.05999999999999996e47

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{54929528941}{2000000} \cdot y\right)}, \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right)}, y\right), c\right), y\right), i\right)\right) \]

      2. *-lowering-*.f64 82.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right)}, y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 82.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -2.5e+34)
     t_1
     (if (<= y 9e+47)
       (/
        (+ t (* y 230661.510616))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2.5e+34) {
		tmp = t_1;
	} else if (y <= 9e+47) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-2.5d+34)) then
        tmp = t_1
    else if (y <= 9d+47) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -2.5e+34) {
		tmp = t_1;
	} else if (y <= 9e+47) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -2.5e+34:
		tmp = t_1
	elif y <= 9e+47:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -2.5e+34)
		tmp = t_1;
	elseif (y <= 9e+47)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -2.5e+34)
		tmp = t_1;
	elseif (y <= 9e+47)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+34], t$95$1, If[LessEqual[y, 9e+47], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4999999999999999e34 or 8.99999999999999958e47 < y

   1. Initial program 5.4%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 5.4%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 66.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 66.6%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 71.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 71.5%

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

   if -2.4999999999999999e34 < y < 8.99999999999999958e47

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

      2. *-lowering-*.f64 81.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

   5. Simplified 81.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+44}:\\ \;\;\;\;\frac{1}{i + y \cdot \left(c + \left(y + a\right) \cdot \left(y \cdot y\right)\right)} \cdot \left(t + y \cdot 230661.510616\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -1.5e+35)
     t_1
     (if (<= y 2.8e+44)
       (*
        (/ 1.0 (+ i (* y (+ c (* (+ y a) (* y y))))))
        (+ t (* y 230661.510616)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -1.5e+35) {
		tmp = t_1;
	} else if (y <= 2.8e+44) {
		tmp = (1.0 / (i + (y * (c + ((y + a) * (y * y)))))) * (t + (y * 230661.510616));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-1.5d+35)) then
        tmp = t_1
    else if (y <= 2.8d+44) then
        tmp = (1.0d0 / (i + (y * (c + ((y + a) * (y * y)))))) * (t + (y * 230661.510616d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -1.5e+35) {
		tmp = t_1;
	} else if (y <= 2.8e+44) {
		tmp = (1.0 / (i + (y * (c + ((y + a) * (y * y)))))) * (t + (y * 230661.510616));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -1.5e+35:
		tmp = t_1
	elif y <= 2.8e+44:
		tmp = (1.0 / (i + (y * (c + ((y + a) * (y * y)))))) * (t + (y * 230661.510616))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -1.5e+35)
		tmp = t_1;
	elseif (y <= 2.8e+44)
		tmp = Float64(Float64(1.0 / Float64(i + Float64(y * Float64(c + Float64(Float64(y + a) * Float64(y * y)))))) * Float64(t + Float64(y * 230661.510616)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -1.5e+35)
		tmp = t_1;
	elseif (y <= 2.8e+44)
		tmp = (1.0 / (i + (y * (c + ((y + a) * (y * y)))))) * (t + (y * 230661.510616));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+35], t$95$1, If[LessEqual[y, 2.8e+44], N[(N[(1.0 / N[(i + N[(y * N[(c + N[(N[(y + a), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.49999999999999995e35 or 2.8000000000000001e44 < y

   1. Initial program 5.4%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 5.4%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 66.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 66.6%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 71.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 71.5%

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

   if -1.49999999999999995e35 < y < 2.8000000000000001e44

   1. Initial program 96.7%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in b around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\color{blue}{\left(y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)}, i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right)}, \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \left({y}^{2} \cdot \left(a + y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)}\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(\left({y}^{2}\right), \left(a + y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \color{blue}{\frac{54929528941}{2000000}}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(\left(y \cdot y\right), \left(a + y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(a + y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      6. +-lowering-+.f64 86.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(a, y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

   7. Simplified 86.4%

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

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(a, y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 73.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(a, y\right)\right)\right)\right), i\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{28832688827}{125000}, y\right), t\right)\right) \]

   10. Simplified 73.3%

       \[\leadsto \frac{1}{y \cdot \left(c + \left(y \cdot y\right) \cdot \left(a + y\right)\right) + i} \cdot \left(\color{blue}{230661.510616 \cdot y} + t\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+44}:\\ \;\;\;\;\frac{1}{i + y \cdot \left(c + \left(y + a\right) \cdot \left(y \cdot y\right)\right)} \cdot \left(t + y \cdot 230661.510616\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+41}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -9.5e+33)
     t_1
     (if (<= y 3.5e+41)
       (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -9.5e+33) {
		tmp = t_1;
	} else if (y <= 3.5e+41) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-9.5d+33)) then
        tmp = t_1
    else if (y <= 3.5d+41) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -9.5e+33) {
		tmp = t_1;
	} else if (y <= 3.5e+41) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -9.5e+33:
		tmp = t_1
	elif y <= 3.5e+41:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -9.5e+33)
		tmp = t_1;
	elseif (y <= 3.5e+41)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -9.5e+33)
		tmp = t_1;
	elseif (y <= 3.5e+41)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+33], t$95$1, If[LessEqual[y, 3.5e+41], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000003e33 or 3.4999999999999999e41 < y

   1. Initial program 6.2%

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

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 6.2%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 66.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 66.1%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 71.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 71.0%

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

   if -9.5000000000000003e33 < y < 3.4999999999999999e41

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{t}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 68.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+41}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -6 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \frac{-1}{\left(0 - i\right) - y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -6e-14)
     t_1
     (if (<= y 1.4e+40)
       (* t (/ -1.0 (- (- 0.0 i) (* y (+ c (* y b))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -6e-14) {
		tmp = t_1;
	} else if (y <= 1.4e+40) {
		tmp = t * (-1.0 / ((0.0 - i) - (y * (c + (y * b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-6d-14)) then
        tmp = t_1
    else if (y <= 1.4d+40) then
        tmp = t * ((-1.0d0) / ((0.0d0 - i) - (y * (c + (y * b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -6e-14) {
		tmp = t_1;
	} else if (y <= 1.4e+40) {
		tmp = t * (-1.0 / ((0.0 - i) - (y * (c + (y * b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -6e-14:
		tmp = t_1
	elif y <= 1.4e+40:
		tmp = t * (-1.0 / ((0.0 - i) - (y * (c + (y * b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -6e-14)
		tmp = t_1;
	elseif (y <= 1.4e+40)
		tmp = Float64(t * Float64(-1.0 / Float64(Float64(0.0 - i) - Float64(y * Float64(c + Float64(y * b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -6e-14)
		tmp = t_1;
	elseif (y <= 1.4e+40)
		tmp = t * (-1.0 / ((0.0 - i) - (y * (c + (y * b)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e-14], t$95$1, If[LessEqual[y, 1.4e+40], N[(t * N[(-1.0 / N[(N[(0.0 - i), $MachinePrecision] - N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.9999999999999997e-14 or 1.4000000000000001e40 < 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. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 11.9%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 62.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 62.2%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 66.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 66.9%

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

   if -5.9999999999999997e-14 < y < 1.4000000000000001e40

   1. Initial program 96.5%

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

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{t \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} - \frac{1}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   5. Simplified 93.4%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{-1}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)}, \mathsf{neg.f64}\left(t\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(\color{blue}{t}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \left(y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(y \cdot \left(a + y\right)\right)\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(a + y\right)\right)\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      8. +-lowering-+.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, y\right)\right)\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

   8. Simplified 71.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \color{blue}{\left(i + y \cdot \left(c + b \cdot y\right)\right)}\right), \mathsf{neg.f64}\left(t\right)\right) \]
   10. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \left(y \cdot \left(c + b \cdot y\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \left(c + b \cdot y\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \left(b \cdot y\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \left(y \cdot b\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

       5. *-lowering-*.f64 70.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, b\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

   11. Simplified 70.0%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \frac{-1}{\left(0 - i\right) - y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -8 \cdot 10^{-14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-122}:\\ \;\;\;\;\frac{t\_1}{i}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{t\_1}{y}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616))) (t_2 (+ x (/ z y))))
   (if (<= y -8e-14)
     t_2
     (if (<= y 2.6e-122) (/ t_1 i) (if (<= y 5.3e+38) (/ (/ t_1 y) c) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -8e-14) {
		tmp = t_2;
	} else if (y <= 2.6e-122) {
		tmp = t_1 / i;
	} else if (y <= 5.3e+38) {
		tmp = (t_1 / y) / c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    t_2 = x + (z / y)
    if (y <= (-8d-14)) then
        tmp = t_2
    else if (y <= 2.6d-122) then
        tmp = t_1 / i
    else if (y <= 5.3d+38) then
        tmp = (t_1 / y) / c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -8e-14) {
		tmp = t_2;
	} else if (y <= 2.6e-122) {
		tmp = t_1 / i;
	} else if (y <= 5.3e+38) {
		tmp = (t_1 / y) / c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	t_2 = x + (z / y)
	tmp = 0
	if y <= -8e-14:
		tmp = t_2
	elif y <= 2.6e-122:
		tmp = t_1 / i
	elif y <= 5.3e+38:
		tmp = (t_1 / y) / c
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	t_2 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -8e-14)
		tmp = t_2;
	elseif (y <= 2.6e-122)
		tmp = Float64(t_1 / i);
	elseif (y <= 5.3e+38)
		tmp = Float64(Float64(t_1 / y) / c);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	t_2 = x + (z / y);
	tmp = 0.0;
	if (y <= -8e-14)
		tmp = t_2;
	elseif (y <= 2.6e-122)
		tmp = t_1 / i;
	elseif (y <= 5.3e+38)
		tmp = (t_1 / y) / c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e-14], t$95$2, If[LessEqual[y, 2.6e-122], N[(t$95$1 / i), $MachinePrecision], If[LessEqual[y, 5.3e+38], N[(N[(t$95$1 / y), $MachinePrecision] / c), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.99999999999999999e-14 or 5.30000000000000024e38 < 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. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 11.9%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 62.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 62.2%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 66.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 66.9%

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

   if -7.99999999999999999e-14 < y < 2.59999999999999975e-122

   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 x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot {y}^{2}\right)}, \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left({y}^{2}\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(y, a\right)}, y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \color{blue}{a}\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      3. *-lowering-*.f64 97.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \color{blue}{a}\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 97.6%

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

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)}{i}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)\right), \color{blue}{i}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \left(y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)\right)\right), i\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)\right)\right), i\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \left(y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)\right)\right)\right), i\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)\right)\right)\right), i\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(x \cdot {y}^{2}\right)\right)\right)\right)\right)\right), i\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \left({y}^{2}\right)\right)\right)\right)\right)\right)\right), i\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \left(y \cdot y\right)\right)\right)\right)\right)\right)\right), i\right) \]

      9. *-lowering-*.f64 67.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right)\right)\right), i\right) \]

   8. Simplified 67.5%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\frac{28832688827}{125000}}\right)\right), i\right) \]
   10. Step-by-step derivation

   11. Simplified 67.5%

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

   if 2.59999999999999975e-122 < y < 5.30000000000000024e38

   1. Initial program 88.8%

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

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{t \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} - \frac{1}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   5. Simplified 78.7%

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

   6. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{\frac{t \cdot \left(\frac{28832688827}{125000} \cdot \frac{1}{t} + \left(\frac{1}{y} + \frac{y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{t}\right)\right)}{c}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(\frac{28832688827}{125000} \cdot \frac{1}{t} + \left(\frac{1}{y} + \frac{y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)}{t}\right)\right)\right), \color{blue}{c}\right) \]

   8. Simplified 35.8%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{t + \frac{28832688827}{125000} \cdot y}{y}\right)}, c\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(t + \frac{28832688827}{125000} \cdot y\right), y\right), c\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \left(\frac{28832688827}{125000} \cdot y\right)\right), y\right), c\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \left(y \cdot \frac{28832688827}{125000}\right)\right), y\right), c\right) \]

       4. *-lowering-*.f64 29.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right)\right), y\right), c\right) \]

   11. Simplified 29.2%

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

Alternative 13: 49.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+164}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.6e-14)
   x
   (if (<= y 4.4e+30)
     (/ t i)
     (if (<= y 2.4e+99) (* z (/ y b)) (if (<= y 2.8e+164) (/ z y) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.6e-14) {
		tmp = x;
	} else if (y <= 4.4e+30) {
		tmp = t / i;
	} else if (y <= 2.4e+99) {
		tmp = z * (y / b);
	} else if (y <= 2.8e+164) {
		tmp = z / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.6d-14)) then
        tmp = x
    else if (y <= 4.4d+30) then
        tmp = t / i
    else if (y <= 2.4d+99) then
        tmp = z * (y / b)
    else if (y <= 2.8d+164) then
        tmp = z / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.6e-14) {
		tmp = x;
	} else if (y <= 4.4e+30) {
		tmp = t / i;
	} else if (y <= 2.4e+99) {
		tmp = z * (y / b);
	} else if (y <= 2.8e+164) {
		tmp = z / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.6e-14:
		tmp = x
	elif y <= 4.4e+30:
		tmp = t / i
	elif y <= 2.4e+99:
		tmp = z * (y / b)
	elif y <= 2.8e+164:
		tmp = z / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.6e-14)
		tmp = x;
	elseif (y <= 4.4e+30)
		tmp = Float64(t / i);
	elseif (y <= 2.4e+99)
		tmp = Float64(z * Float64(y / b));
	elseif (y <= 2.8e+164)
		tmp = Float64(z / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.6e-14)
		tmp = x;
	elseif (y <= 4.4e+30)
		tmp = t / i;
	elseif (y <= 2.4e+99)
		tmp = z * (y / b);
	elseif (y <= 2.8e+164)
		tmp = z / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.6e-14], x, If[LessEqual[y, 4.4e+30], N[(t / i), $MachinePrecision], If[LessEqual[y, 2.4e+99], N[(z * N[(y / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+164], N[(z / y), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.59999999999999997e-14 or 2.8000000000000002e164 < y

   1. Initial program 12.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 54.0%

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

   if -2.59999999999999997e-14 < y < 4.4e30

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 47.7%

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{i}\right) \]

   5. Simplified 47.7%

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

   if 4.4e30 < y < 2.4000000000000001e99

   1. Initial program 20.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 4.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 4.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y \cdot \left(y \cdot y\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{z}\right) \]

   7. Applied egg-rr 6.6%

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

   8. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{b}\right)}, z\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 41.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, b\right), z\right) \]

   10. Simplified 41.4%

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

   if 2.4000000000000001e99 < y < 2.8000000000000002e164

   1. Initial program 0.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 0.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 0.4%

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

   6. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 61.8%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{y}\right) \]

   8. Simplified 61.8%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+164}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+164}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -8.5e-14)
   x
   (if (<= y 1.8e-80)
     (/ t i)
     (if (<= y 3.4e+99) (/ z a) (if (<= y 7.5e+164) (/ z y) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -8.5e-14) {
		tmp = x;
	} else if (y <= 1.8e-80) {
		tmp = t / i;
	} else if (y <= 3.4e+99) {
		tmp = z / a;
	} else if (y <= 7.5e+164) {
		tmp = z / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-8.5d-14)) then
        tmp = x
    else if (y <= 1.8d-80) then
        tmp = t / i
    else if (y <= 3.4d+99) then
        tmp = z / a
    else if (y <= 7.5d+164) then
        tmp = z / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -8.5e-14) {
		tmp = x;
	} else if (y <= 1.8e-80) {
		tmp = t / i;
	} else if (y <= 3.4e+99) {
		tmp = z / a;
	} else if (y <= 7.5e+164) {
		tmp = z / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -8.5e-14:
		tmp = x
	elif y <= 1.8e-80:
		tmp = t / i
	elif y <= 3.4e+99:
		tmp = z / a
	elif y <= 7.5e+164:
		tmp = z / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -8.5e-14)
		tmp = x;
	elseif (y <= 1.8e-80)
		tmp = Float64(t / i);
	elseif (y <= 3.4e+99)
		tmp = Float64(z / a);
	elseif (y <= 7.5e+164)
		tmp = Float64(z / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -8.5e-14)
		tmp = x;
	elseif (y <= 1.8e-80)
		tmp = t / i;
	elseif (y <= 3.4e+99)
		tmp = z / a;
	elseif (y <= 7.5e+164)
		tmp = z / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -8.5e-14], x, If[LessEqual[y, 1.8e-80], N[(t / i), $MachinePrecision], If[LessEqual[y, 3.4e+99], N[(z / a), $MachinePrecision], If[LessEqual[y, 7.5e+164], N[(z / y), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.50000000000000038e-14 or 7.49999999999999976e164 < y

   1. Initial program 12.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 54.0%

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

   if -8.50000000000000038e-14 < y < 1.8e-80

   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

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

      1. /-lowering-/.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{i}\right) \]

   5. Simplified 58.3%

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

   if 1.8e-80 < y < 3.39999999999999984e99

   1. Initial program 63.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 17.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 17.0%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 18.1%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{a}\right) \]

   8. Simplified 18.1%

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

   if 3.39999999999999984e99 < y < 7.49999999999999976e164

   1. Initial program 0.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 0.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 0.4%

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

   6. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 61.8%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{y}\right) \]

   8. Simplified 61.8%

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

Alternative 15: 65.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \frac{-1}{y \cdot \left(0 - c\right) - i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -8.5e-14)
     t_1
     (if (<= y 3.5e+41) (* t (/ -1.0 (- (* y (- 0.0 c)) i))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -8.5e-14) {
		tmp = t_1;
	} else if (y <= 3.5e+41) {
		tmp = t * (-1.0 / ((y * (0.0 - c)) - i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-8.5d-14)) then
        tmp = t_1
    else if (y <= 3.5d+41) then
        tmp = t * ((-1.0d0) / ((y * (0.0d0 - c)) - i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -8.5e-14) {
		tmp = t_1;
	} else if (y <= 3.5e+41) {
		tmp = t * (-1.0 / ((y * (0.0 - c)) - i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -8.5e-14:
		tmp = t_1
	elif y <= 3.5e+41:
		tmp = t * (-1.0 / ((y * (0.0 - c)) - i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -8.5e-14)
		tmp = t_1;
	elseif (y <= 3.5e+41)
		tmp = Float64(t * Float64(-1.0 / Float64(Float64(y * Float64(0.0 - c)) - i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -8.5e-14)
		tmp = t_1;
	elseif (y <= 3.5e+41)
		tmp = t * (-1.0 / ((y * (0.0 - c)) - i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e-14], t$95$1, If[LessEqual[y, 3.5e+41], N[(t * N[(-1.0 / N[(N[(y * N[(0.0 - c), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.50000000000000038e-14 or 3.4999999999999999e41 < 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. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 11.9%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 62.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 62.2%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 66.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 66.9%

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

   if -8.50000000000000038e-14 < y < 3.4999999999999999e41

   1. Initial program 96.5%

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

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{t \cdot \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)} - \frac{1}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   5. Simplified 93.4%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{-1}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)}, \mathsf{neg.f64}\left(t\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \left(i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(\color{blue}{t}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \left(y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(y \cdot \left(a + y\right)\right)\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(a + y\right)\right)\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

      8. +-lowering-+.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, y\right)\right)\right)\right)\right)\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

   8. Simplified 71.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \color{blue}{\left(i + c \cdot y\right)}\right), \mathsf{neg.f64}\left(t\right)\right) \]
   10. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \left(c \cdot y\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \left(y \cdot c\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

       3. *-lowering-*.f64 64.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(i, \mathsf{*.f64}\left(y, c\right)\right)\right), \mathsf{neg.f64}\left(t\right)\right) \]

   11. Simplified 64.1%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \frac{-1}{y \cdot \left(0 - c\right) - i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -6 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -6e-14)
     t_1
     (if (<= y 8.5e-8)
       (/ (+ t (* y 230661.510616)) i)
       (if (<= y 2.2e+99) (* z (/ y b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -6e-14) {
		tmp = t_1;
	} else if (y <= 8.5e-8) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 2.2e+99) {
		tmp = z * (y / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-6d-14)) then
        tmp = t_1
    else if (y <= 8.5d-8) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 2.2d+99) then
        tmp = z * (y / b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -6e-14) {
		tmp = t_1;
	} else if (y <= 8.5e-8) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 2.2e+99) {
		tmp = z * (y / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -6e-14:
		tmp = t_1
	elif y <= 8.5e-8:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 2.2e+99:
		tmp = z * (y / b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -6e-14)
		tmp = t_1;
	elseif (y <= 8.5e-8)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 2.2e+99)
		tmp = Float64(z * Float64(y / b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -6e-14)
		tmp = t_1;
	elseif (y <= 8.5e-8)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 2.2e+99)
		tmp = z * (y / b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e-14], t$95$1, If[LessEqual[y, 8.5e-8], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 2.2e+99], N[(z * N[(y / b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.9999999999999997e-14 or 2.19999999999999978e99 < 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. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 11.5%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 67.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 67.8%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 73.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 73.0%

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

   if -5.9999999999999997e-14 < y < 8.49999999999999935e-8

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot {y}^{2}\right)}, \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left({y}^{2}\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(y, a\right)}, y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \color{blue}{a}\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      3. *-lowering-*.f64 93.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \color{blue}{a}\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 93.9%

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

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)}{i}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)\right), \color{blue}{i}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \left(y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)\right)\right), i\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)\right)\right), i\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \left(y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)\right)\right)\right), i\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)\right)\right)\right), i\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(x \cdot {y}^{2}\right)\right)\right)\right)\right)\right), i\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \left({y}^{2}\right)\right)\right)\right)\right)\right)\right), i\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \left(y \cdot y\right)\right)\right)\right)\right)\right)\right), i\right) \]

      9. *-lowering-*.f64 58.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right)\right)\right), i\right) \]

   8. Simplified 58.9%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\frac{28832688827}{125000}}\right)\right), i\right) \]
   10. Step-by-step derivation

   11. Simplified 58.1%

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

   if 8.49999999999999935e-8 < y < 2.19999999999999978e99

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 11.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 11.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y \cdot \left(y \cdot y\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{z}\right) \]

   7. Applied egg-rr 16.4%

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

   8. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{b}\right)}, z\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 25.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, b\right), z\right) \]

   10. Simplified 25.7%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 56.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -4.8e-14)
     t_1
     (if (<= y 4.7e+30) (/ t i) (if (<= y 2.2e+99) (* z (/ y b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -4.8e-14) {
		tmp = t_1;
	} else if (y <= 4.7e+30) {
		tmp = t / i;
	} else if (y <= 2.2e+99) {
		tmp = z * (y / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-4.8d-14)) then
        tmp = t_1
    else if (y <= 4.7d+30) then
        tmp = t / i
    else if (y <= 2.2d+99) then
        tmp = z * (y / b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -4.8e-14) {
		tmp = t_1;
	} else if (y <= 4.7e+30) {
		tmp = t / i;
	} else if (y <= 2.2e+99) {
		tmp = z * (y / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -4.8e-14:
		tmp = t_1
	elif y <= 4.7e+30:
		tmp = t / i
	elif y <= 2.2e+99:
		tmp = z * (y / b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -4.8e-14)
		tmp = t_1;
	elseif (y <= 4.7e+30)
		tmp = Float64(t / i);
	elseif (y <= 2.2e+99)
		tmp = Float64(z * Float64(y / b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -4.8e-14)
		tmp = t_1;
	elseif (y <= 4.7e+30)
		tmp = t / i;
	elseif (y <= 2.2e+99)
		tmp = z * (y / b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e-14], t$95$1, If[LessEqual[y, 4.7e+30], N[(t / i), $MachinePrecision], If[LessEqual[y, 2.2e+99], N[(z * N[(y / b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8e-14 or 2.19999999999999978e99 < 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. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 11.5%

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

   5. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 67.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   7. Simplified 67.8%

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

   8. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      2. /-lowering-/.f64 73.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 73.0%

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

   if -4.8e-14 < y < 4.6999999999999999e30

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 47.7%

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{i}\right) \]

   5. Simplified 47.7%

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

   if 4.6999999999999999e30 < y < 2.19999999999999978e99

   1. Initial program 20.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 4.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 4.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y \cdot \left(y \cdot y\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{z}\right) \]

   7. Applied egg-rr 6.6%

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

   8. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{b}\right)}, z\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 41.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, b\right), z\right) \]

   10. Simplified 41.4%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \frac{y}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -9.5e-18)
   x
   (if (<= y 1.8e-80) (/ t i) (if (<= y 2.2e+99) (/ z a) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -9.5e-18) {
		tmp = x;
	} else if (y <= 1.8e-80) {
		tmp = t / i;
	} else if (y <= 2.2e+99) {
		tmp = z / a;
	} 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 <= (-9.5d-18)) then
        tmp = x
    else if (y <= 1.8d-80) then
        tmp = t / i
    else if (y <= 2.2d+99) then
        tmp = z / a
    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 <= -9.5e-18) {
		tmp = x;
	} else if (y <= 1.8e-80) {
		tmp = t / i;
	} else if (y <= 2.2e+99) {
		tmp = z / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -9.5e-18:
		tmp = x
	elif y <= 1.8e-80:
		tmp = t / i
	elif y <= 2.2e+99:
		tmp = z / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -9.5e-18)
		tmp = x;
	elseif (y <= 1.8e-80)
		tmp = Float64(t / i);
	elseif (y <= 2.2e+99)
		tmp = Float64(z / a);
	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 <= -9.5e-18)
		tmp = x;
	elseif (y <= 1.8e-80)
		tmp = t / i;
	elseif (y <= 2.2e+99)
		tmp = z / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -9.5e-18], x, If[LessEqual[y, 1.8e-80], N[(t / i), $MachinePrecision], If[LessEqual[y, 2.2e+99], N[(z / a), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5000000000000003e-18 or 2.19999999999999978e99 < 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

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 50.1%

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

   if -9.5000000000000003e-18 < y < 1.8e-80

   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

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

      1. /-lowering-/.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{i}\right) \]

   5. Simplified 58.3%

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

   if 1.8e-80 < y < 2.19999999999999978e99

   1. Initial program 63.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 17.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 17.0%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 18.1%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{a}\right) \]

   8. Simplified 18.1%

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

Alternative 19: 51.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.8e-14) x (if (<= y 4.6e-5) (/ 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 <= -5.8e-14) {
		tmp = x;
	} else if (y <= 4.6e-5) {
		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 <= (-5.8d-14)) then
        tmp = x
    else if (y <= 4.6d-5) 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 <= -5.8e-14) {
		tmp = x;
	} else if (y <= 4.6e-5) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.8e-14:
		tmp = x
	elif y <= 4.6e-5:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.8e-14)
		tmp = x;
	elseif (y <= 4.6e-5)
		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 <= -5.8e-14)
		tmp = x;
	elseif (y <= 4.6e-5)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.8e-14], x, If[LessEqual[y, 4.6e-5], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000005e-14 or 4.6e-5 < y

   1. Initial program 15.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 42.7%

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

   if -5.8000000000000005e-14 < y < 4.6e-5

   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

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

      1. /-lowering-/.f64 50.7%

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{i}\right) \]

   5. Simplified 50.7%

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

Alternative 20: 25.1% 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 53.6%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 24.9%

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

Reproduce

herbie shell --seed 2024161 
(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)))