Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 57.4% → 81.0%

Time: 18.8s

Alternatives: 23

Speedup: 1.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 57.4% 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: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.7e+83)
   (+ x (/ (- z (* x a)) y))
   (if (<= y 1.45e+66)
     (/
      (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
      (+ (* y (+ (* y (+ b (* y (+ y a)))) c)) i))
     (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.7e+83) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 1.45e+66) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / 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 <= (-1.7d+83)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 1.45d+66) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / ((y * ((y * (b + (y * (y + a)))) + c)) + i)
    else
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / 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 <= -1.7e+83) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 1.45e+66) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.7e+83:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 1.45e+66:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * ((y * (b + (y * (y + a)))) + c)) + i)
	else:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.7e+83)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 1.45e+66)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c)) + i));
	else
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.7e+83)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 1.45e+66)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	else
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.7e+83], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+66], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6999999999999999e83

   1. Initial program 2.2%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 54.4%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 76.1%

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

   8. Simplified 76.1%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -1.6999999999999999e83 < y < 1.44999999999999993e66

   1. Initial program 92.2%

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

   if 1.44999999999999993e66 < y

   1. Initial program 0.2%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.2%

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

      1. div-inv N/A

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

      2. frac-2neg N/A

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

      3. metadata-eval N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

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

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

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

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

   6. Applied egg-rr 0.2%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(-1, \color{blue}{\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} - \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right), \color{blue}{\left(\frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y}\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      3. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      12. /-lowering-/.f64 72.5%

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 72.5%

      \[\leadsto \frac{-1}{\color{blue}{\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y} - \frac{1}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + \left(y \cdot y\right) \cdot t\_1}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-61}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot t\_1 + c\right) + i}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ i (* (* y y) t_1)))))
   (if (<= y -1.7e+83)
     (+ x (/ (- z (* x a)) y))
     (if (<= y -6.5e-34)
       t_2
       (if (<= y 2.3e-61)
         (/
          (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
          (+ (* y (+ (* y t_1) c)) i))
         (if (<= y 1.5e+66)
           t_2
           (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + ((y * y) * t_1));
	double tmp;
	if (y <= -1.7e+83) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -6.5e-34) {
		tmp = t_2;
	} else if (y <= 2.3e-61) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * t_1) + c)) + i);
	} else if (y <= 1.5e+66) {
		tmp = t_2;
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b + (y * (y + a))
    t_2 = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + ((y * y) * t_1))
    if (y <= (-1.7d+83)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= (-6.5d-34)) then
        tmp = t_2
    else if (y <= 2.3d-61) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * t_1) + c)) + i)
    else if (y <= 1.5d+66) then
        tmp = t_2
    else
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / 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 t_1 = b + (y * (y + a));
	double t_2 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + ((y * y) * t_1));
	double tmp;
	if (y <= -1.7e+83) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -6.5e-34) {
		tmp = t_2;
	} else if (y <= 2.3e-61) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * t_1) + c)) + i);
	} else if (y <= 1.5e+66) {
		tmp = t_2;
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b + (y * (y + a))
	t_2 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + ((y * y) * t_1))
	tmp = 0
	if y <= -1.7e+83:
		tmp = x + ((z - (x * a)) / y)
	elif y <= -6.5e-34:
		tmp = t_2
	elif y <= 2.3e-61:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * t_1) + c)) + i)
	elif y <= 1.5e+66:
		tmp = t_2
	else:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b + Float64(y * Float64(y + a)))
	t_2 = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(Float64(y * y) * t_1)))
	tmp = 0.0
	if (y <= -1.7e+83)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= -6.5e-34)
		tmp = t_2;
	elseif (y <= 2.3e-61)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(Float64(y * t_1) + c)) + i));
	elseif (y <= 1.5e+66)
		tmp = t_2;
	else
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b + (y * (y + a));
	t_2 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + ((y * y) * t_1));
	tmp = 0.0;
	if (y <= -1.7e+83)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= -6.5e-34)
		tmp = t_2;
	elseif (y <= 2.3e-61)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * t_1) + c)) + i);
	elseif (y <= 1.5e+66)
		tmp = t_2;
	else
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(N[(y * y), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+83], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-34], t$95$2, If[LessEqual[y, 2.3e-61], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * t$95$1), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+66], t$95$2, N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6999999999999999e83

   1. Initial program 2.2%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 54.4%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 76.1%

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

   8. Simplified 76.1%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -1.6999999999999999e83 < y < -6.49999999999999985e-34 or 2.29999999999999992e-61 < y < 1.50000000000000001e66

   1. Initial program 77.9%

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

   3. Taylor expanded in c around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

   5. Simplified 65.7%

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

   if -6.49999999999999985e-34 < y < 2.29999999999999992e-61

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{54929528941}{2000000} \cdot y\right)}, \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 98.0%

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

   5. Simplified 98.0%

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

   if 1.50000000000000001e66 < y

   1. Initial program 0.2%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.2%

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

      1. div-inv N/A

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

      2. frac-2neg N/A

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

      3. metadata-eval N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

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

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

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

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

   6. Applied egg-rr 0.2%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(-1, \color{blue}{\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} - \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right), \color{blue}{\left(\frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y}\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      3. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      12. /-lowering-/.f64 72.5%

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 72.5%

      \[\leadsto \frac{-1}{\color{blue}{\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y} - \frac{1}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + \left(y \cdot y\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-61}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + \left(y \cdot y\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{-1}{\left(y \cdot \left(y \cdot t\_1 + c\right) + i\right) \cdot \frac{-1}{t + y \cdot \left(230661.510616 + x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right)}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + \left(y \cdot y\right) \cdot t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a)))))
   (if (<= y -1.7e+83)
     (+ x (/ (- z (* x a)) y))
     (if (<= y 8.8e-41)
       (/
        -1.0
        (*
         (+ (* y (+ (* y t_1) c)) i)
         (/ -1.0 (+ t (* y (+ 230661.510616 (* x (* y (* y y)))))))))
       (if (<= y 1.5e+66)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ i (* (* y y) t_1)))
         (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double tmp;
	if (y <= -1.7e+83) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 8.8e-41) {
		tmp = -1.0 / (((y * ((y * t_1) + c)) + i) * (-1.0 / (t + (y * (230661.510616 + (x * (y * (y * y))))))));
	} else if (y <= 1.5e+66) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + ((y * y) * t_1));
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = b + (y * (y + a))
    if (y <= (-1.7d+83)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 8.8d-41) then
        tmp = (-1.0d0) / (((y * ((y * t_1) + c)) + i) * ((-1.0d0) / (t + (y * (230661.510616d0 + (x * (y * (y * y))))))))
    else if (y <= 1.5d+66) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + ((y * y) * t_1))
    else
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / 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 t_1 = b + (y * (y + a));
	double tmp;
	if (y <= -1.7e+83) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 8.8e-41) {
		tmp = -1.0 / (((y * ((y * t_1) + c)) + i) * (-1.0 / (t + (y * (230661.510616 + (x * (y * (y * y))))))));
	} else if (y <= 1.5e+66) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + ((y * y) * t_1));
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b + (y * (y + a))
	tmp = 0
	if y <= -1.7e+83:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 8.8e-41:
		tmp = -1.0 / (((y * ((y * t_1) + c)) + i) * (-1.0 / (t + (y * (230661.510616 + (x * (y * (y * y))))))))
	elif y <= 1.5e+66:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + ((y * y) * t_1))
	else:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b + Float64(y * Float64(y + a)))
	tmp = 0.0
	if (y <= -1.7e+83)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 8.8e-41)
		tmp = Float64(-1.0 / Float64(Float64(Float64(y * Float64(Float64(y * t_1) + c)) + i) * Float64(-1.0 / Float64(t + Float64(y * Float64(230661.510616 + Float64(x * Float64(y * Float64(y * y)))))))));
	elseif (y <= 1.5e+66)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(Float64(y * y) * t_1)));
	else
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b + (y * (y + a));
	tmp = 0.0;
	if (y <= -1.7e+83)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 8.8e-41)
		tmp = -1.0 / (((y * ((y * t_1) + c)) + i) * (-1.0 / (t + (y * (230661.510616 + (x * (y * (y * y))))))));
	elseif (y <= 1.5e+66)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + ((y * y) * t_1));
	else
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+83], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e-41], N[(-1.0 / N[(N[(N[(y * N[(N[(y * t$95$1), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision] * N[(-1.0 / N[(t + N[(y * N[(230661.510616 + N[(x * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+66], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(N[(y * y), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6999999999999999e83

   1. Initial program 2.2%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 54.4%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 76.1%

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

   8. Simplified 76.1%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -1.6999999999999999e83 < y < 8.7999999999999999e-41

   1. Initial program 93.7%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 93.5%

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

      1. div-inv N/A

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

      2. frac-2neg N/A

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

      3. metadata-eval N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

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

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

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

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

   6. Applied egg-rr 93.0%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\color{blue}{\left(x \cdot {y}^{3}\right)}, \frac{28832688827}{125000}\right)\right), t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right)\right)\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{*.f64}\left(\mathsf{/.f64}\left(-1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left({y}^{3}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right)}, b\right)\right), c\right)\right), i\right)\right)\right) \]

      2. cube-mult N/A

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

      3. unpow2 N/A

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 87.4%

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

   9. Simplified 87.4%

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

   if 8.7999999999999999e-41 < y < 1.50000000000000001e66

   1. Initial program 85.2%

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

   3. Taylor expanded in c around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

   5. Simplified 74.2%

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

   if 1.50000000000000001e66 < y

   1. Initial program 0.2%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.2%

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

      1. div-inv N/A

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

      2. frac-2neg N/A

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

      3. metadata-eval N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

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

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

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

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

   6. Applied egg-rr 0.2%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(-1, \color{blue}{\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} - \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right), \color{blue}{\left(\frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y}\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      3. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      12. /-lowering-/.f64 72.5%

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 72.5%

      \[\leadsto \frac{-1}{\color{blue}{\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y} - \frac{1}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{-1}{\left(y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i\right) \cdot \frac{-1}{t + y \cdot \left(230661.510616 + x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right)}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + \left(y \cdot y\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t\_1}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+30}:\\ \;\;\;\;\frac{t + y \cdot \left(z \cdot \left(y \cdot y\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ b (* y (+ y a)))) c)) i)))
   (if (<= y -7.6e+63)
     (+ x (/ (- z (* x a)) y))
     (if (<= y 3.6e-93)
       (/ (+ t (* y 230661.510616)) t_1)
       (if (<= y 5e+30)
         (/ (+ t (* y (* z (* y y)))) t_1)
         (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * (b + (y * (y + a)))) + c)) + i;
	double tmp;
	if (y <= -7.6e+63) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 3.6e-93) {
		tmp = (t + (y * 230661.510616)) / t_1;
	} else if (y <= 5e+30) {
		tmp = (t + (y * (z * (y * y)))) / t_1;
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = (y * ((y * (b + (y * (y + a)))) + c)) + i
    if (y <= (-7.6d+63)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 3.6d-93) then
        tmp = (t + (y * 230661.510616d0)) / t_1
    else if (y <= 5d+30) then
        tmp = (t + (y * (z * (y * y)))) / t_1
    else
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / 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 t_1 = (y * ((y * (b + (y * (y + a)))) + c)) + i;
	double tmp;
	if (y <= -7.6e+63) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 3.6e-93) {
		tmp = (t + (y * 230661.510616)) / t_1;
	} else if (y <= 5e+30) {
		tmp = (t + (y * (z * (y * y)))) / t_1;
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * (b + (y * (y + a)))) + c)) + i
	tmp = 0
	if y <= -7.6e+63:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 3.6e-93:
		tmp = (t + (y * 230661.510616)) / t_1
	elif y <= 5e+30:
		tmp = (t + (y * (z * (y * y)))) / t_1
	else:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c)) + i)
	tmp = 0.0
	if (y <= -7.6e+63)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 3.6e-93)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / t_1);
	elseif (y <= 5e+30)
		tmp = Float64(Float64(t + Float64(y * Float64(z * Float64(y * y)))) / t_1);
	else
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * (b + (y * (y + a)))) + c)) + i;
	tmp = 0.0;
	if (y <= -7.6e+63)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 3.6e-93)
		tmp = (t + (y * 230661.510616)) / t_1;
	elseif (y <= 5e+30)
		tmp = (t + (y * (z * (y * y)))) / t_1;
	else
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -7.6e+63], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-93], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 5e+30], N[(N[(t + N[(y * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.6000000000000002e63

   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. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 51.4%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 70.8%

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

   8. Simplified 70.8%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -7.6000000000000002e63 < y < 3.6000000000000002e-93

   1. Initial program 95.4%

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

   3. Taylor expanded in y around 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 87.1%

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

   5. Simplified 87.1%

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

   if 3.6000000000000002e-93 < y < 4.9999999999999998e30

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

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

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

      3. unpow2 N/A

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

      4. *-lowering-*.f64 77.6%

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

   5. Simplified 77.6%

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

   if 4.9999999999999998e30 < y

   1. Initial program 8.2%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 8.2%

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

      1. div-inv N/A

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

      2. frac-2neg N/A

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

      3. metadata-eval N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

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

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

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

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

   6. Applied egg-rr 8.2%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(-1, \color{blue}{\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} - \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right), \color{blue}{\left(\frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y}\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      3. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      12. /-lowering-/.f64 64.5%

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 64.5%

      \[\leadsto \frac{-1}{\color{blue}{\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y} - \frac{1}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+30}:\\ \;\;\;\;\frac{t + y \cdot \left(z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i\\ \mathbf{if}\;y \leq -6 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t\_1}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+31}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ b (* y (+ y a)))) c)) i)))
   (if (<= y -6e+63)
     (+ x (/ (- z (* x a)) y))
     (if (<= y 3.3e-6)
       (/ (+ t (* y 230661.510616)) t_1)
       (if (<= y 1.15e+31)
         (/ (* z (* y (* y y))) t_1)
         (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * (b + (y * (y + a)))) + c)) + i;
	double tmp;
	if (y <= -6e+63) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 3.3e-6) {
		tmp = (t + (y * 230661.510616)) / t_1;
	} else if (y <= 1.15e+31) {
		tmp = (z * (y * (y * y))) / t_1;
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = (y * ((y * (b + (y * (y + a)))) + c)) + i
    if (y <= (-6d+63)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 3.3d-6) then
        tmp = (t + (y * 230661.510616d0)) / t_1
    else if (y <= 1.15d+31) then
        tmp = (z * (y * (y * y))) / t_1
    else
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / 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 t_1 = (y * ((y * (b + (y * (y + a)))) + c)) + i;
	double tmp;
	if (y <= -6e+63) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 3.3e-6) {
		tmp = (t + (y * 230661.510616)) / t_1;
	} else if (y <= 1.15e+31) {
		tmp = (z * (y * (y * y))) / t_1;
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * (b + (y * (y + a)))) + c)) + i
	tmp = 0
	if y <= -6e+63:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 3.3e-6:
		tmp = (t + (y * 230661.510616)) / t_1
	elif y <= 1.15e+31:
		tmp = (z * (y * (y * y))) / t_1
	else:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c)) + i)
	tmp = 0.0
	if (y <= -6e+63)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 3.3e-6)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / t_1);
	elseif (y <= 1.15e+31)
		tmp = Float64(Float64(z * Float64(y * Float64(y * y))) / t_1);
	else
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * (b + (y * (y + a)))) + c)) + i;
	tmp = 0.0;
	if (y <= -6e+63)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 3.3e-6)
		tmp = (t + (y * 230661.510616)) / t_1;
	elseif (y <= 1.15e+31)
		tmp = (z * (y * (y * y))) / t_1;
	else
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -6e+63], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-6], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 1.15e+31], N[(N[(z * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.99999999999999998e63

   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. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 51.4%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 70.8%

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

   8. Simplified 70.8%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -5.99999999999999998e63 < y < 3.30000000000000017e-6

   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 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 85.9%

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

   5. Simplified 85.9%

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

   if 3.30000000000000017e-6 < y < 1.15e31

   1. Initial program 99.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   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 65.7%

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

   5. Simplified 65.7%

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

   if 1.15e31 < y

   1. Initial program 8.2%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 8.2%

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

      1. div-inv N/A

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

      2. frac-2neg N/A

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

      3. metadata-eval N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

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

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

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

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

   6. Applied egg-rr 8.2%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(-1, \color{blue}{\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} - \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right), \color{blue}{\left(\frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y}\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      3. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      12. /-lowering-/.f64 64.5%

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 64.5%

      \[\leadsto \frac{-1}{\color{blue}{\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y} - \frac{1}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+31}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+30}:\\ \;\;\;\;\frac{t + y \cdot \left(z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.4e+63)
   (+ x (/ (- z (* x a)) y))
   (if (<= y 2.8e-8)
     (/ (+ t (* y 230661.510616)) (+ (* y (+ (* y (+ b (* y (+ y a)))) c)) i))
     (if (<= y 2e+30)
       (/ (+ t (* y (* z (* y y)))) (+ i (* y (+ c (* a (* y y))))))
       (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.4e+63) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 2.8e-8) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	} else if (y <= 2e+30) {
		tmp = (t + (y * (z * (y * y)))) / (i + (y * (c + (a * (y * y)))));
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-6.4d+63)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 2.8d-8) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * (b + (y * (y + a)))) + c)) + i)
    else if (y <= 2d+30) then
        tmp = (t + (y * (z * (y * y)))) / (i + (y * (c + (a * (y * y)))))
    else
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.4e+63) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 2.8e-8) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	} else if (y <= 2e+30) {
		tmp = (t + (y * (z * (y * y)))) / (i + (y * (c + (a * (y * y)))));
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.4e+63:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 2.8e-8:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * (b + (y * (y + a)))) + c)) + i)
	elif y <= 2e+30:
		tmp = (t + (y * (z * (y * y)))) / (i + (y * (c + (a * (y * y)))))
	else:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.4e+63)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 2.8e-8)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c)) + i));
	elseif (y <= 2e+30)
		tmp = Float64(Float64(t + Float64(y * Float64(z * Float64(y * y)))) / Float64(i + Float64(y * Float64(c + Float64(a * Float64(y * y))))));
	else
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -6.4e+63)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 2.8e-8)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	elseif (y <= 2e+30)
		tmp = (t + (y * (z * (y * y)))) / (i + (y * (c + (a * (y * y)))));
	else
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.4e+63], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-8], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+30], N[(N[(t + N[(y * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.40000000000000022e63

   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. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 51.4%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 70.8%

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

   8. Simplified 70.8%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -6.40000000000000022e63 < y < 2.7999999999999999e-8

   1. Initial program 95.9%

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

   3. Taylor expanded in 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 85.6%

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

   5. Simplified 85.6%

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

   if 2.7999999999999999e-8 < y < 2e30

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

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

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

      3. unpow2 N/A

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

      4. *-lowering-*.f64 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, y\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(a \cdot {y}^{2}\right)}, c\right), y\right), i\right)\right) \]
   7. Step-by-step derivation

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 70.1%

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

   8. Simplified 70.1%

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

   if 2e30 < y

   1. Initial program 8.2%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 8.2%

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

      1. div-inv N/A

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

      2. frac-2neg N/A

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

      3. metadata-eval N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

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

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

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

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

   6. Applied egg-rr 8.2%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(-1, \color{blue}{\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} - \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right), \color{blue}{\left(\frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y}\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      3. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      12. /-lowering-/.f64 64.5%

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 64.5%

      \[\leadsto \frac{-1}{\color{blue}{\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y} - \frac{1}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+30}:\\ \;\;\;\;\frac{t + y \cdot \left(z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.8e+64)
   (+ x (/ (- z (* x a)) y))
   (if (<= y 1.45e+66)
     (/
      (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
      (+ (* y (+ (* y (+ b (* y (+ y a)))) c)) i))
     (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.8e+64) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 1.45e+66) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / 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 <= (-1.8d+64)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 1.45d+66) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * (b + (y * (y + a)))) + c)) + i)
    else
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / 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 <= -1.8e+64) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 1.45e+66) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.8e+64:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 1.45e+66:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * (b + (y * (y + a)))) + c)) + i)
	else:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.8e+64)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 1.45e+66)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c)) + i));
	else
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.8e+64)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 1.45e+66)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	else
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.8e+64], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+66], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000007e64

   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. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 51.4%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 70.8%

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

   8. Simplified 70.8%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -1.80000000000000007e64 < y < 1.44999999999999993e66

   1. Initial program 93.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{54929528941}{2000000} \cdot y\right)}, \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 80.9%

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

   5. Simplified 80.9%

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

   if 1.44999999999999993e66 < y

   1. Initial program 0.2%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.2%

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

      1. div-inv N/A

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

      2. frac-2neg N/A

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

      3. metadata-eval N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

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

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

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

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

   6. Applied egg-rr 0.2%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(-1, \color{blue}{\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} - \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right), \color{blue}{\left(\frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y}\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      3. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      12. /-lowering-/.f64 72.5%

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 72.5%

      \[\leadsto \frac{-1}{\color{blue}{\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y} - \frac{1}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+199}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+30}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x)))))
   (if (<= y -9.5e+199)
     (+ x (/ (- z (* x a)) y))
     (if (<= y -2e+21)
       t_1
       (if (<= y 1.75e+30)
         (/ (+ t (* y 230661.510616)) (+ 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 = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	double tmp;
	if (y <= -9.5e+199) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -2e+21) {
		tmp = t_1;
	} else if (y <= 1.75e+30) {
		tmp = (t + (y * 230661.510616)) / (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 = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / x))
    if (y <= (-9.5d+199)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= (-2d+21)) then
        tmp = t_1
    else if (y <= 1.75d+30) then
        tmp = (t + (y * 230661.510616d0)) / (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 = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	double tmp;
	if (y <= -9.5e+199) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -2e+21) {
		tmp = t_1;
	} else if (y <= 1.75e+30) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	tmp = 0
	if y <= -9.5e+199:
		tmp = x + ((z - (x * a)) / y)
	elif y <= -2e+21:
		tmp = t_1
	elif y <= 1.75e+30:
		tmp = (t + (y * 230661.510616)) / (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(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)))
	tmp = 0.0
	if (y <= -9.5e+199)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= -2e+21)
		tmp = t_1;
	elseif (y <= 1.75e+30)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / 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 = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	tmp = 0.0;
	if (y <= -9.5e+199)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= -2e+21)
		tmp = t_1;
	elseif (y <= 1.75e+30)
		tmp = (t + (y * 230661.510616)) / (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[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+199], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e+21], t$95$1, If[LessEqual[y, 1.75e+30], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.49999999999999954e199

   1. Initial program 0.0%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 62.7%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 88.7%

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

   8. Simplified 88.7%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -9.49999999999999954e199 < y < -2e21 or 1.75000000000000011e30 < y

   1. Initial program 12.9%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 12.9%

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

      1. div-inv N/A

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

      2. frac-2neg N/A

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

      3. metadata-eval N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

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

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

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

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

   6. Applied egg-rr 12.9%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(-1, \color{blue}{\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} - \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right), \color{blue}{\left(\frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y}\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      3. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      12. /-lowering-/.f64 60.4%

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 60.4%

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

   if -2e21 < y < 1.75000000000000011e30

   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

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 80.2%

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

   8. Simplified 80.2%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+199}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+21}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+30}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.8e+63)
   (+ x (/ (- z (* x a)) y))
   (if (<= y 3.8e+40)
     (/ (+ t (* y 230661.510616)) (+ (* y (+ (* y (+ b (* y (+ y a)))) c)) i))
     (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 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+63) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 3.8e+40) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / 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+63)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 3.8d+40) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * (b + (y * (y + a)))) + c)) + i)
    else
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / 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+63) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 3.8e+40) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	} else {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.8e+63:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 3.8e+40:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * (b + (y * (y + a)))) + c)) + i)
	else:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.8e+63)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 3.8e+40)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c)) + i));
	else
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / 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+63)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 3.8e+40)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * (b + (y * (y + a)))) + c)) + i);
	else
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.8e+63], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+40], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999999e63

   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. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 51.4%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 70.8%

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

   8. Simplified 70.8%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -5.7999999999999999e63 < y < 3.80000000000000004e40

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 79.3%

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

   5. Simplified 79.3%

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

   if 3.80000000000000004e40 < y

   1. Initial program 6.9%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 6.9%

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

      1. div-inv N/A

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

      2. frac-2neg N/A

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

      3. metadata-eval N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

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

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

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

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

   6. Applied egg-rr 6.9%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(-1, \color{blue}{\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y} - \frac{1}{x}\right)}\right) \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{\frac{a}{x} - \frac{z}{{x}^{2}}}{y}\right), \color{blue}{\left(\frac{1}{x}\right)}\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y}\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      3. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right), \left(\frac{\color{blue}{1}}{x}\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \left(\frac{1}{x}\right)\right)\right) \]

      12. /-lowering-/.f64 66.5%

          \[\leadsto \mathsf{/.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right), \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 66.5%

      \[\leadsto \frac{-1}{\color{blue}{\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y} - \frac{1}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-124}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i + \left(y \cdot y\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{27464.7644705}{y} + \left(z - \frac{x \cdot b}{y}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.8e-7)
   (+ x (/ (- z (* x a)) y))
   (if (<= y 4.4e-124)
     (/ (+ t (* y 230661.510616)) (+ i (* y c)))
     (if (<= y 9.6e+36)
       (/ t (+ i (* (* y y) (+ b (* y (+ y a))))))
       (+ x (/ (+ (/ 27464.7644705 y) (- z (/ (* x b) y))) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.8e-7) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 4.4e-124) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 9.6e+36) {
		tmp = t / (i + ((y * y) * (b + (y * (y + a)))));
	} else {
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-6.8d-7)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 4.4d-124) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else if (y <= 9.6d+36) then
        tmp = t / (i + ((y * y) * (b + (y * (y + a)))))
    else
        tmp = x + (((27464.7644705d0 / y) + (z - ((x * b) / y))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.8e-7) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 4.4e-124) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else if (y <= 9.6e+36) {
		tmp = t / (i + ((y * y) * (b + (y * (y + a)))));
	} else {
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.8e-7:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 4.4e-124:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	elif y <= 9.6e+36:
		tmp = t / (i + ((y * y) * (b + (y * (y + a)))))
	else:
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.8e-7)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 4.4e-124)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	elseif (y <= 9.6e+36)
		tmp = Float64(t / Float64(i + Float64(Float64(y * y) * Float64(b + Float64(y * Float64(y + a))))));
	else
		tmp = Float64(x + Float64(Float64(Float64(27464.7644705 / y) + Float64(z - Float64(Float64(x * b) / y))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -6.8e-7)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 4.4e-124)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	elseif (y <= 9.6e+36)
		tmp = t / (i + ((y * y) * (b + (y * (y + a)))));
	else
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.8e-7], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e-124], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e+36], N[(t / N[(i + N[(N[(y * y), $MachinePrecision] * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(27464.7644705 / y), $MachinePrecision] + N[(z - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.79999999999999948e-7

   1. Initial program 17.7%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 42.8%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 57.1%

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

   8. Simplified 57.1%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -6.79999999999999948e-7 < y < 4.3999999999999998e-124

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 91.5%

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

   8. Simplified 91.5%

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

   if 4.3999999999999998e-124 < y < 9.5999999999999997e36

   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 c around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

   5. Simplified 78.0%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 43.6%

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

   if 9.5999999999999997e36 < y

   1. Initial program 8.4%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 52.5%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\frac{b \cdot x}{y} - \left(z + \frac{54929528941}{2000000} \cdot \frac{1}{y}\right)}{y}\right)}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{b \cdot x}{y} - \left(z + \frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), \color{blue}{y}\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(\frac{b \cdot x}{y} - z\right) - \frac{54929528941}{2000000} \cdot \frac{1}{y}\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\frac{b \cdot x}{y} - z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\frac{b \cdot x}{y}\right), z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(b \cdot x\right), y\right), z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \left(\frac{\frac{54929528941}{2000000} \cdot 1}{y}\right)\right), y\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \left(\frac{\frac{54929528941}{2000000}}{y}\right)\right), y\right)\right) \]

      9. /-lowering-/.f64 61.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, y\right)\right), y\right)\right) \]

   8. Simplified 61.1%

      \[\leadsto x - \color{blue}{\frac{\left(\frac{b \cdot x}{y} - z\right) - \frac{27464.7644705}{y}}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-124}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i + \left(y \cdot y\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{27464.7644705}{y} + \left(z - \frac{x \cdot b}{y}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-137}:\\ \;\;\;\;\frac{t\_1}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+82}:\\ \;\;\;\;\frac{t\_1}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616))))
   (if (<= y -6.8e-7)
     (+ x (/ (- z (* x a)) y))
     (if (<= y 1.2e-137)
       (/ t_1 (+ i (* y c)))
       (if (<= y 7e+82)
         (/ t_1 (+ i (* b (* y y))))
         (- (+ x (/ z y)) (/ (* x a) 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);
	double tmp;
	if (y <= -6.8e-7) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 1.2e-137) {
		tmp = t_1 / (i + (y * c));
	} else if (y <= 7e+82) {
		tmp = t_1 / (i + (b * (y * y)));
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    if (y <= (-6.8d-7)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 1.2d-137) then
        tmp = t_1 / (i + (y * c))
    else if (y <= 7d+82) then
        tmp = t_1 / (i + (b * (y * y)))
    else
        tmp = (x + (z / y)) - ((x * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double tmp;
	if (y <= -6.8e-7) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 1.2e-137) {
		tmp = t_1 / (i + (y * c));
	} else if (y <= 7e+82) {
		tmp = t_1 / (i + (b * (y * y)));
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	tmp = 0
	if y <= -6.8e-7:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 1.2e-137:
		tmp = t_1 / (i + (y * c))
	elif y <= 7e+82:
		tmp = t_1 / (i + (b * (y * y)))
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	tmp = 0.0
	if (y <= -6.8e-7)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 1.2e-137)
		tmp = Float64(t_1 / Float64(i + Float64(y * c)));
	elseif (y <= 7e+82)
		tmp = Float64(t_1 / Float64(i + Float64(b * Float64(y * y))));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	tmp = 0.0;
	if (y <= -6.8e-7)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 1.2e-137)
		tmp = t_1 / (i + (y * c));
	elseif (y <= 7e+82)
		tmp = t_1 / (i + (b * (y * y)));
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	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]}, If[LessEqual[y, -6.8e-7], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-137], N[(t$95$1 / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+82], N[(t$95$1 / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.79999999999999948e-7

   1. Initial program 17.7%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 42.8%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 57.1%

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

   8. Simplified 57.1%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -6.79999999999999948e-7 < y < 1.2e-137

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 92.1%

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

   8. Simplified 92.1%

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

   if 1.2e-137 < y < 7.0000000000000001e82

   1. Initial program 82.4%

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

   3. Taylor expanded in y around 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 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in b around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 32.1%

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

   8. Simplified 32.1%

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

   if 7.0000000000000001e82 < y

   1. Initial program 0.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. 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. remove-double-neg N/A

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

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

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

      8. remove-double-neg N/A

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

      9. *-lowering-*.f64 70.2%

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

   5. Simplified 70.2%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-137}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+82}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{i} + \frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+82}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7.4e+31)
   (+ x (/ (- z (* x a)) y))
   (if (<= y 2.25e-61)
     (+ (/ t i) (/ (* y 230661.510616) i))
     (if (<= y 7e+82)
       (/ (+ t (* y 230661.510616)) (* b (* y y)))
       (- (+ x (/ z y)) (/ (* x a) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7.4e+31) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 2.25e-61) {
		tmp = (t / i) + ((y * 230661.510616) / i);
	} else if (y <= 7e+82) {
		tmp = (t + (y * 230661.510616)) / (b * (y * y));
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-7.4d+31)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 2.25d-61) then
        tmp = (t / i) + ((y * 230661.510616d0) / i)
    else if (y <= 7d+82) then
        tmp = (t + (y * 230661.510616d0)) / (b * (y * y))
    else
        tmp = (x + (z / y)) - ((x * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7.4e+31) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 2.25e-61) {
		tmp = (t / i) + ((y * 230661.510616) / i);
	} else if (y <= 7e+82) {
		tmp = (t + (y * 230661.510616)) / (b * (y * y));
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7.4e+31:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 2.25e-61:
		tmp = (t / i) + ((y * 230661.510616) / i)
	elif y <= 7e+82:
		tmp = (t + (y * 230661.510616)) / (b * (y * y))
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7.4e+31)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 2.25e-61)
		tmp = Float64(Float64(t / i) + Float64(Float64(y * 230661.510616) / i));
	elseif (y <= 7e+82)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(b * Float64(y * y)));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -7.4e+31)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 2.25e-61)
		tmp = (t / i) + ((y * 230661.510616) / i);
	elseif (y <= 7e+82)
		tmp = (t + (y * 230661.510616)) / (b * (y * y));
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7.4e+31], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e-61], N[(N[(t / i), $MachinePrecision] + N[(N[(y * 230661.510616), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+82], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.3999999999999996e31

   1. Initial program 10.9%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 47.1%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 62.8%

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

   8. Simplified 62.8%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -7.3999999999999996e31 < y < 2.25e-61

   1. Initial program 98.8%

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

   3. Taylor expanded in c around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

   5. Simplified 82.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i} + \frac{t}{i}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{t}{i} + \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i}} \]

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

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 68.2%

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

   8. Simplified 68.2%

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

   if 2.25e-61 < y < 7.0000000000000001e82

   1. Initial program 74.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 30.3%

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

   5. Simplified 30.3%

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

   6. Taylor expanded in b around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 16.8%

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

   8. Simplified 16.8%

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

   if 7.0000000000000001e82 < y

   1. Initial program 0.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. 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. remove-double-neg N/A

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

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

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

      8. remove-double-neg N/A

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

      9. *-lowering-*.f64 70.2%

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

   5. Simplified 70.2%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{i} + \frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+82}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{i} + \frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+86}:\\ \;\;\;\;\frac{27464.7644705 - x \cdot b}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.5e+30)
   (+ x (/ (- z (* x a)) y))
   (if (<= y 4.8e-55)
     (+ (/ t i) (/ (* y 230661.510616) i))
     (if (<= y 2.15e+86)
       (/ (- 27464.7644705 (* x b)) (* y y))
       (- (+ x (/ z y)) (/ (* x a) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.5e+30) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 4.8e-55) {
		tmp = (t / i) + ((y * 230661.510616) / i);
	} else if (y <= 2.15e+86) {
		tmp = (27464.7644705 - (x * b)) / (y * y);
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.5d+30)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 4.8d-55) then
        tmp = (t / i) + ((y * 230661.510616d0) / i)
    else if (y <= 2.15d+86) then
        tmp = (27464.7644705d0 - (x * b)) / (y * y)
    else
        tmp = (x + (z / y)) - ((x * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.5e+30) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 4.8e-55) {
		tmp = (t / i) + ((y * 230661.510616) / i);
	} else if (y <= 2.15e+86) {
		tmp = (27464.7644705 - (x * b)) / (y * y);
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.5e+30:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 4.8e-55:
		tmp = (t / i) + ((y * 230661.510616) / i)
	elif y <= 2.15e+86:
		tmp = (27464.7644705 - (x * b)) / (y * y)
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.5e+30)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 4.8e-55)
		tmp = Float64(Float64(t / i) + Float64(Float64(y * 230661.510616) / i));
	elseif (y <= 2.15e+86)
		tmp = Float64(Float64(27464.7644705 - Float64(x * b)) / Float64(y * y));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.5e+30)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 4.8e-55)
		tmp = (t / i) + ((y * 230661.510616) / i);
	elseif (y <= 2.15e+86)
		tmp = (27464.7644705 - (x * b)) / (y * y);
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.5e+30], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-55], N[(N[(t / i), $MachinePrecision] + N[(N[(y * 230661.510616), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+86], N[(N[(27464.7644705 - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.50000000000000021e30

   1. Initial program 10.9%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 47.1%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 62.8%

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

   8. Simplified 62.8%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -3.50000000000000021e30 < y < 4.79999999999999983e-55

   1. Initial program 98.8%

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

   3. Taylor expanded in c around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i} + \frac{t}{i}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{t}{i} + \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i}} \]

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

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 67.2%

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

   8. Simplified 67.2%

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

   if 4.79999999999999983e-55 < y < 2.1500000000000001e86

   1. Initial program 71.3%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 13.0%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around 0

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

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

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

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\frac{54929528941}{2000000} + a \cdot \left(a \cdot x - z\right)\right), \left(b \cdot x\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(a \cdot \left(a \cdot x - z\right)\right)\right), \left(b \cdot x\right)\right), \left({y}^{2}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \left(a \cdot x - z\right)\right)\right), \left(b \cdot x\right)\right), \left({y}^{2}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(a \cdot x\right), z\right)\right)\right), \left(b \cdot x\right)\right), \left({y}^{2}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), z\right)\right)\right), \left(b \cdot x\right)\right), \left({y}^{2}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), z\right)\right)\right), \mathsf{*.f64}\left(b, x\right)\right), \left({y}^{2}\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), z\right)\right)\right), \mathsf{*.f64}\left(b, x\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

      9. *-lowering-*.f64 13.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), z\right)\right)\right), \mathsf{*.f64}\left(b, x\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   8. Simplified 13.7%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} - b \cdot x}{{y}^{2}}} \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{54929528941}{2000000} - b \cdot x\right), \color{blue}{\left({y}^{2}\right)}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{54929528941}{2000000}, \left(b \cdot x\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(b, x\right)\right), \left({y}^{2}\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(b, x\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       5. *-lowering-*.f64 14.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(b, x\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   11. Simplified 14.8%

       \[\leadsto \color{blue}{\frac{27464.7644705 - b \cdot x}{y \cdot y}} \]

   if 2.1500000000000001e86 < y

   1. Initial program 0.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. 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. remove-double-neg N/A

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

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

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

      8. remove-double-neg N/A

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

      9. *-lowering-*.f64 71.5%

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

   5. Simplified 71.5%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{i} + \frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+86}:\\ \;\;\;\;\frac{27464.7644705 - x \cdot b}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+36}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{27464.7644705}{y} + \left(z - \frac{x \cdot b}{y}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7e+28)
   (+ x (/ (- z (* x a)) y))
   (if (<= y 2.05e+36)
     (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
     (+ x (/ (+ (/ 27464.7644705 y) (- z (/ (* x b) y))) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7e+28) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 2.05e+36) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-7d+28)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 2.05d+36) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else
        tmp = x + (((27464.7644705d0 / y) + (z - ((x * b) / y))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7e+28) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 2.05e+36) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7e+28:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 2.05e+36:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	else:
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7e+28)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 2.05e+36)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = Float64(x + Float64(Float64(Float64(27464.7644705 / y) + Float64(z - Float64(Float64(x * b) / y))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -7e+28)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 2.05e+36)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	else
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7e+28], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+36], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(27464.7644705 / y), $MachinePrecision] + N[(z - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9999999999999999e28

   1. Initial program 10.9%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 47.1%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 62.8%

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

   8. Simplified 62.8%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -6.9999999999999999e28 < y < 2.05000000000000006e36

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 78.5%

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

   8. Simplified 78.5%

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

   if 2.05000000000000006e36 < y

   1. Initial program 8.4%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 52.5%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\frac{b \cdot x}{y} - \left(z + \frac{54929528941}{2000000} \cdot \frac{1}{y}\right)}{y}\right)}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{b \cdot x}{y} - \left(z + \frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), \color{blue}{y}\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(\frac{b \cdot x}{y} - z\right) - \frac{54929528941}{2000000} \cdot \frac{1}{y}\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\frac{b \cdot x}{y} - z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\frac{b \cdot x}{y}\right), z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(b \cdot x\right), y\right), z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \left(\frac{\frac{54929528941}{2000000} \cdot 1}{y}\right)\right), y\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \left(\frac{\frac{54929528941}{2000000}}{y}\right)\right), y\right)\right) \]

      9. /-lowering-/.f64 61.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, y\right)\right), y\right)\right) \]

   8. Simplified 61.1%

      \[\leadsto x - \color{blue}{\frac{\left(\frac{b \cdot x}{y} - z\right) - \frac{27464.7644705}{y}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+36}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{27464.7644705}{y} + \left(z - \frac{x \cdot b}{y}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{27464.7644705}{y} + \left(z - \frac{x \cdot b}{y}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.8e-7)
   (+ x (/ (- z (* x a)) y))
   (if (<= y 6.2e+34)
     (/ (+ t (* y 230661.510616)) (+ i (* y c)))
     (+ x (/ (+ (/ 27464.7644705 y) (- z (/ (* x b) y))) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.8e-7) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 6.2e+34) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-6.8d-7)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 6.2d+34) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else
        tmp = x + (((27464.7644705d0 / y) + (z - ((x * b) / y))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.8e-7) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 6.2e+34) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.8e-7:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 6.2e+34:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	else:
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.8e-7)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 6.2e+34)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	else
		tmp = Float64(x + Float64(Float64(Float64(27464.7644705 / y) + Float64(z - Float64(Float64(x * b) / y))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -6.8e-7)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 6.2e+34)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	else
		tmp = x + (((27464.7644705 / y) + (z - ((x * b) / y))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.8e-7], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+34], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(27464.7644705 / y), $MachinePrecision] + N[(z - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.79999999999999948e-7

   1. Initial program 17.7%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 42.8%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 57.1%

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

   8. Simplified 57.1%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -6.79999999999999948e-7 < y < 6.19999999999999955e34

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 73.9%

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

   8. Simplified 73.9%

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

   if 6.19999999999999955e34 < y

   1. Initial program 8.4%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 52.5%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\frac{b \cdot x}{y} - \left(z + \frac{54929528941}{2000000} \cdot \frac{1}{y}\right)}{y}\right)}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{b \cdot x}{y} - \left(z + \frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), \color{blue}{y}\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(\frac{b \cdot x}{y} - z\right) - \frac{54929528941}{2000000} \cdot \frac{1}{y}\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\frac{b \cdot x}{y} - z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\frac{b \cdot x}{y}\right), z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(b \cdot x\right), y\right), z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \left(\frac{54929528941}{2000000} \cdot \frac{1}{y}\right)\right), y\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \left(\frac{\frac{54929528941}{2000000} \cdot 1}{y}\right)\right), y\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \left(\frac{\frac{54929528941}{2000000}}{y}\right)\right), y\right)\right) \]

      9. /-lowering-/.f64 61.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), y\right), z\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, y\right)\right), y\right)\right) \]

   8. Simplified 61.1%

      \[\leadsto x - \color{blue}{\frac{\left(\frac{b \cdot x}{y} - z\right) - \frac{27464.7644705}{y}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{27464.7644705}{y} + \left(z - \frac{x \cdot b}{y}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{i} + \frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+86}:\\ \;\;\;\;\frac{27464.7644705 - x \cdot b}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.22e+33)
     t_1
     (if (<= y 4.8e-55)
       (+ (/ t i) (/ (* y 230661.510616) i))
       (if (<= y 2.15e+86) (/ (- 27464.7644705 (* x b)) (* y y)) 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 - (x * a)) / y);
	double tmp;
	if (y <= -1.22e+33) {
		tmp = t_1;
	} else if (y <= 4.8e-55) {
		tmp = (t / i) + ((y * 230661.510616) / i);
	} else if (y <= 2.15e+86) {
		tmp = (27464.7644705 - (x * b)) / (y * y);
	} 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 - (x * a)) / y)
    if (y <= (-1.22d+33)) then
        tmp = t_1
    else if (y <= 4.8d-55) then
        tmp = (t / i) + ((y * 230661.510616d0) / i)
    else if (y <= 2.15d+86) then
        tmp = (27464.7644705d0 - (x * b)) / (y * y)
    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 - (x * a)) / y);
	double tmp;
	if (y <= -1.22e+33) {
		tmp = t_1;
	} else if (y <= 4.8e-55) {
		tmp = (t / i) + ((y * 230661.510616) / i);
	} else if (y <= 2.15e+86) {
		tmp = (27464.7644705 - (x * b)) / (y * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -1.22e+33:
		tmp = t_1
	elif y <= 4.8e-55:
		tmp = (t / i) + ((y * 230661.510616) / i)
	elif y <= 2.15e+86:
		tmp = (27464.7644705 - (x * b)) / (y * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.22e+33)
		tmp = t_1;
	elseif (y <= 4.8e-55)
		tmp = Float64(Float64(t / i) + Float64(Float64(y * 230661.510616) / i));
	elseif (y <= 2.15e+86)
		tmp = Float64(Float64(27464.7644705 - Float64(x * b)) / Float64(y * y));
	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 - (x * a)) / y);
	tmp = 0.0;
	if (y <= -1.22e+33)
		tmp = t_1;
	elseif (y <= 4.8e-55)
		tmp = (t / i) + ((y * 230661.510616) / i);
	elseif (y <= 2.15e+86)
		tmp = (27464.7644705 - (x * b)) / (y * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.22e+33], t$95$1, If[LessEqual[y, 4.8e-55], N[(N[(t / i), $MachinePrecision] + N[(N[(y * 230661.510616), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+86], N[(N[(27464.7644705 - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.22000000000000005e33 or 2.1500000000000001e86 < y

   1. Initial program 6.0%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 52.7%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 66.8%

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

   8. Simplified 66.8%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -1.22000000000000005e33 < y < 4.79999999999999983e-55

   1. Initial program 98.8%

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

   3. Taylor expanded in c around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i} + \frac{t}{i}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{t}{i} + \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i}} \]

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

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 67.2%

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

   8. Simplified 67.2%

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

   if 4.79999999999999983e-55 < y < 2.1500000000000001e86

   1. Initial program 71.3%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 13.0%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around 0

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

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

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

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\frac{54929528941}{2000000} + a \cdot \left(a \cdot x - z\right)\right), \left(b \cdot x\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(a \cdot \left(a \cdot x - z\right)\right)\right), \left(b \cdot x\right)\right), \left({y}^{2}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \left(a \cdot x - z\right)\right)\right), \left(b \cdot x\right)\right), \left({y}^{2}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(a \cdot x\right), z\right)\right)\right), \left(b \cdot x\right)\right), \left({y}^{2}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), z\right)\right)\right), \left(b \cdot x\right)\right), \left({y}^{2}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), z\right)\right)\right), \mathsf{*.f64}\left(b, x\right)\right), \left({y}^{2}\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), z\right)\right)\right), \mathsf{*.f64}\left(b, x\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

      9. *-lowering-*.f64 13.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), z\right)\right)\right), \mathsf{*.f64}\left(b, x\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   8. Simplified 13.7%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{\frac{54929528941}{2000000} - b \cdot x}{{y}^{2}}} \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{54929528941}{2000000} - b \cdot x\right), \color{blue}{\left({y}^{2}\right)}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{54929528941}{2000000}, \left(b \cdot x\right)\right), \left({\color{blue}{y}}^{2}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(b, x\right)\right), \left({y}^{2}\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(b, x\right)\right), \left(y \cdot \color{blue}{y}\right)\right) \]

       5. *-lowering-*.f64 14.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(b, x\right)\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   11. Simplified 14.8%

       \[\leadsto \color{blue}{\frac{27464.7644705 - b \cdot x}{y \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{i} + \frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+86}:\\ \;\;\;\;\frac{27464.7644705 - x \cdot b}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 57.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{i} + \frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+82}:\\ \;\;\;\;\frac{t}{a \cdot \left(y \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -2.7e+31)
     t_1
     (if (<= y 3.2e-32)
       (+ (/ t i) (/ (* y 230661.510616) i))
       (if (<= y 7e+82) (/ t (* a (* y (* y y)))) 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 - (x * a)) / y);
	double tmp;
	if (y <= -2.7e+31) {
		tmp = t_1;
	} else if (y <= 3.2e-32) {
		tmp = (t / i) + ((y * 230661.510616) / i);
	} else if (y <= 7e+82) {
		tmp = t / (a * (y * (y * y)));
	} 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 - (x * a)) / y)
    if (y <= (-2.7d+31)) then
        tmp = t_1
    else if (y <= 3.2d-32) then
        tmp = (t / i) + ((y * 230661.510616d0) / i)
    else if (y <= 7d+82) then
        tmp = t / (a * (y * (y * y)))
    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 - (x * a)) / y);
	double tmp;
	if (y <= -2.7e+31) {
		tmp = t_1;
	} else if (y <= 3.2e-32) {
		tmp = (t / i) + ((y * 230661.510616) / i);
	} else if (y <= 7e+82) {
		tmp = t / (a * (y * (y * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -2.7e+31:
		tmp = t_1
	elif y <= 3.2e-32:
		tmp = (t / i) + ((y * 230661.510616) / i)
	elif y <= 7e+82:
		tmp = t / (a * (y * (y * y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -2.7e+31)
		tmp = t_1;
	elseif (y <= 3.2e-32)
		tmp = Float64(Float64(t / i) + Float64(Float64(y * 230661.510616) / i));
	elseif (y <= 7e+82)
		tmp = Float64(t / Float64(a * Float64(y * Float64(y * y))));
	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 - (x * a)) / y);
	tmp = 0.0;
	if (y <= -2.7e+31)
		tmp = t_1;
	elseif (y <= 3.2e-32)
		tmp = (t / i) + ((y * 230661.510616) / i);
	elseif (y <= 7e+82)
		tmp = t / (a * (y * (y * y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+31], t$95$1, If[LessEqual[y, 3.2e-32], N[(N[(t / i), $MachinePrecision] + N[(N[(y * 230661.510616), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+82], N[(t / N[(a * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.69999999999999986e31 or 7.0000000000000001e82 < y

   1. Initial program 5.9%

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

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 52.2%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

      3. *-lowering-*.f64 66.2%

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

   8. Simplified 66.2%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -2.69999999999999986e31 < y < 3.2000000000000002e-32

   1. Initial program 98.8%

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

   3. Taylor expanded in c around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

   5. Simplified 81.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i} + \frac{t}{i}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{t}{i} + \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i}} \]

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

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 65.0%

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

   8. Simplified 65.0%

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

   if 3.2000000000000002e-32 < y < 7.0000000000000001e82

   1. Initial program 70.0%

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

   3. Taylor expanded in y around 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 23.1%

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

   5. Simplified 23.1%

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

   6. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{*.f64}\left(a, \color{blue}{\left({y}^{3}\right)}\right)\right) \]

      2. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{*.f64}\left(a, \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{*.f64}\left(a, \left(y \cdot {y}^{\color{blue}{2}}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left({y}^{2}\right)}\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{y}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 17.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 17.3%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{a \cdot \left(y \cdot \left(y \cdot y\right)\right)}} \]

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t}{a \cdot {y}^{3}}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(a \cdot {y}^{3}\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{\left({y}^{3}\right)}\right)\right) \]

       3. cube-mult N/A

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(a, \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)\right)\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(a, \left(y \cdot {y}^{\color{blue}{2}}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left({y}^{2}\right)}\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{y}\right)\right)\right)\right) \]

       7. *-lowering-*.f64 16.8%

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

   11. Simplified 16.8%

       \[\leadsto \color{blue}{\frac{t}{a \cdot \left(y \cdot \left(y \cdot y\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{i} + \frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+82}:\\ \;\;\;\;\frac{t}{a \cdot \left(y \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 68.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+44}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.1e-7)
   (+ x (/ (- z (* x a)) y))
   (if (<= y 5.8e+44)
     (/ (+ t (* y 230661.510616)) (+ i (* y c)))
     (- (+ x (/ z y)) (/ (* x a) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.1e-7) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 5.8e+44) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-6.1d-7)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 5.8d+44) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else
        tmp = (x + (z / y)) - ((x * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -6.1e-7) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 5.8e+44) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -6.1e-7:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 5.8e+44:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -6.1e-7)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 5.8e+44)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -6.1e-7)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 5.8e+44)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -6.1e-7], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+44], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.09999999999999983e-7

   1. Initial program 17.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto x - \color{blue}{\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 42.8%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot x - z\right), \color{blue}{y}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), z\right), y\right)\right) \]

      3. *-lowering-*.f64 57.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), z\right), y\right)\right) \]

   8. Simplified 57.1%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -6.09999999999999983e-7 < y < 5.8000000000000004e44

   1. Initial program 98.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 85.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

   5. Simplified 85.3%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\color{blue}{\left(c \cdot y\right)}, i\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 72.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, y\right), i\right)\right) \]

   8. Simplified 72.8%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{c \cdot y} + i} \]

   if 5.8000000000000004e44 < y

   1. Initial program 6.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. 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. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 58.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 58.0%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+44}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 58.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{t}{i} + \frac{y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -5.8e+28)
     t_1
     (if (<= y 5.5e+42) (+ (/ t i) (/ (* y 230661.510616) 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 - (x * a)) / y);
	double tmp;
	if (y <= -5.8e+28) {
		tmp = t_1;
	} else if (y <= 5.5e+42) {
		tmp = (t / i) + ((y * 230661.510616) / 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 - (x * a)) / y)
    if (y <= (-5.8d+28)) then
        tmp = t_1
    else if (y <= 5.5d+42) then
        tmp = (t / i) + ((y * 230661.510616d0) / 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 - (x * a)) / y);
	double tmp;
	if (y <= -5.8e+28) {
		tmp = t_1;
	} else if (y <= 5.5e+42) {
		tmp = (t / i) + ((y * 230661.510616) / i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -5.8e+28:
		tmp = t_1
	elif y <= 5.5e+42:
		tmp = (t / i) + ((y * 230661.510616) / i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -5.8e+28)
		tmp = t_1;
	elseif (y <= 5.5e+42)
		tmp = Float64(Float64(t / i) + Float64(Float64(y * 230661.510616) / 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 - (x * a)) / y);
	tmp = 0.0;
	if (y <= -5.8e+28)
		tmp = t_1;
	elseif (y <= 5.5e+42)
		tmp = (t / i) + ((y * 230661.510616) / i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+28], t$95$1, If[LessEqual[y, 5.5e+42], N[(N[(t / i), $MachinePrecision] + N[(N[(y * 230661.510616), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000002e28 or 5.50000000000000001e42 < y

   1. Initial program 8.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto x - \color{blue}{\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right)\right) \]

   5. Simplified 49.9%

      \[\leadsto \color{blue}{x - \frac{\left(\left(0 - z\right) - \frac{27464.7644705 - \left(b \cdot x - a \cdot \left(\left(0 - z\right) + a \cdot x\right)\right)}{y}\right) + a \cdot x}{y}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot x - z}{y}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot x - z\right), \color{blue}{y}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), z\right), y\right)\right) \]

      3. *-lowering-*.f64 60.4%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), z\right), y\right)\right) \]

   8. Simplified 60.4%

      \[\leadsto x - \color{blue}{\frac{a \cdot x - z}{y}} \]

   if -5.8000000000000002e28 < y < 5.50000000000000001e42

   1. Initial program 97.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right), \color{blue}{\left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \left(y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right), \left(\color{blue}{i} + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \left(y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \left(z + x \cdot y\right)\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \left(x \cdot y\right)\right)\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \left(y \cdot x\right)\right)\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(i, \color{blue}{\left({y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right) \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + \left(b + y \cdot \left(y + a\right)\right) \cdot \left(y \cdot y\right)}} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i} + \frac{t}{i}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{t}{i} + \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{t}{i}\right), \color{blue}{\left(\frac{28832688827}{125000} \cdot \frac{y}{i}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, i\right), \left(\color{blue}{\frac{28832688827}{125000}} \cdot \frac{y}{i}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, i\right), \left(\frac{\frac{28832688827}{125000} \cdot y}{\color{blue}{i}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, i\right), \mathsf{/.f64}\left(\left(\frac{28832688827}{125000} \cdot y\right), \color{blue}{i}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, i\right), \mathsf{/.f64}\left(\left(y \cdot \frac{28832688827}{125000}\right), i\right)\right) \]

      7. *-lowering-*.f64 56.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, i\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), i\right)\right) \]

   8. Simplified 56.5%

      \[\leadsto \color{blue}{\frac{t}{i} + \frac{y \cdot 230661.510616}{i}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{t}{i} + \frac{y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 53.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1950000:\\ \;\;\;\;\frac{t}{i} + \frac{y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -8.5e+32)
   x
   (if (<= y 1950000.0) (+ (/ t i) (/ (* y 230661.510616) i)) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -8.5e+32) {
		tmp = x;
	} else if (y <= 1950000.0) {
		tmp = (t / i) + ((y * 230661.510616) / i);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-8.5d+32)) then
        tmp = x
    else if (y <= 1950000.0d0) then
        tmp = (t / i) + ((y * 230661.510616d0) / i)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -8.5e+32) {
		tmp = x;
	} else if (y <= 1950000.0) {
		tmp = (t / i) + ((y * 230661.510616) / i);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -8.5e+32:
		tmp = x
	elif y <= 1950000.0:
		tmp = (t / i) + ((y * 230661.510616) / i)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -8.5e+32)
		tmp = x;
	elseif (y <= 1950000.0)
		tmp = Float64(Float64(t / i) + Float64(Float64(y * 230661.510616) / i));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -8.5e+32)
		tmp = x;
	elseif (y <= 1950000.0)
		tmp = (t / i) + ((y * 230661.510616) / i);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -8.5e+32], x, If[LessEqual[y, 1950000.0], N[(N[(t / i), $MachinePrecision] + N[(N[(y * 230661.510616), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999998e32 or 1.95e6 < y

   1. Initial program 14.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 45.4%

      \[\leadsto \color{blue}{x} \]

   if -8.4999999999999998e32 < y < 1.95e6

   1. Initial program 98.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right), \color{blue}{\left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \left(y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right), \left(\color{blue}{i} + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \left(y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(y \cdot \left(z + x \cdot y\right)\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \left(z + x \cdot y\right)\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \left(x \cdot y\right)\right)\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \left(y \cdot x\right)\right)\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right)\right), \left(i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{28832688827}{125000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(y, x\right)\right)\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(i, \color{blue}{\left({y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right) \]

   5. Simplified 81.2%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + \left(b + y \cdot \left(y + a\right)\right) \cdot \left(y \cdot y\right)}} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i} + \frac{t}{i}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{t}{i} + \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i}} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{t}{i}\right), \color{blue}{\left(\frac{28832688827}{125000} \cdot \frac{y}{i}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, i\right), \left(\color{blue}{\frac{28832688827}{125000}} \cdot \frac{y}{i}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, i\right), \left(\frac{\frac{28832688827}{125000} \cdot y}{\color{blue}{i}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, i\right), \mathsf{/.f64}\left(\left(\frac{28832688827}{125000} \cdot y\right), \color{blue}{i}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, i\right), \mathsf{/.f64}\left(\left(y \cdot \frac{28832688827}{125000}\right), i\right)\right) \]

      7. *-lowering-*.f64 60.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, i\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), i\right)\right) \]

   8. Simplified 60.7%

      \[\leadsto \color{blue}{\frac{t}{i} + \frac{y \cdot 230661.510616}{i}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 53.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6100000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.52e+29)
   x
   (if (<= y 6100000.0) (/ (+ t (* y 230661.510616)) 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 <= -1.52e+29) {
		tmp = x;
	} else if (y <= 6100000.0) {
		tmp = (t + (y * 230661.510616)) / 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 <= (-1.52d+29)) then
        tmp = x
    else if (y <= 6100000.0d0) then
        tmp = (t + (y * 230661.510616d0)) / 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 <= -1.52e+29) {
		tmp = x;
	} else if (y <= 6100000.0) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.52e+29:
		tmp = x
	elif y <= 6100000.0:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.52e+29)
		tmp = x;
	elseif (y <= 6100000.0)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / 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 <= -1.52e+29)
		tmp = x;
	elseif (y <= 6100000.0)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.52e+29], x, If[LessEqual[y, 6100000.0], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.52e29 or 6.1e6 < y

   1. Initial program 14.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 45.4%

      \[\leadsto \color{blue}{x} \]

   if -1.52e29 < y < 6.1e6

   1. Initial program 98.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 87.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

   5. Simplified 87.7%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \color{blue}{i}\right) \]
   7. Step-by-step derivation

   8. Simplified 60.6%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{i}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6100000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 49.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.7e+30) x (if (<= y 1.15e-54) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.7e+30) {
		tmp = x;
	} else if (y <= 1.15e-54) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.7d+30)) then
        tmp = x
    else if (y <= 1.15d-54) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.7e+30) {
		tmp = x;
	} else if (y <= 1.15e-54) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.7e+30:
		tmp = x
	elif y <= 1.15e-54:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.7e+30)
		tmp = x;
	elseif (y <= 1.15e-54)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.7e+30)
		tmp = x;
	elseif (y <= 1.15e-54)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.7e+30], x, If[LessEqual[y, 1.15e-54], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6999999999999999e30 or 1.1499999999999999e-54 < y

   1. Initial program 21.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 41.7%

      \[\leadsto \color{blue}{x} \]

   if -2.6999999999999999e30 < y < 1.1499999999999999e-54

   1. Initial program 98.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t}{i}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 54.8%

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{i}\right) \]

   5. Simplified 54.8%

      \[\leadsto \color{blue}{\frac{t}{i}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 25.0% 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 57.0%

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 24.2%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024160 
(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)))