Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.2% → 83.2%

Time: 19.1s

Alternatives: 15

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.2% accurate, 0.5× speedup

Math

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

FPCore

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(0 - z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right)\right), y\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(a \cdot x\right)\right), y\right)\right) \]

      12. *-lowering-*.f64 77.6%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{*.f64}\left(a, x\right)\right), y\right)\right) \]

   5. Simplified 77.6%

      \[\leadsto \color{blue}{x - \frac{\left(0 - z\right) + a \cdot x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.3%

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

Alternative 2: 77.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ t_2 := y \cdot t\_1 + i\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{+62}:\\ \;\;\;\;\left(\left(x + \frac{z}{y}\right) + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{1}{y}}{t\_1} \cdot \left(y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t\_2}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot \left(z \cdot \left(y \cdot y\right)\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ y a)) b)) c)) (t_2 (+ (* y t_1) i)))
   (if (<= y -2.45e+62)
     (- (+ (+ x (/ z y)) (/ 27464.7644705 (* y y))) (/ (* x a) y))
     (if (<= y -7.5e-29)
       (*
        (/ (/ 1.0 y) t_1)
        (+
         (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
         t))
       (if (<= y 9.6e-78)
         (/ (+ t (* y 230661.510616)) t_2)
         (if (<= y 1.4e+43)
           (/ (+ t (* y (* z (* y y)))) t_2)
           (+ x (/ (- z (* 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 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = (y * t_1) + i;
	double tmp;
	if (y <= -2.45e+62) {
		tmp = ((x + (z / y)) + (27464.7644705 / (y * y))) - ((x * a) / y);
	} else if (y <= -7.5e-29) {
		tmp = ((1.0 / y) / t_1) * ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t);
	} else if (y <= 9.6e-78) {
		tmp = (t + (y * 230661.510616)) / t_2;
	} else if (y <= 1.4e+43) {
		tmp = (t + (y * (z * (y * y)))) / t_2;
	} else {
		tmp = x + ((z - (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) :: t_2
    real(8) :: tmp
    t_1 = (y * ((y * (y + a)) + b)) + c
    t_2 = (y * t_1) + i
    if (y <= (-2.45d+62)) then
        tmp = ((x + (z / y)) + (27464.7644705d0 / (y * y))) - ((x * a) / y)
    else if (y <= (-7.5d-29)) then
        tmp = ((1.0d0 / y) / t_1) * ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) + t)
    else if (y <= 9.6d-78) then
        tmp = (t + (y * 230661.510616d0)) / t_2
    else if (y <= 1.4d+43) then
        tmp = (t + (y * (z * (y * y)))) / t_2
    else
        tmp = x + ((z - (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 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = (y * t_1) + i;
	double tmp;
	if (y <= -2.45e+62) {
		tmp = ((x + (z / y)) + (27464.7644705 / (y * y))) - ((x * a) / y);
	} else if (y <= -7.5e-29) {
		tmp = ((1.0 / y) / t_1) * ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t);
	} else if (y <= 9.6e-78) {
		tmp = (t + (y * 230661.510616)) / t_2;
	} else if (y <= 1.4e+43) {
		tmp = (t + (y * (z * (y * y)))) / t_2;
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * (y + a)) + b)) + c
	t_2 = (y * t_1) + i
	tmp = 0
	if y <= -2.45e+62:
		tmp = ((x + (z / y)) + (27464.7644705 / (y * y))) - ((x * a) / y)
	elif y <= -7.5e-29:
		tmp = ((1.0 / y) / t_1) * ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t)
	elif y <= 9.6e-78:
		tmp = (t + (y * 230661.510616)) / t_2
	elif y <= 1.4e+43:
		tmp = (t + (y * (z * (y * y)))) / t_2
	else:
		tmp = x + ((z - (x * a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)
	t_2 = Float64(Float64(y * t_1) + i)
	tmp = 0.0
	if (y <= -2.45e+62)
		tmp = Float64(Float64(Float64(x + Float64(z / y)) + Float64(27464.7644705 / Float64(y * y))) - Float64(Float64(x * a) / y));
	elseif (y <= -7.5e-29)
		tmp = Float64(Float64(Float64(1.0 / y) / t_1) * Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t));
	elseif (y <= 9.6e-78)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / t_2);
	elseif (y <= 1.4e+43)
		tmp = Float64(Float64(t + Float64(y * Float64(z * Float64(y * y)))) / t_2);
	else
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * (y + a)) + b)) + c;
	t_2 = (y * t_1) + i;
	tmp = 0.0;
	if (y <= -2.45e+62)
		tmp = ((x + (z / y)) + (27464.7644705 / (y * y))) - ((x * a) / y);
	elseif (y <= -7.5e-29)
		tmp = ((1.0 / y) / t_1) * ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t);
	elseif (y <= 9.6e-78)
		tmp = (t + (y * 230661.510616)) / t_2;
	elseif (y <= 1.4e+43)
		tmp = (t + (y * (z * (y * y)))) / t_2;
	else
		tmp = x + ((z - (x * a)) / y);
	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[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * t$95$1), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -2.45e+62], N[(N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-29], N[(N[(N[(1.0 / y), $MachinePrecision] / t$95$1), $MachinePrecision] * N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e-78], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 1.4e+43], N[(N[(t + N[(y * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.4499999999999998e62

   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

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      8. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, \left(y \cdot y\right)\right)\right), \left(\frac{a \cdot x}{y} + \left(\frac{a \cdot \left(z - a \cdot x\right)}{{y}^{2}} + \frac{b \cdot x}{{y}^{2}}\right)\right)\right) \]

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

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

      10. associate-+r+ N/A

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

   5. Simplified 66.7%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, y\right)\right)\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

      2. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   8. Simplified 74.8%

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

   if -2.4499999999999998e62 < y < -7.50000000000000006e-29

   1. Initial program 66.4%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 66.5%

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

      1. associate-/r/ N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   6. Applied egg-rr 66.3%

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

   7. Taylor expanded in i around 0

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

      1. associate-/r* N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 55.6%

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

   9. Simplified 55.6%

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

   if -7.50000000000000006e-29 < y < 9.59999999999999999e-78

   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 96.6%

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

   5. Simplified 96.6%

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

   if 9.59999999999999999e-78 < y < 1.40000000000000009e43

   1. Initial program 91.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   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 72.3%

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

   5. Simplified 72.3%

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

   if 1.40000000000000009e43 < y

   1. Initial program 0.4%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(0 - z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right)\right), y\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(a \cdot x\right)\right), y\right)\right) \]

      12. *-lowering-*.f64 80.9%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{*.f64}\left(a, x\right)\right), y\right)\right) \]

   5. Simplified 80.9%

      \[\leadsto \color{blue}{x - \frac{\left(0 - z\right) + a \cdot x}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+62}:\\ \;\;\;\;\left(\left(x + \frac{z}{y}\right) + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{1}{y}}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c} \cdot \left(y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot \left(z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ t_2 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+159}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\frac{-1}{x} - \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t\_1}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{t + y \cdot \left(z \cdot \left(y \cdot y\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
        (t_2 (+ x (/ (- z (* x a)) y))))
   (if (<= y -8.8e+159)
     t_2
     (if (<= y -7.2e-14)
       (/ -1.0 (- (/ -1.0 x) (/ (- (/ a x) (/ z (* x x))) y)))
       (if (<= y 5.2e-83)
         (/ (+ t (* y 230661.510616)) t_1)
         (if (<= y 2.5e+44) (/ (+ t (* y (* z (* y y)))) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_2 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -8.8e+159) {
		tmp = t_2;
	} else if (y <= -7.2e-14) {
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y));
	} else if (y <= 5.2e-83) {
		tmp = (t + (y * 230661.510616)) / t_1;
	} else if (y <= 2.5e+44) {
		tmp = (t + (y * (z * (y * y)))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    t_2 = x + ((z - (x * a)) / y)
    if (y <= (-8.8d+159)) then
        tmp = t_2
    else if (y <= (-7.2d-14)) then
        tmp = (-1.0d0) / (((-1.0d0) / x) - (((a / x) - (z / (x * x))) / y))
    else if (y <= 5.2d-83) then
        tmp = (t + (y * 230661.510616d0)) / t_1
    else if (y <= 2.5d+44) then
        tmp = (t + (y * (z * (y * y)))) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_2 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -8.8e+159) {
		tmp = t_2;
	} else if (y <= -7.2e-14) {
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y));
	} else if (y <= 5.2e-83) {
		tmp = (t + (y * 230661.510616)) / t_1;
	} else if (y <= 2.5e+44) {
		tmp = (t + (y * (z * (y * y)))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	t_2 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -8.8e+159:
		tmp = t_2
	elif y <= -7.2e-14:
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y))
	elif y <= 5.2e-83:
		tmp = (t + (y * 230661.510616)) / t_1
	elif y <= 2.5e+44:
		tmp = (t + (y * (z * (y * y)))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	t_2 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -8.8e+159)
		tmp = t_2;
	elseif (y <= -7.2e-14)
		tmp = Float64(-1.0 / Float64(Float64(-1.0 / x) - Float64(Float64(Float64(a / x) - Float64(z / Float64(x * x))) / y)));
	elseif (y <= 5.2e-83)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / t_1);
	elseif (y <= 2.5e+44)
		tmp = Float64(Float64(t + Float64(y * Float64(z * Float64(y * y)))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	t_2 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -8.8e+159)
		tmp = t_2;
	elseif (y <= -7.2e-14)
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y));
	elseif (y <= 5.2e-83)
		tmp = (t + (y * 230661.510616)) / t_1;
	elseif (y <= 2.5e+44)
		tmp = (t + (y * (z * (y * y)))) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.8e+159], t$95$2, If[LessEqual[y, -7.2e-14], N[(-1.0 / N[(N[(-1.0 / x), $MachinePrecision] - N[(N[(N[(a / x), $MachinePrecision] - N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-83], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.5e+44], N[(N[(t + N[(y * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.7999999999999997e159 or 2.4999999999999998e44 < 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

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(0 - z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right)\right), y\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(a \cdot x\right)\right), y\right)\right) \]

      12. *-lowering-*.f64 82.6%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{*.f64}\left(a, x\right)\right), y\right)\right) \]

   5. Simplified 82.6%

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

   if -8.7999999999999997e159 < y < -7.1999999999999996e-14

   1. Initial program 32.7%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 32.7%

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

   5. Taylor expanded in y around -inf

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

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

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

      2. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      10. unpow2 N/A

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

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

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

      12. /-lowering-/.f64 45.6%

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

   7. Simplified 45.6%

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

   if -7.1999999999999996e-14 < y < 5.20000000000000018e-83

   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 94.9%

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

   5. Simplified 94.9%

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

   if 5.20000000000000018e-83 < y < 2.4999999999999998e44

   1. Initial program 91.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   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 72.3%

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

   5. Simplified 72.3%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+159}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\frac{-1}{x} - \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{t + y \cdot \left(z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+161}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\frac{-1}{x} - \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.1e+161)
   (+ x (/ (- z (* x a)) y))
   (if (<= y -7.2e-14)
     (/ -1.0 (- (/ -1.0 x) (/ (- (/ a x) (/ z (* x x))) y)))
     (if (<= y 68000000000000.0)
       (/
        (+ t (* y 230661.510616))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (- (+ 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 <= -4.1e+161) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -7.2e-14) {
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y));
	} else if (y <= 68000000000000.0) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} 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 <= (-4.1d+161)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= (-7.2d-14)) then
        tmp = (-1.0d0) / (((-1.0d0) / x) - (((a / x) - (z / (x * x))) / y))
    else if (y <= 68000000000000.0d0) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    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 <= -4.1e+161) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -7.2e-14) {
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y));
	} else if (y <= 68000000000000.0) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} 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 <= -4.1e+161:
		tmp = x + ((z - (x * a)) / y)
	elif y <= -7.2e-14:
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y))
	elif y <= 68000000000000.0:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	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 <= -4.1e+161)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= -7.2e-14)
		tmp = Float64(-1.0 / Float64(Float64(-1.0 / x) - Float64(Float64(Float64(a / x) - Float64(z / Float64(x * x))) / y)));
	elseif (y <= 68000000000000.0)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = 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 <= -4.1e+161)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= -7.2e-14)
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y));
	elseif (y <= 68000000000000.0)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	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, -4.1e+161], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e-14], N[(-1.0 / N[(N[(-1.0 / x), $MachinePrecision] - N[(N[(N[(a / x), $MachinePrecision] - N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 68000000000000.0], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], 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 < -4.1000000000000001e161

   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

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(0 - z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right)\right), y\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(a \cdot x\right)\right), y\right)\right) \]

      12. *-lowering-*.f64 84.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{*.f64}\left(a, x\right)\right), y\right)\right) \]

   5. Simplified 84.8%

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

   if -4.1000000000000001e161 < y < -7.1999999999999996e-14

   1. Initial program 32.7%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 32.7%

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

   5. Taylor expanded in y around -inf

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

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

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

      2. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      10. unpow2 N/A

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

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

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

      12. /-lowering-/.f64 45.6%

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

   7. Simplified 45.6%

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

   if -7.1999999999999996e-14 < y < 6.8e13

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 86.4%

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

   5. Simplified 86.4%

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

   if 6.8e13 < y

   1. Initial program 7.4%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 7.4%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 73.2%

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

   7. Simplified 73.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+161}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\frac{-1}{x} - \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+158}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\frac{-1}{x} - \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq 58000000000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6.4e+158)
   (+ x (/ (- z (* x a)) y))
   (if (<= y -4.3e-14)
     (/ -1.0 (- (/ -1.0 x) (/ (- (/ a x) (/ z (* x x))) y)))
     (if (<= y 58000000000000.0)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ i (* y (+ c (* y b)))))
       (- (+ 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 <= -6.4e+158) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -4.3e-14) {
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y));
	} else if (y <= 58000000000000.0) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} 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 <= (-6.4d+158)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= (-4.3d-14)) then
        tmp = (-1.0d0) / (((-1.0d0) / x) - (((a / x) - (z / (x * x))) / y))
    else if (y <= 58000000000000.0d0) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * b))))
    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 <= -6.4e+158) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -4.3e-14) {
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y));
	} else if (y <= 58000000000000.0) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} 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 <= -6.4e+158:
		tmp = x + ((z - (x * a)) / y)
	elif y <= -4.3e-14:
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y))
	elif y <= 58000000000000.0:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	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 <= -6.4e+158)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= -4.3e-14)
		tmp = Float64(-1.0 / Float64(Float64(-1.0 / x) - Float64(Float64(Float64(a / x) - Float64(z / Float64(x * x))) / y)));
	elseif (y <= 58000000000000.0)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	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 <= -6.4e+158)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= -4.3e-14)
		tmp = -1.0 / ((-1.0 / x) - (((a / x) - (z / (x * x))) / y));
	elseif (y <= 58000000000000.0)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	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, -6.4e+158], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.3e-14], N[(-1.0 / N[(N[(-1.0 / x), $MachinePrecision] - N[(N[(N[(a / x), $MachinePrecision] - N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 58000000000000.0], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $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 < -6.39999999999999989e158

   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

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(0 - z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right)\right), y\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(a \cdot x\right)\right), y\right)\right) \]

      12. *-lowering-*.f64 84.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{*.f64}\left(a, x\right)\right), y\right)\right) \]

   5. Simplified 84.8%

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

   if -6.39999999999999989e158 < y < -4.29999999999999998e-14

   1. Initial program 32.7%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 32.7%

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

   5. Taylor expanded in y around -inf

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

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

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

      2. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      10. unpow2 N/A

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

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

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

      12. /-lowering-/.f64 45.6%

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

   7. Simplified 45.6%

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

   if -4.29999999999999998e-14 < y < 5.8e13

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{54929528941}{2000000} \cdot y\right)}, \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 80.6%

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

   8. Simplified 80.6%

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

   if 5.8e13 < y

   1. Initial program 7.4%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 7.4%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 73.2%

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

   7. Simplified 73.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+158}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\frac{-1}{x} - \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{y}}\\ \mathbf{elif}\;y \leq 58000000000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+162}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\left(\frac{z}{y \cdot \left(x \cdot x\right)} - \frac{\frac{a}{x}}{y}\right) + \frac{-1}{x}}\\ \mathbf{elif}\;y \leq 3200000000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.15e+162)
   (+ x (/ (- z (* x a)) y))
   (if (<= y -7.2e-14)
     (/ -1.0 (+ (- (/ z (* y (* x x))) (/ (/ a x) y)) (/ -1.0 x)))
     (if (<= y 3200000000000.0)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ i (* y (+ c (* y b)))))
       (- (+ 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 <= -2.15e+162) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -7.2e-14) {
		tmp = -1.0 / (((z / (y * (x * x))) - ((a / x) / y)) + (-1.0 / x));
	} else if (y <= 3200000000000.0) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} 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 <= (-2.15d+162)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= (-7.2d-14)) then
        tmp = (-1.0d0) / (((z / (y * (x * x))) - ((a / x) / y)) + ((-1.0d0) / x))
    else if (y <= 3200000000000.0d0) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * b))))
    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 <= -2.15e+162) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -7.2e-14) {
		tmp = -1.0 / (((z / (y * (x * x))) - ((a / x) / y)) + (-1.0 / x));
	} else if (y <= 3200000000000.0) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	} 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 <= -2.15e+162:
		tmp = x + ((z - (x * a)) / y)
	elif y <= -7.2e-14:
		tmp = -1.0 / (((z / (y * (x * x))) - ((a / x) / y)) + (-1.0 / x))
	elif y <= 3200000000000.0:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	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 <= -2.15e+162)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= -7.2e-14)
		tmp = Float64(-1.0 / Float64(Float64(Float64(z / Float64(y * Float64(x * x))) - Float64(Float64(a / x) / y)) + Float64(-1.0 / x)));
	elseif (y <= 3200000000000.0)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	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 <= -2.15e+162)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= -7.2e-14)
		tmp = -1.0 / (((z / (y * (x * x))) - ((a / x) / y)) + (-1.0 / x));
	elseif (y <= 3200000000000.0)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	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, -2.15e+162], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e-14], N[(-1.0 / N[(N[(N[(z / N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3200000000000.0], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $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 < -2.1500000000000001e162

   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

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(0 - z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right)\right), y\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(a \cdot x\right)\right), y\right)\right) \]

      12. *-lowering-*.f64 84.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{*.f64}\left(a, x\right)\right), y\right)\right) \]

   5. Simplified 84.8%

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

   if -2.1500000000000001e162 < y < -7.1999999999999996e-14

   1. Initial program 32.7%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 32.7%

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

      1. clear-num N/A

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

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

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

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

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

   6. Applied egg-rr 32.7%

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

   7. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

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

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

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

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

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

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

      5. associate-/r* N/A

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

      11. unpow2 N/A

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

      12. *-lowering-*.f64 45.6%

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

   9. Simplified 45.6%

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

   if -7.1999999999999996e-14 < y < 3.2e12

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{54929528941}{2000000} \cdot y\right)}, \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 80.6%

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

   8. Simplified 80.6%

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

   if 3.2e12 < y

   1. Initial program 7.4%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 7.4%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 73.2%

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

   7. Simplified 73.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+162}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\left(\frac{z}{y \cdot \left(x \cdot x\right)} - \frac{\frac{a}{x}}{y}\right) + \frac{-1}{x}}\\ \mathbf{elif}\;y \leq 3200000000000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+157}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\left(\frac{z}{y \cdot \left(x \cdot x\right)} - \frac{\frac{a}{x}}{y}\right) + \frac{-1}{x}}\\ \mathbf{elif}\;y \leq 62000000000000:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.1e+157)
   (+ x (/ (- z (* x a)) y))
   (if (<= y -7.2e-14)
     (/ -1.0 (+ (- (/ z (* y (* x x))) (/ (/ a x) y)) (/ -1.0 x)))
     (if (<= y 62000000000000.0)
       (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (- (+ 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 <= -1.1e+157) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -7.2e-14) {
		tmp = -1.0 / (((z / (y * (x * x))) - ((a / x) / y)) + (-1.0 / x));
	} else if (y <= 62000000000000.0) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} 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 <= (-1.1d+157)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= (-7.2d-14)) then
        tmp = (-1.0d0) / (((z / (y * (x * x))) - ((a / x) / y)) + ((-1.0d0) / x))
    else if (y <= 62000000000000.0d0) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    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 <= -1.1e+157) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= -7.2e-14) {
		tmp = -1.0 / (((z / (y * (x * x))) - ((a / x) / y)) + (-1.0 / x));
	} else if (y <= 62000000000000.0) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} 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 <= -1.1e+157:
		tmp = x + ((z - (x * a)) / y)
	elif y <= -7.2e-14:
		tmp = -1.0 / (((z / (y * (x * x))) - ((a / x) / y)) + (-1.0 / x))
	elif y <= 62000000000000.0:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	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 <= -1.1e+157)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= -7.2e-14)
		tmp = Float64(-1.0 / Float64(Float64(Float64(z / Float64(y * Float64(x * x))) - Float64(Float64(a / x) / y)) + Float64(-1.0 / x)));
	elseif (y <= 62000000000000.0)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	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 <= -1.1e+157)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= -7.2e-14)
		tmp = -1.0 / (((z / (y * (x * x))) - ((a / x) / y)) + (-1.0 / x));
	elseif (y <= 62000000000000.0)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	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, -1.1e+157], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e-14], N[(-1.0 / N[(N[(N[(z / N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 62000000000000.0], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], 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 < -1.1000000000000001e157

   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

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(0 - z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right)\right), y\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(a \cdot x\right)\right), y\right)\right) \]

      12. *-lowering-*.f64 84.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{*.f64}\left(a, x\right)\right), y\right)\right) \]

   5. Simplified 84.8%

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

   if -1.1000000000000001e157 < y < -7.1999999999999996e-14

   1. Initial program 32.7%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 32.7%

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

      1. clear-num N/A

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

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

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

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

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

   6. Applied egg-rr 32.7%

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

   7. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

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

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

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

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

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

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

      5. associate-/r* N/A

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

      11. unpow2 N/A

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

      12. *-lowering-*.f64 45.6%

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

   9. Simplified 45.6%

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

   if -7.1999999999999996e-14 < y < 6.2e13

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 71.0%

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

   if 6.2e13 < y

   1. Initial program 7.4%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 7.4%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 73.2%

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

   7. Simplified 73.2%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+157}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{-1}{\left(\frac{z}{y \cdot \left(x \cdot x\right)} - \frac{\frac{a}{x}}{y}\right) + \frac{-1}{x}}\\ \mathbf{elif}\;y \leq 62000000000000:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ t_2 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+64}:\\ \;\;\;\;\left(t\_2 + \frac{27464.7644705}{y \cdot y}\right) - t\_1\\ \mathbf{elif}\;y \leq 3500000000000:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)) (t_2 (+ x (/ z y))))
   (if (<= y -9e+64)
     (- (+ t_2 (/ 27464.7644705 (* y y))) t_1)
     (if (<= y 3500000000000.0)
       (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (- t_2 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 * a) / y;
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -9e+64) {
		tmp = (t_2 + (27464.7644705 / (y * y))) - t_1;
	} else if (y <= 3500000000000.0) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_2 - 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) :: t_2
    real(8) :: tmp
    t_1 = (x * a) / y
    t_2 = x + (z / y)
    if (y <= (-9d+64)) then
        tmp = (t_2 + (27464.7644705d0 / (y * y))) - t_1
    else if (y <= 3500000000000.0d0) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = t_2 - 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 * a) / y;
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -9e+64) {
		tmp = (t_2 + (27464.7644705 / (y * y))) - t_1;
	} else if (y <= 3500000000000.0) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	t_2 = x + (z / y)
	tmp = 0
	if y <= -9e+64:
		tmp = (t_2 + (27464.7644705 / (y * y))) - t_1
	elif y <= 3500000000000.0:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = t_2 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	t_2 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -9e+64)
		tmp = Float64(Float64(t_2 + Float64(27464.7644705 / Float64(y * y))) - t_1);
	elseif (y <= 3500000000000.0)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(t_2 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	t_2 = x + (z / y);
	tmp = 0.0;
	if (y <= -9e+64)
		tmp = (t_2 + (27464.7644705 / (y * y))) - t_1;
	elseif (y <= 3500000000000.0)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = t_2 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+64], N[(N[(t$95$2 + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[y, 3500000000000.0], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999946e64

   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

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      8. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, \left(y \cdot y\right)\right)\right), \left(\frac{a \cdot x}{y} + \left(\frac{a \cdot \left(z - a \cdot x\right)}{{y}^{2}} + \frac{b \cdot x}{{y}^{2}}\right)\right)\right) \]

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

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

      10. associate-+r+ N/A

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

   5. Simplified 68.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, y\right)\right)\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

      2. *-lowering-*.f64 76.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   8. Simplified 76.2%

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

   if -8.99999999999999946e64 < y < 3.5e12

   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. Taylor expanded in y around 0

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

   5. Simplified 63.4%

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

   if 3.5e12 < y

   1. Initial program 7.4%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 7.4%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 73.2%

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

   7. Simplified 73.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+64}:\\ \;\;\;\;\left(\left(x + \frac{z}{y}\right) + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3500000000000:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot a}{y}\\ t_2 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+41}:\\ \;\;\;\;\left(t\_2 + \frac{27464.7644705}{y \cdot y}\right) - t\_1\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (* x a) y)) (t_2 (+ x (/ z y))))
   (if (<= y -3.6e+41)
     (- (+ t_2 (/ 27464.7644705 (* y y))) t_1)
     (if (<= y 68000000000000.0) (/ t (+ i (* y c))) (- t_2 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 * a) / y;
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -3.6e+41) {
		tmp = (t_2 + (27464.7644705 / (y * y))) - t_1;
	} else if (y <= 68000000000000.0) {
		tmp = t / (i + (y * c));
	} else {
		tmp = t_2 - 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) :: t_2
    real(8) :: tmp
    t_1 = (x * a) / y
    t_2 = x + (z / y)
    if (y <= (-3.6d+41)) then
        tmp = (t_2 + (27464.7644705d0 / (y * y))) - t_1
    else if (y <= 68000000000000.0d0) then
        tmp = t / (i + (y * c))
    else
        tmp = t_2 - 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 * a) / y;
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -3.6e+41) {
		tmp = (t_2 + (27464.7644705 / (y * y))) - t_1;
	} else if (y <= 68000000000000.0) {
		tmp = t / (i + (y * c));
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * a) / y
	t_2 = x + (z / y)
	tmp = 0
	if y <= -3.6e+41:
		tmp = (t_2 + (27464.7644705 / (y * y))) - t_1
	elif y <= 68000000000000.0:
		tmp = t / (i + (y * c))
	else:
		tmp = t_2 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * a) / y)
	t_2 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -3.6e+41)
		tmp = Float64(Float64(t_2 + Float64(27464.7644705 / Float64(y * y))) - t_1);
	elseif (y <= 68000000000000.0)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = Float64(t_2 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * a) / y;
	t_2 = x + (z / y);
	tmp = 0.0;
	if (y <= -3.6e+41)
		tmp = (t_2 + (27464.7644705 / (y * y))) - t_1;
	elseif (y <= 68000000000000.0)
		tmp = t / (i + (y * c));
	else
		tmp = t_2 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+41], N[(N[(t$95$2 + N[(27464.7644705 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[y, 68000000000000.0], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.60000000000000025e41

   1. Initial program 2.0%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

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

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

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

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

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

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

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

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

      8. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, \left(y \cdot y\right)\right)\right), \left(\frac{a \cdot x}{y} + \left(\frac{a \cdot \left(z - a \cdot x\right)}{{y}^{2}} + \frac{b \cdot x}{{y}^{2}}\right)\right)\right) \]

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

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

      10. associate-+r+ N/A

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

   5. Simplified 63.4%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, y\right)\right)\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]
   7. Step-by-step derivation

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

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

      2. *-lowering-*.f64 71.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   8. Simplified 71.2%

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

   if -3.60000000000000025e41 < y < 6.8e13

   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. Step-by-step derivation

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 95.5%

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

      1. clear-num N/A

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

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

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

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

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. *-commutative N/A

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

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

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

      11. unpow2 N/A

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

      12. *-lowering-*.f64 54.1%

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

   9. Simplified 54.1%

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

   10. Taylor expanded in t around inf

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

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

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

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

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 61.6%

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

   12. Simplified 61.6%

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

   if 6.8e13 < y

   1. Initial program 7.4%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 7.4%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 73.2%

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

   7. Simplified 73.2%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+41}:\\ \;\;\;\;\left(\left(x + \frac{z}{y}\right) + \frac{27464.7644705}{y \cdot y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2900000000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7.2e+44)
   (+ x (/ (- z (* x a)) y))
   (if (<= y 2900000000000.0)
     (/ t (+ 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 <= -7.2e+44) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 2900000000000.0) {
		tmp = t / (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 <= (-7.2d+44)) then
        tmp = x + ((z - (x * a)) / y)
    else if (y <= 2900000000000.0d0) then
        tmp = t / (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 <= -7.2e+44) {
		tmp = x + ((z - (x * a)) / y);
	} else if (y <= 2900000000000.0) {
		tmp = t / (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 <= -7.2e+44:
		tmp = x + ((z - (x * a)) / y)
	elif y <= 2900000000000.0:
		tmp = t / (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 <= -7.2e+44)
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	elseif (y <= 2900000000000.0)
		tmp = Float64(t / 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 <= -7.2e+44)
		tmp = x + ((z - (x * a)) / y);
	elseif (y <= 2900000000000.0)
		tmp = t / (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, -7.2e+44], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2900000000000.0], N[(t / 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 < -7.2e44

   1. Initial program 2.0%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(0 - z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right)\right), y\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(a \cdot x\right)\right), y\right)\right) \]

      12. *-lowering-*.f64 71.2%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{*.f64}\left(a, x\right)\right), y\right)\right) \]

   5. Simplified 71.2%

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

   if -7.2e44 < y < 2.9e12

   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. Step-by-step derivation

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 95.5%

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

      1. clear-num N/A

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

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

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

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

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. *-commutative N/A

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

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

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

      11. unpow2 N/A

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

      12. *-lowering-*.f64 54.1%

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

   9. Simplified 54.1%

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

   10. Taylor expanded in t around inf

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

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

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

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

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 61.6%

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

   12. Simplified 61.6%

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

   if 2.9e12 < y

   1. Initial program 7.4%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 7.4%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 73.2%

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

   7. Simplified 73.2%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2900000000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -3.25 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2200000000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -3.25e+41)
     t_1
     (if (<= y 2200000000000.0) (/ t (+ i (* y c))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -3.25e+41) {
		tmp = t_1;
	} else if (y <= 2200000000000.0) {
		tmp = t / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    if (y <= (-3.25d+41)) then
        tmp = t_1
    else if (y <= 2200000000000.0d0) then
        tmp = t / (i + (y * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -3.25e+41) {
		tmp = t_1;
	} else if (y <= 2200000000000.0) {
		tmp = t / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -3.25e+41:
		tmp = t_1
	elif y <= 2200000000000.0:
		tmp = t / (i + (y * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -3.25e+41)
		tmp = t_1;
	elseif (y <= 2200000000000.0)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -3.25e+41)
		tmp = t_1;
	elseif (y <= 2200000000000.0)
		tmp = t / (i + (y * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.25e+41], t$95$1, If[LessEqual[y, 2200000000000.0], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.24999999999999988e41 or 2.2e12 < y

   1. Initial program 4.7%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. sub-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(0 - z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right)\right), y\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(a \cdot x\right)\right), y\right)\right) \]

      12. *-lowering-*.f64 72.2%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{*.f64}\left(a, x\right)\right), y\right)\right) \]

   5. Simplified 72.2%

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

   if -3.24999999999999988e41 < y < 2.2e12

   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. Step-by-step derivation

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 95.5%

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

      1. clear-num N/A

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

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

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

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

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. *-commutative N/A

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

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

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

      11. unpow2 N/A

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

      12. *-lowering-*.f64 54.1%

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

   9. Simplified 54.1%

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

   10. Taylor expanded in t around inf

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

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

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

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

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 61.6%

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

   12. Simplified 61.6%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2200000000000:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -150:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 14200000000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -150.0)
   x
   (if (<= y 14200000000000.0) (/ t i) (if (<= y 5.5e+111) (/ z y) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -150.0) {
		tmp = x;
	} else if (y <= 14200000000000.0) {
		tmp = t / i;
	} else if (y <= 5.5e+111) {
		tmp = z / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-150.0d0)) then
        tmp = x
    else if (y <= 14200000000000.0d0) then
        tmp = t / i
    else if (y <= 5.5d+111) then
        tmp = z / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -150.0) {
		tmp = x;
	} else if (y <= 14200000000000.0) {
		tmp = t / i;
	} else if (y <= 5.5e+111) {
		tmp = z / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -150.0:
		tmp = x
	elif y <= 14200000000000.0:
		tmp = t / i
	elif y <= 5.5e+111:
		tmp = z / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -150.0)
		tmp = x;
	elseif (y <= 14200000000000.0)
		tmp = Float64(t / i);
	elseif (y <= 5.5e+111)
		tmp = Float64(z / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -150.0)
		tmp = x;
	elseif (y <= 14200000000000.0)
		tmp = t / i;
	elseif (y <= 5.5e+111)
		tmp = z / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -150.0], x, If[LessEqual[y, 14200000000000.0], N[(t / i), $MachinePrecision], If[LessEqual[y, 5.5e+111], N[(z / y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -150 or 5.4999999999999998e111 < y

   1. Initial program 7.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 53.2%

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

   if -150 < y < 1.42e13

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 50.4%

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

   5. Simplified 50.4%

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

   if 1.42e13 < y < 5.4999999999999998e111

   1. Initial program 21.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   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 16.8%

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

   5. Simplified 16.8%

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

   6. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 35.0%

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

   8. Simplified 35.0%

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

Alternative 13: 58.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.4e+65) x (if (<= y 1.22e+44) (/ t (+ i (* y c))) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.4e+65) {
		tmp = x;
	} else if (y <= 1.22e+44) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-4.4d+65)) then
        tmp = x
    else if (y <= 1.22d+44) then
        tmp = t / (i + (y * c))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.4e+65) {
		tmp = x;
	} else if (y <= 1.22e+44) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.4e+65:
		tmp = x
	elif y <= 1.22e+44:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.4e+65)
		tmp = x;
	elseif (y <= 1.22e+44)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.4e+65)
		tmp = x;
	elseif (y <= 1.22e+44)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.4e+65], x, If[LessEqual[y, 1.22e+44], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999997e65 or 1.22e44 < y

   1. Initial program 0.3%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 56.3%

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

   if -4.3999999999999997e65 < y < 1.22e44

   1. Initial program 92.1%

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

      1. clear-num N/A

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

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

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

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

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

   4. Applied egg-rr 92.0%

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

      1. clear-num N/A

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

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

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

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

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

   6. Applied egg-rr 92.0%

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

   7. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. *-commutative N/A

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

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

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

      11. unpow2 N/A

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

      12. *-lowering-*.f64 51.0%

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

   9. Simplified 51.0%

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

   10. Taylor expanded in t around inf

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

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

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

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

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 57.9%

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

   12. Simplified 57.9%

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

Alternative 14: 51.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -250:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 105000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -250.0) x (if (<= y 105000.0) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -250.0) {
		tmp = x;
	} else if (y <= 105000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-250.0d0)) then
        tmp = x
    else if (y <= 105000.0d0) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -250.0) {
		tmp = x;
	} else if (y <= 105000.0) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -250.0:
		tmp = x
	elif y <= 105000.0:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -250.0)
		tmp = x;
	elseif (y <= 105000.0)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -250.0)
		tmp = x;
	elseif (y <= 105000.0)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -250.0], x, If[LessEqual[y, 105000.0], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -250 or 105000 < y

   1. Initial program 10.6%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 46.3%

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

   if -250 < y < 105000

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 51.1%

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

   5. Simplified 51.1%

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

Alternative 15: 26.3% 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 54.4%

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

3. Taylor expanded in y around inf

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

5. Simplified 25.2%

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

Reproduce

herbie shell --seed 2024158 
(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)))