Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.7% → 84.1%

Time: 18.2s

Alternatives: 14

Speedup: 2.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.1% accurate, 0.5× speedup

Math

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

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 y)) (* a (/ x 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 / y)) - (a * (x / 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 / y)) - (a * (x / 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 / y)) - (a * (x / 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(Float64(x + Float64(z / y)) - Float64(a * Float64(x / 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 / y)) - (a * (x / 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[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #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 91.8%

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

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

   1. Initial program 0.0%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.0%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 75.5%

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

   7. Simplified 75.5%

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

4. Final simplification 85.6%

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

Alternative 2: 81.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+75}:\\ \;\;\;\;t\_1 - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -9.5e+75)
     (- t_1 (* a (/ x y)))
     (if (<= y -2.75e+54)
       (* y (+ (/ x a) (/ (/ z a) y)))
       (if (<= y 9.2e+47)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -9.5e+75) {
		tmp = t_1 - (a * (x / y));
	} else if (y <= -2.75e+54) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= 9.2e+47) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-9.5d+75)) then
        tmp = t_1 - (a * (x / y))
    else if (y <= (-2.75d+54)) then
        tmp = y * ((x / a) + ((z / a) / y))
    else if (y <= 9.2d+47) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -9.5e+75) {
		tmp = t_1 - (a * (x / y));
	} else if (y <= -2.75e+54) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= 9.2e+47) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -9.5e+75:
		tmp = t_1 - (a * (x / y))
	elif y <= -2.75e+54:
		tmp = y * ((x / a) + ((z / a) / y))
	elif y <= 9.2e+47:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -9.5e+75)
		tmp = Float64(t_1 - Float64(a * Float64(x / y)));
	elseif (y <= -2.75e+54)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(z / a) / y)));
	elseif (y <= 9.2e+47)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -9.5e+75)
		tmp = t_1 - (a * (x / y));
	elseif (y <= -2.75e+54)
		tmp = y * ((x / a) + ((z / a) / y));
	elseif (y <= 9.2e+47)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+75], N[(t$95$1 - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.75e+54], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+47], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.50000000000000061e75

   1. Initial program 0.0%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.0%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 79.5%

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

   7. Simplified 79.5%

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

   if -9.50000000000000061e75 < y < -2.75000000000000013e54

   1. Initial program 13.8%

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

   3. Taylor expanded in a around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 13.4%

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

   5. Simplified 13.4%

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

   6. Taylor expanded in y around inf

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

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

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

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

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

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

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

      4. associate-/r* N/A

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

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

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

      6. /-lowering-/.f64 63.8%

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

   8. Simplified 63.8%

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

   if -2.75000000000000013e54 < y < 9.1999999999999994e47

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

      3. *-lowering-*.f64 88.7%

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

   5. Simplified 88.7%

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

   if 9.1999999999999994e47 < y

   1. Initial program 6.6%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 6.6%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in a around 0

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

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

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

      2. /-lowering-/.f64 76.4%

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

   10. Simplified 76.4%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+75}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ t_2 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+77}:\\ \;\;\;\;t\_2 - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{-80}:\\ \;\;\;\;\frac{t + y \cdot \left(z \cdot \left(y \cdot y\right)\right)}{t\_1}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 y))))
   (if (<= y -9.5e+77)
     (- t_2 (* a (/ x y)))
     (if (<= y -3e+54)
       (* y (+ (/ x a) (/ (/ z a) y)))
       (if (<= y -1.62e-80)
         (/ (+ t (* y (* z (* y y)))) t_1)
         (if (<= y 5.2e+23) (/ (+ t (* y 230661.510616)) 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 / y);
	double tmp;
	if (y <= -9.5e+77) {
		tmp = t_2 - (a * (x / y));
	} else if (y <= -3e+54) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= -1.62e-80) {
		tmp = (t + (y * (z * (y * y)))) / t_1;
	} else if (y <= 5.2e+23) {
		tmp = (t + (y * 230661.510616)) / 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 / y)
    if (y <= (-9.5d+77)) then
        tmp = t_2 - (a * (x / y))
    else if (y <= (-3d+54)) then
        tmp = y * ((x / a) + ((z / a) / y))
    else if (y <= (-1.62d-80)) then
        tmp = (t + (y * (z * (y * y)))) / t_1
    else if (y <= 5.2d+23) then
        tmp = (t + (y * 230661.510616d0)) / 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 / y);
	double tmp;
	if (y <= -9.5e+77) {
		tmp = t_2 - (a * (x / y));
	} else if (y <= -3e+54) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= -1.62e-80) {
		tmp = (t + (y * (z * (y * y)))) / t_1;
	} else if (y <= 5.2e+23) {
		tmp = (t + (y * 230661.510616)) / 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 / y)
	tmp = 0
	if y <= -9.5e+77:
		tmp = t_2 - (a * (x / y))
	elif y <= -3e+54:
		tmp = y * ((x / a) + ((z / a) / y))
	elif y <= -1.62e-80:
		tmp = (t + (y * (z * (y * y)))) / t_1
	elif y <= 5.2e+23:
		tmp = (t + (y * 230661.510616)) / 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(z / y))
	tmp = 0.0
	if (y <= -9.5e+77)
		tmp = Float64(t_2 - Float64(a * Float64(x / y)));
	elseif (y <= -3e+54)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(z / a) / y)));
	elseif (y <= -1.62e-80)
		tmp = Float64(Float64(t + Float64(y * Float64(z * Float64(y * y)))) / t_1);
	elseif (y <= 5.2e+23)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / 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 / y);
	tmp = 0.0;
	if (y <= -9.5e+77)
		tmp = t_2 - (a * (x / y));
	elseif (y <= -3e+54)
		tmp = y * ((x / a) + ((z / a) / y));
	elseif (y <= -1.62e-80)
		tmp = (t + (y * (z * (y * y)))) / t_1;
	elseif (y <= 5.2e+23)
		tmp = (t + (y * 230661.510616)) / 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[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+77], N[(t$95$2 - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e+54], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.62e-80], N[(N[(t + N[(y * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 5.2e+23], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.4999999999999998e77

   1. Initial program 0.0%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.0%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 79.5%

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

   7. Simplified 79.5%

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

   if -9.4999999999999998e77 < y < -2.9999999999999999e54

   1. Initial program 13.8%

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

   3. Taylor expanded in a around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 13.4%

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

   5. Simplified 13.4%

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

   6. Taylor expanded in y around inf

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

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

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

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

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

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

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

      4. associate-/r* N/A

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

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

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

      6. /-lowering-/.f64 63.8%

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

   8. Simplified 63.8%

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

   if -2.9999999999999999e54 < y < -1.62e-80

   1. Initial program 79.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   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 54.2%

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

   5. Simplified 54.2%

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

   if -1.62e-80 < y < 5.19999999999999983e23

   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 92.2%

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

   5. Simplified 92.2%

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

   if 5.19999999999999983e23 < y

   1. Initial program 13.7%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 13.7%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in a around 0

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

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

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

      2. /-lowering-/.f64 71.3%

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

   10. Simplified 71.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+77}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{-80}:\\ \;\;\;\;\frac{t + y \cdot \left(z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ t_2 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+66}:\\ \;\;\;\;t\_1 - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-58}:\\ \;\;\;\;\frac{t + y \cdot \left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right)}{t\_2}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))) (t_2 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (<= y -3.5e+66)
     (- t_1 (* a (/ x y)))
     (if (<= y -4.4e-58)
       (/ (+ t (* y (* x (* y (* y y))))) t_2)
       (if (<= y 1.5e+23) (/ (+ t (* y 230661.510616)) 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 + (z / y);
	double t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -3.5e+66) {
		tmp = t_1 - (a * (x / y));
	} else if (y <= -4.4e-58) {
		tmp = (t + (y * (x * (y * (y * y))))) / t_2;
	} else if (y <= 1.5e+23) {
		tmp = (t + (y * 230661.510616)) / t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + (z / y)
    t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    if (y <= (-3.5d+66)) then
        tmp = t_1 - (a * (x / y))
    else if (y <= (-4.4d-58)) then
        tmp = (t + (y * (x * (y * (y * y))))) / t_2
    else if (y <= 1.5d+23) then
        tmp = (t + (y * 230661.510616d0)) / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -3.5e+66) {
		tmp = t_1 - (a * (x / y));
	} else if (y <= -4.4e-58) {
		tmp = (t + (y * (x * (y * (y * y))))) / t_2;
	} else if (y <= 1.5e+23) {
		tmp = (t + (y * 230661.510616)) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	tmp = 0
	if y <= -3.5e+66:
		tmp = t_1 - (a * (x / y))
	elif y <= -4.4e-58:
		tmp = (t + (y * (x * (y * (y * y))))) / t_2
	elif y <= 1.5e+23:
		tmp = (t + (y * 230661.510616)) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	t_2 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if (y <= -3.5e+66)
		tmp = Float64(t_1 - Float64(a * Float64(x / y)));
	elseif (y <= -4.4e-58)
		tmp = Float64(Float64(t + Float64(y * Float64(x * Float64(y * Float64(y * y))))) / t_2);
	elseif (y <= 1.5e+23)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	tmp = 0.0;
	if (y <= -3.5e+66)
		tmp = t_1 - (a * (x / y));
	elseif (y <= -4.4e-58)
		tmp = (t + (y * (x * (y * (y * y))))) / t_2;
	elseif (y <= 1.5e+23)
		tmp = (t + (y * 230661.510616)) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -3.5e+66], N[(t$95$1 - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.4e-58], N[(N[(t + N[(y * N[(x * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 1.5e+23], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4999999999999997e66

   1. Initial program 0.2%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.2%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 74.4%

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

   7. Simplified 74.4%

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

   if -3.4999999999999997e66 < y < -4.40000000000000011e-58

   1. Initial program 64.8%

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

   3. Taylor expanded in x around inf

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

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

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

      2. cube-mult N/A

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

      3. unpow2 N/A

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

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

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

      5. unpow2 N/A

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

      6. *-lowering-*.f64 45.4%

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

   5. Simplified 45.4%

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

   if -4.40000000000000011e-58 < y < 1.5e23

   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 90.3%

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

   5. Simplified 90.3%

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

   if 1.5e23 < y

   1. Initial program 13.7%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 13.7%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in a around 0

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

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

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

      2. /-lowering-/.f64 71.3%

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

   10. Simplified 71.3%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+66}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-58}:\\ \;\;\;\;\frac{t + y \cdot \left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+76}:\\ \;\;\;\;t\_1 - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+23}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -9.2e+76)
     (- t_1 (* a (/ x y)))
     (if (<= y -3.2e+53)
       (* y (+ (/ x a) (/ (/ z a) y)))
       (if (<= y 5e+23)
         (/
          (+ t (* y 230661.510616))
          (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -9.2e+76) {
		tmp = t_1 - (a * (x / y));
	} else if (y <= -3.2e+53) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= 5e+23) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-9.2d+76)) then
        tmp = t_1 - (a * (x / y))
    else if (y <= (-3.2d+53)) then
        tmp = y * ((x / a) + ((z / a) / y))
    else if (y <= 5d+23) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -9.2e+76) {
		tmp = t_1 - (a * (x / y));
	} else if (y <= -3.2e+53) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= 5e+23) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -9.2e+76:
		tmp = t_1 - (a * (x / y))
	elif y <= -3.2e+53:
		tmp = y * ((x / a) + ((z / a) / y))
	elif y <= 5e+23:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -9.2e+76)
		tmp = Float64(t_1 - Float64(a * Float64(x / y)));
	elseif (y <= -3.2e+53)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(z / a) / y)));
	elseif (y <= 5e+23)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -9.2e+76)
		tmp = t_1 - (a * (x / y));
	elseif (y <= -3.2e+53)
		tmp = y * ((x / a) + ((z / a) / y));
	elseif (y <= 5e+23)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+76], N[(t$95$1 - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e+53], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+23], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.20000000000000005e76

   1. Initial program 0.0%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.0%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 79.5%

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

   7. Simplified 79.5%

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

   if -9.20000000000000005e76 < y < -3.2e53

   1. Initial program 13.8%

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

   3. Taylor expanded in a around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 13.4%

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

   5. Simplified 13.4%

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

   6. Taylor expanded in y around inf

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

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

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

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

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

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

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

      4. associate-/r* N/A

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

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

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

      6. /-lowering-/.f64 63.8%

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

   8. Simplified 63.8%

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

   if -3.2e53 < y < 4.9999999999999999e23

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 81.1%

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

   5. Simplified 81.1%

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

   if 4.9999999999999999e23 < y

   1. Initial program 13.7%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 13.7%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in a around 0

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

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

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

      2. /-lowering-/.f64 71.3%

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

   10. Simplified 71.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+76}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+23}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+74}:\\ \;\;\;\;t\_1 - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -0.00076:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -4.4e+74)
     (- t_1 (* a (/ x y)))
     (if (<= y -0.00076)
       (* y (+ (/ x a) (/ (/ z a) y)))
       (if (<= y 7.5e+21)
         (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -4.4e+74) {
		tmp = t_1 - (a * (x / y));
	} else if (y <= -0.00076) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= 7.5e+21) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-4.4d+74)) then
        tmp = t_1 - (a * (x / y))
    else if (y <= (-0.00076d0)) then
        tmp = y * ((x / a) + ((z / a) / y))
    else if (y <= 7.5d+21) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -4.4e+74) {
		tmp = t_1 - (a * (x / y));
	} else if (y <= -0.00076) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= 7.5e+21) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -4.4e+74:
		tmp = t_1 - (a * (x / y))
	elif y <= -0.00076:
		tmp = y * ((x / a) + ((z / a) / y))
	elif y <= 7.5e+21:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -4.4e+74)
		tmp = Float64(t_1 - Float64(a * Float64(x / y)));
	elseif (y <= -0.00076)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(z / a) / y)));
	elseif (y <= 7.5e+21)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -4.4e+74)
		tmp = t_1 - (a * (x / y));
	elseif (y <= -0.00076)
		tmp = y * ((x / a) + ((z / a) / y));
	elseif (y <= 7.5e+21)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+74], N[(t$95$1 - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.00076], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+21], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4000000000000002e74

   1. Initial program 0.0%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.0%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 79.5%

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

   7. Simplified 79.5%

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

   if -4.4000000000000002e74 < y < -7.6000000000000004e-4

   1. Initial program 40.9%

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

   3. Taylor expanded in a around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 32.2%

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

   5. Simplified 32.2%

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

   6. Taylor expanded in y around inf

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

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

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

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

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

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

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

      4. associate-/r* N/A

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

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

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

      6. /-lowering-/.f64 39.6%

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

   8. Simplified 39.6%

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

   if -7.6000000000000004e-4 < y < 7.5e21

   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 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 82.6%

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

   8. Simplified 82.6%

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

   if 7.5e21 < y

   1. Initial program 13.7%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 13.7%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in a around 0

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

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

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

      2. /-lowering-/.f64 71.3%

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

   10. Simplified 71.3%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+74}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -0.00076:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+76}:\\ \;\;\;\;t\_2 - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -0.00062:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{t\_1}{y \cdot c}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{t\_1}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616))) (t_2 (+ x (/ z y))))
   (if (<= y -1.4e+76)
     (- t_2 (* a (/ x y)))
     (if (<= y -0.00062)
       (* y (+ (/ x a) (/ (/ z a) y)))
       (if (<= y -2.2e-109)
         (/ t_1 (* y c))
         (if (<= y 6.2e+22) (/ t_1 i) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -1.4e+76) {
		tmp = t_2 - (a * (x / y));
	} else if (y <= -0.00062) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= -2.2e-109) {
		tmp = t_1 / (y * c);
	} else if (y <= 6.2e+22) {
		tmp = t_1 / i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    t_2 = x + (z / y)
    if (y <= (-1.4d+76)) then
        tmp = t_2 - (a * (x / y))
    else if (y <= (-0.00062d0)) then
        tmp = y * ((x / a) + ((z / a) / y))
    else if (y <= (-2.2d-109)) then
        tmp = t_1 / (y * c)
    else if (y <= 6.2d+22) then
        tmp = t_1 / i
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -1.4e+76) {
		tmp = t_2 - (a * (x / y));
	} else if (y <= -0.00062) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= -2.2e-109) {
		tmp = t_1 / (y * c);
	} else if (y <= 6.2e+22) {
		tmp = t_1 / i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	t_2 = x + (z / y)
	tmp = 0
	if y <= -1.4e+76:
		tmp = t_2 - (a * (x / y))
	elif y <= -0.00062:
		tmp = y * ((x / a) + ((z / a) / y))
	elif y <= -2.2e-109:
		tmp = t_1 / (y * c)
	elif y <= 6.2e+22:
		tmp = t_1 / i
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	t_2 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -1.4e+76)
		tmp = Float64(t_2 - Float64(a * Float64(x / y)));
	elseif (y <= -0.00062)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(z / a) / y)));
	elseif (y <= -2.2e-109)
		tmp = Float64(t_1 / Float64(y * c));
	elseif (y <= 6.2e+22)
		tmp = Float64(t_1 / i);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	t_2 = x + (z / y);
	tmp = 0.0;
	if (y <= -1.4e+76)
		tmp = t_2 - (a * (x / y));
	elseif (y <= -0.00062)
		tmp = y * ((x / a) + ((z / a) / y));
	elseif (y <= -2.2e-109)
		tmp = t_1 / (y * c);
	elseif (y <= 6.2e+22)
		tmp = t_1 / i;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+76], N[(t$95$2 - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.00062], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.2e-109], N[(t$95$1 / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+22], N[(t$95$1 / i), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.3999999999999999e76

   1. Initial program 0.0%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.0%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 79.5%

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

   7. Simplified 79.5%

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

   if -1.3999999999999999e76 < y < -6.2e-4

   1. Initial program 40.9%

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

   3. Taylor expanded in a around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 32.2%

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

   5. Simplified 32.2%

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

   6. Taylor expanded in y around inf

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

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

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

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

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

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

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

      4. associate-/r* N/A

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

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

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

      6. /-lowering-/.f64 39.6%

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

   8. Simplified 39.6%

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

   if -6.2e-4 < y < -2.1999999999999999e-109

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 42.8%

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

   8. Simplified 42.8%

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

   if -2.1999999999999999e-109 < y < 6.2000000000000004e22

   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 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 62.2%

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

   if 6.2000000000000004e22 < y

   1. Initial program 13.7%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 13.7%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in a around 0

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

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

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

      2. /-lowering-/.f64 71.3%

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

   10. Simplified 71.3%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+76}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -0.00062:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ t_2 := t + y \cdot 230661.510616\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.0006:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{t\_2}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{t\_2}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))) (t_2 (+ t (* y 230661.510616))))
   (if (<= y -2.8e+77)
     t_1
     (if (<= y -0.0006)
       (* y (+ (/ x a) (/ (/ z a) y)))
       (if (<= y -9.5e-109)
         (/ t_2 (* y c))
         (if (<= y 1.6e+22) (/ t_2 i) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double t_2 = t + (y * 230661.510616);
	double tmp;
	if (y <= -2.8e+77) {
		tmp = t_1;
	} else if (y <= -0.0006) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= -9.5e-109) {
		tmp = t_2 / (y * c);
	} else if (y <= 1.6e+22) {
		tmp = t_2 / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / y)
    t_2 = t + (y * 230661.510616d0)
    if (y <= (-2.8d+77)) then
        tmp = t_1
    else if (y <= (-0.0006d0)) then
        tmp = y * ((x / a) + ((z / a) / y))
    else if (y <= (-9.5d-109)) then
        tmp = t_2 / (y * c)
    else if (y <= 1.6d+22) then
        tmp = t_2 / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double t_2 = t + (y * 230661.510616);
	double tmp;
	if (y <= -2.8e+77) {
		tmp = t_1;
	} else if (y <= -0.0006) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= -9.5e-109) {
		tmp = t_2 / (y * c);
	} else if (y <= 1.6e+22) {
		tmp = t_2 / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	t_2 = t + (y * 230661.510616)
	tmp = 0
	if y <= -2.8e+77:
		tmp = t_1
	elif y <= -0.0006:
		tmp = y * ((x / a) + ((z / a) / y))
	elif y <= -9.5e-109:
		tmp = t_2 / (y * c)
	elif y <= 1.6e+22:
		tmp = t_2 / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	t_2 = Float64(t + Float64(y * 230661.510616))
	tmp = 0.0
	if (y <= -2.8e+77)
		tmp = t_1;
	elseif (y <= -0.0006)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(z / a) / y)));
	elseif (y <= -9.5e-109)
		tmp = Float64(t_2 / Float64(y * c));
	elseif (y <= 1.6e+22)
		tmp = Float64(t_2 / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	t_2 = t + (y * 230661.510616);
	tmp = 0.0;
	if (y <= -2.8e+77)
		tmp = t_1;
	elseif (y <= -0.0006)
		tmp = y * ((x / a) + ((z / a) / y));
	elseif (y <= -9.5e-109)
		tmp = t_2 / (y * c);
	elseif (y <= 1.6e+22)
		tmp = t_2 / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+77], t$95$1, If[LessEqual[y, -0.0006], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-109], N[(t$95$2 / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+22], N[(t$95$2 / i), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.8e77 or 1.6e22 < y

   1. Initial program 6.8%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 6.8%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 75.3%

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

   7. Simplified 75.3%

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

   8. Taylor expanded in a around 0

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

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

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

      2. /-lowering-/.f64 75.2%

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

   10. Simplified 75.2%

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

   if -2.8e77 < y < -5.99999999999999947e-4

   1. Initial program 40.9%

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

   3. Taylor expanded in a around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 32.2%

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

   5. Simplified 32.2%

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

   6. Taylor expanded in y around inf

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

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

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

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

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

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

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

      4. associate-/r* N/A

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

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

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

      6. /-lowering-/.f64 39.6%

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

   8. Simplified 39.6%

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

   if -5.99999999999999947e-4 < y < -9.49999999999999933e-109

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 42.8%

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

   8. Simplified 42.8%

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

   if -9.49999999999999933e-109 < y < 1.6e22

   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 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 62.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -0.0006:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+74}:\\ \;\;\;\;t\_1 - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -0.00052:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -7e+74)
     (- t_1 (* a (/ x y)))
     (if (<= y -0.00052)
       (* y (+ (/ x a) (/ (/ z a) y)))
       (if (<= y 1.8e+22) (/ (+ t (* y 230661.510616)) (+ 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 / y);
	double tmp;
	if (y <= -7e+74) {
		tmp = t_1 - (a * (x / y));
	} else if (y <= -0.00052) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= 1.8e+22) {
		tmp = (t + (y * 230661.510616)) / (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 / y)
    if (y <= (-7d+74)) then
        tmp = t_1 - (a * (x / y))
    else if (y <= (-0.00052d0)) then
        tmp = y * ((x / a) + ((z / a) / y))
    else if (y <= 1.8d+22) then
        tmp = (t + (y * 230661.510616d0)) / (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 / y);
	double tmp;
	if (y <= -7e+74) {
		tmp = t_1 - (a * (x / y));
	} else if (y <= -0.00052) {
		tmp = y * ((x / a) + ((z / a) / y));
	} else if (y <= 1.8e+22) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -7e+74:
		tmp = t_1 - (a * (x / y))
	elif y <= -0.00052:
		tmp = y * ((x / a) + ((z / a) / y))
	elif y <= 1.8e+22:
		tmp = (t + (y * 230661.510616)) / (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(z / y))
	tmp = 0.0
	if (y <= -7e+74)
		tmp = Float64(t_1 - Float64(a * Float64(x / y)));
	elseif (y <= -0.00052)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(Float64(z / a) / y)));
	elseif (y <= 1.8e+22)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / 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 / y);
	tmp = 0.0;
	if (y <= -7e+74)
		tmp = t_1 - (a * (x / y));
	elseif (y <= -0.00052)
		tmp = y * ((x / a) + ((z / a) / y));
	elseif (y <= 1.8e+22)
		tmp = (t + (y * 230661.510616)) / (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[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+74], N[(t$95$1 - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.00052], N[(y * N[(N[(x / a), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+22], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.00000000000000029e74

   1. Initial program 0.0%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.0%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 79.5%

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

   7. Simplified 79.5%

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

   if -7.00000000000000029e74 < y < -5.19999999999999954e-4

   1. Initial program 40.9%

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

   3. Taylor expanded in a around inf

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 32.2%

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

   5. Simplified 32.2%

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

   6. Taylor expanded in y around inf

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

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

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

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

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

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

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

      4. associate-/r* N/A

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

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

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

      6. /-lowering-/.f64 39.6%

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

   8. Simplified 39.6%

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

   if -5.19999999999999954e-4 < y < 1.8e22

   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 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 75.5%

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

   8. Simplified 75.5%

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

   if 1.8e22 < y

   1. Initial program 13.7%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 13.7%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in a around 0

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

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

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

      2. /-lowering-/.f64 71.3%

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

   10. Simplified 71.3%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+74}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -0.00052:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{\frac{z}{a}}{y}\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{t\_1}{y \cdot c}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{t\_1}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616))) (t_2 (+ x (/ z y))))
   (if (<= y -3.9e+46)
     t_2
     (if (<= y -9.5e-109) (/ t_1 (* y c)) (if (<= y 5.2e+22) (/ t_1 i) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -3.9e+46) {
		tmp = t_2;
	} else if (y <= -9.5e-109) {
		tmp = t_1 / (y * c);
	} else if (y <= 5.2e+22) {
		tmp = t_1 / i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    t_2 = x + (z / y)
    if (y <= (-3.9d+46)) then
        tmp = t_2
    else if (y <= (-9.5d-109)) then
        tmp = t_1 / (y * c)
    else if (y <= 5.2d+22) then
        tmp = t_1 / i
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = x + (z / y);
	double tmp;
	if (y <= -3.9e+46) {
		tmp = t_2;
	} else if (y <= -9.5e-109) {
		tmp = t_1 / (y * c);
	} else if (y <= 5.2e+22) {
		tmp = t_1 / i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	t_2 = x + (z / y)
	tmp = 0
	if y <= -3.9e+46:
		tmp = t_2
	elif y <= -9.5e-109:
		tmp = t_1 / (y * c)
	elif y <= 5.2e+22:
		tmp = t_1 / i
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	t_2 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -3.9e+46)
		tmp = t_2;
	elseif (y <= -9.5e-109)
		tmp = Float64(t_1 / Float64(y * c));
	elseif (y <= 5.2e+22)
		tmp = Float64(t_1 / i);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	t_2 = x + (z / y);
	tmp = 0.0;
	if (y <= -3.9e+46)
		tmp = t_2;
	elseif (y <= -9.5e-109)
		tmp = t_1 / (y * c);
	elseif (y <= 5.2e+22)
		tmp = t_1 / i;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+46], t$95$2, If[LessEqual[y, -9.5e-109], N[(t$95$1 / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+22], N[(t$95$1 / i), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.89999999999999995e46 or 5.2e22 < y

   1. Initial program 7.3%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 7.3%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in a around 0

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

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

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

      2. /-lowering-/.f64 68.6%

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

   10. Simplified 68.6%

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

   if -3.89999999999999995e46 < y < -9.49999999999999933e-109

   1. Initial program 90.2%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 52.4%

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

   5. Simplified 52.4%

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

   6. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 32.5%

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

   8. Simplified 32.5%

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

   if -9.49999999999999933e-109 < y < 5.2e22

   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 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 62.2%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -1.66 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -1.66e+34)
     t_1
     (if (<= y 3.8e+22) (/ (+ t (* y 230661.510616)) i) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -1.66e+34) {
		tmp = t_1;
	} else if (y <= 3.8e+22) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-1.66d+34)) then
        tmp = t_1
    else if (y <= 3.8d+22) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -1.66e+34) {
		tmp = t_1;
	} else if (y <= 3.8e+22) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -1.66e+34:
		tmp = t_1
	elif y <= 3.8e+22:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -1.66e+34)
		tmp = t_1;
	elseif (y <= 3.8e+22)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -1.66e+34)
		tmp = t_1;
	elseif (y <= 3.8e+22)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.66e+34], t$95$1, If[LessEqual[y, 3.8e+22], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6599999999999999e34 or 3.8000000000000004e22 < y

   1. Initial program 8.1%

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

      1. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 8.1%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in a around 0

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

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

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

      2. /-lowering-/.f64 67.5%

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

   10. Simplified 67.5%

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

   if -1.6599999999999999e34 < y < 3.8000000000000004e22

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 50.2%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{i}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.66 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{z}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -1.8e+53) t_1 (if (<= y 6e+21) (/ t i) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -1.8e+53) {
		tmp = t_1;
	} else if (y <= 6e+21) {
		tmp = t / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-1.8d+53)) then
        tmp = t_1
    else if (y <= 6d+21) then
        tmp = t / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -1.8e+53) {
		tmp = t_1;
	} else if (y <= 6e+21) {
		tmp = t / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -1.8e+53:
		tmp = t_1
	elif y <= 6e+21:
		tmp = t / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -1.8e+53)
		tmp = t_1;
	elseif (y <= 6e+21)
		tmp = Float64(t / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -1.8e+53)
		tmp = t_1;
	elseif (y <= 6e+21)
		tmp = t / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+53], t$95$1, If[LessEqual[y, 6e+21], N[(t / i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e53 or 6e21 < 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. flip-+ N/A

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

      2. clear-num N/A

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

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

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

      4. clear-num N/A

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

      5. flip-+ N/A

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

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

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

   4. Applied egg-rr 7.4%

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

   5. 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. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in a around 0

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

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

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

      2. /-lowering-/.f64 69.7%

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

   10. Simplified 69.7%

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

   if -1.8e53 < y < 6e21

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 47.1%

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

   5. Simplified 47.1%

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

Alternative 13: 50.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.75e+53) x (if (<= y 3.6e+18) (/ 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 <= -1.75e+53) {
		tmp = x;
	} else if (y <= 3.6e+18) {
		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 <= (-1.75d+53)) then
        tmp = x
    else if (y <= 3.6d+18) 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 <= -1.75e+53) {
		tmp = x;
	} else if (y <= 3.6e+18) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.75e+53:
		tmp = x
	elif y <= 3.6e+18:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.75e+53)
		tmp = x;
	elseif (y <= 3.6e+18)
		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 <= -1.75e+53)
		tmp = x;
	elseif (y <= 3.6e+18)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.75e+53], x, If[LessEqual[y, 3.6e+18], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75000000000000009e53 or 3.6e18 < y

   1. Initial program 8.2%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 58.3%

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

   if -1.75000000000000009e53 < y < 3.6e18

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 47.4%

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

   5. Simplified 47.4%

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

Alternative 14: 25.3% 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 56.7%

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

3. Taylor expanded in y around inf

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

5. Simplified 28.0%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024152 
(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)))