Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.3% → 84.5%

Time: 26.2s

Alternatives: 12

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: 56.3% 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: 84.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
           t)
          (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))
   (if (<= t_1 INFINITY) t_1 (/ x (/ (+ a (+ y (/ b y))) y)))))

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around 0 0.0%

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

   5. Simplified 0.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}}} \]

   6. Taylor expanded in y around inf 60.2%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{b}{x \cdot y} + \frac{y}{x}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 60.2%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \color{blue}{\left(\frac{y}{x} + \frac{b}{x \cdot y}\right)}\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      2. *-commutative 60.2%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{\color{blue}{y \cdot x}}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      3. associate-*r/ 60.2%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\color{blue}{\frac{27464.7644705 \cdot 1}{{x}^{2} \cdot y}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      4. metadata-eval 60.2%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{\color{blue}{27464.7644705}}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      5. *-commutative 60.2%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{\color{blue}{y \cdot {x}^{2}}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      6. *-commutative 60.2%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{\color{blue}{y \cdot x}}\right)\right)} \]

   8. Simplified 60.2%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y \cdot x}\right)\right)}} \]

   9. Taylor expanded in x around inf 45.2%

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

       1. associate-/l* 80.2%

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

   11. Simplified 80.2%

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

4. Final simplification 85.6%

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

Alternative 2: 79.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ t_2 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\\ t_3 := \frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -0.015:\\ \;\;\;\;\frac{t_2}{t_1}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{y \cdot t_2 + t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 0.06:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot t_1 + i}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ y a)) b)) c))
        (t_2 (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
        (t_3 (/ x (/ (+ a (+ y (/ b y))) y))))
   (if (<= y -5.5e+97)
     t_3
     (if (<= y -0.015)
       (/ t_2 t_1)
       (if (<= y -1.3e-55)
         (/ (+ (* y t_2) t) (+ i (* y (+ c (* y b)))))
         (if (<= y 0.06)
           (/
            (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
            (+ (* y t_1) i))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))));
	double t_3 = x / ((a + (y + (b / y))) / y);
	double tmp;
	if (y <= -5.5e+97) {
		tmp = t_3;
	} else if (y <= -0.015) {
		tmp = t_2 / t_1;
	} else if (y <= -1.3e-55) {
		tmp = ((y * t_2) + t) / (i + (y * (c + (y * b))));
	} else if (y <= 0.06) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i);
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (y * ((y * (y + a)) + b)) + c
    t_2 = 230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))
    t_3 = x / ((a + (y + (b / y))) / y)
    if (y <= (-5.5d+97)) then
        tmp = t_3
    else if (y <= (-0.015d0)) then
        tmp = t_2 / t_1
    else if (y <= (-1.3d-55)) then
        tmp = ((y * t_2) + t) / (i + (y * (c + (y * b))))
    else if (y <= 0.06d0) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((y * t_1) + i)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))));
	double t_3 = x / ((a + (y + (b / y))) / y);
	double tmp;
	if (y <= -5.5e+97) {
		tmp = t_3;
	} else if (y <= -0.015) {
		tmp = t_2 / t_1;
	} else if (y <= -1.3e-55) {
		tmp = ((y * t_2) + t) / (i + (y * (c + (y * b))));
	} else if (y <= 0.06) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * (y + a)) + b)) + c
	t_2 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))
	t_3 = x / ((a + (y + (b / y))) / y)
	tmp = 0
	if y <= -5.5e+97:
		tmp = t_3
	elif y <= -0.015:
		tmp = t_2 / t_1
	elif y <= -1.3e-55:
		tmp = ((y * t_2) + t) / (i + (y * (c + (y * b))))
	elif y <= 0.06:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)
	t_2 = Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))
	t_3 = Float64(x / Float64(Float64(a + Float64(y + Float64(b / y))) / y))
	tmp = 0.0
	if (y <= -5.5e+97)
		tmp = t_3;
	elseif (y <= -0.015)
		tmp = Float64(t_2 / t_1);
	elseif (y <= -1.3e-55)
		tmp = Float64(Float64(Float64(y * t_2) + t) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 0.06)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(Float64(y * t_1) + i));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * (y + a)) + b)) + c;
	t_2 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))));
	t_3 = x / ((a + (y + (b / y))) / y);
	tmp = 0.0;
	if (y <= -5.5e+97)
		tmp = t_3;
	elseif (y <= -0.015)
		tmp = t_2 / t_1;
	elseif (y <= -1.3e-55)
		tmp = ((y * t_2) + t) / (i + (y * (c + (y * b))));
	elseif (y <= 0.06)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * t_1) + i);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(N[(a + N[(y + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+97], t$95$3, If[LessEqual[y, -0.015], N[(t$95$2 / t$95$1), $MachinePrecision], If[LessEqual[y, -1.3e-55], N[(N[(N[(y * t$95$2), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.06], 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 * t$95$1), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.50000000000000021e97 or 0.059999999999999998 < y

   1. Initial program 4.8%

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

   3. Taylor expanded in t around 0 3.9%

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

   5. Simplified 5.0%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}}} \]

   6. Taylor expanded in y around inf 56.8%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{b}{x \cdot y} + \frac{y}{x}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \color{blue}{\left(\frac{y}{x} + \frac{b}{x \cdot y}\right)}\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      2. *-commutative 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{\color{blue}{y \cdot x}}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      3. associate-*r/ 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\color{blue}{\frac{27464.7644705 \cdot 1}{{x}^{2} \cdot y}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      4. metadata-eval 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{\color{blue}{27464.7644705}}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      5. *-commutative 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{\color{blue}{y \cdot {x}^{2}}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      6. *-commutative 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{\color{blue}{y \cdot x}}\right)\right)} \]

   8. Simplified 56.8%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y \cdot x}\right)\right)}} \]

   9. Taylor expanded in x around inf 43.4%

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

       1. associate-/l* 75.6%

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

   11. Simplified 75.6%

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

   if -5.50000000000000021e97 < y < -0.014999999999999999

   1. Initial program 51.1%

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

   3. Taylor expanded in t around 0 41.5%

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

   5. Simplified 51.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}}} \]

   6. Taylor expanded in i around 0 61.3%

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

   if -0.014999999999999999 < y < -1.2999999999999999e-55

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 90.6%

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

      1. *-commutative 90.6%

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

   5. Simplified 90.6%

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

   if -1.2999999999999999e-55 < y < 0.059999999999999998

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.7%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + y \cdot z\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{elif}\;y \leq -0.015:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 0.06:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\\ t_2 := \frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -0.0029:\\ \;\;\;\;\frac{t_1}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{elif}\;y \leq 4500000000:\\ \;\;\;\;\frac{y \cdot t_1 + t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
        (t_2 (/ x (/ (+ a (+ y (/ b y))) y))))
   (if (<= y -5.5e+97)
     t_2
     (if (<= y -0.0029)
       (/ t_1 (+ (* y (+ (* y (+ y a)) b)) c))
       (if (<= y 4500000000.0)
         (/ (+ (* y t_1) t) (+ i (* y (+ c (* y b)))))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))));
	double t_2 = x / ((a + (y + (b / y))) / y);
	double tmp;
	if (y <= -5.5e+97) {
		tmp = t_2;
	} else if (y <= -0.0029) {
		tmp = t_1 / ((y * ((y * (y + a)) + b)) + c);
	} else if (y <= 4500000000.0) {
		tmp = ((y * t_1) + t) / (i + (y * (c + (y * b))));
	} 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 = 230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))
    t_2 = x / ((a + (y + (b / y))) / y)
    if (y <= (-5.5d+97)) then
        tmp = t_2
    else if (y <= (-0.0029d0)) then
        tmp = t_1 / ((y * ((y * (y + a)) + b)) + c)
    else if (y <= 4500000000.0d0) then
        tmp = ((y * t_1) + t) / (i + (y * (c + (y * b))))
    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 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))));
	double t_2 = x / ((a + (y + (b / y))) / y);
	double tmp;
	if (y <= -5.5e+97) {
		tmp = t_2;
	} else if (y <= -0.0029) {
		tmp = t_1 / ((y * ((y * (y + a)) + b)) + c);
	} else if (y <= 4500000000.0) {
		tmp = ((y * t_1) + t) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))
	t_2 = x / ((a + (y + (b / y))) / y)
	tmp = 0
	if y <= -5.5e+97:
		tmp = t_2
	elif y <= -0.0029:
		tmp = t_1 / ((y * ((y * (y + a)) + b)) + c)
	elif y <= 4500000000.0:
		tmp = ((y * t_1) + t) / (i + (y * (c + (y * b))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))
	t_2 = Float64(x / Float64(Float64(a + Float64(y + Float64(b / y))) / y))
	tmp = 0.0
	if (y <= -5.5e+97)
		tmp = t_2;
	elseif (y <= -0.0029)
		tmp = Float64(t_1 / Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c));
	elseif (y <= 4500000000.0)
		tmp = Float64(Float64(Float64(y * t_1) + t) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))));
	t_2 = x / ((a + (y + (b / y))) / y);
	tmp = 0.0;
	if (y <= -5.5e+97)
		tmp = t_2;
	elseif (y <= -0.0029)
		tmp = t_1 / ((y * ((y * (y + a)) + b)) + c);
	elseif (y <= 4500000000.0)
		tmp = ((y * t_1) + t) / (i + (y * (c + (y * b))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(a + N[(y + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+97], t$95$2, If[LessEqual[y, -0.0029], N[(t$95$1 / N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4500000000.0], N[(N[(N[(y * t$95$1), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.50000000000000021e97 or 4.5e9 < y

   1. Initial program 3.9%

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

   3. Taylor expanded in t around 0 3.1%

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

   5. Simplified 4.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}}} \]

   6. Taylor expanded in y around inf 56.4%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{b}{x \cdot y} + \frac{y}{x}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 56.4%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \color{blue}{\left(\frac{y}{x} + \frac{b}{x \cdot y}\right)}\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      2. *-commutative 56.4%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{\color{blue}{y \cdot x}}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      3. associate-*r/ 56.4%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\color{blue}{\frac{27464.7644705 \cdot 1}{{x}^{2} \cdot y}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      4. metadata-eval 56.4%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{\color{blue}{27464.7644705}}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      5. *-commutative 56.4%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{\color{blue}{y \cdot {x}^{2}}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      6. *-commutative 56.4%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{\color{blue}{y \cdot x}}\right)\right)} \]

   8. Simplified 56.4%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y \cdot x}\right)\right)}} \]

   9. Taylor expanded in x around inf 42.9%

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

       1. associate-/l* 75.4%

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

   11. Simplified 75.4%

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

   if -5.50000000000000021e97 < y < -0.0029

   1. Initial program 51.1%

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

   3. Taylor expanded in t around 0 41.5%

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

   5. Simplified 51.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}}} \]

   6. Taylor expanded in i around 0 61.3%

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

   if -0.0029 < y < 4.5e9

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 95.7%

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

      1. *-commutative 95.7%

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

   5. Simplified 95.7%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{elif}\;y \leq -0.0029:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{elif}\;y \leq 4500000000:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.095:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{elif}\;y \leq 0.06:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ x (/ (+ a (+ y (/ b y))) y))))
   (if (<= y -5.5e+97)
     t_1
     (if (<= y -0.095)
       (/
        (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))
        (+ (* y (+ (* y (+ y a)) b)) c))
       (if (<= y 0.06)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ 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 / ((a + (y + (b / y))) / y);
	double tmp;
	if (y <= -5.5e+97) {
		tmp = t_1;
	} else if (y <= -0.095) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / ((y * ((y * (y + a)) + b)) + c);
	} else if (y <= 0.06) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (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 / ((a + (y + (b / y))) / y)
    if (y <= (-5.5d+97)) then
        tmp = t_1
    else if (y <= (-0.095d0)) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))) / ((y * ((y * (y + a)) + b)) + c)
    else if (y <= 0.06d0) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (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 / ((a + (y + (b / y))) / y);
	double tmp;
	if (y <= -5.5e+97) {
		tmp = t_1;
	} else if (y <= -0.095) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / ((y * ((y * (y + a)) + b)) + c);
	} else if (y <= 0.06) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (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 / ((a + (y + (b / y))) / y)
	tmp = 0
	if y <= -5.5e+97:
		tmp = t_1
	elif y <= -0.095:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / ((y * ((y * (y + a)) + b)) + c)
	elif y <= 0.06:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (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(Float64(a + Float64(y + Float64(b / y))) / y))
	tmp = 0.0
	if (y <= -5.5e+97)
		tmp = t_1;
	elseif (y <= -0.095)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))) / Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c));
	elseif (y <= 0.06)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * 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 / ((a + (y + (b / y))) / y);
	tmp = 0.0;
	if (y <= -5.5e+97)
		tmp = t_1;
	elseif (y <= -0.095)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / ((y * ((y * (y + a)) + b)) + c);
	elseif (y <= 0.06)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (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[(N[(a + N[(y + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+97], t$95$1, If[LessEqual[y, -0.095], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.06], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.50000000000000021e97 or 0.059999999999999998 < y

   1. Initial program 4.8%

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

   3. Taylor expanded in t around 0 3.9%

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

   5. Simplified 5.0%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}}} \]

   6. Taylor expanded in y around inf 56.8%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{b}{x \cdot y} + \frac{y}{x}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \color{blue}{\left(\frac{y}{x} + \frac{b}{x \cdot y}\right)}\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      2. *-commutative 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{\color{blue}{y \cdot x}}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      3. associate-*r/ 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\color{blue}{\frac{27464.7644705 \cdot 1}{{x}^{2} \cdot y}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      4. metadata-eval 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{\color{blue}{27464.7644705}}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      5. *-commutative 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{\color{blue}{y \cdot {x}^{2}}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      6. *-commutative 56.8%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{\color{blue}{y \cdot x}}\right)\right)} \]

   8. Simplified 56.8%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y \cdot x}\right)\right)}} \]

   9. Taylor expanded in x around inf 43.4%

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

       1. associate-/l* 75.6%

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

   11. Simplified 75.6%

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

   if -5.50000000000000021e97 < y < -0.095000000000000001

   1. Initial program 51.1%

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

   3. Taylor expanded in t around 0 41.5%

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

   5. Simplified 51.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}}} \]

   6. Taylor expanded in i around 0 61.3%

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

   if -0.095000000000000001 < y < 0.059999999999999998

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 95.7%

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

      1. *-commutative 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in x around 0 93.5%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{elif}\;y \leq -0.095:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{elif}\;y \leq 0.06:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+34} \lor \neg \left(y \leq 0.06\right):\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6.2e+34) (not (<= y 0.06)))
   (/ x (/ (+ a (+ y (/ b y))) y))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.2e+34) || !(y <= 0.06)) {
		tmp = x / ((a + (y + (b / y))) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-6.2d+34)) .or. (.not. (y <= 0.06d0))) then
        tmp = x / ((a + (y + (b / y))) / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.2e+34) || !(y <= 0.06)) {
		tmp = x / ((a + (y + (b / y))) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6.2e+34) or not (y <= 0.06):
		tmp = x / ((a + (y + (b / y))) / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6.2e+34) || !(y <= 0.06))
		tmp = Float64(x / Float64(Float64(a + Float64(y + Float64(b / y))) / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -6.2e+34) || ~((y <= 0.06)))
		tmp = x / ((a + (y + (b / y))) / y);
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6.2e+34], N[Not[LessEqual[y, 0.06]], $MachinePrecision]], N[(x / N[(N[(a + N[(y + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.19999999999999955e34 or 0.059999999999999998 < y

   1. Initial program 6.9%

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

   3. Taylor expanded in t around 0 5.3%

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

   5. Simplified 7.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}}} \]

   6. Taylor expanded in y around inf 53.9%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{b}{x \cdot y} + \frac{y}{x}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 53.9%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \color{blue}{\left(\frac{y}{x} + \frac{b}{x \cdot y}\right)}\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      2. *-commutative 53.9%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{\color{blue}{y \cdot x}}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      3. associate-*r/ 53.9%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\color{blue}{\frac{27464.7644705 \cdot 1}{{x}^{2} \cdot y}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      4. metadata-eval 53.9%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{\color{blue}{27464.7644705}}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      5. *-commutative 53.9%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{\color{blue}{y \cdot {x}^{2}}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      6. *-commutative 53.9%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{\color{blue}{y \cdot x}}\right)\right)} \]

   8. Simplified 53.9%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y \cdot x}\right)\right)}} \]

   9. Taylor expanded in x around inf 42.3%

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

       1. associate-/l* 71.6%

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

   11. Simplified 71.6%

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

   if -6.19999999999999955e34 < y < 0.059999999999999998

   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 91.8%

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

      1. *-commutative 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in x around 0 89.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+34} \lor \neg \left(y \leq 0.06\right):\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.18 \lor \neg \left(y \leq 1.02 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -0.18) (not (<= y 1.02e-7)))
   (/ x (/ (+ a (+ y (/ b y))) y))
   (/ (+ t (* y 230661.510616)) (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -0.18) || !(y <= 1.02e-7)) {
		tmp = x / ((a + (y + (b / y))) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-0.18d0)) .or. (.not. (y <= 1.02d-7))) then
        tmp = x / ((a + (y + (b / y))) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -0.18) || !(y <= 1.02e-7)) {
		tmp = x / ((a + (y + (b / y))) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -0.18) or not (y <= 1.02e-7):
		tmp = x / ((a + (y + (b / y))) / y)
	else:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -0.18) || !(y <= 1.02e-7))
		tmp = Float64(x / Float64(Float64(a + Float64(y + Float64(b / y))) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -0.18) || ~((y <= 1.02e-7)))
		tmp = x / ((a + (y + (b / y))) / y);
	else
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -0.18], N[Not[LessEqual[y, 1.02e-7]], $MachinePrecision]], N[(x / N[(N[(a + N[(y + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if y < -0.17999999999999999 or 1.02e-7 < y

   1. Initial program 12.3%

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

   3. Taylor expanded in t around 0 10.2%

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

   5. Simplified 12.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}}} \]

   6. Taylor expanded in y around inf 51.5%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{b}{x \cdot y} + \frac{y}{x}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \color{blue}{\left(\frac{y}{x} + \frac{b}{x \cdot y}\right)}\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      2. *-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{\color{blue}{y \cdot x}}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      3. associate-*r/ 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\color{blue}{\frac{27464.7644705 \cdot 1}{{x}^{2} \cdot y}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      4. metadata-eval 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{\color{blue}{27464.7644705}}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      5. *-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{\color{blue}{y \cdot {x}^{2}}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      6. *-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{\color{blue}{y \cdot x}}\right)\right)} \]

   8. Simplified 51.5%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y \cdot x}\right)\right)}} \]

   9. Taylor expanded in x around inf 40.9%

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

       1. associate-/l* 68.0%

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

   11. Simplified 68.0%

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

   if -0.17999999999999999 < y < 1.02e-7

   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 90.5%

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

      1. *-commutative 88.0%

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

   5. Simplified 90.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.18 \lor \neg \left(y \leq 1.02 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0021 \lor \neg \left(y \leq 1.3 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -0.0021) (not (<= y 1.3e-8)))
   (/ x (/ (+ a (+ y (/ b y))) y))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -0.0021) || !(y <= 1.3e-8)) {
		tmp = x / ((a + (y + (b / y))) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-0.0021d0)) .or. (.not. (y <= 1.3d-8))) then
        tmp = x / ((a + (y + (b / y))) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -0.0021) || !(y <= 1.3e-8)) {
		tmp = x / ((a + (y + (b / y))) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -0.0021) or not (y <= 1.3e-8):
		tmp = x / ((a + (y + (b / y))) / y)
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -0.0021) || !(y <= 1.3e-8))
		tmp = Float64(x / Float64(Float64(a + Float64(y + Float64(b / y))) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -0.0021) || ~((y <= 1.3e-8)))
		tmp = x / ((a + (y + (b / y))) / y);
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -0.0021], N[Not[LessEqual[y, 1.3e-8]], $MachinePrecision]], N[(x / N[(N[(a + N[(y + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00209999999999999987 or 1.3000000000000001e-8 < y

   1. Initial program 12.3%

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

   3. Taylor expanded in t around 0 10.2%

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

   5. Simplified 12.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}}} \]

   6. Taylor expanded in y around inf 51.5%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{b}{x \cdot y} + \frac{y}{x}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \color{blue}{\left(\frac{y}{x} + \frac{b}{x \cdot y}\right)}\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      2. *-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{\color{blue}{y \cdot x}}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      3. associate-*r/ 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\color{blue}{\frac{27464.7644705 \cdot 1}{{x}^{2} \cdot y}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      4. metadata-eval 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{\color{blue}{27464.7644705}}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      5. *-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{\color{blue}{y \cdot {x}^{2}}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      6. *-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{\color{blue}{y \cdot x}}\right)\right)} \]

   8. Simplified 51.5%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y \cdot x}\right)\right)}} \]

   9. Taylor expanded in x around inf 40.9%

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

       1. associate-/l* 68.0%

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

   11. Simplified 68.0%

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

   if -0.00209999999999999987 < y < 1.3000000000000001e-8

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 95.6%

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

      1. *-commutative 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in y around 0 88.0%

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

      1. *-commutative 88.0%

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

   8. Simplified 88.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0021 \lor \neg \left(y \leq 1.3 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+32} \lor \neg \left(y \leq 7.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.9e+32) (not (<= y 7.5e-5)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.9e+32) || !(y <= 7.5e-5)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.9d+32)) .or. (.not. (y <= 7.5d-5))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.9e+32) || !(y <= 7.5e-5)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.9e+32) or not (y <= 7.5e-5):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.9e+32) || !(y <= 7.5e-5))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.9e+32) || ~((y <= 7.5e-5)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.9e+32], N[Not[LessEqual[y, 7.5e-5]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.90000000000000003e32 or 7.49999999999999934e-5 < y

   1. Initial program 8.4%

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

   3. Taylor expanded in y around inf 59.4%

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

      1. associate--l+ 59.4%

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

      2. associate-/l* 62.5%

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

   5. Simplified 62.5%

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

   if -2.90000000000000003e32 < y < 7.49999999999999934e-5

   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 45.1%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+32} \lor \neg \left(y \leq 7.5 \cdot 10^{-5}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+32} \lor \neg \left(y \leq 0.055\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.55e+32) (not (<= y 0.055)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/ t (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.55e+32) || !(y <= 0.055)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.55d+32)) .or. (.not. (y <= 0.055d0))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = t / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.55e+32) || !(y <= 0.055)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.55e+32) or not (y <= 0.055):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.55e+32) || !(y <= 0.055))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.55e+32) || ~((y <= 0.055)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.55e+32], N[Not[LessEqual[y, 0.055]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.55000000000000002e32 or 0.0550000000000000003 < y

   1. Initial program 8.4%

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

   3. Taylor expanded in y around inf 59.4%

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

      1. associate--l+ 59.4%

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

      2. associate-/l* 62.5%

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

   5. Simplified 62.5%

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

   if -2.55000000000000002e32 < y < 0.0550000000000000003

   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 92.2%

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

      1. *-commutative 92.2%

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

   5. Simplified 92.2%

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

   6. Taylor expanded in t around inf 69.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+32} \lor \neg \left(y \leq 0.055\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.3 \lor \neg \left(y \leq 8.2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6.3) (not (<= y 8.2e-8)))
   (/ x (/ (+ a (+ y (/ b y))) y))
   (/ t (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.3) || !(y <= 8.2e-8)) {
		tmp = x / ((a + (y + (b / y))) / y);
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-6.3d0)) .or. (.not. (y <= 8.2d-8))) then
        tmp = x / ((a + (y + (b / y))) / y)
    else
        tmp = t / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.3) || !(y <= 8.2e-8)) {
		tmp = x / ((a + (y + (b / y))) / y);
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6.3) or not (y <= 8.2e-8):
		tmp = x / ((a + (y + (b / y))) / y)
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6.3) || !(y <= 8.2e-8))
		tmp = Float64(x / Float64(Float64(a + Float64(y + Float64(b / y))) / y));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -6.3) || ~((y <= 8.2e-8)))
		tmp = x / ((a + (y + (b / y))) / y);
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6.3], N[Not[LessEqual[y, 8.2e-8]], $MachinePrecision]], N[(x / N[(N[(a + N[(y + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.29999999999999982 or 8.20000000000000063e-8 < y

   1. Initial program 12.3%

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

   3. Taylor expanded in t around 0 10.2%

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

   5. Simplified 12.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right)}}} \]

   6. Taylor expanded in y around inf 51.5%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{b}{x \cdot y} + \frac{y}{x}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \color{blue}{\left(\frac{y}{x} + \frac{b}{x \cdot y}\right)}\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      2. *-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{\color{blue}{y \cdot x}}\right)\right) - \left(27464.7644705 \cdot \frac{1}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      3. associate-*r/ 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\color{blue}{\frac{27464.7644705 \cdot 1}{{x}^{2} \cdot y}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      4. metadata-eval 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{\color{blue}{27464.7644705}}{{x}^{2} \cdot y} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      5. *-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{\color{blue}{y \cdot {x}^{2}}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{x \cdot y}\right)\right)} \]

      6. *-commutative 51.5%

         \[\leadsto \frac{y}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{\color{blue}{y \cdot x}}\right)\right)} \]

   8. Simplified 51.5%

      \[\leadsto \frac{y}{\color{blue}{\left(\frac{a}{x} + \left(\frac{y}{x} + \frac{b}{y \cdot x}\right)\right) - \left(\frac{27464.7644705}{y \cdot {x}^{2}} + \left(\frac{z}{{x}^{2}} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)}{y \cdot x}\right)\right)}} \]

   9. Taylor expanded in x around inf 40.9%

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

       1. associate-/l* 68.0%

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

   11. Simplified 68.0%

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

   if -6.29999999999999982 < y < 8.20000000000000063e-8

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 95.6%

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

      1. *-commutative 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in t around inf 72.6%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.3 \lor \neg \left(y \leq 8.2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{\frac{a + \left(y + \frac{b}{y}\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.6% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -19000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-56}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -19000000.0) x (if (<= y 1.8e-56) (/ 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 <= -19000000.0) {
		tmp = x;
	} else if (y <= 1.8e-56) {
		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 <= (-19000000.0d0)) then
        tmp = x
    else if (y <= 1.8d-56) 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 <= -19000000.0) {
		tmp = x;
	} else if (y <= 1.8e-56) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -19000000.0:
		tmp = x
	elif y <= 1.8e-56:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -19000000.0)
		tmp = x;
	elseif (y <= 1.8e-56)
		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 <= -19000000.0)
		tmp = x;
	elseif (y <= 1.8e-56)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -19000000.0], x, If[LessEqual[y, 1.8e-56], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e7 or 1.79999999999999989e-56 < y

   1. Initial program 14.8%

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

   3. Taylor expanded in y around inf 48.1%

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

   if -1.9e7 < y < 1.79999999999999989e-56

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 49.4%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -19000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-56}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 25.4% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.6%

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

3. Taylor expanded in y around inf 27.8%

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

4. Final simplification 27.8%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(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)))