Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.3% → 86.2%

Time: 25.5s

Alternatives: 14

Speedup: 1.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 86.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_3 := {t\_2}^{2}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(\left(230661.510616 \cdot \frac{1}{y \cdot t\_2} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{t\_2}\right) - i \cdot \left(27464.7644705 \cdot \frac{1}{y \cdot t\_3} + \left(230661.510616 \cdot \frac{1}{t\_3 \cdot {y}^{2}} + \left(\frac{z}{t\_3} + \frac{y \cdot x}{t\_3}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y)))))
        (t_2 (+ c (* y (+ b (* y (+ y a))))))
        (t_3 (pow t_2 2.0)))
   (if (<= y -2.5e+87)
     t_1
     (if (<= y -1.3e+38)
       (*
        y
        (-
         (+
          (* 230661.510616 (/ 1.0 (* y t_2)))
          (/ (+ 27464.7644705 (* y (+ z (* y x)))) t_2))
         (*
          i
          (+
           (* 27464.7644705 (/ 1.0 (* y t_3)))
           (+
            (* 230661.510616 (/ 1.0 (* t_3 (pow y 2.0))))
            (+ (/ z t_3) (/ (* y x) t_3)))))))
       (if (<= y 4.5e+63)
         (/
          (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t)
          (fma (fma (fma (+ y a) y b) y c) y i))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double t_2 = c + (y * (b + (y * (y + a))));
	double t_3 = pow(t_2, 2.0);
	double tmp;
	if (y <= -2.5e+87) {
		tmp = t_1;
	} else if (y <= -1.3e+38) {
		tmp = y * (((230661.510616 * (1.0 / (y * t_2))) + ((27464.7644705 + (y * (z + (y * x)))) / t_2)) - (i * ((27464.7644705 * (1.0 / (y * t_3))) + ((230661.510616 * (1.0 / (t_3 * pow(y, 2.0)))) + ((z / t_3) + ((y * x) / t_3))))));
	} else if (y <= 4.5e+63) {
		tmp = fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((y + a), y, b), y, c), y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	t_2 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_3 = t_2 ^ 2.0
	tmp = 0.0
	if (y <= -2.5e+87)
		tmp = t_1;
	elseif (y <= -1.3e+38)
		tmp = Float64(y * Float64(Float64(Float64(230661.510616 * Float64(1.0 / Float64(y * t_2))) + Float64(Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))) / t_2)) - Float64(i * Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * t_3))) + Float64(Float64(230661.510616 * Float64(1.0 / Float64(t_3 * (y ^ 2.0)))) + Float64(Float64(z / t_3) + Float64(Float64(y * x) / t_3)))))));
	elseif (y <= 4.5e+63)
		tmp = Float64(fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(y + a), y, b), y, c), y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Power[t$95$2, 2.0], $MachinePrecision]}, If[LessEqual[y, -2.5e+87], t$95$1, If[LessEqual[y, -1.3e+38], N[(y * N[(N[(N[(230661.510616 * N[(1.0 / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(27464.7644705 * N[(1.0 / N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / N[(t$95$3 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t$95$3), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+63], N[(N[(N[(N[(N[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999999e87 or 4.50000000000000017e63 < y

   1. Initial program 0.5%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. associate--l+ 70.4%

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

      2. associate-/l* 75.3%

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

   5. Simplified 75.3%

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

   if -2.4999999999999999e87 < y < -1.3e38

   1. Initial program 12.1%

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

   3. Taylor expanded in t around 0 12.1%

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

   5. Simplified 21.4%

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

   6. Taylor expanded in i around 0 73.5%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(27464.7644705 \cdot \frac{1}{y \cdot {\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}^{2}} + \left(230661.510616 \cdot \frac{1}{{y}^{2} \cdot {\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}^{2}} + \left(\frac{z}{{\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}^{2}} + \frac{x \cdot y}{{\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}^{2}}\right)\right)\right)\right) + \left(230661.510616 \cdot \frac{1}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + x \cdot y\right)}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}\right)\right)} \]

   if -1.3e38 < y < 4.50000000000000017e63

   1. Initial program 92.5%

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

      1. fma-define 92.5%

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

      2. fma-define 92.5%

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

      3. fma-define 92.5%

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

      4. fma-define 92.5%

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

      5. fma-define 92.5%

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

      6. fma-define 92.5%

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

      7. fma-define 92.5%

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

   3. Simplified 92.5%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+87}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(\left(230661.510616 \cdot \frac{1}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\right) - i \cdot \left(27464.7644705 \cdot \frac{1}{y \cdot {\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}} + \left(230661.510616 \cdot \frac{1}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2} \cdot {y}^{2}} + \left(\frac{z}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}} + \frac{y \cdot x}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 27464.7644705 + y \cdot \left(z + y \cdot x\right)\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ t_3 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_4 := {t\_3}^{2}\\ t_5 := y \cdot t\_3\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(\left(230661.510616 \cdot \frac{1}{t\_5} + \frac{t\_1}{t\_3}\right) - i \cdot \left(27464.7644705 \cdot \frac{1}{y \cdot t\_4} + \left(230661.510616 \cdot \frac{1}{t\_4 \cdot {y}^{2}} + \left(\frac{z}{t\_4} + \frac{y \cdot x}{t\_4}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot t\_1\right)}{i + t\_5}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ 27464.7644705 (* y (+ z (* y x)))))
        (t_2 (+ x (- (/ z y) (* a (/ x y)))))
        (t_3 (+ c (* y (+ b (* y (+ y a))))))
        (t_4 (pow t_3 2.0))
        (t_5 (* y t_3)))
   (if (<= y -3.4e+86)
     t_2
     (if (<= y -6.8e+41)
       (*
        y
        (-
         (+ (* 230661.510616 (/ 1.0 t_5)) (/ t_1 t_3))
         (*
          i
          (+
           (* 27464.7644705 (/ 1.0 (* y t_4)))
           (+
            (* 230661.510616 (/ 1.0 (* t_4 (pow y 2.0))))
            (+ (/ z t_4) (/ (* y x) t_4)))))))
       (if (<= y 7.5e+62)
         (/ (+ t (* y (+ 230661.510616 (* y t_1)))) (+ i t_5))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 27464.7644705 + (y * (z + (y * x)));
	double t_2 = x + ((z / y) - (a * (x / y)));
	double t_3 = c + (y * (b + (y * (y + a))));
	double t_4 = pow(t_3, 2.0);
	double t_5 = y * t_3;
	double tmp;
	if (y <= -3.4e+86) {
		tmp = t_2;
	} else if (y <= -6.8e+41) {
		tmp = y * (((230661.510616 * (1.0 / t_5)) + (t_1 / t_3)) - (i * ((27464.7644705 * (1.0 / (y * t_4))) + ((230661.510616 * (1.0 / (t_4 * pow(y, 2.0)))) + ((z / t_4) + ((y * x) / t_4))))));
	} else if (y <= 7.5e+62) {
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / (i + t_5);
	} 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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = 27464.7644705d0 + (y * (z + (y * x)))
    t_2 = x + ((z / y) - (a * (x / y)))
    t_3 = c + (y * (b + (y * (y + a))))
    t_4 = t_3 ** 2.0d0
    t_5 = y * t_3
    if (y <= (-3.4d+86)) then
        tmp = t_2
    else if (y <= (-6.8d+41)) then
        tmp = y * (((230661.510616d0 * (1.0d0 / t_5)) + (t_1 / t_3)) - (i * ((27464.7644705d0 * (1.0d0 / (y * t_4))) + ((230661.510616d0 * (1.0d0 / (t_4 * (y ** 2.0d0)))) + ((z / t_4) + ((y * x) / t_4))))))
    else if (y <= 7.5d+62) then
        tmp = (t + (y * (230661.510616d0 + (y * t_1)))) / (i + t_5)
    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 = 27464.7644705 + (y * (z + (y * x)));
	double t_2 = x + ((z / y) - (a * (x / y)));
	double t_3 = c + (y * (b + (y * (y + a))));
	double t_4 = Math.pow(t_3, 2.0);
	double t_5 = y * t_3;
	double tmp;
	if (y <= -3.4e+86) {
		tmp = t_2;
	} else if (y <= -6.8e+41) {
		tmp = y * (((230661.510616 * (1.0 / t_5)) + (t_1 / t_3)) - (i * ((27464.7644705 * (1.0 / (y * t_4))) + ((230661.510616 * (1.0 / (t_4 * Math.pow(y, 2.0)))) + ((z / t_4) + ((y * x) / t_4))))));
	} else if (y <= 7.5e+62) {
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / (i + t_5);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 27464.7644705 + (y * (z + (y * x)))
	t_2 = x + ((z / y) - (a * (x / y)))
	t_3 = c + (y * (b + (y * (y + a))))
	t_4 = math.pow(t_3, 2.0)
	t_5 = y * t_3
	tmp = 0
	if y <= -3.4e+86:
		tmp = t_2
	elif y <= -6.8e+41:
		tmp = y * (((230661.510616 * (1.0 / t_5)) + (t_1 / t_3)) - (i * ((27464.7644705 * (1.0 / (y * t_4))) + ((230661.510616 * (1.0 / (t_4 * math.pow(y, 2.0)))) + ((z / t_4) + ((y * x) / t_4))))))
	elif y <= 7.5e+62:
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / (i + t_5)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	t_3 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_4 = t_3 ^ 2.0
	t_5 = Float64(y * t_3)
	tmp = 0.0
	if (y <= -3.4e+86)
		tmp = t_2;
	elseif (y <= -6.8e+41)
		tmp = Float64(y * Float64(Float64(Float64(230661.510616 * Float64(1.0 / t_5)) + Float64(t_1 / t_3)) - Float64(i * Float64(Float64(27464.7644705 * Float64(1.0 / Float64(y * t_4))) + Float64(Float64(230661.510616 * Float64(1.0 / Float64(t_4 * (y ^ 2.0)))) + Float64(Float64(z / t_4) + Float64(Float64(y * x) / t_4)))))));
	elseif (y <= 7.5e+62)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * t_1)))) / Float64(i + t_5));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 27464.7644705 + (y * (z + (y * x)));
	t_2 = x + ((z / y) - (a * (x / y)));
	t_3 = c + (y * (b + (y * (y + a))));
	t_4 = t_3 ^ 2.0;
	t_5 = y * t_3;
	tmp = 0.0;
	if (y <= -3.4e+86)
		tmp = t_2;
	elseif (y <= -6.8e+41)
		tmp = y * (((230661.510616 * (1.0 / t_5)) + (t_1 / t_3)) - (i * ((27464.7644705 * (1.0 / (y * t_4))) + ((230661.510616 * (1.0 / (t_4 * (y ^ 2.0)))) + ((z / t_4) + ((y * x) / t_4))))));
	elseif (y <= 7.5e+62)
		tmp = (t + (y * (230661.510616 + (y * t_1)))) / (i + t_5);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[Power[t$95$3, 2.0], $MachinePrecision]}, Block[{t$95$5 = N[(y * t$95$3), $MachinePrecision]}, If[LessEqual[y, -3.4e+86], t$95$2, If[LessEqual[y, -6.8e+41], N[(y * N[(N[(N[(230661.510616 * N[(1.0 / t$95$5), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 / t$95$3), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(27464.7644705 * N[(1.0 / N[(y * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / N[(t$95$4 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t$95$4), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+62], N[(N[(t + N[(y * N[(230661.510616 + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + t$95$5), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3999999999999998e86 or 7.49999999999999998e62 < y

   1. Initial program 0.5%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. associate--l+ 70.4%

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

      2. associate-/l* 75.3%

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

   5. Simplified 75.3%

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

   if -3.3999999999999998e86 < y < -6.79999999999999996e41

   1. Initial program 12.1%

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

   3. Taylor expanded in t around 0 12.1%

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

   5. Simplified 21.4%

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

   6. Taylor expanded in i around 0 73.5%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(27464.7644705 \cdot \frac{1}{y \cdot {\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}^{2}} + \left(230661.510616 \cdot \frac{1}{{y}^{2} \cdot {\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}^{2}} + \left(\frac{z}{{\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}^{2}} + \frac{x \cdot y}{{\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}^{2}}\right)\right)\right)\right) + \left(230661.510616 \cdot \frac{1}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + x \cdot y\right)}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}\right)\right)} \]

   if -6.79999999999999996e41 < y < 7.49999999999999998e62

   1. Initial program 92.5%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+86}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(\left(230661.510616 \cdot \frac{1}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\right) - i \cdot \left(27464.7644705 \cdot \frac{1}{y \cdot {\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}} + \left(230661.510616 \cdot \frac{1}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2} \cdot {y}^{2}} + \left(\frac{z}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}} + \frac{y \cdot x}{{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}^{2}}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))
   (if (<= t_1 5e+292) t_1 (+ x (- (/ z y) (* a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	double tmp;
	if (t_1 <= 5e+292) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    if (t_1 <= 5d+292) then
        tmp = t_1
    else
        tmp = x + ((z / y) - (a * (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	double tmp;
	if (t_1 <= 5e+292) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	tmp = 0
	if t_1 <= 5e+292:
		tmp = t_1
	else:
		tmp = x + ((z / y) - (a * (x / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))))
	tmp = 0.0
	if (t_1 <= 5e+292)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	tmp = 0.0;
	if (t_1 <= 5e+292)
		tmp = t_1;
	else
		tmp = x + ((z / y) - (a * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+292], t$95$1, N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 4.9999999999999996e292

   1. Initial program 89.1%

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

   if 4.9999999999999996e292 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 1.3%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. associate--l+ 66.4%

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

      2. associate-/l* 71.1%

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

   5. Simplified 71.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t\_1}\\ t_3 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+77}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -0.002:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 300000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t\_1}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1))
        (t_3 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.35e+77)
     t_3
     (if (<= y -0.002)
       t_2
       (if (<= y 300000.0)
         (/ (+ t (* y 230661.510616)) (+ i (* y t_1)))
         (if (<= y 2.45e+64) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.35e+77) {
		tmp = t_3;
	} else if (y <= -0.002) {
		tmp = t_2;
	} else if (y <= 300000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 2.45e+64) {
		tmp = t_2;
	} 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 = c + (y * (b + (y * (y + a))))
    t_2 = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    t_3 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.35d+77)) then
        tmp = t_3
    else if (y <= (-0.002d0)) then
        tmp = t_2
    else if (y <= 300000.0d0) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_1))
    else if (y <= 2.45d+64) then
        tmp = t_2
    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 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.35e+77) {
		tmp = t_3;
	} else if (y <= -0.002) {
		tmp = t_2;
	} else if (y <= 300000.0) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	} else if (y <= 2.45e+64) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	t_3 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.35e+77:
		tmp = t_3
	elif y <= -0.002:
		tmp = t_2
	elif y <= 300000.0:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1))
	elif y <= 2.45e+64:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1)
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.35e+77)
		tmp = t_3;
	elseif (y <= -0.002)
		tmp = t_2;
	elseif (y <= 300000.0)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_1)));
	elseif (y <= 2.45e+64)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	t_3 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.35e+77)
		tmp = t_3;
	elseif (y <= -0.002)
		tmp = t_2;
	elseif (y <= 300000.0)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_1));
	elseif (y <= 2.45e+64)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+77], t$95$3, If[LessEqual[y, -0.002], t$95$2, If[LessEqual[y, 300000.0], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e+64], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3499999999999999e77 or 2.4500000000000001e64 < y

   1. Initial program 0.5%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-/l* 74.0%

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

   5. Simplified 74.0%

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

   if -1.3499999999999999e77 < y < -2e-3 or 3e5 < y < 2.4500000000000001e64

   1. Initial program 47.9%

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

   3. Taylor expanded in t around 0 45.2%

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

   4. Taylor expanded in i around 0 59.0%

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

   if -2e-3 < y < 3e5

   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 89.6%

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

      1. *-commutative 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -0.002:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 300000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+64}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t\_1}\\ t_3 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+77}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1950000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot t\_1}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1))
        (t_3 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -2.35e+77)
     t_3
     (if (<= y -1.85e+27)
       t_2
       (if (<= y 1950000.0)
         (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i (* y t_1)))
         (if (<= y 2.7e+65) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.35e+77) {
		tmp = t_3;
	} else if (y <= -1.85e+27) {
		tmp = t_2;
	} else if (y <= 1950000.0) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 2.7e+65) {
		tmp = t_2;
	} 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 = c + (y * (b + (y * (y + a))))
    t_2 = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    t_3 = x + ((z / y) - (a * (x / y)))
    if (y <= (-2.35d+77)) then
        tmp = t_3
    else if (y <= (-1.85d+27)) then
        tmp = t_2
    else if (y <= 1950000.0d0) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * t_1))
    else if (y <= 2.7d+65) then
        tmp = t_2
    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 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2.35e+77) {
		tmp = t_3;
	} else if (y <= -1.85e+27) {
		tmp = t_2;
	} else if (y <= 1950000.0) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 2.7e+65) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	t_3 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -2.35e+77:
		tmp = t_3
	elif y <= -1.85e+27:
		tmp = t_2
	elif y <= 1950000.0:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1))
	elif y <= 2.7e+65:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1)
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -2.35e+77)
		tmp = t_3;
	elseif (y <= -1.85e+27)
		tmp = t_2;
	elseif (y <= 1950000.0)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * t_1)));
	elseif (y <= 2.7e+65)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	t_3 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -2.35e+77)
		tmp = t_3;
	elseif (y <= -1.85e+27)
		tmp = t_2;
	elseif (y <= 1950000.0)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	elseif (y <= 2.7e+65)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.35e+77], t$95$3, If[LessEqual[y, -1.85e+27], t$95$2, If[LessEqual[y, 1950000.0], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+65], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.35e77 or 2.70000000000000019e65 < y

   1. Initial program 0.5%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-/l* 74.0%

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

   5. Simplified 74.0%

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

   if -2.35e77 < y < -1.85000000000000001e27 or 1.95e6 < y < 2.70000000000000019e65

   1. Initial program 47.6%

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

   3. Taylor expanded in t around 0 44.7%

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

   4. Taylor expanded in i around 0 59.4%

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

   if -1.85000000000000001e27 < y < 1.95e6

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 89.4%

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

      1. *-commutative 89.4%

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

   5. Simplified 89.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+27}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 1950000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+65}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\\ t_2 := \frac{t\_1}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ t_3 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+77}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -75000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 290000:\\ \;\;\;\;\frac{t + y \cdot t\_1}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
        (t_2 (/ t_1 (+ c (* y (+ b (* y (+ y a)))))))
        (t_3 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -2e+77)
     t_3
     (if (<= y -75000.0)
       t_2
       (if (<= y 290000.0)
         (/ (+ t (* y t_1)) (+ i (* y (+ c (* y b)))))
         (if (<= y 1.2e+64) t_2 t_3))))))

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 * (z + (y * x)))));
	double t_2 = t_1 / (c + (y * (b + (y * (y + a)))));
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2e+77) {
		tmp = t_3;
	} else if (y <= -75000.0) {
		tmp = t_2;
	} else if (y <= 290000.0) {
		tmp = (t + (y * t_1)) / (i + (y * (c + (y * b))));
	} else if (y <= 1.2e+64) {
		tmp = t_2;
	} 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 = 230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))
    t_2 = t_1 / (c + (y * (b + (y * (y + a)))))
    t_3 = x + ((z / y) - (a * (x / y)))
    if (y <= (-2d+77)) then
        tmp = t_3
    else if (y <= (-75000.0d0)) then
        tmp = t_2
    else if (y <= 290000.0d0) then
        tmp = (t + (y * t_1)) / (i + (y * (c + (y * b))))
    else if (y <= 1.2d+64) then
        tmp = t_2
    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 = 230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))));
	double t_2 = t_1 / (c + (y * (b + (y * (y + a)))));
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -2e+77) {
		tmp = t_3;
	} else if (y <= -75000.0) {
		tmp = t_2;
	} else if (y <= 290000.0) {
		tmp = (t + (y * t_1)) / (i + (y * (c + (y * b))));
	} else if (y <= 1.2e+64) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))
	t_2 = t_1 / (c + (y * (b + (y * (y + a)))))
	t_3 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -2e+77:
		tmp = t_3
	elif y <= -75000.0:
		tmp = t_2
	elif y <= 290000.0:
		tmp = (t + (y * t_1)) / (i + (y * (c + (y * b))))
	elif y <= 1.2e+64:
		tmp = t_2
	else:
		tmp = t_3
	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(z + Float64(y * x))))))
	t_2 = Float64(t_1 / Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -2e+77)
		tmp = t_3;
	elseif (y <= -75000.0)
		tmp = t_2;
	elseif (y <= 290000.0)
		tmp = Float64(Float64(t + Float64(y * t_1)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 1.2e+64)
		tmp = t_2;
	else
		tmp = t_3;
	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 * (z + (y * x)))));
	t_2 = t_1 / (c + (y * (b + (y * (y + a)))));
	t_3 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -2e+77)
		tmp = t_3;
	elseif (y <= -75000.0)
		tmp = t_2;
	elseif (y <= 290000.0)
		tmp = (t + (y * t_1)) / (i + (y * (c + (y * b))));
	elseif (y <= 1.2e+64)
		tmp = t_2;
	else
		tmp = t_3;
	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[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+77], t$95$3, If[LessEqual[y, -75000.0], t$95$2, If[LessEqual[y, 290000.0], N[(N[(t + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+64], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999997e77 or 1.2e64 < y

   1. Initial program 0.5%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-/l* 74.0%

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

   5. Simplified 74.0%

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

   if -1.99999999999999997e77 < y < -75000 or 2.9e5 < y < 1.2e64

   1. Initial program 49.3%

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

   3. Taylor expanded in t around 0 44.0%

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

   4. Taylor expanded in i around 0 57.4%

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

   if -75000 < y < 2.9e5

   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 93.2%

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

      1. *-commutative 93.2%

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

   5. Simplified 93.2%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -75000:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 290000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+64}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ t_2 := \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t\_1}\\ t_3 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3900000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot t\_1}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ b (* y (+ y a))))))
        (t_2
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1))
        (t_3 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.9e+77)
     t_3
     (if (<= y -2.05e+27)
       t_2
       (if (<= y 3900000.0)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y t_1)))
         (if (<= y 2.75e+65) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.9e+77) {
		tmp = t_3;
	} else if (y <= -2.05e+27) {
		tmp = t_2;
	} else if (y <= 3900000.0) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1));
	} else if (y <= 2.75e+65) {
		tmp = t_2;
	} 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 = c + (y * (b + (y * (y + a))))
    t_2 = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    t_3 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.9d+77)) then
        tmp = t_3
    else if (y <= (-2.05d+27)) then
        tmp = t_2
    else if (y <= 3900000.0d0) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * t_1))
    else if (y <= 2.75d+65) then
        tmp = t_2
    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 = c + (y * (b + (y * (y + a))));
	double t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	double t_3 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.9e+77) {
		tmp = t_3;
	} else if (y <= -2.05e+27) {
		tmp = t_2;
	} else if (y <= 3900000.0) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1));
	} else if (y <= 2.75e+65) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * (b + (y * (y + a))))
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	t_3 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.9e+77:
		tmp = t_3
	elif y <= -2.05e+27:
		tmp = t_2
	elif y <= 3900000.0:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1))
	elif y <= 2.75e+65:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	t_2 = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1)
	t_3 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.9e+77)
		tmp = t_3;
	elseif (y <= -2.05e+27)
		tmp = t_2;
	elseif (y <= 3900000.0)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * t_1)));
	elseif (y <= 2.75e+65)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * (b + (y * (y + a))));
	t_2 = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	t_3 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.9e+77)
		tmp = t_3;
	elseif (y <= -2.05e+27)
		tmp = t_2;
	elseif (y <= 3900000.0)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * t_1));
	elseif (y <= 2.75e+65)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+77], t$95$3, If[LessEqual[y, -2.05e+27], t$95$2, If[LessEqual[y, 3900000.0], 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 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+65], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000001e77 or 2.7499999999999998e65 < y

   1. Initial program 0.5%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-/l* 74.0%

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

   5. Simplified 74.0%

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

   if -1.9000000000000001e77 < y < -2.0500000000000001e27 or 3.9e6 < y < 2.7499999999999998e65

   1. Initial program 47.6%

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

   3. Taylor expanded in t around 0 44.7%

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

   4. Taylor expanded in i around 0 59.4%

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

   if -2.0500000000000001e27 < y < 3.9e6

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 95.4%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+27}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 3900000:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+65}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+27} \lor \neg \left(y \leq 2.2 \cdot 10^{+29}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.95e+27) (not (<= y 2.2e+29)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.95e+27) || !(y <= 2.2e+29)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.95d+27)) .or. (.not. (y <= 2.2d+29))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.95e+27) || !(y <= 2.2e+29)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.95e+27) or not (y <= 2.2e+29):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.95e+27) || !(y <= 2.2e+29))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.95e+27) || ~((y <= 2.2e+29)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.95e+27], N[Not[LessEqual[y, 2.2e+29]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9499999999999999e27 or 2.2000000000000001e29 < y

   1. Initial program 9.5%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. associate--l+ 58.8%

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

      2. associate-/l* 62.7%

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

   5. Simplified 62.7%

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

   if -1.9499999999999999e27 < y < 2.2000000000000001e29

   1. Initial program 95.3%

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

   3. Taylor expanded in y around 0 83.2%

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

      1. *-commutative 83.2%

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

   5. Simplified 83.2%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+27} \lor \neg \left(y \leq 2.2 \cdot 10^{+29}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+27} \lor \neg \left(y \leq 6.1 \cdot 10^{+29}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.4e+27) (not (<= y 6.1e+29)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ t (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.4e+27) || !(y <= 6.1e+29)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.4d+27)) .or. (.not. (y <= 6.1d+29))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.4e+27) || !(y <= 6.1e+29)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.4e+27) or not (y <= 6.1e+29):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.4e+27) || !(y <= 6.1e+29))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.4e+27) || ~((y <= 6.1e+29)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.4e+27], N[Not[LessEqual[y, 6.1e+29]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4e27 or 6.0999999999999998e29 < y

   1. Initial program 9.5%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. associate--l+ 58.8%

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

      2. associate-/l* 62.7%

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

   5. Simplified 62.7%

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

   if -3.4e27 < y < 6.0999999999999998e29

   1. Initial program 95.3%

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

   3. Taylor expanded in t around inf 70.4%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+27} \lor \neg \left(y \leq 6.1 \cdot 10^{+29}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+27} \lor \neg \left(y \leq 95\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.85e+27) (not (<= y 95.0)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ (+ t (* y 230661.510616)) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.85e+27) || !(y <= 95.0)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / 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 <= (-1.85d+27)) .or. (.not. (y <= 95.0d0))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * 230661.510616d0)) / 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 <= -1.85e+27) || !(y <= 95.0)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.85e+27) or not (y <= 95.0):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * 230661.510616)) / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.85e+27) || !(y <= 95.0))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.85e+27) || ~((y <= 95.0)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * 230661.510616)) / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.85e+27], N[Not[LessEqual[y, 95.0]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85000000000000001e27 or 95 < y

   1. Initial program 13.3%

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

   3. Taylor expanded in y around inf 54.5%

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

      1. associate--l+ 54.5%

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

      2. associate-/l* 58.1%

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

   5. Simplified 58.1%

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

   if -1.85000000000000001e27 < y < 95

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 45.8%

      \[\leadsto \color{blue}{y \cdot \left(230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]
   4. Step-by-step derivation

      1. fma-define 45.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

      2. associate-*r/ 45.8%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616 \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      3. metadata-eval 45.8%

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{230661.510616}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. associate-/l* 50.1%

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i} - \color{blue}{c \cdot \frac{t}{{i}^{2}}}, \frac{t}{i}\right) \]

   5. Simplified 50.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{230661.510616}{i} - c \cdot \frac{t}{{i}^{2}}, \frac{t}{i}\right)} \]

   6. Taylor expanded in i around inf 55.0%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+27} \lor \neg \left(y \leq 95\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+27} \lor \neg \left(y \leq 6 \cdot 10^{-7}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.8e+27) (not (<= y 6e-7)))
   (+ x (/ (- z (* x a)) y))
   (/ (+ t (* y 230661.510616)) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.8e+27) || !(y <= 6e-7)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / 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 <= (-2.8d+27)) .or. (.not. (y <= 6d-7))) then
        tmp = x + ((z - (x * a)) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / 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 <= -2.8e+27) || !(y <= 6e-7)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.8e+27) or not (y <= 6e-7):
		tmp = x + ((z - (x * a)) / y)
	else:
		tmp = (t + (y * 230661.510616)) / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.8e+27) || !(y <= 6e-7))
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.8e+27) || ~((y <= 6e-7)))
		tmp = x + ((z - (x * a)) / y);
	else
		tmp = (t + (y * 230661.510616)) / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.8e+27], N[Not[LessEqual[y, 6e-7]], $MachinePrecision]], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999999e27 or 5.9999999999999997e-7 < y

   1. Initial program 15.1%

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

   3. Taylor expanded in t around 0 12.5%

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

   4. Taylor expanded in y around inf 53.4%

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

      1. associate--l+ 53.4%

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

      2. div-sub 53.4%

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

      3. *-commutative 53.4%

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

   6. Simplified 53.4%

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

   if -2.7999999999999999e27 < y < 5.9999999999999997e-7

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 46.9%

      \[\leadsto \color{blue}{y \cdot \left(230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]
   4. Step-by-step derivation

      1. fma-define 47.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

      2. associate-*r/ 47.0%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616 \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      3. metadata-eval 47.0%

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{230661.510616}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. associate-/l* 51.4%

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i} - \color{blue}{c \cdot \frac{t}{{i}^{2}}}, \frac{t}{i}\right) \]

   5. Simplified 51.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{230661.510616}{i} - c \cdot \frac{t}{{i}^{2}}, \frac{t}{i}\right)} \]

   6. Taylor expanded in i around inf 56.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+27} \lor \neg \left(y \leq 6 \cdot 10^{-7}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-7}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.75e+27) x (if (<= y 2.05e-7) (/ (+ t (* y 230661.510616)) i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.75e+27) {
		tmp = x;
	} else if (y <= 2.05e-7) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.75d+27)) then
        tmp = x
    else if (y <= 2.05d-7) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.75e+27) {
		tmp = x;
	} else if (y <= 2.05e-7) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.75e+27:
		tmp = x
	elif y <= 2.05e-7:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.75e+27)
		tmp = x;
	elseif (y <= 2.05e-7)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.75e+27)
		tmp = x;
	elseif (y <= 2.05e-7)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.75e+27], x, If[LessEqual[y, 2.05e-7], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7500000000000001e27 or 2.05e-7 < y

   1. Initial program 15.7%

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

   3. Taylor expanded in y around inf 41.0%

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

   if -1.7500000000000001e27 < y < 2.05e-7

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 47.4%

      \[\leadsto \color{blue}{y \cdot \left(230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]
   4. Step-by-step derivation

      1. fma-define 47.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

      2. associate-*r/ 47.4%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616 \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      3. metadata-eval 47.4%

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{230661.510616}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. associate-/l* 51.8%

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i} - \color{blue}{c \cdot \frac{t}{{i}^{2}}}, \frac{t}{i}\right) \]

   5. Simplified 51.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{230661.510616}{i} - c \cdot \frac{t}{{i}^{2}}, \frac{t}{i}\right)} \]

   6. Taylor expanded in i around inf 56.8%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-7}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-7}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3e+27) x (if (<= y 2.25e-7) (/ 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 <= -3e+27) {
		tmp = x;
	} else if (y <= 2.25e-7) {
		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 <= (-3d+27)) then
        tmp = x
    else if (y <= 2.25d-7) 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 <= -3e+27) {
		tmp = x;
	} else if (y <= 2.25e-7) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3e+27:
		tmp = x
	elif y <= 2.25e-7:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3e+27)
		tmp = x;
	elseif (y <= 2.25e-7)
		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 <= -3e+27)
		tmp = x;
	elseif (y <= 2.25e-7)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3e+27], x, If[LessEqual[y, 2.25e-7], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999976e27 or 2.2499999999999999e-7 < y

   1. Initial program 15.7%

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

   3. Taylor expanded in y around inf 41.0%

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

   if -2.99999999999999976e27 < y < 2.2499999999999999e-7

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 49.2%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-7}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 26.0% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.1%

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

3. Taylor expanded in y around inf 24.2%

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

4. Final simplification 24.2%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(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)))