Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.7% → 84.3%

Time: 23.2s

Alternatives: 19

Speedup: 1.6×

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: 55.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ t_3 := \frac{t}{t_1}\\ t_4 := \frac{z}{a} + \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+21}:\\ \;\;\;\;t_3 + \left(\frac{\frac{27464.7644705}{a}}{y} + t_4\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+50}:\\ \;\;\;\;t_3 + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{\frac{230661.510616}{a}}{y \cdot y} + \left(\frac{\frac{t}{y}}{\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right)} + \left(t_4 + \frac{27464.7644705}{y \cdot a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2 (+ (/ z y) (- x (/ a (/ y x)))))
        (t_3 (/ t t_1))
        (t_4 (+ (/ z a) (/ y (/ a x)))))
   (if (<= y -1.5e+62)
     t_2
     (if (<= y -5.4e+21)
       (+ t_3 (+ (/ (/ 27464.7644705 a) y) t_4))
       (if (<= y 1.15e+50)
         (+
          t_3
          (/
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
           t_1))
         (if (<= y 2.6e+102)
           (+
            (/ (/ 230661.510616 a) (* y y))
            (+
             (/ (/ t y) (fma (fma (+ y a) y b) y c))
             (+ t_4 (/ 27464.7644705 (* y a)))))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double t_3 = t / t_1;
	double t_4 = (z / a) + (y / (a / x));
	double tmp;
	if (y <= -1.5e+62) {
		tmp = t_2;
	} else if (y <= -5.4e+21) {
		tmp = t_3 + (((27464.7644705 / a) / y) + t_4);
	} else if (y <= 1.15e+50) {
		tmp = t_3 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else if (y <= 2.6e+102) {
		tmp = ((230661.510616 / a) / (y * y)) + (((t / y) / fma(fma((y + a), y, b), y, c)) + (t_4 + (27464.7644705 / (y * a))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	t_3 = Float64(t / t_1)
	t_4 = Float64(Float64(z / a) + Float64(y / Float64(a / x)))
	tmp = 0.0
	if (y <= -1.5e+62)
		tmp = t_2;
	elseif (y <= -5.4e+21)
		tmp = Float64(t_3 + Float64(Float64(Float64(27464.7644705 / a) / y) + t_4));
	elseif (y <= 1.15e+50)
		tmp = Float64(t_3 + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_1));
	elseif (y <= 2.6e+102)
		tmp = Float64(Float64(Float64(230661.510616 / a) / Float64(y * y)) + Float64(Float64(Float64(t / y) / fma(fma(Float64(y + a), y, b), y, c)) + Float64(t_4 + Float64(27464.7644705 / Float64(y * a)))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+62], t$95$2, If[LessEqual[y, -5.4e+21], N[(t$95$3 + N[(N[(N[(27464.7644705 / a), $MachinePrecision] / y), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+50], N[(t$95$3 + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+102], N[(N[(N[(230661.510616 / a), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t / y), $MachinePrecision] / N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 + N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5e62 or 2.60000000000000006e102 < y

   1. Initial program 0.4%

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

   2. Taylor expanded in y around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-/l* 82.7%

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

   4. Simplified 82.7%

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

   if -1.5e62 < y < -5.4e21

   1. Initial program 30.0%

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

   2. Taylor expanded in t around inf 30.0%

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

   3. Taylor expanded in a around inf 26.8%

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

      1. *-commutative 26.8%

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

      2. fma-def 26.8%

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

      3. *-commutative 26.8%

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

      4. unpow2 26.8%

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

   5. Simplified 26.8%

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

   6. Taylor expanded in y around inf 36.4%

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

      1. +-commutative 36.4%

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

      2. associate-+r+ 36.4%

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

      3. associate-*r/ 36.4%

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

      4. metadata-eval 36.4%

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

      5. associate-/r* 44.3%

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

      6. +-commutative 44.3%

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

      7. associate-/l* 69.8%

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

   8. Simplified 69.8%

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

   if -5.4e21 < y < 1.14999999999999998e50

   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. Taylor expanded in t around inf 95.3%

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

   if 1.14999999999999998e50 < y < 2.60000000000000006e102

   1. Initial program 2.3%

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

   2. Taylor expanded in t around inf 2.3%

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

   3. Taylor expanded in a around inf 13.3%

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

      1. *-commutative 13.3%

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

      2. fma-def 13.3%

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

      3. *-commutative 13.3%

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

      4. unpow2 13.3%

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

   5. Simplified 13.3%

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

   6. Taylor expanded in i around 0 53.9%

      \[\leadsto \color{blue}{230661.510616 \cdot \frac{1}{{y}^{2} \cdot a} + \left(\frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(\frac{y \cdot x}{a} + \left(27464.7644705 \cdot \frac{1}{a \cdot y} + \frac{z}{a}\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 53.9%

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

      2. associate-*r/ 53.9%

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

      3. metadata-eval 53.9%

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

      4. associate-/r* 53.9%

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

      5. unpow2 53.9%

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

      6. associate-/r* 55.1%

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

      7. +-commutative 55.1%

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

      8. *-commutative 55.1%

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

      9. fma-udef 55.1%

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

      10. fma-def 55.1%

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

      11. +-commutative 55.1%

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

      12. associate-+r+ 55.1%

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

      13. +-commutative 55.1%

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

   8. Simplified 61.0%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(\frac{\frac{27464.7644705}{a}}{y} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+50}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{\frac{230661.510616}{a}}{y \cdot y} + \left(\frac{\frac{t}{y}}{\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right)} + \left(\left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right) + \frac{27464.7644705}{y \cdot a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 2: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \frac{t}{t_1}\\ t_3 := t_2 + \left(\frac{\frac{27464.7644705}{a}}{y} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\right)\\ t_4 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+63}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+49}:\\ \;\;\;\;t_2 + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+102}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2 (/ t t_1))
        (t_3 (+ t_2 (+ (/ (/ 27464.7644705 a) y) (+ (/ z a) (/ y (/ a x))))))
        (t_4 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -1.3e+63)
     t_4
     (if (<= y -1.36e+20)
       t_3
       (if (<= y 9e+49)
         (+
          t_2
          (/
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))
           t_1))
         (if (<= y 3.4e+102) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = t / t_1;
	double t_3 = t_2 + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))));
	double t_4 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.3e+63) {
		tmp = t_4;
	} else if (y <= -1.36e+20) {
		tmp = t_3;
	} else if (y <= 9e+49) {
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else if (y <= 3.4e+102) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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) :: tmp
    t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
    t_2 = t / t_1
    t_3 = t_2 + (((27464.7644705d0 / a) / y) + ((z / a) + (y / (a / x))))
    t_4 = (z / y) + (x - (a / (y / x)))
    if (y <= (-1.3d+63)) then
        tmp = t_4
    else if (y <= (-1.36d+20)) then
        tmp = t_3
    else if (y <= 9d+49) then
        tmp = t_2 + ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))) / t_1)
    else if (y <= 3.4d+102) then
        tmp = t_3
    else
        tmp = t_4
    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 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = t / t_1;
	double t_3 = t_2 + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))));
	double t_4 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.3e+63) {
		tmp = t_4;
	} else if (y <= -1.36e+20) {
		tmp = t_3;
	} else if (y <= 9e+49) {
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	} else if (y <= 3.4e+102) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
	t_2 = t / t_1
	t_3 = t_2 + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))))
	t_4 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -1.3e+63:
		tmp = t_4
	elif y <= -1.36e+20:
		tmp = t_3
	elif y <= 9e+49:
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1)
	elif y <= 3.4e+102:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	t_2 = Float64(t / t_1)
	t_3 = Float64(t_2 + Float64(Float64(Float64(27464.7644705 / a) / y) + Float64(Float64(z / a) + Float64(y / Float64(a / x)))))
	t_4 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.3e+63)
		tmp = t_4;
	elseif (y <= -1.36e+20)
		tmp = t_3;
	elseif (y <= 9e+49)
		tmp = Float64(t_2 + Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) / t_1));
	elseif (y <= 3.4e+102)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	t_2 = t / t_1;
	t_3 = t_2 + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))));
	t_4 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.3e+63)
		tmp = t_4;
	elseif (y <= -1.36e+20)
		tmp = t_3;
	elseif (y <= 9e+49)
		tmp = t_2 + ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) / t_1);
	elseif (y <= 3.4e+102)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(N[(N[(27464.7644705 / a), $MachinePrecision] / y), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+63], t$95$4, If[LessEqual[y, -1.36e+20], t$95$3, If[LessEqual[y, 9e+49], N[(t$95$2 + N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+102], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3000000000000001e63 or 3.4e102 < y

   1. Initial program 0.4%

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

   2. Taylor expanded in y around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-/l* 82.7%

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

   4. Simplified 82.7%

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

   if -1.3000000000000001e63 < y < -1.36e20 or 8.99999999999999965e49 < y < 3.4e102

   1. Initial program 13.6%

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

   2. Taylor expanded in t around inf 13.6%

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

   3. Taylor expanded in a around inf 18.8%

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

      1. *-commutative 18.8%

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

      2. fma-def 18.8%

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

      3. *-commutative 18.8%

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

      4. unpow2 18.8%

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

   5. Simplified 18.8%

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

   6. Taylor expanded in y around inf 46.8%

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

      1. +-commutative 46.8%

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

      2. associate-+r+ 46.8%

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

      3. associate-*r/ 46.8%

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

      4. metadata-eval 46.8%

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

      5. associate-/r* 50.0%

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

      6. +-commutative 50.0%

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

      7. associate-/l* 63.9%

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

   8. Simplified 63.9%

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

   if -1.36e20 < y < 8.99999999999999965e49

   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. Taylor expanded in t around inf 95.3%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+63}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(\frac{\frac{27464.7644705}{a}}{y} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(\frac{\frac{27464.7644705}{a}}{y} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 3: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \frac{t}{t_1} + \left(\frac{\frac{27464.7644705}{a}}{y} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\right)\\ t_3 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+44}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2
         (+ (/ t t_1) (+ (/ (/ 27464.7644705 a) y) (+ (/ z a) (/ y (/ a x))))))
        (t_3 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -7.6e+62)
     t_3
     (if (<= y -8.8e+20)
       t_2
       (if (<= y 5e+44)
         (/ (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))) t_1)
         (if (<= y 2.6e+102) 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 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (t / t_1) + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))));
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -7.6e+62) {
		tmp = t_3;
	} else if (y <= -8.8e+20) {
		tmp = t_2;
	} else if (y <= 5e+44) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	} else if (y <= 2.6e+102) {
		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 = i + (y * (c + (y * ((y * (y + a)) + b))))
    t_2 = (t / t_1) + (((27464.7644705d0 / a) / y) + ((z / a) + (y / (a / x))))
    t_3 = (z / y) + (x - (a / (y / x)))
    if (y <= (-7.6d+62)) then
        tmp = t_3
    else if (y <= (-8.8d+20)) then
        tmp = t_2
    else if (y <= 5d+44) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / t_1
    else if (y <= 2.6d+102) 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 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (t / t_1) + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))));
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -7.6e+62) {
		tmp = t_3;
	} else if (y <= -8.8e+20) {
		tmp = t_2;
	} else if (y <= 5e+44) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	} else if (y <= 2.6e+102) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
	t_2 = (t / t_1) + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))))
	t_3 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -7.6e+62:
		tmp = t_3
	elif y <= -8.8e+20:
		tmp = t_2
	elif y <= 5e+44:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1
	elif y <= 2.6e+102:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	t_2 = Float64(Float64(t / t_1) + Float64(Float64(Float64(27464.7644705 / a) / y) + Float64(Float64(z / a) + Float64(y / Float64(a / x)))))
	t_3 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -7.6e+62)
		tmp = t_3;
	elseif (y <= -8.8e+20)
		tmp = t_2;
	elseif (y <= 5e+44)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / t_1);
	elseif (y <= 2.6e+102)
		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 = i + (y * (c + (y * ((y * (y + a)) + b))));
	t_2 = (t / t_1) + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))));
	t_3 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -7.6e+62)
		tmp = t_3;
	elseif (y <= -8.8e+20)
		tmp = t_2;
	elseif (y <= 5e+44)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	elseif (y <= 2.6e+102)
		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[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(N[(27464.7644705 / a), $MachinePrecision] / y), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.6e+62], t$95$3, If[LessEqual[y, -8.8e+20], t$95$2, If[LessEqual[y, 5e+44], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.6e+102], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.59999999999999967e62 or 2.60000000000000006e102 < y

   1. Initial program 0.4%

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

   2. Taylor expanded in y around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-/l* 82.7%

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

   4. Simplified 82.7%

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

   if -7.59999999999999967e62 < y < -8.8e20 or 4.9999999999999996e44 < y < 2.60000000000000006e102

   1. Initial program 16.6%

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

   2. Taylor expanded in t around inf 16.6%

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

   3. Taylor expanded in a around inf 18.5%

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

      1. *-commutative 18.5%

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

      2. fma-def 18.5%

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

      3. *-commutative 18.5%

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

      4. unpow2 18.5%

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

   5. Simplified 18.5%

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

   6. Taylor expanded in y around inf 45.5%

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

      1. +-commutative 45.5%

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

      2. associate-+r+ 45.5%

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

      3. associate-*r/ 45.5%

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

      4. metadata-eval 45.5%

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

      5. associate-/r* 48.5%

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

      6. +-commutative 48.5%

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

      7. associate-/l* 61.9%

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

   8. Simplified 61.9%

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

   if -8.8e20 < y < 4.9999999999999996e44

   1. Initial program 95.2%

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

   2. Taylor expanded in x around 0 92.5%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+62}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(\frac{\frac{27464.7644705}{a}}{y} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+44}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(\frac{\frac{27464.7644705}{a}}{y} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 4: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \frac{t}{t_1} + \left(\frac{\frac{27464.7644705}{a}}{y} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\right)\\ t_3 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2
         (+ (/ t t_1) (+ (/ (/ 27464.7644705 a) y) (+ (/ z a) (/ y (/ a x))))))
        (t_3 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -5e+62)
     t_3
     (if (<= y -5.4e+21)
       t_2
       (if (<= y 1.02e+51)
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
          t_1)
         (if (<= y 2.6e+102) 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 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (t / t_1) + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))));
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -5e+62) {
		tmp = t_3;
	} else if (y <= -5.4e+21) {
		tmp = t_2;
	} else if (y <= 1.02e+51) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	} else if (y <= 2.6e+102) {
		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 = i + (y * (c + (y * ((y * (y + a)) + b))))
    t_2 = (t / t_1) + (((27464.7644705d0 / a) / y) + ((z / a) + (y / (a / x))))
    t_3 = (z / y) + (x - (a / (y / x)))
    if (y <= (-5d+62)) then
        tmp = t_3
    else if (y <= (-5.4d+21)) then
        tmp = t_2
    else if (y <= 1.02d+51) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / t_1
    else if (y <= 2.6d+102) 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 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (t / t_1) + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))));
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -5e+62) {
		tmp = t_3;
	} else if (y <= -5.4e+21) {
		tmp = t_2;
	} else if (y <= 1.02e+51) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	} else if (y <= 2.6e+102) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
	t_2 = (t / t_1) + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))))
	t_3 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -5e+62:
		tmp = t_3
	elif y <= -5.4e+21:
		tmp = t_2
	elif y <= 1.02e+51:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1
	elif y <= 2.6e+102:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	t_2 = Float64(Float64(t / t_1) + Float64(Float64(Float64(27464.7644705 / a) / y) + Float64(Float64(z / a) + Float64(y / Float64(a / x)))))
	t_3 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -5e+62)
		tmp = t_3;
	elseif (y <= -5.4e+21)
		tmp = t_2;
	elseif (y <= 1.02e+51)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / t_1);
	elseif (y <= 2.6e+102)
		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 = i + (y * (c + (y * ((y * (y + a)) + b))));
	t_2 = (t / t_1) + (((27464.7644705 / a) / y) + ((z / a) + (y / (a / x))));
	t_3 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -5e+62)
		tmp = t_3;
	elseif (y <= -5.4e+21)
		tmp = t_2;
	elseif (y <= 1.02e+51)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1;
	elseif (y <= 2.6e+102)
		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[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(N[(27464.7644705 / a), $MachinePrecision] / y), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+62], t$95$3, If[LessEqual[y, -5.4e+21], t$95$2, If[LessEqual[y, 1.02e+51], 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] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.6e+102], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000029e62 or 2.60000000000000006e102 < y

   1. Initial program 0.4%

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

   2. Taylor expanded in y around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-/l* 82.7%

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

   4. Simplified 82.7%

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

   if -5.00000000000000029e62 < y < -5.4e21 or 1.02e51 < y < 2.60000000000000006e102

   1. Initial program 13.6%

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

   2. Taylor expanded in t around inf 13.6%

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

   3. Taylor expanded in a around inf 18.8%

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

      1. *-commutative 18.8%

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

      2. fma-def 18.8%

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

      3. *-commutative 18.8%

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

      4. unpow2 18.8%

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

   5. Simplified 18.8%

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

   6. Taylor expanded in y around inf 46.8%

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

      1. +-commutative 46.8%

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

      2. associate-+r+ 46.8%

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

      3. associate-*r/ 46.8%

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

      4. metadata-eval 46.8%

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

      5. associate-/r* 50.0%

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

      6. +-commutative 50.0%

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

      7. associate-/l* 63.9%

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

   8. Simplified 63.9%

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

   if -5.4e21 < y < 1.02e51

   1. Initial program 95.3%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+62}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(\frac{\frac{27464.7644705}{a}}{y} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(\frac{\frac{27464.7644705}{a}}{y} + \left(\frac{z}{a} + \frac{y}{\frac{a}{x}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 5: 78.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ t_2 := t_1 + \left(\frac{z}{a} + \frac{y \cdot x}{a}\right)\\ t_3 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1.62 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;t_1 + \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+45}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ t (+ i (* y (+ c (* y (+ (* y (+ y a)) b)))))))
        (t_2 (+ t_1 (+ (/ z a) (/ (* y x) a))))
        (t_3 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -1.62e+62)
     t_3
     (if (<= y -1.1e+34)
       (+ t_1 (/ y (/ a x)))
       (if (<= y -5.4e+21)
         t_2
         (if (<= y 3e+45)
           (/
            (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
            (+ i (* y (+ c (* y b)))))
           (if (<= y 3.2e+102) 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 = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	double t_2 = t_1 + ((z / a) + ((y * x) / a));
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.62e+62) {
		tmp = t_3;
	} else if (y <= -1.1e+34) {
		tmp = t_1 + (y / (a / x));
	} else if (y <= -5.4e+21) {
		tmp = t_2;
	} else if (y <= 3e+45) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else if (y <= 3.2e+102) {
		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 = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    t_2 = t_1 + ((z / a) + ((y * x) / a))
    t_3 = (z / y) + (x - (a / (y / x)))
    if (y <= (-1.62d+62)) then
        tmp = t_3
    else if (y <= (-1.1d+34)) then
        tmp = t_1 + (y / (a / x))
    else if (y <= (-5.4d+21)) then
        tmp = t_2
    else if (y <= 3d+45) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    else if (y <= 3.2d+102) 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 = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	double t_2 = t_1 + ((z / a) + ((y * x) / a));
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -1.62e+62) {
		tmp = t_3;
	} else if (y <= -1.1e+34) {
		tmp = t_1 + (y / (a / x));
	} else if (y <= -5.4e+21) {
		tmp = t_2;
	} else if (y <= 3e+45) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else if (y <= 3.2e+102) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	t_2 = t_1 + ((z / a) + ((y * x) / a))
	t_3 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -1.62e+62:
		tmp = t_3
	elif y <= -1.1e+34:
		tmp = t_1 + (y / (a / x))
	elif y <= -5.4e+21:
		tmp = t_2
	elif y <= 3e+45:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	elif y <= 3.2e+102:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))))
	t_2 = Float64(t_1 + Float64(Float64(z / a) + Float64(Float64(y * x) / a)))
	t_3 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1.62e+62)
		tmp = t_3;
	elseif (y <= -1.1e+34)
		tmp = Float64(t_1 + Float64(y / Float64(a / x)));
	elseif (y <= -5.4e+21)
		tmp = t_2;
	elseif (y <= 3e+45)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 3.2e+102)
		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 = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	t_2 = t_1 + ((z / a) + ((y * x) / a));
	t_3 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1.62e+62)
		tmp = t_3;
	elseif (y <= -1.1e+34)
		tmp = t_1 + (y / (a / x));
	elseif (y <= -5.4e+21)
		tmp = t_2;
	elseif (y <= 3e+45)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	elseif (y <= 3.2e+102)
		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[(t / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(N[(z / a), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.62e+62], t$95$3, If[LessEqual[y, -1.1e+34], N[(t$95$1 + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.4e+21], t$95$2, If[LessEqual[y, 3e+45], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+102], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6199999999999999e62 or 3.1999999999999999e102 < y

   1. Initial program 0.4%

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

   2. Taylor expanded in y around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-/l* 82.7%

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

   4. Simplified 82.7%

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

   if -1.6199999999999999e62 < y < -1.1000000000000001e34

   1. Initial program 28.2%

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

   2. Taylor expanded in t around inf 28.2%

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

   3. Taylor expanded in a around inf 23.6%

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

      1. *-commutative 23.6%

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

      2. fma-def 23.6%

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

      3. *-commutative 23.6%

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

      4. unpow2 23.6%

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

   5. Simplified 23.6%

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

   6. Taylor expanded in y around inf 17.2%

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

      1. associate-/l* 52.3%

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

   8. Simplified 52.3%

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

   if -1.1000000000000001e34 < y < -5.4e21 or 3.00000000000000011e45 < y < 3.1999999999999999e102

   1. Initial program 12.0%

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

   2. Taylor expanded in t around inf 12.0%

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

   3. Taylor expanded in a around inf 16.4%

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

      1. *-commutative 16.4%

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

      2. fma-def 16.4%

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

      3. *-commutative 16.4%

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

      4. unpow2 16.4%

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

   5. Simplified 16.4%

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

   6. Taylor expanded in y around inf 53.9%

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

   if -5.4e21 < y < 3.00000000000000011e45

   1. Initial program 95.2%

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

   2. Taylor expanded in x around 0 92.5%

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

   3. Taylor expanded in y around 0 87.8%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{+62}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(\frac{z}{a} + \frac{y \cdot x}{a}\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+45}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(\frac{z}{a} + \frac{y \cdot x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 6: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ t_2 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{t_2}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;\frac{t}{t_2} + \left(\frac{z}{a} + \frac{y \cdot x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x)))))
        (t_2 (+ i (* y (+ c (* y (+ (* y (+ y a)) b)))))))
   (if (<= y -1.65e+47)
     t_1
     (if (<= y 1.05e+46)
       (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) t_2)
       (if (<= y 2.1e+103) (+ (/ t t_2) (+ (/ z a) (/ (* y x) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double t_2 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double tmp;
	if (y <= -1.65e+47) {
		tmp = t_1;
	} else if (y <= 1.05e+46) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	} else if (y <= 2.1e+103) {
		tmp = (t / t_2) + ((z / a) + ((y * x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    t_2 = i + (y * (c + (y * ((y * (y + a)) + b))))
    if (y <= (-1.65d+47)) then
        tmp = t_1
    else if (y <= 1.05d+46) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / t_2
    else if (y <= 2.1d+103) then
        tmp = (t / t_2) + ((z / a) + ((y * x) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double t_2 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double tmp;
	if (y <= -1.65e+47) {
		tmp = t_1;
	} else if (y <= 1.05e+46) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	} else if (y <= 2.1e+103) {
		tmp = (t / t_2) + ((z / a) + ((y * x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	t_2 = i + (y * (c + (y * ((y * (y + a)) + b))))
	tmp = 0
	if y <= -1.65e+47:
		tmp = t_1
	elif y <= 1.05e+46:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2
	elif y <= 2.1e+103:
		tmp = (t / t_2) + ((z / a) + ((y * x) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	t_2 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	tmp = 0.0
	if (y <= -1.65e+47)
		tmp = t_1;
	elseif (y <= 1.05e+46)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / t_2);
	elseif (y <= 2.1e+103)
		tmp = Float64(Float64(t / t_2) + Float64(Float64(z / a) + Float64(Float64(y * x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	t_2 = i + (y * (c + (y * ((y * (y + a)) + b))));
	tmp = 0.0;
	if (y <= -1.65e+47)
		tmp = t_1;
	elseif (y <= 1.05e+46)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	elseif (y <= 2.1e+103)
		tmp = (t / t_2) + ((z / a) + ((y * x) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+47], t$95$1, If[LessEqual[y, 1.05e+46], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 2.1e+103], N[(N[(t / t$95$2), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e47 or 2.1000000000000002e103 < 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. Taylor expanded in y around inf 75.5%

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

      1. associate--l+ 75.5%

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

      2. associate-/l* 79.5%

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

   4. Simplified 79.5%

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

   if -1.65e47 < y < 1.05e46

   1. Initial program 92.7%

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

   2. Taylor expanded in z around inf 88.2%

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

      1. *-commutative 88.2%

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

      2. unpow2 88.2%

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

   4. Simplified 88.2%

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

   if 1.05e46 < y < 2.1000000000000002e103

   1. Initial program 8.0%

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

   2. Taylor expanded in t around inf 8.0%

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

   3. Taylor expanded in a around inf 13.1%

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

      1. *-commutative 13.1%

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

      2. fma-def 13.1%

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

      3. *-commutative 13.1%

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

      4. unpow2 13.1%

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

   5. Simplified 13.1%

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

   6. Taylor expanded in y around inf 51.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+47}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(\frac{z}{a} + \frac{y \cdot x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 7: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{t_1} + \left(\frac{z}{a} + \frac{y \cdot x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -4.4e+49)
     t_2
     (if (<= y 4.5e+42)
       (/ (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))) t_1)
       (if (<= y 2.6e+102) (+ (/ t t_1) (+ (/ z a) (/ (* y x) a))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -4.4e+49) {
		tmp = t_2;
	} else if (y <= 4.5e+42) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	} else if (y <= 2.6e+102) {
		tmp = (t / t_1) + ((z / a) + ((y * x) / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
    t_2 = (z / y) + (x - (a / (y / x)))
    if (y <= (-4.4d+49)) then
        tmp = t_2
    else if (y <= 4.5d+42) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / t_1
    else if (y <= 2.6d+102) then
        tmp = (t / t_1) + ((z / a) + ((y * x) / a))
    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 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -4.4e+49) {
		tmp = t_2;
	} else if (y <= 4.5e+42) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	} else if (y <= 2.6e+102) {
		tmp = (t / t_1) + ((z / a) + ((y * x) / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
	t_2 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -4.4e+49:
		tmp = t_2
	elif y <= 4.5e+42:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1
	elif y <= 2.6e+102:
		tmp = (t / t_1) + ((z / a) + ((y * x) / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -4.4e+49)
		tmp = t_2;
	elseif (y <= 4.5e+42)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / t_1);
	elseif (y <= 2.6e+102)
		tmp = Float64(Float64(t / t_1) + Float64(Float64(z / a) + Float64(Float64(y * x) / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	t_2 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -4.4e+49)
		tmp = t_2;
	elseif (y <= 4.5e+42)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	elseif (y <= 2.6e+102)
		tmp = (t / t_1) + ((z / a) + ((y * x) / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+49], t$95$2, If[LessEqual[y, 4.5e+42], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.6e+102], N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4000000000000001e49 or 2.60000000000000006e102 < 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. Taylor expanded in y around inf 75.5%

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

      1. associate--l+ 75.5%

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

      2. associate-/l* 79.5%

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

   4. Simplified 79.5%

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

   if -4.4000000000000001e49 < y < 4.50000000000000012e42

   1. Initial program 92.7%

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

   2. Taylor expanded in x around 0 89.5%

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

   if 4.50000000000000012e42 < y < 2.60000000000000006e102

   1. Initial program 8.0%

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

   2. Taylor expanded in t around inf 8.0%

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

   3. Taylor expanded in a around inf 13.1%

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

      1. *-commutative 13.1%

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

      2. fma-def 13.1%

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

      3. *-commutative 13.1%

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

      4. unpow2 13.1%

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

   5. Simplified 13.1%

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

   6. Taylor expanded in y around inf 51.2%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \left(\frac{z}{a} + \frac{y \cdot x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 8: 78.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -9.4 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+31}:\\ \;\;\;\;t_1 + \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+20}:\\ \;\;\;\;t_1 + \frac{z}{a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ t (+ i (* y (+ c (* y (+ (* y (+ y a)) b)))))))
        (t_2 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -9.4e+61)
     t_2
     (if (<= y -7.5e+31)
       (+ t_1 (/ y (/ a x)))
       (if (<= y -5.2e+20)
         (+ t_1 (/ z a))
         (if (<= y 3.2e+51)
           (/
            (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
            (+ i (* y (+ c (* y b)))))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -9.4e+61) {
		tmp = t_2;
	} else if (y <= -7.5e+31) {
		tmp = t_1 + (y / (a / x));
	} else if (y <= -5.2e+20) {
		tmp = t_1 + (z / a);
	} else if (y <= 3.2e+51) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    t_2 = (z / y) + (x - (a / (y / x)))
    if (y <= (-9.4d+61)) then
        tmp = t_2
    else if (y <= (-7.5d+31)) then
        tmp = t_1 + (y / (a / x))
    else if (y <= (-5.2d+20)) then
        tmp = t_1 + (z / a)
    else if (y <= 3.2d+51) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -9.4e+61) {
		tmp = t_2;
	} else if (y <= -7.5e+31) {
		tmp = t_1 + (y / (a / x));
	} else if (y <= -5.2e+20) {
		tmp = t_1 + (z / a);
	} else if (y <= 3.2e+51) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	t_2 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -9.4e+61:
		tmp = t_2
	elif y <= -7.5e+31:
		tmp = t_1 + (y / (a / x))
	elif y <= -5.2e+20:
		tmp = t_1 + (z / a)
	elif y <= 3.2e+51:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -9.4e+61)
		tmp = t_2;
	elseif (y <= -7.5e+31)
		tmp = Float64(t_1 + Float64(y / Float64(a / x)));
	elseif (y <= -5.2e+20)
		tmp = Float64(t_1 + Float64(z / a));
	elseif (y <= 3.2e+51)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	t_2 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -9.4e+61)
		tmp = t_2;
	elseif (y <= -7.5e+31)
		tmp = t_1 + (y / (a / x));
	elseif (y <= -5.2e+20)
		tmp = t_1 + (z / a);
	elseif (y <= 3.2e+51)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.4e+61], t$95$2, If[LessEqual[y, -7.5e+31], N[(t$95$1 + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.2e+20], N[(t$95$1 + N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+51], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.3999999999999997e61 or 3.2000000000000002e51 < y

   1. Initial program 0.7%

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

   2. Taylor expanded in y around inf 70.6%

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

      1. associate--l+ 70.6%

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

      2. associate-/l* 74.3%

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

   4. Simplified 74.3%

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

   if -9.3999999999999997e61 < y < -7.5e31

   1. Initial program 28.2%

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

   2. Taylor expanded in t around inf 28.2%

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

   3. Taylor expanded in a around inf 23.6%

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

      1. *-commutative 23.6%

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

      2. fma-def 23.6%

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

      3. *-commutative 23.6%

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

      4. unpow2 23.6%

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

   5. Simplified 23.6%

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

   6. Taylor expanded in y around inf 17.2%

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

      1. associate-/l* 52.3%

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

   8. Simplified 52.3%

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

   if -7.5e31 < y < -5.2e20

   1. Initial program 34.6%

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

   2. Taylor expanded in t around inf 34.6%

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

   3. Taylor expanded in a around inf 35.3%

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

      1. *-commutative 35.3%

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

      2. fma-def 35.3%

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

      3. *-commutative 35.3%

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

      4. unpow2 35.3%

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

   5. Simplified 35.3%

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

   6. Taylor expanded in z around inf 68.6%

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

   if -5.2e20 < y < 3.2000000000000002e51

   1. Initial program 94.5%

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

   2. Taylor expanded in x around 0 91.2%

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

   3. Taylor expanded in y around 0 86.5%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{z}{a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 9: 76.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)\\ t_2 := \frac{t}{t_1}\\ t_3 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -9.9 \cdot 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;t_2 + \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+17}:\\ \;\;\;\;t_2 + \frac{z}{a}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-15}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))
        (t_2 (/ t t_1))
        (t_3 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -9.9e+61)
     t_3
     (if (<= y -4.8e+33)
       (+ t_2 (/ y (/ a x)))
       (if (<= y -3.7e+17)
         (+ t_2 (/ z a))
         (if (<= y 1.9e-15) (/ (+ t (* y 230661.510616)) t_1) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = t / t_1;
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -9.9e+61) {
		tmp = t_3;
	} else if (y <= -4.8e+33) {
		tmp = t_2 + (y / (a / x));
	} else if (y <= -3.7e+17) {
		tmp = t_2 + (z / a);
	} else if (y <= 1.9e-15) {
		tmp = (t + (y * 230661.510616)) / t_1;
	} 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 = i + (y * (c + (y * ((y * (y + a)) + b))))
    t_2 = t / t_1
    t_3 = (z / y) + (x - (a / (y / x)))
    if (y <= (-9.9d+61)) then
        tmp = t_3
    else if (y <= (-4.8d+33)) then
        tmp = t_2 + (y / (a / x))
    else if (y <= (-3.7d+17)) then
        tmp = t_2 + (z / a)
    else if (y <= 1.9d-15) then
        tmp = (t + (y * 230661.510616d0)) / t_1
    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 = i + (y * (c + (y * ((y * (y + a)) + b))));
	double t_2 = t / t_1;
	double t_3 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -9.9e+61) {
		tmp = t_3;
	} else if (y <= -4.8e+33) {
		tmp = t_2 + (y / (a / x));
	} else if (y <= -3.7e+17) {
		tmp = t_2 + (z / a);
	} else if (y <= 1.9e-15) {
		tmp = (t + (y * 230661.510616)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))))
	t_2 = t / t_1
	t_3 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -9.9e+61:
		tmp = t_3
	elif y <= -4.8e+33:
		tmp = t_2 + (y / (a / x))
	elif y <= -3.7e+17:
		tmp = t_2 + (z / a)
	elif y <= 1.9e-15:
		tmp = (t + (y * 230661.510616)) / t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))
	t_2 = Float64(t / t_1)
	t_3 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -9.9e+61)
		tmp = t_3;
	elseif (y <= -4.8e+33)
		tmp = Float64(t_2 + Float64(y / Float64(a / x)));
	elseif (y <= -3.7e+17)
		tmp = Float64(t_2 + Float64(z / a));
	elseif (y <= 1.9e-15)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i + (y * (c + (y * ((y * (y + a)) + b))));
	t_2 = t / t_1;
	t_3 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -9.9e+61)
		tmp = t_3;
	elseif (y <= -4.8e+33)
		tmp = t_2 + (y / (a / x));
	elseif (y <= -3.7e+17)
		tmp = t_2 + (z / a);
	elseif (y <= 1.9e-15)
		tmp = (t + (y * 230661.510616)) / t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.9e+61], t$95$3, If[LessEqual[y, -4.8e+33], N[(t$95$2 + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.7e+17], N[(t$95$2 + N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-15], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.9000000000000004e61 or 1.9000000000000001e-15 < y

   1. Initial program 6.2%

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

   2. Taylor expanded in y around inf 64.7%

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

      1. associate--l+ 64.7%

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

      2. associate-/l* 67.9%

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

   4. Simplified 67.9%

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

   if -9.9000000000000004e61 < y < -4.8e33

   1. Initial program 28.2%

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

   2. Taylor expanded in t around inf 28.2%

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

   3. Taylor expanded in a around inf 23.6%

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

      1. *-commutative 23.6%

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

      2. fma-def 23.6%

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

      3. *-commutative 23.6%

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

      4. unpow2 23.6%

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

   5. Simplified 23.6%

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

   6. Taylor expanded in y around inf 17.2%

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

      1. associate-/l* 52.3%

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

   8. Simplified 52.3%

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

   if -4.8e33 < y < -3.7e17

   1. Initial program 34.6%

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

   2. Taylor expanded in t around inf 34.6%

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

   3. Taylor expanded in a around inf 35.3%

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

      1. *-commutative 35.3%

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

      2. fma-def 35.3%

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

      3. *-commutative 35.3%

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

      4. unpow2 35.3%

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

   5. Simplified 35.3%

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

   6. Taylor expanded in z around inf 68.6%

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

   if -3.7e17 < y < 1.9000000000000001e-15

   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. Taylor expanded in y around 0 93.7%

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

      1. *-commutative 93.7%

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

   4. Simplified 93.7%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.9 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)} + \frac{z}{a}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-15}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 10: 76.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+61} \lor \neg \left(y \leq 1.9 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -9.2e+61) (not (<= y 1.9e-15)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9.2e+61) || !(y <= 1.9e-15)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-9.2d+61)) .or. (.not. (y <= 1.9d-15))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9.2e+61) || !(y <= 1.9e-15)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -9.2e+61) or not (y <= 1.9e-15):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -9.2e+61) || !(y <= 1.9e-15))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -9.2e+61) || ~((y <= 1.9e-15)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -9.2e+61], N[Not[LessEqual[y, 1.9e-15]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.1999999999999998e61 or 1.9000000000000001e-15 < y

   1. Initial program 6.2%

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

   2. Taylor expanded in y around inf 64.7%

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

      1. associate--l+ 64.7%

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

      2. associate-/l* 67.9%

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

   4. Simplified 67.9%

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

   if -9.1999999999999998e61 < y < 1.9000000000000001e-15

   1. Initial program 93.7%

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

   2. Taylor expanded in y around 0 86.8%

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

      1. *-commutative 86.8%

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

   4. Simplified 86.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+61} \lor \neg \left(y \leq 1.9 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \]

Alternative 11: 59.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{t_1}{y \cdot c}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-123}:\\ \;\;\;\;\frac{t_1}{i}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-76}:\\ \;\;\;\;\frac{230661.510616}{c} + \frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-15}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616))) (t_2 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -9.2e+61)
     t_2
     (if (<= y -8.8e-82)
       (/ t_1 (* y c))
       (if (<= y 9e-123)
         (/ t_1 i)
         (if (<= y 1.9e-76)
           (+ (/ 230661.510616 c) (/ t (* y c)))
           (if (<= y 1.32e-15) (/ t i) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -9.2e+61) {
		tmp = t_2;
	} else if (y <= -8.8e-82) {
		tmp = t_1 / (y * c);
	} else if (y <= 9e-123) {
		tmp = t_1 / i;
	} else if (y <= 1.9e-76) {
		tmp = (230661.510616 / c) + (t / (y * c));
	} else if (y <= 1.32e-15) {
		tmp = t / i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    t_2 = (z / y) + (x - (a / (y / x)))
    if (y <= (-9.2d+61)) then
        tmp = t_2
    else if (y <= (-8.8d-82)) then
        tmp = t_1 / (y * c)
    else if (y <= 9d-123) then
        tmp = t_1 / i
    else if (y <= 1.9d-76) then
        tmp = (230661.510616d0 / c) + (t / (y * c))
    else if (y <= 1.32d-15) then
        tmp = t / i
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -9.2e+61) {
		tmp = t_2;
	} else if (y <= -8.8e-82) {
		tmp = t_1 / (y * c);
	} else if (y <= 9e-123) {
		tmp = t_1 / i;
	} else if (y <= 1.9e-76) {
		tmp = (230661.510616 / c) + (t / (y * c));
	} else if (y <= 1.32e-15) {
		tmp = t / i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	t_2 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -9.2e+61:
		tmp = t_2
	elif y <= -8.8e-82:
		tmp = t_1 / (y * c)
	elif y <= 9e-123:
		tmp = t_1 / i
	elif y <= 1.9e-76:
		tmp = (230661.510616 / c) + (t / (y * c))
	elif y <= 1.32e-15:
		tmp = t / i
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	t_2 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -9.2e+61)
		tmp = t_2;
	elseif (y <= -8.8e-82)
		tmp = Float64(t_1 / Float64(y * c));
	elseif (y <= 9e-123)
		tmp = Float64(t_1 / i);
	elseif (y <= 1.9e-76)
		tmp = Float64(Float64(230661.510616 / c) + Float64(t / Float64(y * c)));
	elseif (y <= 1.32e-15)
		tmp = Float64(t / i);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	t_2 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -9.2e+61)
		tmp = t_2;
	elseif (y <= -8.8e-82)
		tmp = t_1 / (y * c);
	elseif (y <= 9e-123)
		tmp = t_1 / i;
	elseif (y <= 1.9e-76)
		tmp = (230661.510616 / c) + (t / (y * c));
	elseif (y <= 1.32e-15)
		tmp = t / i;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+61], t$95$2, If[LessEqual[y, -8.8e-82], N[(t$95$1 / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-123], N[(t$95$1 / i), $MachinePrecision], If[LessEqual[y, 1.9e-76], N[(N[(230661.510616 / c), $MachinePrecision] + N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e-15], N[(t / i), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.1999999999999998e61 or 1.31999999999999995e-15 < y

   1. Initial program 6.2%

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

   2. Taylor expanded in y around inf 64.7%

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

      1. associate--l+ 64.7%

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

      2. associate-/l* 67.9%

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

   4. Simplified 67.9%

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

   if -9.1999999999999998e61 < y < -8.79999999999999943e-82

   1. Initial program 69.9%

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

   2. Taylor expanded in c around inf 28.9%

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

   3. Taylor expanded in y around 0 25.3%

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

      1. *-commutative 25.3%

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

   5. Simplified 25.3%

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

   6. Taylor expanded in y around 0 26.0%

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

   if -8.79999999999999943e-82 < y < 8.99999999999999986e-123

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 52.0%

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

   3. Taylor expanded in i around inf 79.5%

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

   if 8.99999999999999986e-123 < y < 1.9000000000000001e-76

   1. Initial program 99.5%

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

   2. Taylor expanded in c around inf 80.4%

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

   3. Taylor expanded in y around 0 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in y around 0 80.3%

      \[\leadsto \color{blue}{230661.510616 \cdot \frac{1}{c} + \frac{t}{c \cdot y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 80.4%

         \[\leadsto \color{blue}{\frac{230661.510616 \cdot 1}{c}} + \frac{t}{c \cdot y} \]

      2. metadata-eval 80.4%

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

      3. *-commutative 80.4%

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

   8. Simplified 80.4%

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

   if 1.9000000000000001e-76 < y < 1.31999999999999995e-15

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 28.5%

      \[\leadsto \color{blue}{\frac{t}{i}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-123}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-76}:\\ \;\;\;\;\frac{230661.510616}{c} + \frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-15}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 12: 59.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-73}:\\ \;\;\;\;\frac{230661.510616}{c} + \frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (/ z y) (- x (/ a (/ y x))))))
   (if (<= y -9.2e+61)
     t_1
     (if (<= y -5.1e-81)
       (/ (+ t (* y 230661.510616)) (* y c))
       (if (<= y 9.5e-122)
         (/ (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))) i)
         (if (<= y 5.4e-73)
           (+ (/ 230661.510616 c) (/ t (* y c)))
           (if (<= y 1.8e-15) (/ t i) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -9.2e+61) {
		tmp = t_1;
	} else if (y <= -5.1e-81) {
		tmp = (t + (y * 230661.510616)) / (y * c);
	} else if (y <= 9.5e-122) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	} else if (y <= 5.4e-73) {
		tmp = (230661.510616 / c) + (t / (y * c));
	} else if (y <= 1.8e-15) {
		tmp = t / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / y) + (x - (a / (y / x)))
    if (y <= (-9.2d+61)) then
        tmp = t_1
    else if (y <= (-5.1d-81)) then
        tmp = (t + (y * 230661.510616d0)) / (y * c)
    else if (y <= 9.5d-122) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / i
    else if (y <= 5.4d-73) then
        tmp = (230661.510616d0 / c) + (t / (y * c))
    else if (y <= 1.8d-15) then
        tmp = t / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z / y) + (x - (a / (y / x)));
	double tmp;
	if (y <= -9.2e+61) {
		tmp = t_1;
	} else if (y <= -5.1e-81) {
		tmp = (t + (y * 230661.510616)) / (y * c);
	} else if (y <= 9.5e-122) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	} else if (y <= 5.4e-73) {
		tmp = (230661.510616 / c) + (t / (y * c));
	} else if (y <= 1.8e-15) {
		tmp = t / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z / y) + (x - (a / (y / x)))
	tmp = 0
	if y <= -9.2e+61:
		tmp = t_1
	elif y <= -5.1e-81:
		tmp = (t + (y * 230661.510616)) / (y * c)
	elif y <= 9.5e-122:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i
	elif y <= 5.4e-73:
		tmp = (230661.510616 / c) + (t / (y * c))
	elif y <= 1.8e-15:
		tmp = t / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -9.2e+61)
		tmp = t_1;
	elseif (y <= -5.1e-81)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(y * c));
	elseif (y <= 9.5e-122)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / i);
	elseif (y <= 5.4e-73)
		tmp = Float64(Float64(230661.510616 / c) + Float64(t / Float64(y * c)));
	elseif (y <= 1.8e-15)
		tmp = Float64(t / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z / y) + (x - (a / (y / x)));
	tmp = 0.0;
	if (y <= -9.2e+61)
		tmp = t_1;
	elseif (y <= -5.1e-81)
		tmp = (t + (y * 230661.510616)) / (y * c);
	elseif (y <= 9.5e-122)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / i;
	elseif (y <= 5.4e-73)
		tmp = (230661.510616 / c) + (t / (y * c));
	elseif (y <= 1.8e-15)
		tmp = t / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+61], t$95$1, If[LessEqual[y, -5.1e-81], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-122], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 5.4e-73], N[(N[(230661.510616 / c), $MachinePrecision] + N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-15], N[(t / i), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.1999999999999998e61 or 1.8000000000000001e-15 < y

   1. Initial program 6.2%

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

   2. Taylor expanded in y around inf 64.7%

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

      1. associate--l+ 64.7%

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

      2. associate-/l* 67.9%

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

   4. Simplified 67.9%

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

   if -9.1999999999999998e61 < y < -5.10000000000000027e-81

   1. Initial program 69.9%

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

   2. Taylor expanded in c around inf 28.9%

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

   3. Taylor expanded in y around 0 25.3%

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

      1. *-commutative 25.3%

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

   5. Simplified 25.3%

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

   6. Taylor expanded in y around 0 26.0%

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

   if -5.10000000000000027e-81 < y < 9.5000000000000002e-122

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.8%

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

   3. Taylor expanded in i around inf 79.5%

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

   if 9.5000000000000002e-122 < y < 5.39999999999999989e-73

   1. Initial program 99.5%

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

   2. Taylor expanded in c around inf 80.4%

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

   3. Taylor expanded in y around 0 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in y around 0 80.3%

      \[\leadsto \color{blue}{230661.510616 \cdot \frac{1}{c} + \frac{t}{c \cdot y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 80.4%

         \[\leadsto \color{blue}{\frac{230661.510616 \cdot 1}{c}} + \frac{t}{c \cdot y} \]

      2. metadata-eval 80.4%

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

      3. *-commutative 80.4%

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

   8. Simplified 80.4%

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

   if 5.39999999999999989e-73 < y < 1.8000000000000001e-15

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 28.5%

      \[\leadsto \color{blue}{\frac{t}{i}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-73}:\\ \;\;\;\;\frac{230661.510616}{c} + \frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 13: 68.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+61} \lor \neg \left(y \leq 1.9 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -9.2e+61) (not (<= y 1.9e-15)))
   (+ (/ z y) (- x (/ a (/ y x))))
   (/ t (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9.2e+61) || !(y <= 1.9e-15)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-9.2d+61)) .or. (.not. (y <= 1.9d-15))) then
        tmp = (z / y) + (x - (a / (y / x)))
    else
        tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9.2e+61) || !(y <= 1.9e-15)) {
		tmp = (z / y) + (x - (a / (y / x)));
	} else {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -9.2e+61) or not (y <= 1.9e-15):
		tmp = (z / y) + (x - (a / (y / x)))
	else:
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -9.2e+61) || !(y <= 1.9e-15))
		tmp = Float64(Float64(z / y) + Float64(x - Float64(a / Float64(y / x))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -9.2e+61) || ~((y <= 1.9e-15)))
		tmp = (z / y) + (x - (a / (y / x)));
	else
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -9.2e+61], N[Not[LessEqual[y, 1.9e-15]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] + N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.1999999999999998e61 or 1.9000000000000001e-15 < y

   1. Initial program 6.2%

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

   2. Taylor expanded in y around inf 64.7%

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

      1. associate--l+ 64.7%

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

      2. associate-/l* 67.9%

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

   4. Simplified 67.9%

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

   if -9.1999999999999998e61 < y < 1.9000000000000001e-15

   1. Initial program 93.7%

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

   2. Taylor expanded in t around inf 74.0%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+61} \lor \neg \left(y \leq 1.9 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{z}{y} + \left(x - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \]

Alternative 14: 52.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-80}:\\ \;\;\;\;\frac{t_1}{y \cdot c}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{t_1}{i}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{230661.510616}{c} + \frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616))))
   (if (<= y -4.1e+58)
     x
     (if (<= y -3.4e-80)
       (/ t_1 (* y c))
       (if (<= y 9.5e-122)
         (/ t_1 i)
         (if (<= y 7.2e-78)
           (+ (/ 230661.510616 c) (/ t (* y c)))
           (if (<= y 2.55e+36) (/ t i) x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double tmp;
	if (y <= -4.1e+58) {
		tmp = x;
	} else if (y <= -3.4e-80) {
		tmp = t_1 / (y * c);
	} else if (y <= 9.5e-122) {
		tmp = t_1 / i;
	} else if (y <= 7.2e-78) {
		tmp = (230661.510616 / c) + (t / (y * c));
	} else if (y <= 2.55e+36) {
		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) :: t_1
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    if (y <= (-4.1d+58)) then
        tmp = x
    else if (y <= (-3.4d-80)) then
        tmp = t_1 / (y * c)
    else if (y <= 9.5d-122) then
        tmp = t_1 / i
    else if (y <= 7.2d-78) then
        tmp = (230661.510616d0 / c) + (t / (y * c))
    else if (y <= 2.55d+36) 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 t_1 = t + (y * 230661.510616);
	double tmp;
	if (y <= -4.1e+58) {
		tmp = x;
	} else if (y <= -3.4e-80) {
		tmp = t_1 / (y * c);
	} else if (y <= 9.5e-122) {
		tmp = t_1 / i;
	} else if (y <= 7.2e-78) {
		tmp = (230661.510616 / c) + (t / (y * c));
	} else if (y <= 2.55e+36) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	tmp = 0
	if y <= -4.1e+58:
		tmp = x
	elif y <= -3.4e-80:
		tmp = t_1 / (y * c)
	elif y <= 9.5e-122:
		tmp = t_1 / i
	elif y <= 7.2e-78:
		tmp = (230661.510616 / c) + (t / (y * c))
	elif y <= 2.55e+36:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	tmp = 0.0
	if (y <= -4.1e+58)
		tmp = x;
	elseif (y <= -3.4e-80)
		tmp = Float64(t_1 / Float64(y * c));
	elseif (y <= 9.5e-122)
		tmp = Float64(t_1 / i);
	elseif (y <= 7.2e-78)
		tmp = Float64(Float64(230661.510616 / c) + Float64(t / Float64(y * c)));
	elseif (y <= 2.55e+36)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	tmp = 0.0;
	if (y <= -4.1e+58)
		tmp = x;
	elseif (y <= -3.4e-80)
		tmp = t_1 / (y * c);
	elseif (y <= 9.5e-122)
		tmp = t_1 / i;
	elseif (y <= 7.2e-78)
		tmp = (230661.510616 / c) + (t / (y * c));
	elseif (y <= 2.55e+36)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+58], x, If[LessEqual[y, -3.4e-80], N[(t$95$1 / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-122], N[(t$95$1 / i), $MachinePrecision], If[LessEqual[y, 7.2e-78], N[(N[(230661.510616 / c), $MachinePrecision] + N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e+36], N[(t / i), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.1e58 or 2.54999999999999986e36 < y

   1. Initial program 3.2%

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

   2. Taylor expanded in y around inf 54.8%

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

   if -4.1e58 < y < -3.4000000000000001e-80

   1. Initial program 72.4%

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

   2. Taylor expanded in c around inf 30.0%

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

   3. Taylor expanded in y around 0 26.1%

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

      1. *-commutative 26.1%

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

   5. Simplified 26.1%

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

   6. Taylor expanded in y around 0 27.0%

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

   if -3.4000000000000001e-80 < y < 9.5000000000000002e-122

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 52.0%

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

   3. Taylor expanded in i around inf 79.5%

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

   if 9.5000000000000002e-122 < y < 7.2000000000000005e-78

   1. Initial program 99.5%

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

   2. Taylor expanded in c around inf 80.4%

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

   3. Taylor expanded in y around 0 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in y around 0 80.3%

      \[\leadsto \color{blue}{230661.510616 \cdot \frac{1}{c} + \frac{t}{c \cdot y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 80.4%

         \[\leadsto \color{blue}{\frac{230661.510616 \cdot 1}{c}} + \frac{t}{c \cdot y} \]

      2. metadata-eval 80.4%

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

      3. *-commutative 80.4%

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

   8. Simplified 80.4%

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

   if 7.2000000000000005e-78 < y < 2.54999999999999986e36

   1. Initial program 71.3%

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

   2. Taylor expanded in y around 0 15.8%

      \[\leadsto \color{blue}{\frac{t}{i}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-80}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{230661.510616}{c} + \frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 52.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-74}:\\ \;\;\;\;\frac{230661.510616}{c} + \frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.5e-58)
   x
   (if (<= y 9.5e-122)
     (/ (+ t (* y 230661.510616)) i)
     (if (<= y 3.05e-74)
       (+ (/ 230661.510616 c) (/ t (* y c)))
       (if (<= y 2.4e+36) (/ 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 <= -5.5e-58) {
		tmp = x;
	} else if (y <= 9.5e-122) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 3.05e-74) {
		tmp = (230661.510616 / c) + (t / (y * c));
	} else if (y <= 2.4e+36) {
		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 <= (-5.5d-58)) then
        tmp = x
    else if (y <= 9.5d-122) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 3.05d-74) then
        tmp = (230661.510616d0 / c) + (t / (y * c))
    else if (y <= 2.4d+36) 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 <= -5.5e-58) {
		tmp = x;
	} else if (y <= 9.5e-122) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 3.05e-74) {
		tmp = (230661.510616 / c) + (t / (y * c));
	} else if (y <= 2.4e+36) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.5e-58:
		tmp = x
	elif y <= 9.5e-122:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 3.05e-74:
		tmp = (230661.510616 / c) + (t / (y * c))
	elif y <= 2.4e+36:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.5e-58)
		tmp = x;
	elseif (y <= 9.5e-122)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 3.05e-74)
		tmp = Float64(Float64(230661.510616 / c) + Float64(t / Float64(y * c)));
	elseif (y <= 2.4e+36)
		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 <= -5.5e-58)
		tmp = x;
	elseif (y <= 9.5e-122)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 3.05e-74)
		tmp = (230661.510616 / c) + (t / (y * c));
	elseif (y <= 2.4e+36)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.5e-58], x, If[LessEqual[y, 9.5e-122], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 3.05e-74], N[(N[(230661.510616 / c), $MachinePrecision] + N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+36], N[(t / i), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.49999999999999996e-58 or 2.39999999999999992e36 < y

   1. Initial program 12.2%

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

   2. Taylor expanded in y around inf 47.8%

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

   if -5.49999999999999996e-58 < y < 9.5000000000000002e-122

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 50.3%

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

   3. Taylor expanded in i around inf 76.3%

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

   if 9.5000000000000002e-122 < y < 3.0499999999999999e-74

   1. Initial program 99.5%

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

   2. Taylor expanded in c around inf 80.4%

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

   3. Taylor expanded in y around 0 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in y around 0 80.3%

      \[\leadsto \color{blue}{230661.510616 \cdot \frac{1}{c} + \frac{t}{c \cdot y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 80.4%

         \[\leadsto \color{blue}{\frac{230661.510616 \cdot 1}{c}} + \frac{t}{c \cdot y} \]

      2. metadata-eval 80.4%

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

      3. *-commutative 80.4%

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

   8. Simplified 80.4%

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

   if 3.0499999999999999e-74 < y < 2.39999999999999992e36

   1. Initial program 71.3%

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

   2. Taylor expanded in y around 0 15.8%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-74}:\\ \;\;\;\;\frac{230661.510616}{c} + \frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 49.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.1e+58)
   x
   (if (<= y 2.5e-122)
     (/ t i)
     (if (<= y 1.86e-28) (/ t (* y c)) (if (<= y 2.45e+36) (/ 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 <= -4.1e+58) {
		tmp = x;
	} else if (y <= 2.5e-122) {
		tmp = t / i;
	} else if (y <= 1.86e-28) {
		tmp = t / (y * c);
	} else if (y <= 2.45e+36) {
		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 <= (-4.1d+58)) then
        tmp = x
    else if (y <= 2.5d-122) then
        tmp = t / i
    else if (y <= 1.86d-28) then
        tmp = t / (y * c)
    else if (y <= 2.45d+36) 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 <= -4.1e+58) {
		tmp = x;
	} else if (y <= 2.5e-122) {
		tmp = t / i;
	} else if (y <= 1.86e-28) {
		tmp = t / (y * c);
	} else if (y <= 2.45e+36) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.1e+58:
		tmp = x
	elif y <= 2.5e-122:
		tmp = t / i
	elif y <= 1.86e-28:
		tmp = t / (y * c)
	elif y <= 2.45e+36:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.1e+58)
		tmp = x;
	elseif (y <= 2.5e-122)
		tmp = Float64(t / i);
	elseif (y <= 1.86e-28)
		tmp = Float64(t / Float64(y * c));
	elseif (y <= 2.45e+36)
		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 <= -4.1e+58)
		tmp = x;
	elseif (y <= 2.5e-122)
		tmp = t / i;
	elseif (y <= 1.86e-28)
		tmp = t / (y * c);
	elseif (y <= 2.45e+36)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.1e+58], x, If[LessEqual[y, 2.5e-122], N[(t / i), $MachinePrecision], If[LessEqual[y, 1.86e-28], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e+36], N[(t / i), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1e58 or 2.4499999999999999e36 < y

   1. Initial program 3.2%

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

   2. Taylor expanded in y around inf 54.8%

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

   if -4.1e58 < y < 2.4999999999999999e-122 or 1.86e-28 < y < 2.4499999999999999e36

   1. Initial program 90.3%

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

   2. Taylor expanded in y around 0 53.5%

      \[\leadsto \color{blue}{\frac{t}{i}} \]

   if 2.4999999999999999e-122 < y < 1.86e-28

   1. Initial program 99.4%

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

   2. Taylor expanded in c around inf 69.8%

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

   3. Taylor expanded in y around 0 62.4%

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

      1. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in y around 0 48.7%

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

      1. *-commutative 48.7%

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

   8. Simplified 48.7%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 53.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+36}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.5e-58) x (if (<= y 2.55e+36) (/ (+ 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 <= -5.5e-58) {
		tmp = x;
	} else if (y <= 2.55e+36) {
		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 <= (-5.5d-58)) then
        tmp = x
    else if (y <= 2.55d+36) 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 <= -5.5e-58) {
		tmp = x;
	} else if (y <= 2.55e+36) {
		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 <= -5.5e-58:
		tmp = x
	elif y <= 2.55e+36:
		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 <= -5.5e-58)
		tmp = x;
	elseif (y <= 2.55e+36)
		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 <= -5.5e-58)
		tmp = x;
	elseif (y <= 2.55e+36)
		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, -5.5e-58], x, If[LessEqual[y, 2.55e+36], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999996e-58 or 2.54999999999999986e36 < y

   1. Initial program 12.2%

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

   2. Taylor expanded in y around inf 47.8%

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

   if -5.49999999999999996e-58 < y < 2.54999999999999986e36

   1. Initial program 95.6%

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

   2. Taylor expanded in y around 0 42.5%

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

   3. Taylor expanded in i around inf 63.4%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+36}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 50.8% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.1e+58) x (if (<= y 2.9e+36) (/ 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 <= -4.1e+58) {
		tmp = x;
	} else if (y <= 2.9e+36) {
		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 <= (-4.1d+58)) then
        tmp = x
    else if (y <= 2.9d+36) 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 <= -4.1e+58) {
		tmp = x;
	} else if (y <= 2.9e+36) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.1e+58:
		tmp = x
	elif y <= 2.9e+36:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.1e+58)
		tmp = x;
	elseif (y <= 2.9e+36)
		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 <= -4.1e+58)
		tmp = x;
	elseif (y <= 2.9e+36)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.1e+58], x, If[LessEqual[y, 2.9e+36], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1e58 or 2.9e36 < y

   1. Initial program 3.2%

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

   2. Taylor expanded in y around inf 54.8%

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

   if -4.1e58 < y < 2.9e36

   1. Initial program 91.2%

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

   2. Taylor expanded in y around 0 50.1%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+36}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 25.9% 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 50.0%

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

2. Taylor expanded in y around inf 27.6%

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

3. Final simplification 27.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023224 
(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)))