Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.6% → 81.2%

Time: 27.8s

Alternatives: 18

Speedup: 2.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.6% 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: 81.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6.7 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.018:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
          (+ i (* y (+ c (* y (+ b (* y (+ y a)))))))))
        (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -6.7e+24)
     t_2
     (if (<= y 4.8e-53)
       t_1
       (if (<= y 0.018)
         (/
          (+
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
           t)
          (+ i (* y (+ c (* y b)))))
         (if (<= y 1.2e+52) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -6.7e+24) {
		tmp = t_2;
	} else if (y <= 4.8e-53) {
		tmp = t_1;
	} else if (y <= 0.018) {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * b))));
	} else if (y <= 1.2e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-6.7d+24)) then
        tmp = t_2
    else if (y <= 4.8d-53) then
        tmp = t_1
    else if (y <= 0.018d0) then
        tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) + t) / (i + (y * (c + (y * b))))
    else if (y <= 1.2d+52) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -6.7e+24) {
		tmp = t_2;
	} else if (y <= 4.8e-53) {
		tmp = t_1;
	} else if (y <= 0.018) {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * b))));
	} else if (y <= 1.2e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -6.7e+24:
		tmp = t_2
	elif y <= 4.8e-53:
		tmp = t_1
	elif y <= 0.018:
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * b))))
	elif y <= 1.2e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -6.7e+24)
		tmp = t_2;
	elseif (y <= 4.8e-53)
		tmp = t_1;
	elseif (y <= 0.018)
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 1.2e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -6.7e+24)
		tmp = t_2;
	elseif (y <= 4.8e-53)
		tmp = t_1;
	elseif (y <= 0.018)
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * b))));
	elseif (y <= 1.2e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(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 * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.7e+24], t$95$2, If[LessEqual[y, 4.8e-53], t$95$1, If[LessEqual[y, 0.018], N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.6999999999999999e24 or 1.2e52 < 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 72.6%

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

      1. associate--l+ 72.6%

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

      2. associate-/l* 73.6%

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

   4. Simplified 73.6%

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

   if -6.6999999999999999e24 < y < 4.80000000000000015e-53 or 0.0179999999999999986 < y < 1.2e52

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0 94.9%

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

   if 4.80000000000000015e-53 < y < 0.0179999999999999986

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 99.3%

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

      1. *-commutative 99.3%

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

   4. Simplified 99.3%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+24}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 0.018:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 2: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
           t)
          (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))
   (if (<= t_1 2e+303) t_1 (+ x (- (/ z y) (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	double tmp;
	if (t_1 <= 2e+303) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a / (y / 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 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) + t) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    if (t_1 <= 2d+303) then
        tmp = t_1
    else
        tmp = x + ((z / y) - (a / (y / 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 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	double tmp;
	if (t_1 <= 2e+303) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	tmp = 0
	if t_1 <= 2e+303:
		tmp = t_1
	else:
		tmp = x + ((z / y) - (a / (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))))
	tmp = 0.0
	if (t_1 <= 2e+303)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	tmp = 0.0;
	if (t_1 <= 2e+303)
		tmp = t_1;
	else
		tmp = x + ((z / y) - (a / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+303], t$95$1, N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2e303

   1. Initial program 93.9%

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

   if 2e303 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 1.3%

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

   2. Taylor expanded in y around inf 73.4%

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

      1. associate--l+ 73.4%

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

      2. associate-/l* 74.4%

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

   4. Simplified 74.4%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 3: 79.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6.7 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-26}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+40}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -6.7e+24)
     t_1
     (if (<= y -4.1e-26)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
        (* y (+ c (* y (+ b (* y (+ y a)))))))
       (if (<= y 1.22e+40)
         (/
          (+
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
           t)
          (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -6.7e+24) {
		tmp = t_1;
	} else if (y <= -4.1e-26) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (y * (c + (y * (b + (y * (y + a))))));
	} else if (y <= 1.22e+40) {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    if (y <= (-6.7d+24)) then
        tmp = t_1
    else if (y <= (-4.1d-26)) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (y * (c + (y * (b + (y * (y + a))))))
    else if (y <= 1.22d+40) then
        tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) + t) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -6.7e+24) {
		tmp = t_1;
	} else if (y <= -4.1e-26) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (y * (c + (y * (b + (y * (y + a))))));
	} else if (y <= 1.22e+40) {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -6.7e+24:
		tmp = t_1
	elif y <= -4.1e-26:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (y * (c + (y * (b + (y * (y + a))))))
	elif y <= 1.22e+40:
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -6.7e+24)
		tmp = t_1;
	elseif (y <= -4.1e-26)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))));
	elseif (y <= 1.22e+40)
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -6.7e+24)
		tmp = t_1;
	elseif (y <= -4.1e-26)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (y * (c + (y * (b + (y * (y + a))))));
	elseif (y <= 1.22e+40)
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.7e+24], t$95$1, If[LessEqual[y, -4.1e-26], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e+40], N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.6999999999999999e24 or 1.22000000000000004e40 < y

   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 y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 73.2%

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

   4. Simplified 73.2%

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

   if -6.6999999999999999e24 < y < -4.0999999999999999e-26

   1. Initial program 90.1%

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

   2. Taylor expanded in x around 0 90.1%

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

   3. Taylor expanded in i around 0 90.1%

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

   if -4.0999999999999999e-26 < y < 1.22000000000000004e40

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 93.4%

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

      1. *-commutative 93.4%

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

   4. Simplified 93.4%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+24}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-26}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+40}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 4: 78.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6.7 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{t_1}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+39}:\\ \;\;\;\;\frac{t_1}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))))
        (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -6.7e+24)
     t_2
     (if (<= y -6.2e-29)
       (/ t_1 (* y (+ c (* y (+ b (* y (+ y a)))))))
       (if (<= y 9e+39) (/ t_1 (+ 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 + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -6.7e+24) {
		tmp = t_2;
	} else if (y <= -6.2e-29) {
		tmp = t_1 / (y * (c + (y * (b + (y * (y + a))))));
	} else if (y <= 9e+39) {
		tmp = t_1 / (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 + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-6.7d+24)) then
        tmp = t_2
    else if (y <= (-6.2d-29)) then
        tmp = t_1 / (y * (c + (y * (b + (y * (y + a))))))
    else if (y <= 9d+39) then
        tmp = t_1 / (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 + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -6.7e+24) {
		tmp = t_2;
	} else if (y <= -6.2e-29) {
		tmp = t_1 / (y * (c + (y * (b + (y * (y + a))))));
	} else if (y <= 9e+39) {
		tmp = t_1 / (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 + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -6.7e+24:
		tmp = t_2
	elif y <= -6.2e-29:
		tmp = t_1 / (y * (c + (y * (b + (y * (y + a))))))
	elif y <= 9e+39:
		tmp = t_1 / (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(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z))))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -6.7e+24)
		tmp = t_2;
	elseif (y <= -6.2e-29)
		tmp = Float64(t_1 / Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))));
	elseif (y <= 9e+39)
		tmp = Float64(t_1 / 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 + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))));
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -6.7e+24)
		tmp = t_2;
	elseif (y <= -6.2e-29)
		tmp = t_1 / (y * (c + (y * (b + (y * (y + a))))));
	elseif (y <= 9e+39)
		tmp = t_1 / (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[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.7e+24], t$95$2, If[LessEqual[y, -6.2e-29], N[(t$95$1 / N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+39], N[(t$95$1 / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.6999999999999999e24 or 8.99999999999999991e39 < y

   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 y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 73.2%

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

   4. Simplified 73.2%

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

   if -6.6999999999999999e24 < y < -6.20000000000000052e-29

   1. Initial program 90.1%

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

   2. Taylor expanded in x around 0 90.1%

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

   3. Taylor expanded in i around 0 90.1%

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

   if -6.20000000000000052e-29 < y < 8.99999999999999991e39

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 93.4%

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

      1. *-commutative 93.4%

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

   4. Simplified 93.4%

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

   5. Taylor expanded in x around 0 88.4%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+24}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+39}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 5: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2600000000:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{c + y \cdot b}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+ t (* y 230661.510616))
          (+ i (* y (+ c (* y (+ b (* y (+ y a)))))))))
        (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -5.5e+24)
     t_2
     (if (<= y 4.5e-43)
       t_1
       (if (<= y 2600000000.0)
         (/
          (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)
          (+ c (* y b)))
         (if (<= y 7.8e+41) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -5.5e+24) {
		tmp = t_2;
	} else if (y <= 4.5e-43) {
		tmp = t_1;
	} else if (y <= 2600000000.0) {
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / (c + (y * b));
	} else if (y <= 7.8e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-5.5d+24)) then
        tmp = t_2
    else if (y <= 4.5d-43) then
        tmp = t_1
    else if (y <= 2600000000.0d0) then
        tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0) / (c + (y * b))
    else if (y <= 7.8d+41) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -5.5e+24) {
		tmp = t_2;
	} else if (y <= 4.5e-43) {
		tmp = t_1;
	} else if (y <= 2600000000.0) {
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / (c + (y * b));
	} else if (y <= 7.8e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -5.5e+24:
		tmp = t_2
	elif y <= 4.5e-43:
		tmp = t_1
	elif y <= 2600000000.0:
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / (c + (y * b))
	elif y <= 7.8e+41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -5.5e+24)
		tmp = t_2;
	elseif (y <= 4.5e-43)
		tmp = t_1;
	elseif (y <= 2600000000.0)
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616) / Float64(c + Float64(y * b)));
	elseif (y <= 7.8e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * 230661.510616)) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -5.5e+24)
		tmp = t_2;
	elseif (y <= 4.5e-43)
		tmp = t_1;
	elseif (y <= 2600000000.0)
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / (c + (y * b));
	elseif (y <= 7.8e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+24], t$95$2, If[LessEqual[y, 4.5e-43], t$95$1, If[LessEqual[y, 2600000000.0], N[(N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision] / N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+41], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000002e24 or 7.7999999999999994e41 < y

   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 y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 73.2%

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

   4. Simplified 73.2%

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

   if -5.5000000000000002e24 < y < 4.50000000000000025e-43 or 2.6e9 < y < 7.7999999999999994e41

   1. Initial program 96.7%

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

   2. Taylor expanded in y around 0 87.3%

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

      1. *-commutative 81.9%

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

   4. Simplified 87.3%

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

   if 4.50000000000000025e-43 < y < 2.6e9

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 99.3%

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

      1. *-commutative 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in i around 0 83.1%

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

   6. Taylor expanded in t around 0 65.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 2600000000:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{c + y \cdot b}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 6: 77.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+24} \lor \neg \left(y \leq 1.85 \cdot 10^{+43}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.6e+24) (not (<= y 1.85e+43)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.6e+24) || !(y <= 1.85e+43)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.6d+24)) .or. (.not. (y <= 1.85d+43))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.6e+24) || !(y <= 1.85e+43)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.6e+24) or not (y <= 1.85e+43):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.6e+24) || !(y <= 1.85e+43))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.6e+24) || ~((y <= 1.85e+43)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * (y + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.6e+24], N[Not[LessEqual[y, 1.85e+43]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5999999999999999e24 or 1.85e43 < y

   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 y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 73.2%

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

   4. Simplified 73.2%

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

   if -1.5999999999999999e24 < y < 1.85e43

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 84.8%

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

      1. *-commutative 78.6%

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

   4. Simplified 84.8%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+24} \lor \neg \left(y \leq 1.85 \cdot 10^{+43}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \end{array} \]

Alternative 7: 78.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+22} \lor \neg \left(y \leq 4.8 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.05e+22) (not (<= y 4.8e+38)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.05e+22) || !(y <= 4.8e+38)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.05d+22)) .or. (.not. (y <= 4.8d+38))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.05e+22) || !(y <= 4.8e+38)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.05e+22) or not (y <= 4.8e+38):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.05e+22) || !(y <= 4.8e+38))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.05e+22) || ~((y <= 4.8e+38)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.05e+22], N[Not[LessEqual[y, 4.8e+38]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0499999999999999e22 or 4.80000000000000035e38 < y

   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 y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 73.2%

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

   4. Simplified 73.2%

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

   if -2.0499999999999999e22 < y < 4.80000000000000035e38

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 89.4%

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

      1. *-commutative 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in x around 0 84.7%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+22} \lor \neg \left(y \leq 4.8 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 8: 74.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ t_2 := c + y \cdot b\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t_2}\\ \mathbf{elif}\;y \leq 12000000000:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{t_2}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+41}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))) (t_2 (+ c (* y b))))
   (if (<= y -1.05e+24)
     t_1
     (if (<= y 4.2e-54)
       (/ (+ t (* y 230661.510616)) (+ i (* y t_2)))
       (if (<= y 12000000000.0)
         (/ (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616) t_2)
         (if (<= y 1.65e+41)
           (/ t (+ i (* y (+ c (* y (+ b (* y (+ y 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 = x + ((z / y) - (a / (y / x)));
	double t_2 = c + (y * b);
	double tmp;
	if (y <= -1.05e+24) {
		tmp = t_1;
	} else if (y <= 4.2e-54) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 12000000000.0) {
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	} else if (y <= 1.65e+41) {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + 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 = x + ((z / y) - (a / (y / x)))
    t_2 = c + (y * b)
    if (y <= (-1.05d+24)) then
        tmp = t_1
    else if (y <= 4.2d-54) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_2))
    else if (y <= 12000000000.0d0) then
        tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0) / t_2
    else if (y <= 1.65d+41) then
        tmp = t / (i + (y * (c + (y * (b + (y * (y + 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 = x + ((z / y) - (a / (y / x)));
	double t_2 = c + (y * b);
	double tmp;
	if (y <= -1.05e+24) {
		tmp = t_1;
	} else if (y <= 4.2e-54) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 12000000000.0) {
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	} else if (y <= 1.65e+41) {
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	t_2 = c + (y * b)
	tmp = 0
	if y <= -1.05e+24:
		tmp = t_1
	elif y <= 4.2e-54:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2))
	elif y <= 12000000000.0:
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2
	elif y <= 1.65e+41:
		tmp = t / (i + (y * (c + (y * (b + (y * (y + a)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	t_2 = Float64(c + Float64(y * b))
	tmp = 0.0
	if (y <= -1.05e+24)
		tmp = t_1;
	elseif (y <= 4.2e-54)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_2)));
	elseif (y <= 12000000000.0)
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2);
	elseif (y <= 1.65e+41)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	t_2 = c + (y * b);
	tmp = 0.0;
	if (y <= -1.05e+24)
		tmp = t_1;
	elseif (y <= 4.2e-54)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	elseif (y <= 12000000000.0)
		tmp = ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616) / t_2;
	elseif (y <= 1.65e+41)
		tmp = t / (i + (y * (c + (y * (b + (y * (y + 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[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+24], t$95$1, If[LessEqual[y, 4.2e-54], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 12000000000.0], N[(N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 1.65e+41], N[(t / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.0500000000000001e24 or 1.65e41 < y

   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 y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 73.2%

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

   4. Simplified 73.2%

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

   if -1.0500000000000001e24 < y < 4.2e-54

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 93.3%

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

      1. *-commutative 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in y around 0 86.9%

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

      1. *-commutative 86.9%

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

   7. Simplified 86.9%

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

   if 4.2e-54 < y < 1.2e10

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 91.7%

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

      1. *-commutative 91.7%

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

   4. Simplified 91.7%

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

   5. Taylor expanded in i around 0 70.7%

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

   6. Taylor expanded in t around 0 56.7%

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

   if 1.2e10 < y < 1.65e41

   1. Initial program 58.5%

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

   2. Taylor expanded in t around inf 44.2%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+24}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 12000000000:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}{c + y \cdot b}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+41}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 9: 74.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+24} \lor \neg \left(y \leq 5.6 \cdot 10^{+40}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.8e+24) (not (<= y 5.6e+40)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.8e+24) || !(y <= 5.6e+40)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-5.8d+24)) .or. (.not. (y <= 5.6d+40))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.8e+24) || !(y <= 5.6e+40)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5.8e+24) or not (y <= 5.6e+40):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5.8e+24) || !(y <= 5.6e+40))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5.8e+24) || ~((y <= 5.6e+40)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5.8e+24], N[Not[LessEqual[y, 5.6e+40]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999958e24 or 5.6000000000000003e40 < y

   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 y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 73.2%

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

   4. Simplified 73.2%

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

   if -5.79999999999999958e24 < y < 5.6000000000000003e40

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 89.4%

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

      1. *-commutative 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in y around 0 78.6%

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

      1. *-commutative 78.6%

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

   7. Simplified 78.6%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+24} \lor \neg \left(y \leq 5.6 \cdot 10^{+40}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 10: 74.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+24} \lor \neg \left(y \leq 2.75 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.12e+24) (not (<= y 2.75e+38)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.12e+24) || !(y <= 2.75e+38)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.12d+24)) .or. (.not. (y <= 2.75d+38))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.12e+24) || !(y <= 2.75e+38)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.12e+24) or not (y <= 2.75e+38):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.12e+24) || !(y <= 2.75e+38))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.12e+24) || ~((y <= 2.75e+38)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.12e+24], N[Not[LessEqual[y, 2.75e+38]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - 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 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.12e24 or 2.7500000000000002e38 < y

   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 y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 73.2%

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

   4. Simplified 73.2%

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

   if -1.12e24 < y < 2.7500000000000002e38

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 89.4%

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

      1. *-commutative 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in y around 0 77.7%

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

      1. *-commutative 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+24} \lor \neg \left(y \leq 2.75 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 11: 59.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-145}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -3.5e+60)
     t_1
     (if (<= y 9e-145)
       (/ (+ t (* y 230661.510616)) i)
       (if (<= y 1.55e+38) (/ t (* y (+ c (* y b)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -3.5e+60) {
		tmp = t_1;
	} else if (y <= 9e-145) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 1.55e+38) {
		tmp = t / (y * (c + (y * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    if (y <= (-3.5d+60)) then
        tmp = t_1
    else if (y <= 9d-145) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 1.55d+38) then
        tmp = t / (y * (c + (y * b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -3.5e+60) {
		tmp = t_1;
	} else if (y <= 9e-145) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 1.55e+38) {
		tmp = t / (y * (c + (y * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -3.5e+60:
		tmp = t_1
	elif y <= 9e-145:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 1.55e+38:
		tmp = t / (y * (c + (y * b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -3.5e+60)
		tmp = t_1;
	elseif (y <= 9e-145)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 1.55e+38)
		tmp = Float64(t / Float64(y * Float64(c + Float64(y * b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -3.5e+60)
		tmp = t_1;
	elseif (y <= 9e-145)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 1.55e+38)
		tmp = t / (y * (c + (y * b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+60], t$95$1, If[LessEqual[y, 9e-145], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 1.55e+38], N[(t / N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000002e60 or 1.55000000000000009e38 < y

   1. Initial program 2.2%

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

   2. Taylor expanded in y around inf 74.8%

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

      1. associate--l+ 74.8%

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

      2. associate-/l* 75.8%

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

   4. Simplified 75.8%

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

   if -3.5000000000000002e60 < y < 9.0000000000000001e-145

   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 i around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. +-commutative 60.3%

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

      3. +-commutative 60.3%

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

      4. +-commutative 60.3%

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

      5. fma-udef 60.3%

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

      6. fma-def 60.3%

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

      7. fma-def 60.3%

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

      8. fma-def 60.3%

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

      9. fma-udef 60.3%

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

      10. *-commutative 60.3%

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

      11. fma-def 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in y around 0 57.6%

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

      1. *-commutative 57.6%

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

   7. Simplified 57.6%

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

   if 9.0000000000000001e-145 < y < 1.55000000000000009e38

   1. Initial program 92.1%

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

   2. Taylor expanded in y around 0 80.0%

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

      1. *-commutative 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in i around 0 61.0%

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

   6. Taylor expanded in t around inf 34.9%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+60}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-145}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 12: 53.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-145}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.6e+60)
   x
   (if (<= y 6.5e-145)
     (/ (+ t (* y 230661.510616)) i)
     (if (<= y 4.1e+40) (/ t (* y (+ c (* y b)))) (- x (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.6e+60) {
		tmp = x;
	} else if (y <= 6.5e-145) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 4.1e+40) {
		tmp = t / (y * (c + (y * b)));
	} else {
		tmp = x - (a / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.6d+60)) then
        tmp = x
    else if (y <= 6.5d-145) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 4.1d+40) then
        tmp = t / (y * (c + (y * b)))
    else
        tmp = x - (a / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.6e+60) {
		tmp = x;
	} else if (y <= 6.5e-145) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 4.1e+40) {
		tmp = t / (y * (c + (y * b)));
	} else {
		tmp = x - (a / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.6e+60:
		tmp = x
	elif y <= 6.5e-145:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 4.1e+40:
		tmp = t / (y * (c + (y * b)))
	else:
		tmp = x - (a / (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.6e+60)
		tmp = x;
	elseif (y <= 6.5e-145)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 4.1e+40)
		tmp = Float64(t / Float64(y * Float64(c + Float64(y * b))));
	else
		tmp = Float64(x - Float64(a / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.6e+60)
		tmp = x;
	elseif (y <= 6.5e-145)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 4.1e+40)
		tmp = t / (y * (c + (y * b)));
	else
		tmp = x - (a / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.6e+60], x, If[LessEqual[y, 6.5e-145], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 4.1e+40], N[(t / N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.59999999999999995e60

   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 61.0%

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

   if -1.59999999999999995e60 < y < 6.5000000000000002e-145

   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 i around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. +-commutative 60.3%

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

      3. +-commutative 60.3%

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

      4. +-commutative 60.3%

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

      5. fma-udef 60.3%

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

      6. fma-def 60.3%

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

      7. fma-def 60.3%

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

      8. fma-def 60.3%

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

      9. fma-udef 60.3%

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

      10. *-commutative 60.3%

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

      11. fma-def 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in y around 0 57.6%

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

      1. *-commutative 57.6%

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

   7. Simplified 57.6%

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

   if 6.5000000000000002e-145 < y < 4.1000000000000002e40

   1. Initial program 92.1%

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

   2. Taylor expanded in y around 0 80.0%

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

      1. *-commutative 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in i around 0 61.0%

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

   6. Taylor expanded in t around inf 34.9%

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

   if 4.1000000000000002e40 < y

   1. Initial program 3.9%

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

   2. Taylor expanded in z around 0 0.7%

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

   3. Taylor expanded in y around inf 65.0%

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

      1. mul-1-neg 65.0%

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

      2. unsub-neg 65.0%

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

      3. associate-/l* 65.1%

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

   5. Simplified 65.1%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-145}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 13: 67.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+21} \lor \neg \left(y \leq 3.35 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8.2e+21) (not (<= y 3.35e+38)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/ t (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.2e+21) || !(y <= 3.35e+38)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-8.2d+21)) .or. (.not. (y <= 3.35d+38))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = t / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.2e+21) || !(y <= 3.35e+38)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -8.2e+21) or not (y <= 3.35e+38):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -8.2e+21) || !(y <= 3.35e+38))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -8.2e+21) || ~((y <= 3.35e+38)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -8.2e+21], N[Not[LessEqual[y, 3.35e+38]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2e21 or 3.35000000000000012e38 < y

   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 y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. associate-/l* 73.2%

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

   4. Simplified 73.2%

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

   if -8.2e21 < y < 3.35000000000000012e38

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 89.4%

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

      1. *-commutative 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in t around inf 65.7%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+21} \lor \neg \left(y \leq 3.35 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 14: 49.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-149}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.6e+60)
   x
   (if (<= y 1.3e-149)
     (/ t i)
     (if (<= y 1.25e+34) (/ t (* y c)) (- x (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.6e+60) {
		tmp = x;
	} else if (y <= 1.3e-149) {
		tmp = t / i;
	} else if (y <= 1.25e+34) {
		tmp = t / (y * c);
	} else {
		tmp = x - (a / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.6d+60)) then
        tmp = x
    else if (y <= 1.3d-149) then
        tmp = t / i
    else if (y <= 1.25d+34) then
        tmp = t / (y * c)
    else
        tmp = x - (a / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.6e+60) {
		tmp = x;
	} else if (y <= 1.3e-149) {
		tmp = t / i;
	} else if (y <= 1.25e+34) {
		tmp = t / (y * c);
	} else {
		tmp = x - (a / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.6e+60:
		tmp = x
	elif y <= 1.3e-149:
		tmp = t / i
	elif y <= 1.25e+34:
		tmp = t / (y * c)
	else:
		tmp = x - (a / (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.6e+60)
		tmp = x;
	elseif (y <= 1.3e-149)
		tmp = Float64(t / i);
	elseif (y <= 1.25e+34)
		tmp = Float64(t / Float64(y * c));
	else
		tmp = Float64(x - Float64(a / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.6e+60)
		tmp = x;
	elseif (y <= 1.3e-149)
		tmp = t / i;
	elseif (y <= 1.25e+34)
		tmp = t / (y * c);
	else
		tmp = x - (a / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.6e+60], x, If[LessEqual[y, 1.3e-149], N[(t / i), $MachinePrecision], If[LessEqual[y, 1.25e+34], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.59999999999999995e60

   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 61.0%

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

   if -1.59999999999999995e60 < y < 1.29999999999999999e-149

   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 y around 0 52.2%

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

   if 1.29999999999999999e-149 < y < 1.25e34

   1. Initial program 94.3%

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

   2. Taylor expanded in y around 0 82.0%

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

      1. *-commutative 82.0%

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

   4. Simplified 82.0%

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

   5. Taylor expanded in i around 0 60.2%

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

   6. Taylor expanded in y around 0 28.6%

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

      1. *-commutative 28.6%

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

   8. Simplified 28.6%

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

   if 1.25e34 < y

   1. Initial program 5.6%

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

   2. Taylor expanded in z around 0 2.5%

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

   3. Taylor expanded in y around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

      3. associate-/l* 63.2%

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

   5. Simplified 63.2%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-149}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 15: 52.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-145}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.6e+60)
   x
   (if (<= y 9e-145)
     (/ (+ t (* y 230661.510616)) i)
     (if (<= y 4.4e+27) (/ t (* y c)) (- x (/ a (/ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.6e+60) {
		tmp = x;
	} else if (y <= 9e-145) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 4.4e+27) {
		tmp = t / (y * c);
	} else {
		tmp = x - (a / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.6d+60)) then
        tmp = x
    else if (y <= 9d-145) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 4.4d+27) then
        tmp = t / (y * c)
    else
        tmp = x - (a / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.6e+60) {
		tmp = x;
	} else if (y <= 9e-145) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 4.4e+27) {
		tmp = t / (y * c);
	} else {
		tmp = x - (a / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.6e+60:
		tmp = x
	elif y <= 9e-145:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 4.4e+27:
		tmp = t / (y * c)
	else:
		tmp = x - (a / (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.6e+60)
		tmp = x;
	elseif (y <= 9e-145)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 4.4e+27)
		tmp = Float64(t / Float64(y * c));
	else
		tmp = Float64(x - Float64(a / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.6e+60)
		tmp = x;
	elseif (y <= 9e-145)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 4.4e+27)
		tmp = t / (y * c);
	else
		tmp = x - (a / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.6e+60], x, If[LessEqual[y, 9e-145], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 4.4e+27], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.59999999999999995e60

   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 61.0%

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

   if -1.59999999999999995e60 < y < 9.0000000000000001e-145

   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 i around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. +-commutative 60.3%

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

      3. +-commutative 60.3%

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

      4. +-commutative 60.3%

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

      5. fma-udef 60.3%

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

      6. fma-def 60.3%

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

      7. fma-def 60.3%

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

      8. fma-def 60.3%

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

      9. fma-udef 60.3%

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

      10. *-commutative 60.3%

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

      11. fma-def 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in y around 0 57.6%

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

      1. *-commutative 57.6%

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

   7. Simplified 57.6%

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

   if 9.0000000000000001e-145 < y < 4.3999999999999997e27

   1. Initial program 94.2%

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

   2. Taylor expanded in y around 0 81.6%

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

      1. *-commutative 81.6%

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

   4. Simplified 81.6%

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

   5. Taylor expanded in i around 0 61.6%

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

   6. Taylor expanded in y around 0 29.1%

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

      1. *-commutative 29.1%

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

   8. Simplified 29.1%

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

   if 4.3999999999999997e27 < y

   1. Initial program 5.6%

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

   2. Taylor expanded in z around 0 2.5%

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

   3. Taylor expanded in y around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

      3. associate-/l* 63.2%

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

   5. Simplified 63.2%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-145}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \end{array} \]

Alternative 16: 49.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-149}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 95000:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.6e+60)
   x
   (if (<= y 5.2e-149) (/ t i) (if (<= y 95000.0) (/ t (* y c)) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.6e+60) {
		tmp = x;
	} else if (y <= 5.2e-149) {
		tmp = t / i;
	} else if (y <= 95000.0) {
		tmp = t / (y * c);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.6d+60)) then
        tmp = x
    else if (y <= 5.2d-149) then
        tmp = t / i
    else if (y <= 95000.0d0) then
        tmp = t / (y * c)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.6e+60) {
		tmp = x;
	} else if (y <= 5.2e-149) {
		tmp = t / i;
	} else if (y <= 95000.0) {
		tmp = t / (y * c);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.6e+60:
		tmp = x
	elif y <= 5.2e-149:
		tmp = t / i
	elif y <= 95000.0:
		tmp = t / (y * c)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.6e+60)
		tmp = x;
	elseif (y <= 5.2e-149)
		tmp = Float64(t / i);
	elseif (y <= 95000.0)
		tmp = Float64(t / Float64(y * c));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.6e+60)
		tmp = x;
	elseif (y <= 5.2e-149)
		tmp = t / i;
	elseif (y <= 95000.0)
		tmp = t / (y * c);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.6e+60], x, If[LessEqual[y, 5.2e-149], N[(t / i), $MachinePrecision], If[LessEqual[y, 95000.0], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999995e60 or 95000 < y

   1. Initial program 6.4%

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

   2. Taylor expanded in y around inf 59.0%

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

   if -1.59999999999999995e60 < y < 5.19999999999999998e-149

   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 y around 0 52.2%

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

   if 5.19999999999999998e-149 < y < 95000

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 93.5%

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

      1. *-commutative 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in i around 0 67.7%

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

   6. Taylor expanded in y around 0 33.0%

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

      1. *-commutative 33.0%

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

   8. Simplified 33.0%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-149}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 95000:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 50.9% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.65e+60) x (if (<= y 2.2e-11) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.65e+60) {
		tmp = x;
	} else if (y <= 2.2e-11) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.65d+60)) then
        tmp = x
    else if (y <= 2.2d-11) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.65e+60) {
		tmp = x;
	} else if (y <= 2.2e-11) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.65e+60:
		tmp = x
	elif y <= 2.2e-11:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.65e+60)
		tmp = x;
	elseif (y <= 2.2e-11)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.65e+60)
		tmp = x;
	elseif (y <= 2.2e-11)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.65e+60], x, If[LessEqual[y, 2.2e-11], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6499999999999999e60 or 2.2000000000000002e-11 < y

   1. Initial program 8.8%

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

   2. Taylor expanded in y around inf 57.6%

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

   if -1.6499999999999999e60 < y < 2.2000000000000002e-11

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 44.3%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 25.8% 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 55.5%

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

2. Taylor expanded in y around inf 28.5%

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

3. Final simplification 28.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023333 
(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)))