Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.4% → 85.2%

Time: 28.7s

Alternatives: 21

Speedup: 2.5×

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: 56.4% 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: 85.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+39} \lor \neg \left(y \leq 3.6 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.15e+39) (not (<= y 3.6e+52)))
   (* (/ y (+ (+ y a) (/ b y))) x)
   (/
    (+ (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))) t)
    (+ i (* y (+ (* y (+ b (* y (+ y a)))) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.15e+39) || !(y <= 3.6e+52)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) + t) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	}
	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 <= (-2.15d+39)) .or. (.not. (y <= 3.6d+52))) then
        tmp = (y / ((y + a) + (b / y))) * x
    else
        tmp = ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))) + t) / (i + (y * ((y * (b + (y * (y + a)))) + c)))
    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 <= -2.15e+39) || !(y <= 3.6e+52)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) + t) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.15e+39) or not (y <= 3.6e+52):
		tmp = (y / ((y + a) + (b / y))) * x
	else:
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) + t) / (i + (y * ((y * (b + (y * (y + a)))) + c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.15e+39) || !(y <= 3.6e+52))
		tmp = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x);
	else
		tmp = Float64(Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))) + t) / Float64(i + Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.15e+39) || ~((y <= 3.6e+52)))
		tmp = (y / ((y + a) + (b / y))) * x;
	else
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))) + t) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.15e+39], N[Not[LessEqual[y, 3.6e+52]], $MachinePrecision]], N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15e39 or 3.6e52 < y

   1. Initial program 1.4%

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

   2. Taylor expanded in t around 0 1.4%

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

      1. *-commutative 1.4%

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

      2. associate-/l* 1.6%

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

      3. +-commutative 1.6%

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

      4. *-commutative 1.6%

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

      5. fma-udef 1.6%

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

      6. fma-udef 1.6%

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

      7. fma-udef 1.6%

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

      8. +-commutative 1.6%

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

   4. Simplified 1.6%

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

   5. Taylor expanded in y around -inf 60.8%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in x around inf 66.3%

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

      1. associate-+r+ 66.3%

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

   10. Simplified 66.3%

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

       1. associate-/r/ 75.3%

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

   12. Applied egg-rr 75.3%

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

   if -2.15e39 < y < 3.6e52

   1. Initial program 93.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+39} \lor \neg \left(y \leq 3.6 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \end{array} \]

Alternative 2: 81.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+29} \lor \neg \left(y \leq 2.1 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.1e+29) (not (<= y 2.1e+54)))
   (* (/ y (+ (+ y a) (/ b y))) x)
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ (* y (+ b (* y (+ y a)))) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.1e+29) || !(y <= 2.1e+54)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	}
	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 <= (-5.1d+29)) .or. (.not. (y <= 2.1d+54))) then
        tmp = (y / ((y + a) + (b / y))) * x
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)))
    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 <= -5.1e+29) || !(y <= 2.1e+54)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5.1e+29) or not (y <= 2.1e+54):
		tmp = (y / ((y + a) + (b / y))) * x
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5.1e+29) || !(y <= 2.1e+54))
		tmp = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / 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(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5.1e+29) || ~((y <= 2.1e+54)))
		tmp = (y / ((y + a) + (b / y))) * x;
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5.1e+29], N[Not[LessEqual[y, 2.1e+54]], $MachinePrecision]], N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $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[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1000000000000001e29 or 2.09999999999999986e54 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in t around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.4%

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

      3. +-commutative 4.4%

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

      4. *-commutative 4.4%

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

      5. fma-udef 4.4%

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

      6. fma-udef 4.4%

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

      7. fma-udef 4.4%

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

      8. +-commutative 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in y around -inf 59.4%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. associate-+r+ 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 73.2%

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

   12. Applied egg-rr 73.2%

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

   if -5.1000000000000001e29 < y < 2.09999999999999986e54

   1. Initial program 94.8%

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

   2. Taylor expanded in x around 0 89.5%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+29} \lor \neg \left(y \leq 2.1 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \end{array} \]

Alternative 3: 78.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ t_2 := y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\\ \mathbf{if}\;y \leq -9 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-46}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t_2}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+52}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (/ y (+ (+ y a) (/ b y))) x))
        (t_2 (+ (* y (+ b (* y (+ y a)))) c)))
   (if (<= y -9e+28)
     t_1
     (if (<= y 2.15e-46)
       (/ (+ t (* y 230661.510616)) (+ i (* y t_2)))
       (if (<= y 1.45e+52)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_2)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y / ((y + a) + (b / y))) * x;
	double t_2 = (y * (b + (y * (y + a)))) + c;
	double tmp;
	if (y <= -9e+28) {
		tmp = t_1;
	} else if (y <= 2.15e-46) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 1.45e+52) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / ((y + a) + (b / y))) * x
    t_2 = (y * (b + (y * (y + a)))) + c
    if (y <= (-9d+28)) then
        tmp = t_1
    else if (y <= 2.15d-46) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_2))
    else if (y <= 1.45d+52) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y / ((y + a) + (b / y))) * x;
	double t_2 = (y * (b + (y * (y + a)))) + c;
	double tmp;
	if (y <= -9e+28) {
		tmp = t_1;
	} else if (y <= 2.15e-46) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 1.45e+52) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y / ((y + a) + (b / y))) * x
	t_2 = (y * (b + (y * (y + a)))) + c
	tmp = 0
	if y <= -9e+28:
		tmp = t_1
	elif y <= 2.15e-46:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2))
	elif y <= 1.45e+52:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x)
	t_2 = Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c)
	tmp = 0.0
	if (y <= -9e+28)
		tmp = t_1;
	elseif (y <= 2.15e-46)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_2)));
	elseif (y <= 1.45e+52)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y / ((y + a) + (b / y))) * x;
	t_2 = (y * (b + (y * (y + a)))) + c;
	tmp = 0.0;
	if (y <= -9e+28)
		tmp = t_1;
	elseif (y <= 2.15e-46)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	elseif (y <= 1.45e+52)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, If[LessEqual[y, -9e+28], t$95$1, If[LessEqual[y, 2.15e-46], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+52], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999994e28 or 1.45e52 < y

   1. Initial program 5.0%

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

   2. Taylor expanded in t around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.4%

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

      3. +-commutative 4.4%

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

      4. *-commutative 4.4%

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

      5. fma-udef 4.4%

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

      6. fma-udef 4.4%

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

      7. fma-udef 4.4%

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

      8. +-commutative 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in y around -inf 58.9%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in x around inf 64.1%

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

      1. associate-+r+ 64.1%

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

   10. Simplified 64.1%

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

       1. associate-/r/ 72.6%

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

   12. Applied egg-rr 72.6%

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

   if -8.9999999999999994e28 < y < 2.15000000000000018e-46

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0 86.8%

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

      1. *-commutative 86.8%

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

   4. Simplified 86.8%

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

   if 2.15000000000000018e-46 < y < 1.45e52

   1. Initial program 71.5%

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

   2. Taylor expanded in t around 0 55.1%

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

      1. *-commutative 55.1%

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

      2. associate-/l* 66.3%

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

      3. +-commutative 66.3%

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

      4. *-commutative 66.3%

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

      5. fma-udef 66.3%

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

      6. fma-udef 66.3%

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

      7. fma-udef 66.3%

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

      8. +-commutative 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in i around 0 60.7%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+28}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-46}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+52}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(b + y \cdot \left(y + a\right)\right) + c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \end{array} \]

Alternative 4: 78.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\\ t_2 := \frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot t_1}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+52}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ b (* y (+ y a)))) c))
        (t_2 (* (/ y (+ (+ y a) (/ b y))) x)))
   (if (<= y -1.35e+29)
     t_2
     (if (<= y 5.4e-46)
       (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i (* y t_1)))
       (if (<= y 3.5e+52)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))) t_1)
         (if (<= y 3.6e+52) (/ t (* b (* y y))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * (b + (y * (y + a)))) + c;
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -1.35e+29) {
		tmp = t_2;
	} else if (y <= 5.4e-46) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 3.5e+52) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else if (y <= 3.6e+52) {
		tmp = t / (b * (y * y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * (b + (y * (y + a)))) + c
    t_2 = (y / ((y + a) + (b / y))) * x
    if (y <= (-1.35d+29)) then
        tmp = t_2
    else if (y <= 5.4d-46) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * t_1))
    else if (y <= 3.5d+52) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / t_1
    else if (y <= 3.6d+52) then
        tmp = t / (b * (y * y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * (b + (y * (y + a)))) + c;
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -1.35e+29) {
		tmp = t_2;
	} else if (y <= 5.4e-46) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 3.5e+52) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	} else if (y <= 3.6e+52) {
		tmp = t / (b * (y * y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * (b + (y * (y + a)))) + c
	t_2 = (y / ((y + a) + (b / y))) * x
	tmp = 0
	if y <= -1.35e+29:
		tmp = t_2
	elif y <= 5.4e-46:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1))
	elif y <= 3.5e+52:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1
	elif y <= 3.6e+52:
		tmp = t / (b * (y * y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c)
	t_2 = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x)
	tmp = 0.0
	if (y <= -1.35e+29)
		tmp = t_2;
	elseif (y <= 5.4e-46)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * t_1)));
	elseif (y <= 3.5e+52)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / t_1);
	elseif (y <= 3.6e+52)
		tmp = Float64(t / Float64(b * Float64(y * y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * (b + (y * (y + a)))) + c;
	t_2 = (y / ((y + a) + (b / y))) * x;
	tmp = 0.0;
	if (y <= -1.35e+29)
		tmp = t_2;
	elseif (y <= 5.4e-46)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	elseif (y <= 3.5e+52)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / t_1;
	elseif (y <= 3.6e+52)
		tmp = t / (b * (y * y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -1.35e+29], t$95$2, If[LessEqual[y, 5.4e-46], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+52], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 3.6e+52], N[(t / N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35e29 or 3.6e52 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in t around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.4%

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

      3. +-commutative 4.4%

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

      4. *-commutative 4.4%

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

      5. fma-udef 4.4%

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

      6. fma-udef 4.4%

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

      7. fma-udef 4.4%

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

      8. +-commutative 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in y around -inf 59.4%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. associate-+r+ 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 73.2%

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

   12. Applied egg-rr 73.2%

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

   if -1.35e29 < y < 5.4e-46

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0 88.1%

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

      1. *-commutative 88.1%

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

   4. Simplified 88.1%

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

   if 5.4e-46 < y < 3.5e52

   1. Initial program 71.5%

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

   2. Taylor expanded in t around 0 55.1%

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

      1. *-commutative 55.1%

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

      2. associate-/l* 66.3%

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

      3. +-commutative 66.3%

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

      4. *-commutative 66.3%

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

      5. fma-udef 66.3%

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

      6. fma-udef 66.3%

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

      7. fma-udef 66.3%

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

      8. +-commutative 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in i around 0 60.7%

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

   if 3.5e52 < y < 3.6e52

   1. Initial program 100.0%

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

      1. div-inv 100.0%

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

      2. *-commutative 100.0%

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

      3. fma-def 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-def 100.0%

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

      6. *-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. fma-def 100.0%

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

      9. *-commutative 100.0%

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

      10. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in b around inf 100.0%

      \[\leadsto \color{blue}{\frac{t}{{y}^{2} \cdot b}} \]
   6. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{t}{\color{blue}{b \cdot {y}^{2}}} \]

      2. unpow2 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+52}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{y \cdot \left(b + y \cdot \left(y + a\right)\right) + c}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \end{array} \]

Alternative 5: 81.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+29} \lor \neg \left(y \leq 3.6 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.4e+29) (not (<= y 3.6e+52)))
   (* (/ y (+ (+ y a) (/ b y))) x)
   (/
    (+ t (* y (+ 230661.510616 (* z (* y y)))))
    (+ i (* y (+ (* y (+ b (* y (+ y a)))) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.4e+29) || !(y <= 3.6e+52)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	}
	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 <= (-2.4d+29)) .or. (.not. (y <= 3.6d+52))) then
        tmp = (y / ((y + a) + (b / y))) * x
    else
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)))
    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 <= -2.4e+29) || !(y <= 3.6e+52)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.4e+29) or not (y <= 3.6e+52):
		tmp = (y / ((y + a) + (b / y))) * x
	else:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.4e+29) || !(y <= 3.6e+52))
		tmp = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x);
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(i + Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.4e+29) || ~((y <= 3.6e+52)))
		tmp = (y / ((y + a) + (b / y))) * x;
	else
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.4e+29], N[Not[LessEqual[y, 3.6e+52]], $MachinePrecision]], N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4000000000000001e29 or 3.6e52 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in t around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.4%

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

      3. +-commutative 4.4%

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

      4. *-commutative 4.4%

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

      5. fma-udef 4.4%

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

      6. fma-udef 4.4%

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

      7. fma-udef 4.4%

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

      8. +-commutative 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in y around -inf 59.4%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. associate-+r+ 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 73.2%

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

   12. Applied egg-rr 73.2%

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

   if -2.4000000000000001e29 < y < 3.6e52

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 88.3%

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

      1. *-commutative 88.3%

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

      2. unpow2 88.3%

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

   4. Simplified 88.3%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+29} \lor \neg \left(y \leq 3.6 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \end{array} \]

Alternative 6: 64.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ t_2 := \frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{if}\;y \leq -9 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{y \cdot \left(c \cdot 4.335357023065617 \cdot 10^{-6} - i \cdot 5.162090511591658 \cdot 10^{-7}\right) + i \cdot 4.335357023065617 \cdot 10^{-6}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 17000000:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ t (+ i (* y (+ c (* y (+ b (* y y))))))))
        (t_2 (* (/ y (+ (+ y a) (/ b y))) x)))
   (if (<= y -9e+28)
     t_2
     (if (<= y 7.5e-196)
       t_1
       (if (<= y 1.12e-131)
         (/
          y
          (+
           (* y (- (* c 4.335357023065617e-6) (* i 5.162090511591658e-7)))
           (* i 4.335357023065617e-6)))
         (if (<= y 8.2e-59)
           t_1
           (if (<= y 17000000.0)
             (/
              (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))
              c)
             (if (<= y 3.6e+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 / (i + (y * (c + (y * (b + (y * y))))));
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -9e+28) {
		tmp = t_2;
	} else if (y <= 7.5e-196) {
		tmp = t_1;
	} else if (y <= 1.12e-131) {
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6));
	} else if (y <= 8.2e-59) {
		tmp = t_1;
	} else if (y <= 17000000.0) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / c;
	} else if (y <= 3.6e+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 / (i + (y * (c + (y * (b + (y * y))))))
    t_2 = (y / ((y + a) + (b / y))) * x
    if (y <= (-9d+28)) then
        tmp = t_2
    else if (y <= 7.5d-196) then
        tmp = t_1
    else if (y <= 1.12d-131) then
        tmp = y / ((y * ((c * 4.335357023065617d-6) - (i * 5.162090511591658d-7))) + (i * 4.335357023065617d-6))
    else if (y <= 8.2d-59) then
        tmp = t_1
    else if (y <= 17000000.0d0) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))) / c
    else if (y <= 3.6d+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 / (i + (y * (c + (y * (b + (y * y))))));
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -9e+28) {
		tmp = t_2;
	} else if (y <= 7.5e-196) {
		tmp = t_1;
	} else if (y <= 1.12e-131) {
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6));
	} else if (y <= 8.2e-59) {
		tmp = t_1;
	} else if (y <= 17000000.0) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / c;
	} else if (y <= 3.6e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t / (i + (y * (c + (y * (b + (y * y))))))
	t_2 = (y / ((y + a) + (b / y))) * x
	tmp = 0
	if y <= -9e+28:
		tmp = t_2
	elif y <= 7.5e-196:
		tmp = t_1
	elif y <= 1.12e-131:
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6))
	elif y <= 8.2e-59:
		tmp = t_1
	elif y <= 17000000.0:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / c
	elif y <= 3.6e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * y)))))))
	t_2 = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x)
	tmp = 0.0
	if (y <= -9e+28)
		tmp = t_2;
	elseif (y <= 7.5e-196)
		tmp = t_1;
	elseif (y <= 1.12e-131)
		tmp = Float64(y / Float64(Float64(y * Float64(Float64(c * 4.335357023065617e-6) - Float64(i * 5.162090511591658e-7))) + Float64(i * 4.335357023065617e-6)));
	elseif (y <= 8.2e-59)
		tmp = t_1;
	elseif (y <= 17000000.0)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))) / c);
	elseif (y <= 3.6e+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 / (i + (y * (c + (y * (b + (y * y))))));
	t_2 = (y / ((y + a) + (b / y))) * x;
	tmp = 0.0;
	if (y <= -9e+28)
		tmp = t_2;
	elseif (y <= 7.5e-196)
		tmp = t_1;
	elseif (y <= 1.12e-131)
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6));
	elseif (y <= 8.2e-59)
		tmp = t_1;
	elseif (y <= 17000000.0)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))) / c;
	elseif (y <= 3.6e+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[(t / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -9e+28], t$95$2, If[LessEqual[y, 7.5e-196], t$95$1, If[LessEqual[y, 1.12e-131], N[(y / N[(N[(y * N[(N[(c * 4.335357023065617e-6), $MachinePrecision] - N[(i * 5.162090511591658e-7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * 4.335357023065617e-6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-59], t$95$1, If[LessEqual[y, 17000000.0], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 3.6e+52], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.9999999999999994e28 or 3.6e52 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in t around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.4%

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

      3. +-commutative 4.4%

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

      4. *-commutative 4.4%

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

      5. fma-udef 4.4%

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

      6. fma-udef 4.4%

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

      7. fma-udef 4.4%

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

      8. +-commutative 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in y around -inf 59.4%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. associate-+r+ 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 73.2%

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

   12. Applied egg-rr 73.2%

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

   if -8.9999999999999994e28 < y < 7.5e-196 or 1.12000000000000001e-131 < y < 8.1999999999999991e-59 or 1.7e7 < y < 3.6e52

   1. Initial program 94.8%

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

      1. div-inv 94.6%

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

      2. *-commutative 94.6%

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

      3. fma-def 94.6%

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

      4. *-commutative 94.6%

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

      5. fma-def 94.6%

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

      6. *-commutative 94.6%

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

      7. fma-def 94.6%

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

      8. fma-def 94.6%

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

      9. *-commutative 94.6%

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

      10. fma-def 94.6%

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

   3. Applied egg-rr 94.6%

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

   4. Taylor expanded in y around 0 70.9%

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

   5. Taylor expanded in a around 0 69.3%

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

      1. *-commutative 69.3%

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

      2. +-commutative 69.3%

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

      3. unpow2 69.3%

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

   7. Simplified 69.3%

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

   if 7.5e-196 < y < 1.12000000000000001e-131

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-/l* 82.4%

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

      3. +-commutative 82.4%

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

      4. *-commutative 82.4%

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

      5. fma-udef 82.4%

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

      6. fma-udef 82.4%

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

      7. fma-udef 82.4%

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

      8. +-commutative 82.4%

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

   4. Simplified 82.4%

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

   5. Taylor expanded in y around 0 79.8%

      \[\leadsto \frac{y}{\color{blue}{y \cdot \left(4.335357023065617 \cdot 10^{-6} \cdot c - 5.162090511591658 \cdot 10^{-7} \cdot i\right) + 4.335357023065617 \cdot 10^{-6} \cdot i}} \]

   if 8.1999999999999991e-59 < y < 1.7e7

   1. Initial program 91.6%

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

   2. Taylor expanded in t around 0 62.6%

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

      1. *-commutative 62.6%

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

      2. associate-/l* 70.1%

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

      3. +-commutative 70.1%

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

      4. *-commutative 70.1%

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

      5. fma-udef 70.1%

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

      6. fma-udef 70.1%

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

      7. fma-udef 70.1%

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

      8. +-commutative 70.1%

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

   4. Simplified 70.1%

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

   5. Taylor expanded in c around inf 47.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+28}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{y \cdot \left(c \cdot 4.335357023065617 \cdot 10^{-6} - i \cdot 5.162090511591658 \cdot 10^{-7}\right) + i \cdot 4.335357023065617 \cdot 10^{-6}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 17000000:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}{c}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \end{array} \]

Alternative 7: 66.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ t_2 := \frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{if}\;y \leq -9 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{y \cdot \left(c \cdot 4.335357023065617 \cdot 10^{-6} - i \cdot 5.162090511591658 \cdot 10^{-7}\right) + i \cdot 4.335357023065617 \cdot 10^{-6}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ t (+ i (* y (+ (* y (+ b (* y (+ y a)))) c)))))
        (t_2 (* (/ y (+ (+ y a) (/ b y))) x)))
   (if (<= y -9e+28)
     t_2
     (if (<= y 7.5e-196)
       t_1
       (if (<= y 2.3e-131)
         (/
          y
          (+
           (* y (- (* c 4.335357023065617e-6) (* i 5.162090511591658e-7)))
           (* i 4.335357023065617e-6)))
         (if (<= y 3.6e+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 / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -9e+28) {
		tmp = t_2;
	} else if (y <= 7.5e-196) {
		tmp = t_1;
	} else if (y <= 2.3e-131) {
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6));
	} else if (y <= 3.6e+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 / (i + (y * ((y * (b + (y * (y + a)))) + c)))
    t_2 = (y / ((y + a) + (b / y))) * x
    if (y <= (-9d+28)) then
        tmp = t_2
    else if (y <= 7.5d-196) then
        tmp = t_1
    else if (y <= 2.3d-131) then
        tmp = y / ((y * ((c * 4.335357023065617d-6) - (i * 5.162090511591658d-7))) + (i * 4.335357023065617d-6))
    else if (y <= 3.6d+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 / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -9e+28) {
		tmp = t_2;
	} else if (y <= 7.5e-196) {
		tmp = t_1;
	} else if (y <= 2.3e-131) {
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6));
	} else if (y <= 3.6e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t / (i + (y * ((y * (b + (y * (y + a)))) + c)))
	t_2 = (y / ((y + a) + (b / y))) * x
	tmp = 0
	if y <= -9e+28:
		tmp = t_2
	elif y <= 7.5e-196:
		tmp = t_1
	elif y <= 2.3e-131:
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6))
	elif y <= 3.6e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t / Float64(i + Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c))))
	t_2 = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x)
	tmp = 0.0
	if (y <= -9e+28)
		tmp = t_2;
	elseif (y <= 7.5e-196)
		tmp = t_1;
	elseif (y <= 2.3e-131)
		tmp = Float64(y / Float64(Float64(y * Float64(Float64(c * 4.335357023065617e-6) - Float64(i * 5.162090511591658e-7))) + Float64(i * 4.335357023065617e-6)));
	elseif (y <= 3.6e+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 / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	t_2 = (y / ((y + a) + (b / y))) * x;
	tmp = 0.0;
	if (y <= -9e+28)
		tmp = t_2;
	elseif (y <= 7.5e-196)
		tmp = t_1;
	elseif (y <= 2.3e-131)
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6));
	elseif (y <= 3.6e+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[(t / N[(i + N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -9e+28], t$95$2, If[LessEqual[y, 7.5e-196], t$95$1, If[LessEqual[y, 2.3e-131], N[(y / N[(N[(y * N[(N[(c * 4.335357023065617e-6), $MachinePrecision] - N[(i * 5.162090511591658e-7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * 4.335357023065617e-6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999994e28 or 3.6e52 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in t around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.4%

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

      3. +-commutative 4.4%

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

      4. *-commutative 4.4%

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

      5. fma-udef 4.4%

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

      6. fma-udef 4.4%

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

      7. fma-udef 4.4%

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

      8. +-commutative 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in y around -inf 59.4%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. associate-+r+ 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 73.2%

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

   12. Applied egg-rr 73.2%

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

   if -8.9999999999999994e28 < y < 7.5e-196 or 2.30000000000000022e-131 < y < 3.6e52

   1. Initial program 94.5%

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

   2. Taylor expanded in t around inf 66.9%

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

   if 7.5e-196 < y < 2.30000000000000022e-131

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-/l* 82.4%

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

      3. +-commutative 82.4%

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

      4. *-commutative 82.4%

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

      5. fma-udef 82.4%

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

      6. fma-udef 82.4%

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

      7. fma-udef 82.4%

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

      8. +-commutative 82.4%

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

   4. Simplified 82.4%

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

   5. Taylor expanded in y around 0 79.8%

      \[\leadsto \frac{y}{\color{blue}{y \cdot \left(4.335357023065617 \cdot 10^{-6} \cdot c - 5.162090511591658 \cdot 10^{-7} \cdot i\right) + 4.335357023065617 \cdot 10^{-6} \cdot i}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+28}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{y \cdot \left(c \cdot 4.335357023065617 \cdot 10^{-6} - i \cdot 5.162090511591658 \cdot 10^{-7}\right) + i \cdot 4.335357023065617 \cdot 10^{-6}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \end{array} \]

Alternative 8: 76.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+28} \lor \neg \left(y \leq 3.6 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -9e+28) (not (<= y 3.6e+52)))
   (* (/ y (+ (+ y a) (/ b y))) x)
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ (* y (+ b (* y (+ y a)))) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9e+28) || !(y <= 3.6e+52)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	}
	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 <= (-9d+28)) .or. (.not. (y <= 3.6d+52))) then
        tmp = (y / ((y + a) + (b / y))) * x
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * ((y * (b + (y * (y + a)))) + c)))
    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 <= -9e+28) || !(y <= 3.6e+52)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -9e+28) or not (y <= 3.6e+52):
		tmp = (y / ((y + a) + (b / y))) * x
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * (b + (y * (y + a)))) + c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -9e+28) || !(y <= 3.6e+52))
		tmp = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x);
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(Float64(y * Float64(b + Float64(y * Float64(y + a)))) + c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -9e+28) || ~((y <= 3.6e+52)))
		tmp = (y / ((y + a) + (b / y))) * x;
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * (b + (y * (y + a)))) + c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -9e+28], N[Not[LessEqual[y, 3.6e+52]], $MachinePrecision]], N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999994e28 or 3.6e52 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in t around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.4%

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

      3. +-commutative 4.4%

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

      4. *-commutative 4.4%

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

      5. fma-udef 4.4%

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

      6. fma-udef 4.4%

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

      7. fma-udef 4.4%

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

      8. +-commutative 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in y around -inf 59.4%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. associate-+r+ 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 73.2%

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

   12. Applied egg-rr 73.2%

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

   if -8.9999999999999994e28 < y < 3.6e52

   1. Initial program 94.8%

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

   2. Taylor expanded in y around 0 80.1%

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

      1. *-commutative 80.1%

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

   4. Simplified 80.1%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+28} \lor \neg \left(y \leq 3.6 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(b + y \cdot \left(y + a\right)\right) + c\right)}\\ \end{array} \]

Alternative 9: 68.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ t_2 := \frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-129}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ t (+ i (* y (+ c (* y (+ b (* y y))))))))
        (t_2 (* (/ y (+ (+ y a) (/ b y))) x)))
   (if (<= y -1.05e+29)
     t_2
     (if (<= y 5.8e-196)
       t_1
       (if (<= y 1.3e-129)
         (/ (+ t (* y 230661.510616)) (+ i (* b (* y y))))
         (if (<= y 3.6e+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 / (i + (y * (c + (y * (b + (y * y))))));
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -1.05e+29) {
		tmp = t_2;
	} else if (y <= 5.8e-196) {
		tmp = t_1;
	} else if (y <= 1.3e-129) {
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	} else if (y <= 3.6e+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 / (i + (y * (c + (y * (b + (y * y))))))
    t_2 = (y / ((y + a) + (b / y))) * x
    if (y <= (-1.05d+29)) then
        tmp = t_2
    else if (y <= 5.8d-196) then
        tmp = t_1
    else if (y <= 1.3d-129) then
        tmp = (t + (y * 230661.510616d0)) / (i + (b * (y * y)))
    else if (y <= 3.6d+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 / (i + (y * (c + (y * (b + (y * y))))));
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -1.05e+29) {
		tmp = t_2;
	} else if (y <= 5.8e-196) {
		tmp = t_1;
	} else if (y <= 1.3e-129) {
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	} else if (y <= 3.6e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t / (i + (y * (c + (y * (b + (y * y))))))
	t_2 = (y / ((y + a) + (b / y))) * x
	tmp = 0
	if y <= -1.05e+29:
		tmp = t_2
	elif y <= 5.8e-196:
		tmp = t_1
	elif y <= 1.3e-129:
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)))
	elif y <= 3.6e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * y)))))))
	t_2 = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x)
	tmp = 0.0
	if (y <= -1.05e+29)
		tmp = t_2;
	elseif (y <= 5.8e-196)
		tmp = t_1;
	elseif (y <= 1.3e-129)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(b * Float64(y * y))));
	elseif (y <= 3.6e+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 / (i + (y * (c + (y * (b + (y * y))))));
	t_2 = (y / ((y + a) + (b / y))) * x;
	tmp = 0.0;
	if (y <= -1.05e+29)
		tmp = t_2;
	elseif (y <= 5.8e-196)
		tmp = t_1;
	elseif (y <= 1.3e-129)
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	elseif (y <= 3.6e+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[(t / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -1.05e+29], t$95$2, If[LessEqual[y, 5.8e-196], t$95$1, If[LessEqual[y, 1.3e-129], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0500000000000001e29 or 3.6e52 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in t around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.4%

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

      3. +-commutative 4.4%

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

      4. *-commutative 4.4%

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

      5. fma-udef 4.4%

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

      6. fma-udef 4.4%

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

      7. fma-udef 4.4%

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

      8. +-commutative 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in y around -inf 59.4%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. associate-+r+ 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 73.2%

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

   12. Applied egg-rr 73.2%

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

   if -1.0500000000000001e29 < y < 5.79999999999999974e-196 or 1.3e-129 < y < 3.6e52

   1. Initial program 94.5%

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

      1. div-inv 94.3%

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

      2. *-commutative 94.3%

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

      3. fma-def 94.3%

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

      4. *-commutative 94.3%

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

      5. fma-def 94.3%

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

      6. *-commutative 94.3%

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

      7. fma-def 94.3%

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

      8. fma-def 94.3%

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

      9. *-commutative 94.3%

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

      10. fma-def 94.3%

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

   3. Applied egg-rr 94.3%

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

   4. Taylor expanded in y around 0 66.7%

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

   5. Taylor expanded in a around 0 63.8%

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

      1. *-commutative 63.8%

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

      2. +-commutative 63.8%

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

      3. unpow2 63.8%

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

   7. Simplified 63.8%

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

   if 5.79999999999999974e-196 < y < 1.3e-129

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 99.4%

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

      1. *-commutative 99.4%

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

      2. unpow2 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in b around inf 69.0%

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

      1. *-commutative 69.0%

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

      2. unpow2 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in z around 0 69.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-129}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \end{array} \]

Alternative 10: 65.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ t_2 := \frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{y \cdot \left(c \cdot 4.335357023065617 \cdot 10^{-6} - i \cdot 5.162090511591658 \cdot 10^{-7}\right) + i \cdot 4.335357023065617 \cdot 10^{-6}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ t (+ i (* y (+ c (* y (+ b (* y y))))))))
        (t_2 (* (/ y (+ (+ y a) (/ b y))) x)))
   (if (<= y -9.5e+28)
     t_2
     (if (<= y 7.5e-196)
       t_1
       (if (<= y 1.12e-131)
         (/
          y
          (+
           (* y (- (* c 4.335357023065617e-6) (* i 5.162090511591658e-7)))
           (* i 4.335357023065617e-6)))
         (if (<= y 3.6e+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 / (i + (y * (c + (y * (b + (y * y))))));
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -9.5e+28) {
		tmp = t_2;
	} else if (y <= 7.5e-196) {
		tmp = t_1;
	} else if (y <= 1.12e-131) {
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6));
	} else if (y <= 3.6e+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 / (i + (y * (c + (y * (b + (y * y))))))
    t_2 = (y / ((y + a) + (b / y))) * x
    if (y <= (-9.5d+28)) then
        tmp = t_2
    else if (y <= 7.5d-196) then
        tmp = t_1
    else if (y <= 1.12d-131) then
        tmp = y / ((y * ((c * 4.335357023065617d-6) - (i * 5.162090511591658d-7))) + (i * 4.335357023065617d-6))
    else if (y <= 3.6d+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 / (i + (y * (c + (y * (b + (y * y))))));
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -9.5e+28) {
		tmp = t_2;
	} else if (y <= 7.5e-196) {
		tmp = t_1;
	} else if (y <= 1.12e-131) {
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6));
	} else if (y <= 3.6e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t / (i + (y * (c + (y * (b + (y * y))))))
	t_2 = (y / ((y + a) + (b / y))) * x
	tmp = 0
	if y <= -9.5e+28:
		tmp = t_2
	elif y <= 7.5e-196:
		tmp = t_1
	elif y <= 1.12e-131:
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6))
	elif y <= 3.6e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * y)))))))
	t_2 = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x)
	tmp = 0.0
	if (y <= -9.5e+28)
		tmp = t_2;
	elseif (y <= 7.5e-196)
		tmp = t_1;
	elseif (y <= 1.12e-131)
		tmp = Float64(y / Float64(Float64(y * Float64(Float64(c * 4.335357023065617e-6) - Float64(i * 5.162090511591658e-7))) + Float64(i * 4.335357023065617e-6)));
	elseif (y <= 3.6e+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 / (i + (y * (c + (y * (b + (y * y))))));
	t_2 = (y / ((y + a) + (b / y))) * x;
	tmp = 0.0;
	if (y <= -9.5e+28)
		tmp = t_2;
	elseif (y <= 7.5e-196)
		tmp = t_1;
	elseif (y <= 1.12e-131)
		tmp = y / ((y * ((c * 4.335357023065617e-6) - (i * 5.162090511591658e-7))) + (i * 4.335357023065617e-6));
	elseif (y <= 3.6e+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[(t / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -9.5e+28], t$95$2, If[LessEqual[y, 7.5e-196], t$95$1, If[LessEqual[y, 1.12e-131], N[(y / N[(N[(y * N[(N[(c * 4.335357023065617e-6), $MachinePrecision] - N[(i * 5.162090511591658e-7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * 4.335357023065617e-6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.49999999999999927e28 or 3.6e52 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in t around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.4%

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

      3. +-commutative 4.4%

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

      4. *-commutative 4.4%

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

      5. fma-udef 4.4%

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

      6. fma-udef 4.4%

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

      7. fma-udef 4.4%

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

      8. +-commutative 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in y around -inf 59.4%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. associate-+r+ 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 73.2%

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

   12. Applied egg-rr 73.2%

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

   if -9.49999999999999927e28 < y < 7.5e-196 or 1.12000000000000001e-131 < y < 3.6e52

   1. Initial program 94.5%

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

      1. div-inv 94.3%

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

      2. *-commutative 94.3%

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

      3. fma-def 94.3%

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

      4. *-commutative 94.3%

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

      5. fma-def 94.3%

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

      6. *-commutative 94.3%

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

      7. fma-def 94.3%

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

      8. fma-def 94.3%

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

      9. *-commutative 94.3%

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

      10. fma-def 94.3%

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

   3. Applied egg-rr 94.3%

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

   4. Taylor expanded in y around 0 66.7%

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

   5. Taylor expanded in a around 0 63.8%

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

      1. *-commutative 63.8%

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

      2. +-commutative 63.8%

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

      3. unpow2 63.8%

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

   7. Simplified 63.8%

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

   if 7.5e-196 < y < 1.12000000000000001e-131

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-/l* 82.4%

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

      3. +-commutative 82.4%

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

      4. *-commutative 82.4%

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

      5. fma-udef 82.4%

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

      6. fma-udef 82.4%

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

      7. fma-udef 82.4%

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

      8. +-commutative 82.4%

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

   4. Simplified 82.4%

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

   5. Taylor expanded in y around 0 79.8%

      \[\leadsto \frac{y}{\color{blue}{y \cdot \left(4.335357023065617 \cdot 10^{-6} \cdot c - 5.162090511591658 \cdot 10^{-7} \cdot i\right) + 4.335357023065617 \cdot 10^{-6} \cdot i}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{y \cdot \left(c \cdot 4.335357023065617 \cdot 10^{-6} - i \cdot 5.162090511591658 \cdot 10^{-7}\right) + i \cdot 4.335357023065617 \cdot 10^{-6}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \end{array} \]

Alternative 11: 74.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-20} \lor \neg \left(y \leq 1.2\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.3e-20) (not (<= y 1.2)))
   (* (/ y (+ (+ y a) (/ b y))) x)
   (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) (+ i (* y c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.3e-20) || !(y <= 1.2)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c));
	}
	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 <= (-1.3d-20)) .or. (.not. (y <= 1.2d0))) then
        tmp = (y / ((y + a) + (b / y))) * x
    else
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / (i + (y * c))
    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 <= -1.3e-20) || !(y <= 1.2)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.3e-20) or not (y <= 1.2):
		tmp = (y / ((y + a) + (b / y))) * x
	else:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.3e-20) || !(y <= 1.2))
		tmp = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x);
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(i + Float64(y * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.3e-20) || ~((y <= 1.2)))
		tmp = (y / ((y + a) + (b / y))) * x;
	else
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.3e-20], N[Not[LessEqual[y, 1.2]], $MachinePrecision]], N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999997e-20 or 1.19999999999999996 < y

   1. Initial program 13.3%

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

   2. Taylor expanded in t around 0 9.8%

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

      1. *-commutative 9.8%

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

      2. associate-/l* 12.0%

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

      3. +-commutative 12.0%

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

      4. *-commutative 12.0%

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

      5. fma-udef 12.0%

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

      6. fma-udef 12.0%

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

      7. fma-udef 12.0%

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

      8. +-commutative 12.0%

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

   4. Simplified 12.0%

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

   5. Taylor expanded in y around -inf 52.5%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in x around inf 57.1%

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

      1. associate-+r+ 57.1%

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

   10. Simplified 57.1%

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

       1. associate-/r/ 64.4%

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

   12. Applied egg-rr 64.4%

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

   if -1.29999999999999997e-20 < y < 1.19999999999999996

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 96.5%

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

      1. *-commutative 96.5%

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

      2. unpow2 96.5%

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

   4. Simplified 96.5%

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

   5. Taylor expanded in y around 0 83.5%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-20} \lor \neg \left(y \leq 1.2\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \end{array} \]

Alternative 12: 66.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{1}{i + y \cdot c}\\ t_2 := \frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{if}\;y \leq -4 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-133}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* t (/ 1.0 (+ i (* y c)))))
        (t_2 (* (/ y (+ (+ y a) (/ b y))) x)))
   (if (<= y -4e-21)
     t_2
     (if (<= y 7.5e-196)
       t_1
       (if (<= y 1.2e-133)
         (+ (* 230661.510616 (/ y i)) (/ t i))
         (if (<= y 1.65e-32) 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 * (1.0 / (i + (y * c)));
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -4e-21) {
		tmp = t_2;
	} else if (y <= 7.5e-196) {
		tmp = t_1;
	} else if (y <= 1.2e-133) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else if (y <= 1.65e-32) {
		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 * (1.0d0 / (i + (y * c)))
    t_2 = (y / ((y + a) + (b / y))) * x
    if (y <= (-4d-21)) then
        tmp = t_2
    else if (y <= 7.5d-196) then
        tmp = t_1
    else if (y <= 1.2d-133) then
        tmp = (230661.510616d0 * (y / i)) + (t / i)
    else if (y <= 1.65d-32) 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 * (1.0 / (i + (y * c)));
	double t_2 = (y / ((y + a) + (b / y))) * x;
	double tmp;
	if (y <= -4e-21) {
		tmp = t_2;
	} else if (y <= 7.5e-196) {
		tmp = t_1;
	} else if (y <= 1.2e-133) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else if (y <= 1.65e-32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t * (1.0 / (i + (y * c)))
	t_2 = (y / ((y + a) + (b / y))) * x
	tmp = 0
	if y <= -4e-21:
		tmp = t_2
	elif y <= 7.5e-196:
		tmp = t_1
	elif y <= 1.2e-133:
		tmp = (230661.510616 * (y / i)) + (t / i)
	elif y <= 1.65e-32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t * Float64(1.0 / Float64(i + Float64(y * c))))
	t_2 = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x)
	tmp = 0.0
	if (y <= -4e-21)
		tmp = t_2;
	elseif (y <= 7.5e-196)
		tmp = t_1;
	elseif (y <= 1.2e-133)
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + Float64(t / i));
	elseif (y <= 1.65e-32)
		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 * (1.0 / (i + (y * c)));
	t_2 = (y / ((y + a) + (b / y))) * x;
	tmp = 0.0;
	if (y <= -4e-21)
		tmp = t_2;
	elseif (y <= 7.5e-196)
		tmp = t_1;
	elseif (y <= 1.2e-133)
		tmp = (230661.510616 * (y / i)) + (t / i);
	elseif (y <= 1.65e-32)
		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[(t * N[(1.0 / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -4e-21], t$95$2, If[LessEqual[y, 7.5e-196], t$95$1, If[LessEqual[y, 1.2e-133], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-32], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999963e-21 or 1.65000000000000013e-32 < y

   1. Initial program 16.9%

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

   2. Taylor expanded in t around 0 12.9%

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

      1. *-commutative 12.9%

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

      2. associate-/l* 15.0%

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

      3. +-commutative 15.0%

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

      4. *-commutative 15.0%

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

      5. fma-udef 15.0%

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

      6. fma-udef 15.0%

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

      7. fma-udef 15.0%

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

      8. +-commutative 15.0%

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

   4. Simplified 15.0%

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

   5. Taylor expanded in y around -inf 50.4%

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

   7. Simplified 51.0%

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

   8. Taylor expanded in x around inf 54.9%

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

      1. associate-+r+ 54.9%

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

   10. Simplified 54.9%

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

       1. associate-/r/ 61.9%

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

   12. Applied egg-rr 61.9%

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

   if -3.99999999999999963e-21 < y < 7.5e-196 or 1.2e-133 < y < 1.65000000000000013e-32

   1. Initial program 99.7%

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

      1. div-inv 99.5%

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

      2. *-commutative 99.5%

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

      3. fma-def 99.5%

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

      4. *-commutative 99.5%

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

      5. fma-def 99.5%

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

      6. *-commutative 99.5%

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

      7. fma-def 99.5%

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

      8. fma-def 99.5%

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

      9. *-commutative 99.5%

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

      10. fma-def 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in y around 0 76.3%

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

   5. Taylor expanded in y around 0 67.1%

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

   if 7.5e-196 < y < 1.2e-133

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf 99.5%

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

      1. *-commutative 99.5%

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

      2. unpow2 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in b around inf 76.0%

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

      1. *-commutative 76.0%

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

      2. unpow2 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in y around 0 74.0%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \frac{1}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-133}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \frac{1}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \end{array} \]

Alternative 13: 58.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{1}{i + y \cdot c}\\ t_2 := \frac{y}{\frac{y + a}{x}}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-133}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* t (/ 1.0 (+ i (* y c))))) (t_2 (/ y (/ (+ y a) x))))
   (if (<= y -1.3e-20)
     t_2
     (if (<= y 7.2e-196)
       t_1
       (if (<= y 1.15e-133)
         (+ (* 230661.510616 (/ y i)) (/ t i))
         (if (<= y 1.65e-32) 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 * (1.0 / (i + (y * c)));
	double t_2 = y / ((y + a) / x);
	double tmp;
	if (y <= -1.3e-20) {
		tmp = t_2;
	} else if (y <= 7.2e-196) {
		tmp = t_1;
	} else if (y <= 1.15e-133) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else if (y <= 1.65e-32) {
		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 * (1.0d0 / (i + (y * c)))
    t_2 = y / ((y + a) / x)
    if (y <= (-1.3d-20)) then
        tmp = t_2
    else if (y <= 7.2d-196) then
        tmp = t_1
    else if (y <= 1.15d-133) then
        tmp = (230661.510616d0 * (y / i)) + (t / i)
    else if (y <= 1.65d-32) 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 * (1.0 / (i + (y * c)));
	double t_2 = y / ((y + a) / x);
	double tmp;
	if (y <= -1.3e-20) {
		tmp = t_2;
	} else if (y <= 7.2e-196) {
		tmp = t_1;
	} else if (y <= 1.15e-133) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else if (y <= 1.65e-32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t * (1.0 / (i + (y * c)))
	t_2 = y / ((y + a) / x)
	tmp = 0
	if y <= -1.3e-20:
		tmp = t_2
	elif y <= 7.2e-196:
		tmp = t_1
	elif y <= 1.15e-133:
		tmp = (230661.510616 * (y / i)) + (t / i)
	elif y <= 1.65e-32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t * Float64(1.0 / Float64(i + Float64(y * c))))
	t_2 = Float64(y / Float64(Float64(y + a) / x))
	tmp = 0.0
	if (y <= -1.3e-20)
		tmp = t_2;
	elseif (y <= 7.2e-196)
		tmp = t_1;
	elseif (y <= 1.15e-133)
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + Float64(t / i));
	elseif (y <= 1.65e-32)
		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 * (1.0 / (i + (y * c)));
	t_2 = y / ((y + a) / x);
	tmp = 0.0;
	if (y <= -1.3e-20)
		tmp = t_2;
	elseif (y <= 7.2e-196)
		tmp = t_1;
	elseif (y <= 1.15e-133)
		tmp = (230661.510616 * (y / i)) + (t / i);
	elseif (y <= 1.65e-32)
		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[(t * N[(1.0 / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(N[(y + a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e-20], t$95$2, If[LessEqual[y, 7.2e-196], t$95$1, If[LessEqual[y, 1.15e-133], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-32], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.29999999999999997e-20 or 1.65000000000000013e-32 < y

   1. Initial program 16.9%

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

   2. Taylor expanded in t around 0 12.9%

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

      1. *-commutative 12.9%

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

      2. associate-/l* 15.0%

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

      3. +-commutative 15.0%

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

      4. *-commutative 15.0%

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

      5. fma-udef 15.0%

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

      6. fma-udef 15.0%

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

      7. fma-udef 15.0%

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

      8. +-commutative 15.0%

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

   4. Simplified 15.0%

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

   5. Taylor expanded in y around -inf 50.4%

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

   7. Simplified 51.0%

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

   8. Taylor expanded in x around inf 54.9%

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

      1. associate-+r+ 54.9%

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

   10. Simplified 54.9%

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

   11. Taylor expanded in b around 0 40.4%

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

       1. associate-/l* 52.5%

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

       2. +-commutative 52.5%

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

   13. Simplified 52.5%

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

   if -1.29999999999999997e-20 < y < 7.2000000000000001e-196 or 1.15e-133 < y < 1.65000000000000013e-32

   1. Initial program 99.7%

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

      1. div-inv 99.5%

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

      2. *-commutative 99.5%

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

      3. fma-def 99.5%

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

      4. *-commutative 99.5%

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

      5. fma-def 99.5%

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

      6. *-commutative 99.5%

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

      7. fma-def 99.5%

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

      8. fma-def 99.5%

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

      9. *-commutative 99.5%

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

      10. fma-def 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in y around 0 76.3%

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

   5. Taylor expanded in y around 0 67.1%

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

   if 7.2000000000000001e-196 < y < 1.15e-133

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf 99.5%

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

      1. *-commutative 99.5%

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

      2. unpow2 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in b around inf 76.0%

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

      1. *-commutative 76.0%

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

      2. unpow2 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in y around 0 74.0%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{\frac{y + a}{x}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \frac{1}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-133}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \frac{1}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y + a}{x}}\\ \end{array} \]

Alternative 14: 64.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+28} \lor \neg \left(y \leq 3.6 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + b \cdot \left(y \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -9e+28) (not (<= y 3.6e+52)))
   (* (/ y (+ (+ y a) (/ b y))) x)
   (/ (+ t (* y 230661.510616)) (+ i (* b (* y y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9e+28) || !(y <= 3.6e+52)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-9d+28)) .or. (.not. (y <= 3.6d+52))) then
        tmp = (y / ((y + a) + (b / y))) * x
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (b * (y * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9e+28) || !(y <= 3.6e+52)) {
		tmp = (y / ((y + a) + (b / y))) * x;
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -9e+28) or not (y <= 3.6e+52):
		tmp = (y / ((y + a) + (b / y))) * x
	else:
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -9e+28) || !(y <= 3.6e+52))
		tmp = Float64(Float64(y / Float64(Float64(y + a) + Float64(b / y))) * x);
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(b * Float64(y * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -9e+28) || ~((y <= 3.6e+52)))
		tmp = (y / ((y + a) + (b / y))) * x;
	else
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -9e+28], N[Not[LessEqual[y, 3.6e+52]], $MachinePrecision]], N[(N[(y / N[(N[(y + a), $MachinePrecision] + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999994e28 or 3.6e52 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in t around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.4%

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

      3. +-commutative 4.4%

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

      4. *-commutative 4.4%

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

      5. fma-udef 4.4%

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

      6. fma-udef 4.4%

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

      7. fma-udef 4.4%

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

      8. +-commutative 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in y around -inf 59.4%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. associate-+r+ 64.6%

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

   10. Simplified 64.6%

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

       1. associate-/r/ 73.2%

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

   12. Applied egg-rr 73.2%

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

   if -8.9999999999999994e28 < y < 3.6e52

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 88.3%

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

      1. *-commutative 88.3%

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

      2. unpow2 88.3%

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

   4. Simplified 88.3%

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

   5. Taylor expanded in b around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. unpow2 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in z around 0 55.0%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+28} \lor \neg \left(y \leq 3.6 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{\left(y + a\right) + \frac{b}{y}} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + b \cdot \left(y \cdot y\right)}\\ \end{array} \]

Alternative 15: 49.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{y + a}{x}}\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-129}:\\ \;\;\;\;\frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ y (/ (+ y a) x))))
   (if (<= y -6.4e-24)
     t_1
     (if (<= y 7.5e-196)
       (/ t i)
       (if (<= y 3.8e-129)
         (/ (* y 230661.510616) i)
         (if (<= y 1.65e-32) (/ t i) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y / ((y + a) / x);
	double tmp;
	if (y <= -6.4e-24) {
		tmp = t_1;
	} else if (y <= 7.5e-196) {
		tmp = t / i;
	} else if (y <= 3.8e-129) {
		tmp = (y * 230661.510616) / i;
	} else if (y <= 1.65e-32) {
		tmp = t / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / ((y + a) / x)
    if (y <= (-6.4d-24)) then
        tmp = t_1
    else if (y <= 7.5d-196) then
        tmp = t / i
    else if (y <= 3.8d-129) then
        tmp = (y * 230661.510616d0) / i
    else if (y <= 1.65d-32) then
        tmp = t / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = y / ((y + a) / x);
	double tmp;
	if (y <= -6.4e-24) {
		tmp = t_1;
	} else if (y <= 7.5e-196) {
		tmp = t / i;
	} else if (y <= 3.8e-129) {
		tmp = (y * 230661.510616) / i;
	} else if (y <= 1.65e-32) {
		tmp = t / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = y / ((y + a) / x)
	tmp = 0
	if y <= -6.4e-24:
		tmp = t_1
	elif y <= 7.5e-196:
		tmp = t / i
	elif y <= 3.8e-129:
		tmp = (y * 230661.510616) / i
	elif y <= 1.65e-32:
		tmp = t / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(y / Float64(Float64(y + a) / x))
	tmp = 0.0
	if (y <= -6.4e-24)
		tmp = t_1;
	elseif (y <= 7.5e-196)
		tmp = Float64(t / i);
	elseif (y <= 3.8e-129)
		tmp = Float64(Float64(y * 230661.510616) / i);
	elseif (y <= 1.65e-32)
		tmp = Float64(t / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = y / ((y + a) / x);
	tmp = 0.0;
	if (y <= -6.4e-24)
		tmp = t_1;
	elseif (y <= 7.5e-196)
		tmp = t / i;
	elseif (y <= 3.8e-129)
		tmp = (y * 230661.510616) / i;
	elseif (y <= 1.65e-32)
		tmp = t / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y / N[(N[(y + a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e-24], t$95$1, If[LessEqual[y, 7.5e-196], N[(t / i), $MachinePrecision], If[LessEqual[y, 3.8e-129], N[(N[(y * 230661.510616), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 1.65e-32], N[(t / i), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.40000000000000025e-24 or 1.65000000000000013e-32 < y

   1. Initial program 18.0%

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

   2. Taylor expanded in t around 0 13.4%

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

      1. *-commutative 13.4%

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

      2. associate-/l* 15.6%

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

      3. +-commutative 15.6%

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

      4. *-commutative 15.6%

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

      5. fma-udef 15.6%

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

      6. fma-udef 15.6%

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

      7. fma-udef 15.6%

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

      8. +-commutative 15.6%

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

   4. Simplified 15.6%

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

   5. Taylor expanded in y around -inf 49.7%

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

   7. Simplified 50.3%

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

   8. Taylor expanded in x around inf 54.1%

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

      1. associate-+r+ 54.1%

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

   10. Simplified 54.1%

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

   11. Taylor expanded in b around 0 39.9%

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

       1. associate-/l* 51.8%

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

       2. +-commutative 51.8%

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

   13. Simplified 51.8%

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

   if -6.40000000000000025e-24 < y < 7.5e-196 or 3.79999999999999985e-129 < y < 1.65000000000000013e-32

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 52.9%

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

   if 7.5e-196 < y < 3.79999999999999985e-129

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/l* 75.0%

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

      3. +-commutative 75.0%

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

      4. *-commutative 75.0%

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

      5. fma-udef 75.0%

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

      6. fma-udef 75.0%

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

      7. fma-udef 75.0%

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

      8. +-commutative 75.0%

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

   4. Simplified 75.0%

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

   5. Taylor expanded in i around inf 56.4%

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

   6. Taylor expanded in y around 0 54.7%

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

      1. associate-*r/ 56.4%

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

   8. Simplified 56.4%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{\frac{y + a}{x}}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-129}:\\ \;\;\;\;\frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y + a}{x}}\\ \end{array} \]

Alternative 16: 58.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-21} \lor \neg \left(y \leq 1.65 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{y}{\frac{y + a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{1}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.2e-21) (not (<= y 1.65e-32)))
   (/ y (/ (+ y a) x))
   (* t (/ 1.0 (+ i (* y c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.2e-21) || !(y <= 1.65e-32)) {
		tmp = y / ((y + a) / x);
	} else {
		tmp = t * (1.0 / (i + (y * c)));
	}
	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 <= (-1.2d-21)) .or. (.not. (y <= 1.65d-32))) then
        tmp = y / ((y + a) / x)
    else
        tmp = t * (1.0d0 / (i + (y * c)))
    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 <= -1.2e-21) || !(y <= 1.65e-32)) {
		tmp = y / ((y + a) / x);
	} else {
		tmp = t * (1.0 / (i + (y * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.2e-21) or not (y <= 1.65e-32):
		tmp = y / ((y + a) / x)
	else:
		tmp = t * (1.0 / (i + (y * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.2e-21) || !(y <= 1.65e-32))
		tmp = Float64(y / Float64(Float64(y + a) / x));
	else
		tmp = Float64(t * Float64(1.0 / Float64(i + Float64(y * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.2e-21) || ~((y <= 1.65e-32)))
		tmp = y / ((y + a) / x);
	else
		tmp = t * (1.0 / (i + (y * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.2e-21], N[Not[LessEqual[y, 1.65e-32]], $MachinePrecision]], N[(y / N[(N[(y + a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e-21 or 1.65000000000000013e-32 < y

   1. Initial program 16.9%

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

   2. Taylor expanded in t around 0 12.9%

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

      1. *-commutative 12.9%

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

      2. associate-/l* 15.0%

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

      3. +-commutative 15.0%

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

      4. *-commutative 15.0%

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

      5. fma-udef 15.0%

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

      6. fma-udef 15.0%

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

      7. fma-udef 15.0%

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

      8. +-commutative 15.0%

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

   4. Simplified 15.0%

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

   5. Taylor expanded in y around -inf 50.4%

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

   7. Simplified 51.0%

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

   8. Taylor expanded in x around inf 54.9%

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

      1. associate-+r+ 54.9%

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

   10. Simplified 54.9%

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

   11. Taylor expanded in b around 0 40.4%

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

       1. associate-/l* 52.5%

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

       2. +-commutative 52.5%

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

   13. Simplified 52.5%

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

   if -1.2e-21 < y < 1.65000000000000013e-32

   1. Initial program 99.7%

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

      1. div-inv 99.5%

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

      2. *-commutative 99.5%

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

      3. fma-def 99.5%

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

      4. *-commutative 99.5%

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

      5. fma-def 99.5%

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

      6. *-commutative 99.5%

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

      7. fma-def 99.5%

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

      8. fma-def 99.5%

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

      9. *-commutative 99.5%

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

      10. fma-def 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in y around 0 72.3%

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

   5. Taylor expanded in y around 0 63.9%

      \[\leadsto t \cdot \frac{1}{\color{blue}{i + c \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-21} \lor \neg \left(y \leq 1.65 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{y}{\frac{y + a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{1}{i + y \cdot c}\\ \end{array} \]

Alternative 17: 48.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-129}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.5e-6)
   x
   (if (<= y 7.2e-196)
     (/ t i)
     (if (<= y 5.1e-129)
       (* 230661.510616 (/ y i))
       (if (<= y 3.6e+52) (/ t i) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.5e-6) {
		tmp = x;
	} else if (y <= 7.2e-196) {
		tmp = t / i;
	} else if (y <= 5.1e-129) {
		tmp = 230661.510616 * (y / i);
	} else if (y <= 3.6e+52) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-4.5d-6)) then
        tmp = x
    else if (y <= 7.2d-196) then
        tmp = t / i
    else if (y <= 5.1d-129) then
        tmp = 230661.510616d0 * (y / i)
    else if (y <= 3.6d+52) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.5e-6) {
		tmp = x;
	} else if (y <= 7.2e-196) {
		tmp = t / i;
	} else if (y <= 5.1e-129) {
		tmp = 230661.510616 * (y / i);
	} else if (y <= 3.6e+52) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.5e-6:
		tmp = x
	elif y <= 7.2e-196:
		tmp = t / i
	elif y <= 5.1e-129:
		tmp = 230661.510616 * (y / i)
	elif y <= 3.6e+52:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.5e-6)
		tmp = x;
	elseif (y <= 7.2e-196)
		tmp = Float64(t / i);
	elseif (y <= 5.1e-129)
		tmp = Float64(230661.510616 * Float64(y / i));
	elseif (y <= 3.6e+52)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.5e-6)
		tmp = x;
	elseif (y <= 7.2e-196)
		tmp = t / i;
	elseif (y <= 5.1e-129)
		tmp = 230661.510616 * (y / i);
	elseif (y <= 3.6e+52)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.5e-6], x, If[LessEqual[y, 7.2e-196], N[(t / i), $MachinePrecision], If[LessEqual[y, 5.1e-129], N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+52], N[(t / i), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.50000000000000011e-6 or 3.6e52 < y

   1. Initial program 8.0%

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

   2. Taylor expanded in y around inf 49.6%

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

   if -4.50000000000000011e-6 < y < 7.2000000000000001e-196 or 5.0999999999999999e-129 < y < 3.6e52

   1. Initial program 95.8%

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

   2. Taylor expanded in y around 0 44.3%

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

   if 7.2000000000000001e-196 < y < 5.0999999999999999e-129

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/l* 75.0%

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

      3. +-commutative 75.0%

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

      4. *-commutative 75.0%

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

      5. fma-udef 75.0%

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

      6. fma-udef 75.0%

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

      7. fma-udef 75.0%

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

      8. +-commutative 75.0%

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

   4. Simplified 75.0%

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

   5. Taylor expanded in y around 0 54.7%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-129}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 48.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-129}:\\ \;\;\;\;\frac{y}{i \cdot 4.335357023065617 \cdot 10^{-6}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7e-7)
   x
   (if (<= y 7.5e-196)
     (/ t i)
     (if (<= y 7e-129)
       (/ y (* i 4.335357023065617e-6))
       (if (<= y 1.6e+53) (/ 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 <= -7e-7) {
		tmp = x;
	} else if (y <= 7.5e-196) {
		tmp = t / i;
	} else if (y <= 7e-129) {
		tmp = y / (i * 4.335357023065617e-6);
	} else if (y <= 1.6e+53) {
		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 <= (-7d-7)) then
        tmp = x
    else if (y <= 7.5d-196) then
        tmp = t / i
    else if (y <= 7d-129) then
        tmp = y / (i * 4.335357023065617d-6)
    else if (y <= 1.6d+53) 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 <= -7e-7) {
		tmp = x;
	} else if (y <= 7.5e-196) {
		tmp = t / i;
	} else if (y <= 7e-129) {
		tmp = y / (i * 4.335357023065617e-6);
	} else if (y <= 1.6e+53) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7e-7:
		tmp = x
	elif y <= 7.5e-196:
		tmp = t / i
	elif y <= 7e-129:
		tmp = y / (i * 4.335357023065617e-6)
	elif y <= 1.6e+53:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7e-7)
		tmp = x;
	elseif (y <= 7.5e-196)
		tmp = Float64(t / i);
	elseif (y <= 7e-129)
		tmp = Float64(y / Float64(i * 4.335357023065617e-6));
	elseif (y <= 1.6e+53)
		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 <= -7e-7)
		tmp = x;
	elseif (y <= 7.5e-196)
		tmp = t / i;
	elseif (y <= 7e-129)
		tmp = y / (i * 4.335357023065617e-6);
	elseif (y <= 1.6e+53)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7e-7], x, If[LessEqual[y, 7.5e-196], N[(t / i), $MachinePrecision], If[LessEqual[y, 7e-129], N[(y / N[(i * 4.335357023065617e-6), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+53], N[(t / i), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.99999999999999968e-7 or 1.6e53 < y

   1. Initial program 8.0%

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

   2. Taylor expanded in y around inf 49.6%

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

   if -6.99999999999999968e-7 < y < 7.5e-196 or 6.9999999999999995e-129 < y < 1.6e53

   1. Initial program 95.8%

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

   2. Taylor expanded in y around 0 44.3%

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

   if 7.5e-196 < y < 6.9999999999999995e-129

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/l* 75.0%

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

      3. +-commutative 75.0%

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

      4. *-commutative 75.0%

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

      5. fma-udef 75.0%

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

      6. fma-udef 75.0%

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

      7. fma-udef 75.0%

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

      8. +-commutative 75.0%

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

   4. Simplified 75.0%

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

   5. Taylor expanded in y around 0 56.2%

      \[\leadsto \frac{y}{\color{blue}{4.335357023065617 \cdot 10^{-6} \cdot i}} \]
   6. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto \frac{y}{\color{blue}{i \cdot 4.335357023065617 \cdot 10^{-6}}} \]

   7. Simplified 56.2%

      \[\leadsto \frac{y}{\color{blue}{i \cdot 4.335357023065617 \cdot 10^{-6}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-129}:\\ \;\;\;\;\frac{y}{i \cdot 4.335357023065617 \cdot 10^{-6}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 48.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-129}:\\ \;\;\;\;\frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.5e-6)
   x
   (if (<= y 7.5e-196)
     (/ t i)
     (if (<= y 3.8e-129)
       (/ (* y 230661.510616) i)
       (if (<= y 3.6e+52) (/ t i) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.5e-6) {
		tmp = x;
	} else if (y <= 7.5e-196) {
		tmp = t / i;
	} else if (y <= 3.8e-129) {
		tmp = (y * 230661.510616) / i;
	} else if (y <= 3.6e+52) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-4.5d-6)) then
        tmp = x
    else if (y <= 7.5d-196) then
        tmp = t / i
    else if (y <= 3.8d-129) then
        tmp = (y * 230661.510616d0) / i
    else if (y <= 3.6d+52) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.5e-6) {
		tmp = x;
	} else if (y <= 7.5e-196) {
		tmp = t / i;
	} else if (y <= 3.8e-129) {
		tmp = (y * 230661.510616) / i;
	} else if (y <= 3.6e+52) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.5e-6:
		tmp = x
	elif y <= 7.5e-196:
		tmp = t / i
	elif y <= 3.8e-129:
		tmp = (y * 230661.510616) / i
	elif y <= 3.6e+52:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.5e-6)
		tmp = x;
	elseif (y <= 7.5e-196)
		tmp = Float64(t / i);
	elseif (y <= 3.8e-129)
		tmp = Float64(Float64(y * 230661.510616) / i);
	elseif (y <= 3.6e+52)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.5e-6)
		tmp = x;
	elseif (y <= 7.5e-196)
		tmp = t / i;
	elseif (y <= 3.8e-129)
		tmp = (y * 230661.510616) / i;
	elseif (y <= 3.6e+52)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.5e-6], x, If[LessEqual[y, 7.5e-196], N[(t / i), $MachinePrecision], If[LessEqual[y, 3.8e-129], N[(N[(y * 230661.510616), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 3.6e+52], N[(t / i), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.50000000000000011e-6 or 3.6e52 < y

   1. Initial program 8.0%

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

   2. Taylor expanded in y around inf 49.6%

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

   if -4.50000000000000011e-6 < y < 7.5e-196 or 3.79999999999999985e-129 < y < 3.6e52

   1. Initial program 95.8%

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

   2. Taylor expanded in y around 0 44.3%

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

   if 7.5e-196 < y < 3.79999999999999985e-129

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/l* 75.0%

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

      3. +-commutative 75.0%

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

      4. *-commutative 75.0%

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

      5. fma-udef 75.0%

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

      6. fma-udef 75.0%

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

      7. fma-udef 75.0%

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

      8. +-commutative 75.0%

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

   4. Simplified 75.0%

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

   5. Taylor expanded in i around inf 56.4%

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

   6. Taylor expanded in y around 0 54.7%

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

      1. associate-*r/ 56.4%

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

   8. Simplified 56.4%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-129}:\\ \;\;\;\;\frac{y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 50.2% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.4e-6) x (if (<= y 3.6e+52) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.4e-6) {
		tmp = x;
	} else if (y <= 3.6e+52) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-4.4d-6)) then
        tmp = x
    else if (y <= 3.6d+52) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.4e-6) {
		tmp = x;
	} else if (y <= 3.6e+52) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.4e-6:
		tmp = x
	elif y <= 3.6e+52:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.4e-6)
		tmp = x;
	elseif (y <= 3.6e+52)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.4e-6)
		tmp = x;
	elseif (y <= 3.6e+52)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.4e-6], x, If[LessEqual[y, 3.6e+52], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4000000000000002e-6 or 3.6e52 < y

   1. Initial program 8.0%

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

   2. Taylor expanded in y around inf 49.6%

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

   if -4.4000000000000002e-6 < y < 3.6e52

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 41.7%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 25.4% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.4%

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

2. Taylor expanded in y around inf 25.7%

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

3. Final simplification 25.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023230 
(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)))