Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.2% → 84.8%

Time: 25.2s

Alternatives: 17

Speedup: 1.9×

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: 56.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{t_1} \leq 2 \cdot 10^{+248}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t_1} + \left(x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (<=
        (/
         (+
          (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
          t)
         t_1)
        2e+248)
     (/
      (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t)
      (fma (fma (fma (+ y a) y b) y c) y i))
     (+ (/ t t_1) (+ x (- (/ z y) (/ a (/ y x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if ((((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / t_1) <= 2e+248) {
		tmp = fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((y + a), y, b), y, c), y, i);
	} else {
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))) + t) / t_1) <= 2e+248)
		tmp = Float64(fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(y + a), y, b), y, c), y, i));
	else
		tmp = Float64(Float64(t / t_1) + Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[N[(N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / t$95$1), $MachinePrecision], 2e+248], N[(N[(N[(N[(N[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(N[(t / t$95$1), $MachinePrecision] + N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2.00000000000000009e248

   1. Initial program 91.7%

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

      1. fma-def 91.7%

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

      2. fma-def 91.7%

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

      3. fma-def 91.7%

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

      4. fma-def 91.7%

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

      5. fma-def 91.7%

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

      6. fma-def 91.7%

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

      7. fma-def 91.7%

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

   3. Simplified 91.7%

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

   if 2.00000000000000009e248 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 3.7%

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

   2. Taylor expanded in t around 0 3.7%

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

   3. Taylor expanded in y around inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq 2 \cdot 10^{+248}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \left(x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\right)\\ \end{array} \]

Alternative 2: 84.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ t_2 := \frac{t}{t_1}\\ t_3 := y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)\\ \mathbf{if}\;\frac{t_3 + t}{t_1} \leq 2 \cdot 10^{+248}:\\ \;\;\;\;t_2 + \frac{t_3}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2 + \left(x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
        (t_2 (/ t t_1))
        (t_3
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))))
   (if (<= (/ (+ t_3 t) t_1) 2e+248)
     (+ t_2 (/ t_3 t_1))
     (+ t_2 (+ x (- (/ z y) (/ a (/ y x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_2 = t / t_1;
	double t_3 = y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))));
	double tmp;
	if (((t_3 + t) / t_1) <= 2e+248) {
		tmp = t_2 + (t_3 / t_1);
	} else {
		tmp = t_2 + (x + ((z / y) - (a / (y / x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    t_2 = t / t_1
    t_3 = y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z)))))
    if (((t_3 + t) / t_1) <= 2d+248) then
        tmp = t_2 + (t_3 / t_1)
    else
        tmp = t_2 + (x + ((z / y) - (a / (y / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_2 = t / t_1;
	double t_3 = y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))));
	double tmp;
	if (((t_3 + t) / t_1) <= 2e+248) {
		tmp = t_2 + (t_3 / t_1);
	} else {
		tmp = t_2 + (x + ((z / y) - (a / (y / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	t_2 = t / t_1
	t_3 = y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))
	tmp = 0
	if ((t_3 + t) / t_1) <= 2e+248:
		tmp = t_2 + (t_3 / t_1)
	else:
		tmp = t_2 + (x + ((z / y) - (a / (y / x))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	t_2 = Float64(t / t_1)
	t_3 = Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))))
	tmp = 0.0
	if (Float64(Float64(t_3 + t) / t_1) <= 2e+248)
		tmp = Float64(t_2 + Float64(t_3 / t_1));
	else
		tmp = Float64(t_2 + Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	t_2 = t / t_1;
	t_3 = y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))));
	tmp = 0.0;
	if (((t_3 + t) / t_1) <= 2e+248)
		tmp = t_2 + (t_3 / t_1);
	else
		tmp = t_2 + (x + ((z / y) - (a / (y / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$2 = N[(t / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$3 + t), $MachinePrecision] / t$95$1), $MachinePrecision], 2e+248], N[(t$95$2 + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2.00000000000000009e248

   1. Initial program 91.7%

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

   2. Taylor expanded in t around 0 91.7%

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

   if 2.00000000000000009e248 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 3.7%

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

   2. Taylor expanded in t around 0 3.7%

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

   3. Taylor expanded in y around inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq 2 \cdot 10^{+248}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \left(x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\right)\\ \end{array} \]

Alternative 3: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ t_2 := \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{t_1}\\ \mathbf{if}\;t_2 \leq 2 \cdot 10^{+248}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t_1} + \left(x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
        (t_2
         (/
          (+
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
           t)
          t_1)))
   (if (<= t_2 2e+248) t_2 (+ (/ t t_1) (+ x (- (/ z y) (/ a (/ y x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_2 = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / t_1;
	double tmp;
	if (t_2 <= 2e+248) {
		tmp = t_2;
	} else {
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    t_2 = ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z)))))) + t) / t_1
    if (t_2 <= 2d+248) then
        tmp = t_2
    else
        tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_2 = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / t_1;
	double tmp;
	if (t_2 <= 2e+248) {
		tmp = t_2;
	} else {
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	t_2 = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / t_1
	tmp = 0
	if t_2 <= 2e+248:
		tmp = t_2
	else:
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	t_2 = Float64(Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))) + t) / t_1)
	tmp = 0.0
	if (t_2 <= 2e+248)
		tmp = t_2;
	else
		tmp = Float64(Float64(t / t_1) + Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	t_2 = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / t_1;
	tmp = 0.0;
	if (t_2 <= 2e+248)
		tmp = t_2;
	else
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, 2e+248], t$95$2, N[(N[(t / t$95$1), $MachinePrecision] + N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < 2.00000000000000009e248

   1. Initial program 91.7%

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

   if 2.00000000000000009e248 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 3.7%

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

   2. Taylor expanded in t around 0 3.7%

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

   3. Taylor expanded in y around inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq 2 \cdot 10^{+248}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \left(x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\right)\\ \end{array} \]

Alternative 4: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.55e+111)
   x
   (if (<= y -2.3e+15)
     (/ (+ (* x y) z) a)
     (if (<= y -1.95e+15)
       x
       (if (<= y 1.9e+39)
         (/
          (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
          (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
         (- (+ x (/ z y)) (/ (* x a) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.55e+111) {
		tmp = x;
	} else if (y <= -2.3e+15) {
		tmp = ((x * y) + z) / a;
	} else if (y <= -1.95e+15) {
		tmp = x;
	} else if (y <= 1.9e+39) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (x + (z / y)) - ((x * a) / 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 <= (-1.55d+111)) then
        tmp = x
    else if (y <= (-2.3d+15)) then
        tmp = ((x * y) + z) / a
    else if (y <= (-1.95d+15)) then
        tmp = x
    else if (y <= 1.9d+39) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = (x + (z / y)) - ((x * a) / 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 <= -1.55e+111) {
		tmp = x;
	} else if (y <= -2.3e+15) {
		tmp = ((x * y) + z) / a;
	} else if (y <= -1.95e+15) {
		tmp = x;
	} else if (y <= 1.9e+39) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.55e+111:
		tmp = x
	elif y <= -2.3e+15:
		tmp = ((x * y) + z) / a
	elif y <= -1.95e+15:
		tmp = x
	elif y <= 1.9e+39:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.55e+111)
		tmp = x;
	elseif (y <= -2.3e+15)
		tmp = Float64(Float64(Float64(x * y) + z) / a);
	elseif (y <= -1.95e+15)
		tmp = x;
	elseif (y <= 1.9e+39)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.55e+111)
		tmp = x;
	elseif (y <= -2.3e+15)
		tmp = ((x * y) + z) / a;
	elseif (y <= -1.95e+15)
		tmp = x;
	elseif (y <= 1.9e+39)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.55e+111], x, If[LessEqual[y, -2.3e+15], N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -1.95e+15], x, If[LessEqual[y, 1.9e+39], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.55e111 or -2.3e15 < y < -1.95e15

   1. Initial program 1.9%

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

   2. Taylor expanded in y around inf 80.8%

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

   if -1.55e111 < y < -2.3e15

   1. Initial program 28.6%

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

   2. Taylor expanded in a around inf 0.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)\right) \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)}{{a}^{2} \cdot {y}^{6}} + \left(\frac{t}{a \cdot {y}^{3}} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{a \cdot {y}^{2}}\right)} \]

   3. Taylor expanded in y around -inf 24.1%

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

      1. +-commutative 24.1%

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

      2. mul-1-neg 24.1%

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

      3. unsub-neg 24.1%

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

   5. Simplified 30.6%

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

   6. Taylor expanded in a around inf 31.7%

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

      1. sub-neg 31.7%

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

      2. mul-1-neg 31.7%

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

      3. remove-double-neg 31.7%

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

      4. *-commutative 31.7%

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

   8. Simplified 31.7%

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

   if -1.95e15 < y < 1.8999999999999999e39

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 88.9%

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

      1. *-commutative 88.9%

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

   4. Simplified 88.9%

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

   if 1.8999999999999999e39 < y

   1. Initial program 4.0%

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

   2. Taylor expanded in y around inf 66.9%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 5: 81.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+55} \lor \neg \left(y \leq 1.2 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{t}{t_1} + \left(x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (or (<= y -6.5e+55) (not (<= y 1.2e+36)))
     (+ (/ t t_1) (+ x (- (/ z y) (/ a (/ y x)))))
     (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) 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 * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if ((y <= -6.5e+55) || !(y <= 1.2e+36)) {
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / 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 * ((y * (y + a)) + b)) + c)) + i
    if ((y <= (-6.5d+55)) .or. (.not. (y <= 1.2d+36))) then
        tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))))
    else
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / 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 * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if ((y <= -6.5e+55) || !(y <= 1.2e+36)) {
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	tmp = 0
	if (y <= -6.5e+55) or not (y <= 1.2e+36):
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))))
	else:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if ((y <= -6.5e+55) || !(y <= 1.2e+36))
		tmp = Float64(Float64(t / t_1) + Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x)))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	tmp = 0.0;
	if ((y <= -6.5e+55) || ~((y <= 1.2e+36)))
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))));
	else
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / 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 * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[Or[LessEqual[y, -6.5e+55], N[Not[LessEqual[y, 1.2e+36]], $MachinePrecision]], N[(N[(t / t$95$1), $MachinePrecision] + N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000027e55 or 1.19999999999999996e36 < y

   1. Initial program 2.1%

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

   2. Taylor expanded in t around 0 2.1%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. associate-/l* 75.7%

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

   5. Simplified 75.7%

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

   if -6.50000000000000027e55 < y < 1.19999999999999996e36

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf 90.5%

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

      1. *-commutative 90.5%

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

      2. unpow2 90.5%

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

   4. Simplified 90.5%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+55} \lor \neg \left(y \leq 1.2 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \left(x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 6: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+56} \lor \neg \left(y \leq 1.65 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{t}{t_1} + \left(x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (or (<= y -2.6e+56) (not (<= y 1.65e+38)))
     (+ (/ t t_1) (+ x (- (/ z y) (/ a (/ y x)))))
     (/ (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))))) 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 * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if ((y <= -2.6e+56) || !(y <= 1.65e+38)) {
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / 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 * ((y * (y + a)) + b)) + c)) + i
    if ((y <= (-2.6d+56)) .or. (.not. (y <= 1.65d+38))) then
        tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / 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 * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if ((y <= -2.6e+56) || !(y <= 1.65e+38)) {
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	tmp = 0
	if (y <= -2.6e+56) or not (y <= 1.65e+38):
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if ((y <= -2.6e+56) || !(y <= 1.65e+38))
		tmp = Float64(Float64(t / t_1) + Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x)))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	tmp = 0.0;
	if ((y <= -2.6e+56) || ~((y <= 1.65e+38)))
		tmp = (t / t_1) + (x + ((z / y) - (a / (y / x))));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / 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 * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[Or[LessEqual[y, -2.6e+56], N[Not[LessEqual[y, 1.65e+38]], $MachinePrecision]], N[(N[(t / t$95$1), $MachinePrecision] + N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000011e56 or 1.65e38 < y

   1. Initial program 2.1%

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

   2. Taylor expanded in t around 0 2.1%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. associate-/l* 75.7%

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

   5. Simplified 75.7%

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

   if -2.60000000000000011e56 < y < 1.65e38

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0 92.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+56} \lor \neg \left(y \leq 1.65 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \left(x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 7: 77.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.45e+60)
   x
   (if (<= y 2.8e+45)
     (/
      (+ t (* y (+ 230661.510616 (* z (* y y)))))
      (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
     (- (+ x (/ z y)) (/ (* x a) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.45e+60) {
		tmp = x;
	} else if (y <= 2.8e+45) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (x + (z / y)) - ((x * a) / 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 <= (-2.45d+60)) then
        tmp = x
    else if (y <= 2.8d+45) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = (x + (z / y)) - ((x * a) / 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 <= -2.45e+60) {
		tmp = x;
	} else if (y <= 2.8e+45) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.45e+60:
		tmp = x
	elif y <= 2.8e+45:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.45e+60)
		tmp = x;
	elseif (y <= 2.8e+45)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.45e+60)
		tmp = x;
	elseif (y <= 2.8e+45)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.45e+60], x, If[LessEqual[y, 2.8e+45], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4500000000000001e60

   1. Initial program 0.2%

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

   2. Taylor expanded in y around inf 71.2%

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

   if -2.4500000000000001e60 < y < 2.7999999999999999e45

   1. Initial program 96.2%

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

   2. Taylor expanded in z around inf 89.9%

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

      1. *-commutative 89.9%

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

      2. unpow2 89.9%

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

   4. Simplified 89.9%

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

   if 2.7999999999999999e45 < y

   1. Initial program 4.0%

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

   2. Taylor expanded in y around inf 66.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 8: 68.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq -450000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-84}:\\ \;\;\;\;\frac{t_1}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-186}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{t_1}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y (+ 230661.510616 (* z (* y y)))))))
   (if (<= y -4.4e+109)
     x
     (if (<= y -2.6e+15)
       (/ (+ (* x y) z) a)
       (if (<= y -450000.0)
         x
         (if (<= y -1.4e-84)
           (/ t_1 (+ i (* b (* y y))))
           (if (<= y -1.4e-186)
             (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
             (if (<= y 4.2e+33)
               (/ t_1 (+ i (* y c)))
               (- (+ x (/ z y)) (/ (* x a) y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * (230661.510616 + (z * (y * y))));
	double tmp;
	if (y <= -4.4e+109) {
		tmp = x;
	} else if (y <= -2.6e+15) {
		tmp = ((x * y) + z) / a;
	} else if (y <= -450000.0) {
		tmp = x;
	} else if (y <= -1.4e-84) {
		tmp = t_1 / (i + (b * (y * y)));
	} else if (y <= -1.4e-186) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 4.2e+33) {
		tmp = t_1 / (i + (y * c));
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y * (230661.510616d0 + (z * (y * y))))
    if (y <= (-4.4d+109)) then
        tmp = x
    else if (y <= (-2.6d+15)) then
        tmp = ((x * y) + z) / a
    else if (y <= (-450000.0d0)) then
        tmp = x
    else if (y <= (-1.4d-84)) then
        tmp = t_1 / (i + (b * (y * y)))
    else if (y <= (-1.4d-186)) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= 4.2d+33) then
        tmp = t_1 / (i + (y * c))
    else
        tmp = (x + (z / y)) - ((x * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * (230661.510616 + (z * (y * y))));
	double tmp;
	if (y <= -4.4e+109) {
		tmp = x;
	} else if (y <= -2.6e+15) {
		tmp = ((x * y) + z) / a;
	} else if (y <= -450000.0) {
		tmp = x;
	} else if (y <= -1.4e-84) {
		tmp = t_1 / (i + (b * (y * y)));
	} else if (y <= -1.4e-186) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 4.2e+33) {
		tmp = t_1 / (i + (y * c));
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * (230661.510616 + (z * (y * y))))
	tmp = 0
	if y <= -4.4e+109:
		tmp = x
	elif y <= -2.6e+15:
		tmp = ((x * y) + z) / a
	elif y <= -450000.0:
		tmp = x
	elif y <= -1.4e-84:
		tmp = t_1 / (i + (b * (y * y)))
	elif y <= -1.4e-186:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= 4.2e+33:
		tmp = t_1 / (i + (y * c))
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y)))))
	tmp = 0.0
	if (y <= -4.4e+109)
		tmp = x;
	elseif (y <= -2.6e+15)
		tmp = Float64(Float64(Float64(x * y) + z) / a);
	elseif (y <= -450000.0)
		tmp = x;
	elseif (y <= -1.4e-84)
		tmp = Float64(t_1 / Float64(i + Float64(b * Float64(y * y))));
	elseif (y <= -1.4e-186)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= 4.2e+33)
		tmp = Float64(t_1 / Float64(i + Float64(y * c)));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * (230661.510616 + (z * (y * y))));
	tmp = 0.0;
	if (y <= -4.4e+109)
		tmp = x;
	elseif (y <= -2.6e+15)
		tmp = ((x * y) + z) / a;
	elseif (y <= -450000.0)
		tmp = x;
	elseif (y <= -1.4e-84)
		tmp = t_1 / (i + (b * (y * y)));
	elseif (y <= -1.4e-186)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= 4.2e+33)
		tmp = t_1 / (i + (y * c));
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+109], x, If[LessEqual[y, -2.6e+15], N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -450000.0], x, If[LessEqual[y, -1.4e-84], N[(t$95$1 / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-186], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+33], N[(t$95$1 / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.3999999999999998e109 or -2.6e15 < y < -4.5e5

   1. Initial program 3.7%

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

   2. Taylor expanded in y around inf 79.4%

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

   if -4.3999999999999998e109 < y < -2.6e15

   1. Initial program 28.6%

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

   2. Taylor expanded in a around inf 0.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)\right) \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)}{{a}^{2} \cdot {y}^{6}} + \left(\frac{t}{a \cdot {y}^{3}} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{a \cdot {y}^{2}}\right)} \]

   3. Taylor expanded in y around -inf 24.1%

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

      1. +-commutative 24.1%

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

      2. mul-1-neg 24.1%

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

      3. unsub-neg 24.1%

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

   5. Simplified 30.6%

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

   6. Taylor expanded in a around inf 31.7%

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

      1. sub-neg 31.7%

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

      2. mul-1-neg 31.7%

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

      3. remove-double-neg 31.7%

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

      4. *-commutative 31.7%

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

   8. Simplified 31.7%

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

   if -4.5e5 < y < -1.39999999999999991e-84

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 88.7%

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

      1. *-commutative 88.7%

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

      2. unpow2 88.7%

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

   4. Simplified 88.7%

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

   5. Taylor expanded in b around inf 70.7%

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

      1. unpow2 70.7%

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

   7. Simplified 70.7%

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

   if -1.39999999999999991e-84 < y < -1.39999999999999992e-186

   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 t around inf 90.4%

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

   if -1.39999999999999992e-186 < y < 4.2000000000000001e33

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 95.1%

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

      1. *-commutative 95.1%

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

      2. unpow2 95.1%

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

   4. Simplified 95.1%

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

   5. Taylor expanded in y around 0 85.9%

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

      1. *-commutative 85.9%

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

   7. Simplified 85.9%

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

   if 4.2000000000000001e33 < y

   1. Initial program 4.0%

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

   2. Taylor expanded in y around inf 66.9%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq -450000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-84}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-186}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 9: 72.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -7.8e+108)
   x
   (if (<= y -2.15e-10)
     (/ (+ (* x y) z) a)
     (if (<= y 1.2e+40)
       (/
        (+ t (* y 230661.510616))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (- (+ x (/ z y)) (/ (* x a) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -7.8e+108) {
		tmp = x;
	} else if (y <= -2.15e-10) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 1.2e+40) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (x + (z / y)) - ((x * a) / 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 <= (-7.8d+108)) then
        tmp = x
    else if (y <= (-2.15d-10)) then
        tmp = ((x * y) + z) / a
    else if (y <= 1.2d+40) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = (x + (z / y)) - ((x * a) / 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 <= -7.8e+108) {
		tmp = x;
	} else if (y <= -2.15e-10) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 1.2e+40) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -7.8e+108:
		tmp = x
	elif y <= -2.15e-10:
		tmp = ((x * y) + z) / a
	elif y <= 1.2e+40:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -7.8e+108)
		tmp = x;
	elseif (y <= -2.15e-10)
		tmp = Float64(Float64(Float64(x * y) + z) / a);
	elseif (y <= 1.2e+40)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -7.8e+108)
		tmp = x;
	elseif (y <= -2.15e-10)
		tmp = ((x * y) + z) / a;
	elseif (y <= 1.2e+40)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -7.8e+108], x, If[LessEqual[y, -2.15e-10], N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.2e+40], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.79999999999999969e108

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 80.4%

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

   if -7.79999999999999969e108 < y < -2.15000000000000007e-10

   1. Initial program 46.2%

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

   2. Taylor expanded in a around inf 0.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)\right) \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)}{{a}^{2} \cdot {y}^{6}} + \left(\frac{t}{a \cdot {y}^{3}} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{a \cdot {y}^{2}}\right)} \]

   3. Taylor expanded in y around -inf 18.5%

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

      1. +-commutative 18.5%

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

      2. mul-1-neg 18.5%

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

      3. unsub-neg 18.5%

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

   5. Simplified 23.4%

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

   6. Taylor expanded in a around inf 29.3%

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

      1. sub-neg 29.3%

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

      2. mul-1-neg 29.3%

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

      3. remove-double-neg 29.3%

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

      4. *-commutative 29.3%

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

   8. Simplified 29.3%

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

   if -2.15000000000000007e-10 < y < 1.2e40

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 90.1%

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

      1. *-commutative 90.1%

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

   4. Simplified 90.1%

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

   if 1.2e40 < y

   1. Initial program 4.0%

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

   2. Taylor expanded in y around inf 66.9%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 10: 65.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.05e+111)
   x
   (if (<= y -2.15e-10)
     (/ (+ (* x y) z) a)
     (if (<= y 3.8e+31)
       (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (- (+ x (/ z y)) (/ (* x a) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.05e+111) {
		tmp = x;
	} else if (y <= -2.15e-10) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 3.8e+31) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (x + (z / y)) - ((x * a) / 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 <= (-1.05d+111)) then
        tmp = x
    else if (y <= (-2.15d-10)) then
        tmp = ((x * y) + z) / a
    else if (y <= 3.8d+31) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else
        tmp = (x + (z / y)) - ((x * a) / 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 <= -1.05e+111) {
		tmp = x;
	} else if (y <= -2.15e-10) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 3.8e+31) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.05e+111:
		tmp = x
	elif y <= -2.15e-10:
		tmp = ((x * y) + z) / a
	elif y <= 3.8e+31:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.05e+111)
		tmp = x;
	elseif (y <= -2.15e-10)
		tmp = Float64(Float64(Float64(x * y) + z) / a);
	elseif (y <= 3.8e+31)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.05e+111)
		tmp = x;
	elseif (y <= -2.15e-10)
		tmp = ((x * y) + z) / a;
	elseif (y <= 3.8e+31)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.05e+111], x, If[LessEqual[y, -2.15e-10], N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 3.8e+31], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.04999999999999997e111

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 80.4%

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

   if -1.04999999999999997e111 < y < -2.15000000000000007e-10

   1. Initial program 46.2%

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

   2. Taylor expanded in a around inf 0.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)\right) \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)}{{a}^{2} \cdot {y}^{6}} + \left(\frac{t}{a \cdot {y}^{3}} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{a \cdot {y}^{2}}\right)} \]

   3. Taylor expanded in y around -inf 18.5%

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

      1. +-commutative 18.5%

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

      2. mul-1-neg 18.5%

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

      3. unsub-neg 18.5%

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

   5. Simplified 23.4%

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

   6. Taylor expanded in a around inf 29.3%

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

      1. sub-neg 29.3%

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

      2. mul-1-neg 29.3%

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

      3. remove-double-neg 29.3%

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

      4. *-commutative 29.3%

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

   8. Simplified 29.3%

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

   if -2.15000000000000007e-10 < y < 3.8000000000000001e31

   1. Initial program 98.9%

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

   2. Taylor expanded in t around inf 79.7%

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

   if 3.8000000000000001e31 < y

   1. Initial program 4.0%

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

   2. Taylor expanded in y around inf 66.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 11: 70.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.6e+109)
   x
   (if (<= y -2.15e-10)
     (/ (+ (* x y) z) a)
     (if (<= y 3.5e+35)
       (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) (+ i (* y c)))
       (- (+ x (/ z y)) (/ (* x a) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.6e+109) {
		tmp = x;
	} else if (y <= -2.15e-10) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 3.5e+35) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c));
	} else {
		tmp = (x + (z / y)) - ((x * a) / 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 <= (-3.6d+109)) then
        tmp = x
    else if (y <= (-2.15d-10)) then
        tmp = ((x * y) + z) / a
    else if (y <= 3.5d+35) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / (i + (y * c))
    else
        tmp = (x + (z / y)) - ((x * a) / 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 <= -3.6e+109) {
		tmp = x;
	} else if (y <= -2.15e-10) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 3.5e+35) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c));
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.6e+109:
		tmp = x
	elif y <= -2.15e-10:
		tmp = ((x * y) + z) / a
	elif y <= 3.5e+35:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c))
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.6e+109)
		tmp = x;
	elseif (y <= -2.15e-10)
		tmp = Float64(Float64(Float64(x * y) + z) / a);
	elseif (y <= 3.5e+35)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / Float64(i + Float64(y * c)));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.6e+109)
		tmp = x;
	elseif (y <= -2.15e-10)
		tmp = ((x * y) + z) / a;
	elseif (y <= 3.5e+35)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / (i + (y * c));
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.6e+109], x, If[LessEqual[y, -2.15e-10], N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 3.5e+35], 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], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.6e109

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 80.4%

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

   if -3.6e109 < y < -2.15000000000000007e-10

   1. Initial program 46.2%

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

   2. Taylor expanded in a around inf 0.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)\right) \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)}{{a}^{2} \cdot {y}^{6}} + \left(\frac{t}{a \cdot {y}^{3}} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{a \cdot {y}^{2}}\right)} \]

   3. Taylor expanded in y around -inf 18.5%

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

      1. +-commutative 18.5%

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

      2. mul-1-neg 18.5%

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

      3. unsub-neg 18.5%

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

   5. Simplified 23.4%

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

   6. Taylor expanded in a around inf 29.3%

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

      1. sub-neg 29.3%

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

      2. mul-1-neg 29.3%

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

      3. remove-double-neg 29.3%

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

      4. *-commutative 29.3%

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

   8. Simplified 29.3%

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

   if -2.15000000000000007e-10 < y < 3.5000000000000001e35

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 96.4%

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

      1. *-commutative 96.4%

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

      2. unpow2 96.4%

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

   4. Simplified 96.4%

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

   5. Taylor expanded in y around 0 82.3%

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

      1. *-commutative 82.3%

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

   7. Simplified 82.3%

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

   if 3.5000000000000001e35 < y

   1. Initial program 4.0%

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

   2. Taylor expanded in y around inf 66.9%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 12: 61.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{i + y \cdot c} + 230661.510616 \cdot \frac{y}{i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.8e+108)
   x
   (if (<= y -5.6e-45)
     (/ (+ (* x y) z) a)
     (if (<= y 5.6e-5)
       (+ (/ t (+ i (* y c))) (* 230661.510616 (/ y i)))
       (- (+ x (/ z y)) (/ (* x a) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5.8e+108) {
		tmp = x;
	} else if (y <= -5.6e-45) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 5.6e-5) {
		tmp = (t / (i + (y * c))) + (230661.510616 * (y / i));
	} else {
		tmp = (x + (z / y)) - ((x * a) / 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 <= (-5.8d+108)) then
        tmp = x
    else if (y <= (-5.6d-45)) then
        tmp = ((x * y) + z) / a
    else if (y <= 5.6d-5) then
        tmp = (t / (i + (y * c))) + (230661.510616d0 * (y / i))
    else
        tmp = (x + (z / y)) - ((x * a) / 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 <= -5.8e+108) {
		tmp = x;
	} else if (y <= -5.6e-45) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 5.6e-5) {
		tmp = (t / (i + (y * c))) + (230661.510616 * (y / i));
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.8e+108:
		tmp = x
	elif y <= -5.6e-45:
		tmp = ((x * y) + z) / a
	elif y <= 5.6e-5:
		tmp = (t / (i + (y * c))) + (230661.510616 * (y / i))
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.8e+108)
		tmp = x;
	elseif (y <= -5.6e-45)
		tmp = Float64(Float64(Float64(x * y) + z) / a);
	elseif (y <= 5.6e-5)
		tmp = Float64(Float64(t / Float64(i + Float64(y * c))) + Float64(230661.510616 * Float64(y / i)));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -5.8e+108)
		tmp = x;
	elseif (y <= -5.6e-45)
		tmp = ((x * y) + z) / a;
	elseif (y <= 5.6e-5)
		tmp = (t / (i + (y * c))) + (230661.510616 * (y / i));
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.8e+108], x, If[LessEqual[y, -5.6e-45], N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 5.6e-5], N[(N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.80000000000000015e108

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 80.4%

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

   if -5.80000000000000015e108 < y < -5.6000000000000003e-45

   1. Initial program 58.4%

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

   2. Taylor expanded in a around inf 8.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)\right) \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)}{{a}^{2} \cdot {y}^{6}} + \left(\frac{t}{a \cdot {y}^{3}} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{a \cdot {y}^{2}}\right)} \]

   3. Taylor expanded in y around -inf 19.1%

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

      1. +-commutative 19.1%

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

      2. mul-1-neg 19.1%

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

      3. unsub-neg 19.1%

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

   5. Simplified 22.8%

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

   6. Taylor expanded in a around inf 27.3%

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

      1. sub-neg 27.3%

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

      2. mul-1-neg 27.3%

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

      3. remove-double-neg 27.3%

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

      4. *-commutative 27.3%

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

   8. Simplified 27.3%

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

   if -5.6000000000000003e-45 < y < 5.59999999999999992e-5

   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 t around 0 99.7%

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

   3. Taylor expanded in y around 0 79.0%

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

   4. Taylor expanded in y around 0 76.2%

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

      1. *-commutative 76.2%

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

   6. Simplified 76.2%

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

   if 5.59999999999999992e-5 < y

   1. Initial program 12.6%

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

   2. Taylor expanded in y around inf 60.4%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{i + y \cdot c} + 230661.510616 \cdot \frac{y}{i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 13: 57.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.1e+111)
   x
   (if (<= y -1.5e-43)
     (/ (+ (* x y) z) a)
     (if (<= y 4.9e-5)
       (/ (+ t (* y 230661.510616)) i)
       (- (+ x (/ z y)) (/ (* x a) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.1e+111) {
		tmp = x;
	} else if (y <= -1.5e-43) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 4.9e-5) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = (x + (z / y)) - ((x * a) / 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 <= (-1.1d+111)) then
        tmp = x
    else if (y <= (-1.5d-43)) then
        tmp = ((x * y) + z) / a
    else if (y <= 4.9d-5) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = (x + (z / y)) - ((x * a) / 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 <= -1.1e+111) {
		tmp = x;
	} else if (y <= -1.5e-43) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 4.9e-5) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.1e+111:
		tmp = x
	elif y <= -1.5e-43:
		tmp = ((x * y) + z) / a
	elif y <= 4.9e-5:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.1e+111)
		tmp = x;
	elseif (y <= -1.5e-43)
		tmp = Float64(Float64(Float64(x * y) + z) / a);
	elseif (y <= 4.9e-5)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.1e+111)
		tmp = x;
	elseif (y <= -1.5e-43)
		tmp = ((x * y) + z) / a;
	elseif (y <= 4.9e-5)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = (x + (z / y)) - ((x * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.1e+111], x, If[LessEqual[y, -1.5e-43], N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 4.9e-5], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.09999999999999999e111

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 80.4%

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

   if -1.09999999999999999e111 < y < -1.50000000000000002e-43

   1. Initial program 58.4%

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

   2. Taylor expanded in a around inf 8.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)\right) \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)}{{a}^{2} \cdot {y}^{6}} + \left(\frac{t}{a \cdot {y}^{3}} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{a \cdot {y}^{2}}\right)} \]

   3. Taylor expanded in y around -inf 19.1%

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

      1. +-commutative 19.1%

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

      2. mul-1-neg 19.1%

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

      3. unsub-neg 19.1%

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

   5. Simplified 22.8%

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

   6. Taylor expanded in a around inf 27.3%

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

      1. sub-neg 27.3%

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

      2. mul-1-neg 27.3%

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

      3. remove-double-neg 27.3%

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

      4. *-commutative 27.3%

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

   8. Simplified 27.3%

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

   if -1.50000000000000002e-43 < y < 4.9e-5

   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 t around 0 99.7%

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

   3. Taylor expanded in y around 0 79.0%

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

   4. Taylor expanded in i around inf 64.4%

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

   5. Taylor expanded in i around 0 64.5%

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

      1. *-commutative 64.5%

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

   7. Simplified 64.5%

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

   if 4.9e-5 < y

   1. Initial program 12.6%

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

   2. Taylor expanded in y around inf 60.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]

Alternative 14: 55.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.5e+108)
   x
   (if (<= y -1.5e-43)
     (/ (+ (* x y) z) a)
     (if (<= y 1.45e-5) (/ (+ t (* y 230661.510616)) i) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.5e+108) {
		tmp = x;
	} else if (y <= -1.5e-43) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 1.45e-5) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-4.5d+108)) then
        tmp = x
    else if (y <= (-1.5d-43)) then
        tmp = ((x * y) + z) / a
    else if (y <= 1.45d-5) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.5e+108) {
		tmp = x;
	} else if (y <= -1.5e-43) {
		tmp = ((x * y) + z) / a;
	} else if (y <= 1.45e-5) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -4.5e+108:
		tmp = x
	elif y <= -1.5e-43:
		tmp = ((x * y) + z) / a
	elif y <= 1.45e-5:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.5e+108)
		tmp = x;
	elseif (y <= -1.5e-43)
		tmp = Float64(Float64(Float64(x * y) + z) / a);
	elseif (y <= 1.45e-5)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -4.5e+108)
		tmp = x;
	elseif (y <= -1.5e-43)
		tmp = ((x * y) + z) / a;
	elseif (y <= 1.45e-5)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.5e+108], x, If[LessEqual[y, -1.5e-43], N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.45e-5], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5e108 or 1.45e-5 < y

   1. Initial program 7.1%

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

   2. Taylor expanded in y around inf 61.2%

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

   if -4.5e108 < y < -1.50000000000000002e-43

   1. Initial program 58.4%

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

   2. Taylor expanded in a around inf 8.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)\right) \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)\right)}{{a}^{2} \cdot {y}^{6}} + \left(\frac{t}{a \cdot {y}^{3}} + \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)}{a \cdot {y}^{2}}\right)} \]

   3. Taylor expanded in y around -inf 19.1%

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

      1. +-commutative 19.1%

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

      2. mul-1-neg 19.1%

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

      3. unsub-neg 19.1%

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

   5. Simplified 22.8%

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

   6. Taylor expanded in a around inf 27.3%

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

      1. sub-neg 27.3%

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

      2. mul-1-neg 27.3%

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

      3. remove-double-neg 27.3%

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

      4. *-commutative 27.3%

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

   8. Simplified 27.3%

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

   if -1.50000000000000002e-43 < y < 1.45e-5

   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 t around 0 99.7%

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

   3. Taylor expanded in y around 0 79.0%

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

   4. Taylor expanded in i around inf 64.4%

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

   5. Taylor expanded in i around 0 64.5%

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

      1. *-commutative 64.5%

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

   7. Simplified 64.5%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot y + z}{a}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 55.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -960:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -960.0) x (if (<= y 6e-5) (/ (+ t (* y 230661.510616)) i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -960.0) {
		tmp = x;
	} else if (y <= 6e-5) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-960.0d0)) then
        tmp = x
    else if (y <= 6d-5) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -960.0) {
		tmp = x;
	} else if (y <= 6e-5) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -960.0:
		tmp = x
	elif y <= 6e-5:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -960.0)
		tmp = x;
	elseif (y <= 6e-5)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -960.0)
		tmp = x;
	elseif (y <= 6e-5)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -960.0], x, If[LessEqual[y, 6e-5], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -960 or 6.00000000000000015e-5 < y

   1. Initial program 10.9%

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

   2. Taylor expanded in y around inf 54.6%

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

   if -960 < y < 6.00000000000000015e-5

   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 t around 0 99.6%

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

   3. Taylor expanded in y around 0 74.3%

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

   4. Taylor expanded in i around inf 60.7%

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

   5. Taylor expanded in i around 0 60.8%

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

      1. *-commutative 60.8%

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

   7. Simplified 60.8%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -960:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 51.5% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -520:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -520.0) x (if (<= y 1.9e-5) (/ 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 <= -520.0) {
		tmp = x;
	} else if (y <= 1.9e-5) {
		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 <= (-520.0d0)) then
        tmp = x
    else if (y <= 1.9d-5) 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 <= -520.0) {
		tmp = x;
	} else if (y <= 1.9e-5) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -520.0:
		tmp = x
	elif y <= 1.9e-5:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -520.0)
		tmp = x;
	elseif (y <= 1.9e-5)
		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 <= -520.0)
		tmp = x;
	elseif (y <= 1.9e-5)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -520.0], x, If[LessEqual[y, 1.9e-5], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -520 or 1.9000000000000001e-5 < y

   1. Initial program 10.9%

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

   2. Taylor expanded in y around inf 54.6%

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

   if -520 < y < 1.9000000000000001e-5

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 55.4%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -520:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 26.6% 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 53.2%

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

2. Taylor expanded in y around inf 30.2%

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

3. Final simplification 30.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023293 
(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)))