Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 57.1% → 85.1%

Time: 20.6s

Alternatives: 18

Speedup: 2.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 57.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.1% accurate, 0.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/
    (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))
   (+ 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 tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		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 = x + ((z / y) - (a / (y / x)));
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   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. Step-by-step derivation

      1. fma-def 96.2%

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

      2. fma-def 96.2%

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

      3. fma-def 96.2%

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

      4. fma-def 96.2%

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

      5. fma-def 96.2%

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

      6. fma-def 96.2%

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

      7. fma-def 96.2%

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

   3. Simplified 96.2%

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

   if +inf.0 < (/.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 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 68.4%

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

      1. associate--l+ 68.4%

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

      2. associate-/l* 69.2%

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

   4. Simplified 69.2%

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

4. Final simplification 85.9%

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

Alternative 2: 85.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 96.2%

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

   if +inf.0 < (/.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 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 68.4%

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

      1. associate--l+ 68.4%

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

      2. associate-/l* 69.2%

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

   4. Simplified 69.2%

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

4. Final simplification 85.9%

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

Alternative 3: 81.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ t_2 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{t_2}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x)))))
        (t_2 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (<= y -4.3e+43)
     t_1
     (if (<= y 5.5e-5)
       (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) t_2)
       (if (<= y 2.4e+66)
         (/
          (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* y y)))))))
          t_2)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -4.3e+43) {
		tmp = t_1;
	} else if (y <= 5.5e-5) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	} else if (y <= 2.4e+66) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
    if (y <= (-4.3d+43)) then
        tmp = t_1
    else if (y <= 5.5d-5) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / t_2
    else if (y <= 2.4d+66) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (y * y))))))) / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -4.3e+43) {
		tmp = t_1;
	} else if (y <= 5.5e-5) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	} else if (y <= 2.4e+66) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i
	tmp = 0
	if y <= -4.3e+43:
		tmp = t_1
	elif y <= 5.5e-5:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2
	elif y <= 2.4e+66:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	t_2 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if (y <= -4.3e+43)
		tmp = t_1;
	elseif (y <= 5.5e-5)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / t_2);
	elseif (y <= 2.4e+66)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * Float64(y * y))))))) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	tmp = 0.0;
	if (y <= -4.3e+43)
		tmp = t_1;
	elseif (y <= 5.5e-5)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	elseif (y <= 2.4e+66)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -4.3e+43], t$95$1, If[LessEqual[y, 5.5e-5], N[(N[(t + N[(y * N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 2.4e+66], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3e43 or 2.4000000000000002e66 < y

   1. Initial program 4.2%

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

   2. Taylor expanded in y around inf 69.1%

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

      1. associate--l+ 69.1%

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

      2. associate-/l* 69.9%

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

   4. Simplified 69.9%

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

   if -4.3e43 < y < 5.5000000000000002e-5

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 94.9%

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

      1. *-commutative 94.9%

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

      2. unpow2 94.9%

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

   4. Simplified 94.9%

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

   if 5.5000000000000002e-5 < y < 2.4000000000000002e66

   1. Initial program 81.1%

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

   2. Taylor expanded in x around inf 81.5%

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

      1. unpow2 81.5%

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

   4. Simplified 81.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+43}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 4: 76.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y + a\right) + b\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7200000:\\ \;\;\;\;\frac{y \cdot z}{t_1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+38}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot t_1 + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ y a)) b)) (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -1e+102)
     t_2
     (if (<= y -7200000.0)
       (/ (* y z) t_1)
       (if (<= y 1.9e+38)
         (/
          (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
          (+ (* y (+ (* y t_1) c)) i))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * (y + a)) + b;
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1e+102) {
		tmp = t_2;
	} else if (y <= -7200000.0) {
		tmp = (y * z) / t_1;
	} else if (y <= 1.9e+38) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * t_1) + c)) + i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * (y + a)) + b
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-1d+102)) then
        tmp = t_2
    else if (y <= (-7200000.0d0)) then
        tmp = (y * z) / t_1
    else if (y <= 1.9d+38) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * t_1) + c)) + i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * (y + a)) + b;
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -1e+102) {
		tmp = t_2;
	} else if (y <= -7200000.0) {
		tmp = (y * z) / t_1;
	} else if (y <= 1.9e+38) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * t_1) + c)) + i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * (y + a)) + b
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -1e+102:
		tmp = t_2
	elif y <= -7200000.0:
		tmp = (y * z) / t_1
	elif y <= 1.9e+38:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * t_1) + c)) + i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(y + a)) + b)
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -1e+102)
		tmp = t_2;
	elseif (y <= -7200000.0)
		tmp = Float64(Float64(y * z) / t_1);
	elseif (y <= 1.9e+38)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(Float64(y * t_1) + c)) + i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * (y + a)) + b;
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -1e+102)
		tmp = t_2;
	elseif (y <= -7200000.0)
		tmp = (y * z) / t_1;
	elseif (y <= 1.9e+38)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * t_1) + c)) + i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+102], t$95$2, If[LessEqual[y, -7200000.0], N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 1.9e+38], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * t$95$1), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999977e101 or 1.8999999999999999e38 < y

   1. Initial program 3.5%

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

   2. Taylor expanded in y around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -9.99999999999999977e101 < y < -7.2e6

   1. Initial program 30.2%

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

   2. Taylor expanded in z around inf 18.6%

      \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   3. Taylor expanded in c around 0 18.5%

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

      1. associate-/l* 27.5%

         \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}}} \]

      2. unpow2 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \color{blue}{\left(y \cdot y\right)} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}} \]

      3. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(a + y\right) + b\right)}}{z}} \]

      4. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(y \cdot \color{blue}{\left(y + a\right)} + b\right)}{z}} \]

      5. *-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(\color{blue}{\left(y + a\right) \cdot y} + b\right)}{z}} \]

      6. fma-udef 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\mathsf{fma}\left(y + a, y, b\right)}}{z}} \]

   5. Simplified 27.5%

      \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \mathsf{fma}\left(y + a, y, b\right)}{z}}} \]

   6. Taylor expanded in i around 0 49.3%

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

   if -7.2e6 < y < 1.8999999999999999e38

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 85.3%

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

      1. *-commutative 85.3%

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

   4. Simplified 85.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+102}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -7200000:\\ \;\;\;\;\frac{y \cdot z}{y \cdot \left(y + a\right) + b}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+38}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 5: 80.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+45} \lor \neg \left(y \leq 1.56 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.75e+45) (not (<= y 1.56e+38)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* z (* y y)))))
    (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.75e+45) || !(y <= 1.56e+38)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.75d+45)) .or. (.not. (y <= 1.56d+38))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.75e+45) || !(y <= 1.56e+38)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.75e+45) or not (y <= 1.56e+38):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.75e+45) || !(y <= 1.56e+38))
		tmp = 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))))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.75e+45) || ~((y <= 1.56e+38)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.75e+45], N[Not[LessEqual[y, 1.56e+38]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(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]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75000000000000011e45 or 1.5599999999999999e38 < y

   1. Initial program 5.9%

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

   2. Taylor expanded in y around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-/l* 69.0%

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

   4. Simplified 69.0%

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

   if -1.75000000000000011e45 < y < 1.5599999999999999e38

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 91.3%

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

      1. *-commutative 91.3%

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

      2. unpow2 91.3%

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

   4. Simplified 91.3%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+45} \lor \neg \left(y \leq 1.56 \cdot 10^{+38}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 6: 75.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y + a\right) + b\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6300000:\\ \;\;\;\;\frac{y \cdot z}{t_1}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+36}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot t_1 + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ y a)) b)) (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.2e+101)
     t_2
     (if (<= y -6300000.0)
       (/ (* y z) t_1)
       (if (<= y 1.35e+36)
         (/ (+ t (* y 230661.510616)) (+ (* y (+ (* y t_1) c)) i))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * (y + a)) + b;
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+101) {
		tmp = t_2;
	} else if (y <= -6300000.0) {
		tmp = (y * z) / t_1;
	} else if (y <= 1.35e+36) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * t_1) + c)) + i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * (y + a)) + b
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-2.2d+101)) then
        tmp = t_2
    else if (y <= (-6300000.0d0)) then
        tmp = (y * z) / t_1
    else if (y <= 1.35d+36) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * t_1) + c)) + i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * (y + a)) + b;
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+101) {
		tmp = t_2;
	} else if (y <= -6300000.0) {
		tmp = (y * z) / t_1;
	} else if (y <= 1.35e+36) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * t_1) + c)) + i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * (y + a)) + b
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -2.2e+101:
		tmp = t_2
	elif y <= -6300000.0:
		tmp = (y * z) / t_1
	elif y <= 1.35e+36:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * t_1) + c)) + i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(y + a)) + b)
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.2e+101)
		tmp = t_2;
	elseif (y <= -6300000.0)
		tmp = Float64(Float64(y * z) / t_1);
	elseif (y <= 1.35e+36)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * t_1) + c)) + i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * (y + a)) + b;
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.2e+101)
		tmp = t_2;
	elseif (y <= -6300000.0)
		tmp = (y * z) / t_1;
	elseif (y <= 1.35e+36)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * t_1) + c)) + i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+101], t$95$2, If[LessEqual[y, -6300000.0], N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 1.35e+36], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * t$95$1), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2000000000000001e101 or 1.35e36 < y

   1. Initial program 3.5%

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

   2. Taylor expanded in y around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -2.2000000000000001e101 < y < -6.3e6

   1. Initial program 30.2%

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

   2. Taylor expanded in z around inf 18.6%

      \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   3. Taylor expanded in c around 0 18.5%

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

      1. associate-/l* 27.5%

         \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}}} \]

      2. unpow2 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \color{blue}{\left(y \cdot y\right)} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}} \]

      3. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(a + y\right) + b\right)}}{z}} \]

      4. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(y \cdot \color{blue}{\left(y + a\right)} + b\right)}{z}} \]

      5. *-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(\color{blue}{\left(y + a\right) \cdot y} + b\right)}{z}} \]

      6. fma-udef 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\mathsf{fma}\left(y + a, y, b\right)}}{z}} \]

   5. Simplified 27.5%

      \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \mathsf{fma}\left(y + a, y, b\right)}{z}}} \]

   6. Taylor expanded in i around 0 49.3%

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

   if -6.3e6 < y < 1.35e36

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 85.0%

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

      1. *-commutative 85.0%

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

   4. Simplified 85.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -6300000:\\ \;\;\;\;\frac{y \cdot z}{y \cdot \left(y + a\right) + b}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+36}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 7: 74.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -62000:\\ \;\;\;\;\frac{y \cdot z}{y \cdot \left(y + a\right) + b}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.2e+101)
     t_1
     (if (<= y -62000.0)
       (/ (* y z) (+ (* y (+ y a)) b))
       (if (<= y 1.15e+24)
         (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+101) {
		tmp = t_1;
	} else if (y <= -62000.0) {
		tmp = (y * z) / ((y * (y + a)) + b);
	} else if (y <= 1.15e+24) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    if (y <= (-2.2d+101)) then
        tmp = t_1
    else if (y <= (-62000.0d0)) then
        tmp = (y * z) / ((y * (y + a)) + b)
    else if (y <= 1.15d+24) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+101) {
		tmp = t_1;
	} else if (y <= -62000.0) {
		tmp = (y * z) / ((y * (y + a)) + b);
	} else if (y <= 1.15e+24) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -2.2e+101:
		tmp = t_1
	elif y <= -62000.0:
		tmp = (y * z) / ((y * (y + a)) + b)
	elif y <= 1.15e+24:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.2e+101)
		tmp = t_1;
	elseif (y <= -62000.0)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * Float64(y + a)) + b));
	elseif (y <= 1.15e+24)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.2e+101)
		tmp = t_1;
	elseif (y <= -62000.0)
		tmp = (y * z) / ((y * (y + a)) + b);
	elseif (y <= 1.15e+24)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+101], t$95$1, If[LessEqual[y, -62000.0], N[(N[(y * z), $MachinePrecision] / N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+24], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2000000000000001e101 or 1.15e24 < y

   1. Initial program 3.5%

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

   2. Taylor expanded in y around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -2.2000000000000001e101 < y < -62000

   1. Initial program 30.2%

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

   2. Taylor expanded in z around inf 18.6%

      \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   3. Taylor expanded in c around 0 18.5%

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

      1. associate-/l* 27.5%

         \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}}} \]

      2. unpow2 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \color{blue}{\left(y \cdot y\right)} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}} \]

      3. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(a + y\right) + b\right)}}{z}} \]

      4. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(y \cdot \color{blue}{\left(y + a\right)} + b\right)}{z}} \]

      5. *-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(\color{blue}{\left(y + a\right) \cdot y} + b\right)}{z}} \]

      6. fma-udef 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\mathsf{fma}\left(y + a, y, b\right)}}{z}} \]

   5. Simplified 27.5%

      \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \mathsf{fma}\left(y + a, y, b\right)}{z}}} \]

   6. Taylor expanded in i around 0 49.3%

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

   if -62000 < y < 1.15e24

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 85.0%

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

      1. *-commutative 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in y around 0 80.7%

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

      1. *-commutative 80.7%

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

   7. Simplified 80.7%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -62000:\\ \;\;\;\;\frac{y \cdot z}{y \cdot \left(y + a\right) + b}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+24}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 8: 58.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{i + b \cdot \left(y \cdot y\right)}\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.25 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-128}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ t (+ i (* b (* y y))))) (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -9.2e+37)
     t_2
     (if (<= y 4.25e-162)
       t_1
       (if (<= y 6.6e-128)
         (/ (+ t (* y 230661.510616)) (* y c))
         (if (<= y 1.36e+32) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (i + (b * (y * y)));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -9.2e+37) {
		tmp = t_2;
	} else if (y <= 4.25e-162) {
		tmp = t_1;
	} else if (y <= 6.6e-128) {
		tmp = (t + (y * 230661.510616)) / (y * c);
	} else if (y <= 1.36e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (i + (b * (y * y)))
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-9.2d+37)) then
        tmp = t_2
    else if (y <= 4.25d-162) then
        tmp = t_1
    else if (y <= 6.6d-128) then
        tmp = (t + (y * 230661.510616d0)) / (y * c)
    else if (y <= 1.36d+32) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (i + (b * (y * y)));
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -9.2e+37) {
		tmp = t_2;
	} else if (y <= 4.25e-162) {
		tmp = t_1;
	} else if (y <= 6.6e-128) {
		tmp = (t + (y * 230661.510616)) / (y * c);
	} else if (y <= 1.36e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t / (i + (b * (y * y)))
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -9.2e+37:
		tmp = t_2
	elif y <= 4.25e-162:
		tmp = t_1
	elif y <= 6.6e-128:
		tmp = (t + (y * 230661.510616)) / (y * c)
	elif y <= 1.36e+32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t / Float64(i + Float64(b * Float64(y * y))))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -9.2e+37)
		tmp = t_2;
	elseif (y <= 4.25e-162)
		tmp = t_1;
	elseif (y <= 6.6e-128)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(y * c));
	elseif (y <= 1.36e+32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t / (i + (b * (y * y)));
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -9.2e+37)
		tmp = t_2;
	elseif (y <= 4.25e-162)
		tmp = t_1;
	elseif (y <= 6.6e-128)
		tmp = (t + (y * 230661.510616)) / (y * c);
	elseif (y <= 1.36e+32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+37], t$95$2, If[LessEqual[y, 4.25e-162], t$95$1, If[LessEqual[y, 6.6e-128], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.36e+32], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.2000000000000001e37 or 1.3599999999999999e32 < y

   1. Initial program 5.9%

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

   2. Taylor expanded in y around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-/l* 69.0%

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

   4. Simplified 69.0%

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

   if -9.2000000000000001e37 < y < 4.24999999999999977e-162 or 6.6e-128 < y < 1.3599999999999999e32

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 80.6%

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

      1. *-commutative 80.6%

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

   4. Simplified 80.6%

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

   5. Taylor expanded in b around inf 61.1%

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

      1. *-commutative 61.1%

         \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{{y}^{2} \cdot b} + i} \]

      2. unpow2 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in y around 0 57.3%

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

   if 4.24999999999999977e-162 < y < 6.6e-128

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.8%

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

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in c around inf 70.2%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+37}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 4.25 \cdot 10^{-162}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-128}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 9: 69.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -470:\\ \;\;\;\;\frac{y \cdot z}{y \cdot \left(y + a\right) + b}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+28}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.2e+101)
     t_1
     (if (<= y -470.0)
       (/ (* y z) (+ (* y (+ y a)) b))
       (if (<= y -1.6e-63)
         (/ t (+ i (* b (* y y))))
         (if (<= y 1.1e+28)
           (/ (+ t (* y 230661.510616)) (+ i (* y c)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+101) {
		tmp = t_1;
	} else if (y <= -470.0) {
		tmp = (y * z) / ((y * (y + a)) + b);
	} else if (y <= -1.6e-63) {
		tmp = t / (i + (b * (y * y)));
	} else if (y <= 1.1e+28) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    if (y <= (-2.2d+101)) then
        tmp = t_1
    else if (y <= (-470.0d0)) then
        tmp = (y * z) / ((y * (y + a)) + b)
    else if (y <= (-1.6d-63)) then
        tmp = t / (i + (b * (y * y)))
    else if (y <= 1.1d+28) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+101) {
		tmp = t_1;
	} else if (y <= -470.0) {
		tmp = (y * z) / ((y * (y + a)) + b);
	} else if (y <= -1.6e-63) {
		tmp = t / (i + (b * (y * y)));
	} else if (y <= 1.1e+28) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -2.2e+101:
		tmp = t_1
	elif y <= -470.0:
		tmp = (y * z) / ((y * (y + a)) + b)
	elif y <= -1.6e-63:
		tmp = t / (i + (b * (y * y)))
	elif y <= 1.1e+28:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.2e+101)
		tmp = t_1;
	elseif (y <= -470.0)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * Float64(y + a)) + b));
	elseif (y <= -1.6e-63)
		tmp = Float64(t / Float64(i + Float64(b * Float64(y * y))));
	elseif (y <= 1.1e+28)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.2e+101)
		tmp = t_1;
	elseif (y <= -470.0)
		tmp = (y * z) / ((y * (y + a)) + b);
	elseif (y <= -1.6e-63)
		tmp = t / (i + (b * (y * y)));
	elseif (y <= 1.1e+28)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+101], t$95$1, If[LessEqual[y, -470.0], N[(N[(y * z), $MachinePrecision] / N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-63], N[(t / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+28], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2000000000000001e101 or 1.09999999999999993e28 < y

   1. Initial program 3.5%

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

   2. Taylor expanded in y around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -2.2000000000000001e101 < y < -470

   1. Initial program 30.2%

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

   2. Taylor expanded in z around inf 18.6%

      \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   3. Taylor expanded in c around 0 18.5%

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

      1. associate-/l* 27.5%

         \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}}} \]

      2. unpow2 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \color{blue}{\left(y \cdot y\right)} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}} \]

      3. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(a + y\right) + b\right)}}{z}} \]

      4. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(y \cdot \color{blue}{\left(y + a\right)} + b\right)}{z}} \]

      5. *-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(\color{blue}{\left(y + a\right) \cdot y} + b\right)}{z}} \]

      6. fma-udef 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\mathsf{fma}\left(y + a, y, b\right)}}{z}} \]

   5. Simplified 27.5%

      \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \mathsf{fma}\left(y + a, y, b\right)}{z}}} \]

   6. Taylor expanded in i around 0 49.3%

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

   if -470 < y < -1.59999999999999994e-63

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 54.9%

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

      1. *-commutative 54.9%

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

   4. Simplified 54.9%

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

   5. Taylor expanded in b around inf 48.3%

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

      1. *-commutative 48.3%

         \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{{y}^{2} \cdot b} + i} \]

      2. unpow2 48.3%

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

   7. Simplified 48.3%

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

   8. Taylor expanded in y around 0 44.2%

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

   if -1.59999999999999994e-63 < y < 1.09999999999999993e28

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 88.3%

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

      1. *-commutative 88.3%

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

   4. Simplified 88.3%

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

   5. Taylor expanded in y around 0 78.8%

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

      1. *-commutative 78.8%

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

   7. Simplified 78.8%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -470:\\ \;\;\;\;\frac{y \cdot z}{y \cdot \left(y + a\right) + b}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+28}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 10: 70.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot 230661.510616\\ t_2 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -360:\\ \;\;\;\;\frac{y \cdot z}{y \cdot \left(y + a\right) + b}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-49}:\\ \;\;\;\;\frac{t_1}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{t_1}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (* y 230661.510616))) (t_2 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.2e+101)
     t_2
     (if (<= y -360.0)
       (/ (* y z) (+ (* y (+ y a)) b))
       (if (<= y -1.45e-49)
         (/ t_1 (+ i (* b (* y y))))
         (if (<= y 1.15e+25) (/ t_1 (+ i (* y c))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+101) {
		tmp = t_2;
	} else if (y <= -360.0) {
		tmp = (y * z) / ((y * (y + a)) + b);
	} else if (y <= -1.45e-49) {
		tmp = t_1 / (i + (b * (y * y)));
	} else if (y <= 1.15e+25) {
		tmp = t_1 / (i + (y * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * 230661.510616d0)
    t_2 = x + ((z / y) - (a / (y / x)))
    if (y <= (-2.2d+101)) then
        tmp = t_2
    else if (y <= (-360.0d0)) then
        tmp = (y * z) / ((y * (y + a)) + b)
    else if (y <= (-1.45d-49)) then
        tmp = t_1 / (i + (b * (y * y)))
    else if (y <= 1.15d+25) then
        tmp = t_1 / (i + (y * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * 230661.510616);
	double t_2 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+101) {
		tmp = t_2;
	} else if (y <= -360.0) {
		tmp = (y * z) / ((y * (y + a)) + b);
	} else if (y <= -1.45e-49) {
		tmp = t_1 / (i + (b * (y * y)));
	} else if (y <= 1.15e+25) {
		tmp = t_1 / (i + (y * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * 230661.510616)
	t_2 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -2.2e+101:
		tmp = t_2
	elif y <= -360.0:
		tmp = (y * z) / ((y * (y + a)) + b)
	elif y <= -1.45e-49:
		tmp = t_1 / (i + (b * (y * y)))
	elif y <= 1.15e+25:
		tmp = t_1 / (i + (y * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * 230661.510616))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.2e+101)
		tmp = t_2;
	elseif (y <= -360.0)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * Float64(y + a)) + b));
	elseif (y <= -1.45e-49)
		tmp = Float64(t_1 / Float64(i + Float64(b * Float64(y * y))));
	elseif (y <= 1.15e+25)
		tmp = Float64(t_1 / Float64(i + Float64(y * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * 230661.510616);
	t_2 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.2e+101)
		tmp = t_2;
	elseif (y <= -360.0)
		tmp = (y * z) / ((y * (y + a)) + b);
	elseif (y <= -1.45e-49)
		tmp = t_1 / (i + (b * (y * y)));
	elseif (y <= 1.15e+25)
		tmp = t_1 / (i + (y * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+101], t$95$2, If[LessEqual[y, -360.0], N[(N[(y * z), $MachinePrecision] / N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-49], N[(t$95$1 / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+25], N[(t$95$1 / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2000000000000001e101 or 1.1499999999999999e25 < y

   1. Initial program 3.5%

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

   2. Taylor expanded in y around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -2.2000000000000001e101 < y < -360

   1. Initial program 30.2%

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

   2. Taylor expanded in z around inf 18.6%

      \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   3. Taylor expanded in c around 0 18.5%

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

      1. associate-/l* 27.5%

         \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}}} \]

      2. unpow2 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \color{blue}{\left(y \cdot y\right)} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}} \]

      3. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(a + y\right) + b\right)}}{z}} \]

      4. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(y \cdot \color{blue}{\left(y + a\right)} + b\right)}{z}} \]

      5. *-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(\color{blue}{\left(y + a\right) \cdot y} + b\right)}{z}} \]

      6. fma-udef 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\mathsf{fma}\left(y + a, y, b\right)}}{z}} \]

   5. Simplified 27.5%

      \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \mathsf{fma}\left(y + a, y, b\right)}{z}}} \]

   6. Taylor expanded in i around 0 49.3%

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

   if -360 < y < -1.45e-49

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 58.9%

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

      1. *-commutative 58.9%

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

   4. Simplified 58.9%

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

   5. Taylor expanded in b around inf 51.8%

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

      1. *-commutative 51.8%

         \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{{y}^{2} \cdot b} + i} \]

      2. unpow2 51.8%

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

   7. Simplified 51.8%

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

   if -1.45e-49 < y < 1.1499999999999999e25

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 87.6%

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

      1. *-commutative 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in y around 0 78.3%

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

      1. *-commutative 78.3%

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

   7. Simplified 78.3%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -360:\\ \;\;\;\;\frac{y \cdot z}{y \cdot \left(y + a\right) + b}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-49}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 11: 54.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-123}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ t (+ i (* b (* y y))))))
   (if (<= y -1.95e+39)
     x
     (if (<= y -7e-82)
       t_1
       (if (<= y 4.7e-123)
         (/ (+ t (* y 230661.510616)) i)
         (if (<= y 4.5e+35) t_1 x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (i + (b * (y * y)));
	double tmp;
	if (y <= -1.95e+39) {
		tmp = x;
	} else if (y <= -7e-82) {
		tmp = t_1;
	} else if (y <= 4.7e-123) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 4.5e+35) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (i + (b * (y * y)))
    if (y <= (-1.95d+39)) then
        tmp = x
    else if (y <= (-7d-82)) then
        tmp = t_1
    else if (y <= 4.7d-123) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 4.5d+35) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (i + (b * (y * y)));
	double tmp;
	if (y <= -1.95e+39) {
		tmp = x;
	} else if (y <= -7e-82) {
		tmp = t_1;
	} else if (y <= 4.7e-123) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 4.5e+35) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t / (i + (b * (y * y)))
	tmp = 0
	if y <= -1.95e+39:
		tmp = x
	elif y <= -7e-82:
		tmp = t_1
	elif y <= 4.7e-123:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 4.5e+35:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t / Float64(i + Float64(b * Float64(y * y))))
	tmp = 0.0
	if (y <= -1.95e+39)
		tmp = x;
	elseif (y <= -7e-82)
		tmp = t_1;
	elseif (y <= 4.7e-123)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 4.5e+35)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t / (i + (b * (y * y)));
	tmp = 0.0;
	if (y <= -1.95e+39)
		tmp = x;
	elseif (y <= -7e-82)
		tmp = t_1;
	elseif (y <= 4.7e-123)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 4.5e+35)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.95e+39], x, If[LessEqual[y, -7e-82], t$95$1, If[LessEqual[y, 4.7e-123], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 4.5e+35], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.95e39 or 4.4999999999999997e35 < y

   1. Initial program 5.9%

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

   2. Taylor expanded in y around inf 52.4%

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

   if -1.95e39 < y < -6.9999999999999997e-82 or 4.7000000000000002e-123 < y < 4.4999999999999997e35

   1. Initial program 93.1%

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

   2. Taylor expanded in y around 0 58.7%

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

      1. *-commutative 58.7%

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

   4. Simplified 58.7%

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

   5. Taylor expanded in b around inf 37.5%

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

      1. *-commutative 37.5%

         \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{{y}^{2} \cdot b} + i} \]

      2. unpow2 37.5%

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

   7. Simplified 37.5%

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

   8. Taylor expanded in y around 0 33.4%

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

   if -6.9999999999999997e-82 < y < 4.7000000000000002e-123

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 98.0%

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

      1. *-commutative 98.0%

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

   4. Simplified 98.0%

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

   5. Taylor expanded in i around inf 74.2%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-82}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-123}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 51.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ t (+ i (* b (* y y))))))
   (if (<= y -9.2e+39)
     x
     (if (<= y 4.2e-162)
       t_1
       (if (<= y 7.6e-132)
         (/ (+ t (* y 230661.510616)) (* y c))
         (if (<= y 1.26e+29) t_1 x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (i + (b * (y * y)));
	double tmp;
	if (y <= -9.2e+39) {
		tmp = x;
	} else if (y <= 4.2e-162) {
		tmp = t_1;
	} else if (y <= 7.6e-132) {
		tmp = (t + (y * 230661.510616)) / (y * c);
	} else if (y <= 1.26e+29) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (i + (b * (y * y)))
    if (y <= (-9.2d+39)) then
        tmp = x
    else if (y <= 4.2d-162) then
        tmp = t_1
    else if (y <= 7.6d-132) then
        tmp = (t + (y * 230661.510616d0)) / (y * c)
    else if (y <= 1.26d+29) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t / (i + (b * (y * y)));
	double tmp;
	if (y <= -9.2e+39) {
		tmp = x;
	} else if (y <= 4.2e-162) {
		tmp = t_1;
	} else if (y <= 7.6e-132) {
		tmp = (t + (y * 230661.510616)) / (y * c);
	} else if (y <= 1.26e+29) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t / (i + (b * (y * y)))
	tmp = 0
	if y <= -9.2e+39:
		tmp = x
	elif y <= 4.2e-162:
		tmp = t_1
	elif y <= 7.6e-132:
		tmp = (t + (y * 230661.510616)) / (y * c)
	elif y <= 1.26e+29:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t / Float64(i + Float64(b * Float64(y * y))))
	tmp = 0.0
	if (y <= -9.2e+39)
		tmp = x;
	elseif (y <= 4.2e-162)
		tmp = t_1;
	elseif (y <= 7.6e-132)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(y * c));
	elseif (y <= 1.26e+29)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t / (i + (b * (y * y)));
	tmp = 0.0;
	if (y <= -9.2e+39)
		tmp = x;
	elseif (y <= 4.2e-162)
		tmp = t_1;
	elseif (y <= 7.6e-132)
		tmp = (t + (y * 230661.510616)) / (y * c);
	elseif (y <= 1.26e+29)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+39], x, If[LessEqual[y, 4.2e-162], t$95$1, If[LessEqual[y, 7.6e-132], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+29], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.20000000000000047e39 or 1.26e29 < y

   1. Initial program 5.9%

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

   2. Taylor expanded in y around inf 52.4%

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

   if -9.20000000000000047e39 < y < 4.2e-162 or 7.5999999999999994e-132 < y < 1.26e29

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 80.6%

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

      1. *-commutative 80.6%

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

   4. Simplified 80.6%

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

   5. Taylor expanded in b around inf 61.1%

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

      1. *-commutative 61.1%

         \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{{y}^{2} \cdot b} + i} \]

      2. unpow2 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in y around 0 57.3%

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

   if 4.2e-162 < y < 7.5999999999999994e-132

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.8%

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

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in c around inf 70.2%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-162}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 67.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -95000:\\ \;\;\;\;\frac{y \cdot z}{y \cdot \left(y + a\right) + b}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.2e+101)
     t_1
     (if (<= y -95000.0)
       (/ (* y z) (+ (* y (+ y a)) b))
       (if (<= y 1.02e+34) (/ t (+ i (* y (+ c (* y b))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+101) {
		tmp = t_1;
	} else if (y <= -95000.0) {
		tmp = (y * z) / ((y * (y + a)) + b);
	} else if (y <= 1.02e+34) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    if (y <= (-2.2d+101)) then
        tmp = t_1
    else if (y <= (-95000.0d0)) then
        tmp = (y * z) / ((y * (y + a)) + b)
    else if (y <= 1.02d+34) then
        tmp = t / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.2e+101) {
		tmp = t_1;
	} else if (y <= -95000.0) {
		tmp = (y * z) / ((y * (y + a)) + b);
	} else if (y <= 1.02e+34) {
		tmp = t / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -2.2e+101:
		tmp = t_1
	elif y <= -95000.0:
		tmp = (y * z) / ((y * (y + a)) + b)
	elif y <= 1.02e+34:
		tmp = t / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -2.2e+101)
		tmp = t_1;
	elseif (y <= -95000.0)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * Float64(y + a)) + b));
	elseif (y <= 1.02e+34)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -2.2e+101)
		tmp = t_1;
	elseif (y <= -95000.0)
		tmp = (y * z) / ((y * (y + a)) + b);
	elseif (y <= 1.02e+34)
		tmp = t / (i + (y * (c + (y * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+101], t$95$1, If[LessEqual[y, -95000.0], N[(N[(y * z), $MachinePrecision] / N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+34], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2000000000000001e101 or 1.02e34 < y

   1. Initial program 3.5%

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

   2. Taylor expanded in y around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. associate-/l* 76.1%

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

   4. Simplified 76.1%

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

   if -2.2000000000000001e101 < y < -95000

   1. Initial program 30.2%

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

   2. Taylor expanded in z around inf 18.6%

      \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   3. Taylor expanded in c around 0 18.5%

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

      1. associate-/l* 27.5%

         \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + {y}^{2} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}}} \]

      2. unpow2 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \color{blue}{\left(y \cdot y\right)} \cdot \left(b + y \cdot \left(a + y\right)\right)}{z}} \]

      3. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(a + y\right) + b\right)}}{z}} \]

      4. +-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(y \cdot \color{blue}{\left(y + a\right)} + b\right)}{z}} \]

      5. *-commutative 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \left(\color{blue}{\left(y + a\right) \cdot y} + b\right)}{z}} \]

      6. fma-udef 27.5%

         \[\leadsto \frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \color{blue}{\mathsf{fma}\left(y + a, y, b\right)}}{z}} \]

   5. Simplified 27.5%

      \[\leadsto \color{blue}{\frac{{y}^{3}}{\frac{i + \left(y \cdot y\right) \cdot \mathsf{fma}\left(y + a, y, b\right)}{z}}} \]

   6. Taylor expanded in i around 0 49.3%

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

   if -95000 < y < 1.02e34

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 85.0%

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

      1. *-commutative 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in y around 0 80.7%

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

      1. *-commutative 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in y around 0 71.3%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -95000:\\ \;\;\;\;\frac{y \cdot z}{y \cdot \left(y + a\right) + b}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 14: 67.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+40} \lor \neg \left(y \leq 4.1 \cdot 10^{+27}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7.4e+40) (not (<= y 4.1e+27)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/ t (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7.4e+40) || !(y <= 4.1e+27)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-7.4d+40)) .or. (.not. (y <= 4.1d+27))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = t / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7.4e+40) || !(y <= 4.1e+27)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -7.4e+40) or not (y <= 4.1e+27):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -7.4e+40) || !(y <= 4.1e+27))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -7.4e+40) || ~((y <= 4.1e+27)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -7.4e+40], N[Not[LessEqual[y, 4.1e+27]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4e40 or 4.1000000000000002e27 < y

   1. Initial program 5.9%

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

   2. Taylor expanded in y around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. associate-/l* 69.0%

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

   4. Simplified 69.0%

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

   if -7.4e40 < y < 4.1000000000000002e27

   1. Initial program 97.1%

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

   2. Taylor expanded in y around 0 81.9%

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

      1. *-commutative 81.9%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. *-commutative 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in y around 0 68.8%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+40} \lor \neg \left(y \leq 4.1 \cdot 10^{+27}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 15: 53.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3150000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3150000.0)
   x
   (if (<= y 1.2e-6) (+ (* 230661.510616 (/ y i)) (/ 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 <= -3150000.0) {
		tmp = x;
	} else if (y <= 1.2e-6) {
		tmp = (230661.510616 * (y / i)) + (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 <= (-3150000.0d0)) then
        tmp = x
    else if (y <= 1.2d-6) then
        tmp = (230661.510616d0 * (y / i)) + (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 <= -3150000.0) {
		tmp = x;
	} else if (y <= 1.2e-6) {
		tmp = (230661.510616 * (y / i)) + (t / i);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3150000.0:
		tmp = x
	elif y <= 1.2e-6:
		tmp = (230661.510616 * (y / i)) + (t / i)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3150000.0)
		tmp = x;
	elseif (y <= 1.2e-6)
		tmp = Float64(Float64(230661.510616 * Float64(y / i)) + 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 <= -3150000.0)
		tmp = x;
	elseif (y <= 1.2e-6)
		tmp = (230661.510616 * (y / i)) + (t / i);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3150000.0], x, If[LessEqual[y, 1.2e-6], N[(N[(230661.510616 * N[(y / i), $MachinePrecision]), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.15e6 or 1.1999999999999999e-6 < y

   1. Initial program 15.1%

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

   2. Taylor expanded in y around inf 45.8%

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

   if -3.15e6 < y < 1.1999999999999999e-6

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 89.0%

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

      1. *-commutative 89.0%

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

   4. Simplified 89.0%

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

   5. Taylor expanded in b around inf 64.7%

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

      1. *-commutative 64.7%

         \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{{y}^{2} \cdot b} + i} \]

      2. unpow2 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in y around 0 57.5%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3150000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;230661.510616 \cdot \frac{y}{i} + \frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 53.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6500:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -6500.0) x (if (<= y 1.2e-6) (/ (+ 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 <= -6500.0) {
		tmp = x;
	} else if (y <= 1.2e-6) {
		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 <= (-6500.0d0)) then
        tmp = x
    else if (y <= 1.2d-6) 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 <= -6500.0) {
		tmp = x;
	} else if (y <= 1.2e-6) {
		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 <= -6500.0:
		tmp = x
	elif y <= 1.2e-6:
		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 <= -6500.0)
		tmp = x;
	elseif (y <= 1.2e-6)
		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 <= -6500.0)
		tmp = x;
	elseif (y <= 1.2e-6)
		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, -6500.0], x, If[LessEqual[y, 1.2e-6], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -6500 or 1.1999999999999999e-6 < y

   1. Initial program 15.1%

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

   2. Taylor expanded in y around inf 45.8%

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

   if -6500 < y < 1.1999999999999999e-6

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 89.0%

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

      1. *-commutative 89.0%

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

   4. Simplified 89.0%

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

   5. Taylor expanded in i around inf 57.5%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6500:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 49.1% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-65}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.5e-30) x (if (<= y 1.4e-65) (/ 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 <= -3.5e-30) {
		tmp = x;
	} else if (y <= 1.4e-65) {
		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 <= (-3.5d-30)) then
        tmp = x
    else if (y <= 1.4d-65) 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 <= -3.5e-30) {
		tmp = x;
	} else if (y <= 1.4e-65) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.5e-30:
		tmp = x
	elif y <= 1.4e-65:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.5e-30)
		tmp = x;
	elseif (y <= 1.4e-65)
		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 <= -3.5e-30)
		tmp = x;
	elseif (y <= 1.4e-65)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.5e-30], x, If[LessEqual[y, 1.4e-65], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5000000000000003e-30 or 1.4e-65 < y

   1. Initial program 28.0%

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

   2. Taylor expanded in y around inf 39.5%

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

   if -3.5000000000000003e-30 < y < 1.4e-65

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 62.4%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-65}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 25.3% 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 59.7%

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

2. Taylor expanded in y around inf 23.5%

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

3. Final simplification 23.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023297 
(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)))