Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.5% → 83.8%

Time: 36.3s

Alternatives: 17

Speedup: 3.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.5% 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: 83.8% accurate, 0.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
        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 * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + 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(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))) + 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[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 95.4%

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

      1. fma-def 95.4%

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

      2. fma-def 95.4%

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

      3. fma-def 95.4%

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

      4. fma-def 95.4%

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

      5. fma-def 95.4%

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

      6. fma-def 95.4%

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

      7. fma-def 95.4%

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

   3. Simplified 95.4%

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

   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 71.9%

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

      1. associate--l+ 71.9%

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

      2. associate-/l* 76.7%

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

   4. Simplified 76.7%

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

4. Final simplification 89.5%

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

Alternative 2: 83.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
           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 * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + 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 * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + 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 * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + 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(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))) + 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 * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + 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[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 95.4%

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

   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 71.9%

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

      1. associate--l+ 71.9%

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

      2. associate-/l* 76.7%

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

   4. Simplified 76.7%

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

4. Final simplification 89.5%

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

Alternative 3: 80.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ t_2 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;y \leq -3 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{t_2}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+56}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{t_2}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+130}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -3e+50)
     t_1
     (if (<= y 1.12e-6)
       (/ (+ t (* y (+ 230661.510616 (* z (* y y))))) t_2)
       (if (<= y 2.3e+56)
         (/
          (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
          t_2)
         (if (<= y 2.1e+130)
           (+ (+ (/ 27464.7644705 (* y a)) (/ z a)) (/ x (/ a y)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double t_2 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if (y <= -3e+50) {
		tmp = t_1;
	} else if (y <= 1.12e-6) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	} else if (y <= 2.3e+56) {
		tmp = (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) / t_2;
	} else if (y <= 2.1e+130) {
		tmp = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	} 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 <= (-3d+50)) then
        tmp = t_1
    else if (y <= 1.12d-6) then
        tmp = (t + (y * (230661.510616d0 + (z * (y * y))))) / t_2
    else if (y <= 2.3d+56) then
        tmp = (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z)))))) / t_2
    else if (y <= 2.1d+130) then
        tmp = ((27464.7644705d0 / (y * a)) + (z / a)) + (x / (a / y))
    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 <= -3e+50) {
		tmp = t_1;
	} else if (y <= 1.12e-6) {
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	} else if (y <= 2.3e+56) {
		tmp = (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) / t_2;
	} else if (y <= 2.1e+130) {
		tmp = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	} 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 <= -3e+50:
		tmp = t_1
	elif y <= 1.12e-6:
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2
	elif y <= 2.3e+56:
		tmp = (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) / t_2
	elif y <= 2.1e+130:
		tmp = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y))
	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 <= -3e+50)
		tmp = t_1;
	elseif (y <= 1.12e-6)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(z * Float64(y * y))))) / t_2);
	elseif (y <= 2.3e+56)
		tmp = Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))) / t_2);
	elseif (y <= 2.1e+130)
		tmp = Float64(Float64(Float64(27464.7644705 / Float64(y * a)) + Float64(z / a)) + Float64(x / Float64(a / y)));
	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 <= -3e+50)
		tmp = t_1;
	elseif (y <= 1.12e-6)
		tmp = (t + (y * (230661.510616 + (z * (y * y))))) / t_2;
	elseif (y <= 2.3e+56)
		tmp = (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) / t_2;
	elseif (y <= 2.1e+130)
		tmp = ((27464.7644705 / (y * a)) + (z / a)) + (x / (a / y));
	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, -3e+50], t$95$1, If[LessEqual[y, 1.12e-6], 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, 2.3e+56], N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 2.1e+130], N[(N[(N[(27464.7644705 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.9999999999999998e50 or 2.0999999999999999e130 < y

   1. Initial program 2.8%

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

   2. Taylor expanded in y around inf 73.7%

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

      1. associate--l+ 73.7%

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

      2. associate-/l* 79.0%

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

   4. Simplified 79.0%

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

   if -2.9999999999999998e50 < y < 1.12000000000000008e-6

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 90.0%

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

      1. *-commutative 90.0%

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

      2. unpow2 90.0%

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

   4. Simplified 90.0%

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

   if 1.12000000000000008e-6 < y < 2.30000000000000015e56

   1. Initial program 73.7%

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

   2. Taylor expanded in t around 0 73.7%

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

   if 2.30000000000000015e56 < y < 2.0999999999999999e130

   1. Initial program 0.6%

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

   2. Taylor expanded in a around inf 0.7%

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right)}{a \cdot {y}^{3}}} \]

   3. Taylor expanded in y around inf 29.0%

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

      1. associate-+r+ 29.0%

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

      2. associate-*r/ 29.0%

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

      3. metadata-eval 29.0%

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

      4. *-commutative 29.0%

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

      5. associate-/l* 46.3%

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

   5. Simplified 46.3%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+50}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+56}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+130}:\\ \;\;\;\;\left(\frac{27464.7644705}{y \cdot a} + \frac{z}{a}\right) + \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 4: 79.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+45} \lor \neg \left(y \leq 7.5 \cdot 10^{+64}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.05e+45) (not (<= y 7.5e+64)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* 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 <= -1.05e+45) || !(y <= 7.5e+64)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (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 <= (-1.05d+45)) .or. (.not. (y <= 7.5d+64))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (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 <= -1.05e+45) || !(y <= 7.5e+64)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (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 <= -1.05e+45) or not (y <= 7.5e+64):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (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 <= -1.05e+45) || !(y <= 7.5e+64))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * 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 <= -1.05e+45) || ~((y <= 7.5e+64)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (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, -1.05e+45], N[Not[LessEqual[y, 7.5e+64]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $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 < -1.04999999999999997e45 or 7.5000000000000005e64 < y

   1. Initial program 2.6%

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

   2. Taylor expanded in y around inf 70.0%

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

      1. associate--l+ 70.0%

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

      2. associate-/l* 74.6%

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

   4. Simplified 74.6%

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

   if -1.04999999999999997e45 < y < 7.5000000000000005e64

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 90.5%

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

      1. unpow2 90.5%

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

   4. Simplified 90.5%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+45} \lor \neg \left(y \leq 7.5 \cdot 10^{+64}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 5: 76.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+60}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -3.8e+49)
     t_1
     (if (<= y 1.25e-46)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (if (<= y 2.1e+60)
         (/
          (+
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
           t)
          (+ i (* b (* y y))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -3.8e+49) {
		tmp = t_1;
	} else if (y <= 1.25e-46) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 2.1e+60) {
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / (i + (b * (y * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    if (y <= (-3.8d+49)) then
        tmp = t_1
    else if (y <= 1.25d-46) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= 2.1d+60) then
        tmp = ((y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z)))))) + t) / (i + (b * (y * y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -3.8e+49) {
		tmp = t_1;
	} else if (y <= 1.25e-46) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 2.1e+60) {
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / (i + (b * (y * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -3.8e+49:
		tmp = t_1
	elif y <= 1.25e-46:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= 2.1e+60:
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / (i + (b * (y * y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -3.8e+49)
		tmp = t_1;
	elseif (y <= 1.25e-46)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= 2.1e+60)
		tmp = Float64(Float64(Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))) + t) / Float64(i + Float64(b * Float64(y * y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -3.8e+49)
		tmp = t_1;
	elseif (y <= 1.25e-46)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= 2.1e+60)
		tmp = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / (i + (b * (y * y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+49], t$95$1, If[LessEqual[y, 1.25e-46], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+60], N[(N[(N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999999e49 or 2.1000000000000001e60 < y

   1. Initial program 2.5%

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

   2. Taylor expanded in y around inf 70.8%

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

      1. associate--l+ 70.8%

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

      2. associate-/l* 75.5%

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

   4. Simplified 75.5%

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

   if -3.7999999999999999e49 < y < 1.24999999999999998e-46

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 89.5%

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

      1. *-commutative 89.5%

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

   4. Simplified 89.5%

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

   if 1.24999999999999998e-46 < y < 2.1000000000000001e60

   1. Initial program 81.9%

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

   2. Taylor expanded in b around inf 67.6%

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

      1. unpow2 67.6%

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

   4. Simplified 67.6%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+49}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+60}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 6: 80.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+50} \lor \neg \left(y \leq 2 \cdot 10^{+43}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.5e+50) (not (<= y 2e+43)))
   (+ 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 <= -5.5e+50) || !(y <= 2e+43)) {
		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 <= (-5.5d+50)) .or. (.not. (y <= 2d+43))) 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 <= -5.5e+50) || !(y <= 2e+43)) {
		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 <= -5.5e+50) or not (y <= 2e+43):
		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 <= -5.5e+50) || !(y <= 2e+43))
		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 <= -5.5e+50) || ~((y <= 2e+43)))
		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, -5.5e+50], N[Not[LessEqual[y, 2e+43]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(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 < -5.4999999999999998e50 or 2.00000000000000003e43 < y

   1. Initial program 4.8%

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

   2. Taylor expanded in y around inf 68.8%

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

      1. associate--l+ 68.8%

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

      2. associate-/l* 73.3%

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

   4. Simplified 73.3%

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

   if -5.4999999999999998e50 < y < 2.00000000000000003e43

   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 z around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. unpow2 87.2%

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

   4. Simplified 87.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+50} \lor \neg \left(y \leq 2 \cdot 10^{+43}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]

Alternative 7: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y}} + \frac{y}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -6.5e+50)
     t_1
     (if (<= y 2.7e-6)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (if (<= y 3.2e+69) (+ (/ x (/ b (* y y))) (/ y (/ b z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -6.5e+50) {
		tmp = t_1;
	} else if (y <= 2.7e-6) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 3.2e+69) {
		tmp = (x / (b / (y * y))) + (y / (b / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a / (y / x)))
    if (y <= (-6.5d+50)) then
        tmp = t_1
    else if (y <= 2.7d-6) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= 3.2d+69) then
        tmp = (x / (b / (y * y))) + (y / (b / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -6.5e+50) {
		tmp = t_1;
	} else if (y <= 2.7e-6) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 3.2e+69) {
		tmp = (x / (b / (y * y))) + (y / (b / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a / (y / x)))
	tmp = 0
	if y <= -6.5e+50:
		tmp = t_1
	elif y <= 2.7e-6:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= 3.2e+69:
		tmp = (x / (b / (y * y))) + (y / (b / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))))
	tmp = 0.0
	if (y <= -6.5e+50)
		tmp = t_1;
	elseif (y <= 2.7e-6)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= 3.2e+69)
		tmp = Float64(Float64(x / Float64(b / Float64(y * y))) + Float64(y / Float64(b / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a / (y / x)));
	tmp = 0.0;
	if (y <= -6.5e+50)
		tmp = t_1;
	elseif (y <= 2.7e-6)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= 3.2e+69)
		tmp = (x / (b / (y * y))) + (y / (b / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+50], t$95$1, If[LessEqual[y, 2.7e-6], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+69], N[(N[(x / N[(b / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000003e50 or 3.19999999999999985e69 < y

   1. Initial program 2.6%

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

   2. Taylor expanded in y around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. associate-/l* 77.2%

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

   4. Simplified 77.2%

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

   if -6.5000000000000003e50 < y < 2.69999999999999998e-6

   1. Initial program 98.5%

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

   2. Taylor expanded in y around 0 86.6%

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

      1. *-commutative 86.6%

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

   4. Simplified 86.6%

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

   if 2.69999999999999998e-6 < y < 3.19999999999999985e69

   1. Initial program 54.5%

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

   2. Taylor expanded in b around inf 48.3%

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

      1. unpow2 48.3%

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

   4. Simplified 48.3%

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

   5. Taylor expanded in y around inf 35.4%

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

      1. *-commutative 35.4%

         \[\leadsto \frac{\color{blue}{{y}^{2} \cdot x}}{b} + \frac{y \cdot z}{b} \]

      2. unpow2 35.4%

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

      3. associate-/l* 35.4%

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

   7. Simplified 35.4%

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

   8. Taylor expanded in y around 0 35.4%

      \[\leadsto \color{blue}{\frac{x \cdot {y}^{2}}{b}} + \frac{y}{\frac{b}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 41.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{b}{{y}^{2}}}} + \frac{y}{\frac{b}{z}} \]

      2. unpow2 41.7%

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

   10. Simplified 41.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{b}{y \cdot y}}} + \frac{y}{\frac{b}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-6}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y}} + \frac{y}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 8: 71.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-84}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y}} + \frac{y}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -4.2e+49)
     t_1
     (if (<= y -8e-84)
       (/ t (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (if (<= y 1.75e-51)
         (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i (* y c)))
         (if (<= y 1.1e-10)
           (/ (+ t (* y 230661.510616)) (+ i (* b (* y y))))
           (if (<= y 4.5e-5)
             (/ t (* y c))
             (if (<= y 3.5e+69)
               (+ (/ x (/ b (* y y))) (/ y (/ b z)))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -4.2e+49) {
		tmp = t_1;
	} else if (y <= -8e-84) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 1.75e-51) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c));
	} else if (y <= 1.1e-10) {
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	} else if (y <= 4.5e-5) {
		tmp = t / (y * c);
	} else if (y <= 3.5e+69) {
		tmp = (x / (b / (y * y))) + (y / (b / z));
	} 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 <= (-4.2d+49)) then
        tmp = t_1
    else if (y <= (-8d-84)) then
        tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= 1.75d-51) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * c))
    else if (y <= 1.1d-10) then
        tmp = (t + (y * 230661.510616d0)) / (i + (b * (y * y)))
    else if (y <= 4.5d-5) then
        tmp = t / (y * c)
    else if (y <= 3.5d+69) then
        tmp = (x / (b / (y * y))) + (y / (b / z))
    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 <= -4.2e+49) {
		tmp = t_1;
	} else if (y <= -8e-84) {
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 1.75e-51) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c));
	} else if (y <= 1.1e-10) {
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	} else if (y <= 4.5e-5) {
		tmp = t / (y * c);
	} else if (y <= 3.5e+69) {
		tmp = (x / (b / (y * y))) + (y / (b / z));
	} 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 <= -4.2e+49:
		tmp = t_1
	elif y <= -8e-84:
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= 1.75e-51:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c))
	elif y <= 1.1e-10:
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)))
	elif y <= 4.5e-5:
		tmp = t / (y * c)
	elif y <= 3.5e+69:
		tmp = (x / (b / (y * y))) + (y / (b / z))
	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 <= -4.2e+49)
		tmp = t_1;
	elseif (y <= -8e-84)
		tmp = Float64(t / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= 1.75e-51)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * c)));
	elseif (y <= 1.1e-10)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(b * Float64(y * y))));
	elseif (y <= 4.5e-5)
		tmp = Float64(t / Float64(y * c));
	elseif (y <= 3.5e+69)
		tmp = Float64(Float64(x / Float64(b / Float64(y * y))) + Float64(y / Float64(b / z)));
	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 <= -4.2e+49)
		tmp = t_1;
	elseif (y <= -8e-84)
		tmp = t / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= 1.75e-51)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c));
	elseif (y <= 1.1e-10)
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	elseif (y <= 4.5e-5)
		tmp = t / (y * c);
	elseif (y <= 3.5e+69)
		tmp = (x / (b / (y * y))) + (y / (b / z));
	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, -4.2e+49], t$95$1, If[LessEqual[y, -8e-84], N[(t / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-51], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-10], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-5], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+69], N[(N[(x / N[(b / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.20000000000000022e49 or 3.49999999999999987e69 < y

   1. Initial program 2.6%

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

   2. Taylor expanded in y around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. associate-/l* 77.2%

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

   4. Simplified 77.2%

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

   if -4.20000000000000022e49 < y < -8.0000000000000003e-84

   1. Initial program 93.3%

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

   2. Taylor expanded in t around inf 54.1%

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

   if -8.0000000000000003e-84 < y < 1.7499999999999999e-51

   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 96.8%

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

      1. *-commutative 96.8%

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

   4. Simplified 96.8%

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

   5. Taylor expanded in y around 0 92.4%

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

      1. *-commutative 92.4%

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

   7. Simplified 92.4%

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

   if 1.7499999999999999e-51 < y < 1.09999999999999995e-10

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 85.5%

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

      1. unpow2 85.5%

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

   4. Simplified 85.5%

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

   5. Taylor expanded in y around 0 56.0%

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

      1. *-commutative 56.0%

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

   7. Simplified 56.0%

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

   if 1.09999999999999995e-10 < y < 4.50000000000000028e-5

   1. Initial program 98.4%

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

   2. Taylor expanded in t around inf 98.4%

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

   3. Taylor expanded in c around inf 98.4%

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

      1. *-commutative 98.4%

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

   5. Simplified 98.4%

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

   if 4.50000000000000028e-5 < y < 3.49999999999999987e69

   1. Initial program 54.5%

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

   2. Taylor expanded in b around inf 48.3%

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

      1. unpow2 48.3%

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

   4. Simplified 48.3%

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

   5. Taylor expanded in y around inf 35.4%

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

      1. *-commutative 35.4%

         \[\leadsto \frac{\color{blue}{{y}^{2} \cdot x}}{b} + \frac{y \cdot z}{b} \]

      2. unpow2 35.4%

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

      3. associate-/l* 35.4%

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

   7. Simplified 35.4%

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

   8. Taylor expanded in y around 0 35.4%

      \[\leadsto \color{blue}{\frac{x \cdot {y}^{2}}{b}} + \frac{y}{\frac{b}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 41.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{b}{{y}^{2}}}} + \frac{y}{\frac{b}{z}} \]

      2. unpow2 41.7%

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

   10. Simplified 41.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{b}{y \cdot y}}} + \frac{y}{\frac{b}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-84}:\\ \;\;\;\;\frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-51}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y}} + \frac{y}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 9: 75.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y}} + \frac{y}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.8e+49)
     t_1
     (if (<= y 7.6e-5)
       (/
        (+ t (* y 230661.510616))
        (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
       (if (<= y 3.2e+69) (+ (/ x (/ b (* y y))) (/ y (/ b z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.8e+49) {
		tmp = t_1;
	} else if (y <= 7.6e-5) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 3.2e+69) {
		tmp = (x / (b / (y * y))) + (y / (b / z));
	} 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 <= (-2.8d+49)) then
        tmp = t_1
    else if (y <= 7.6d-5) then
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    else if (y <= 3.2d+69) then
        tmp = (x / (b / (y * y))) + (y / (b / z))
    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 <= -2.8e+49) {
		tmp = t_1;
	} else if (y <= 7.6e-5) {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	} else if (y <= 3.2e+69) {
		tmp = (x / (b / (y * y))) + (y / (b / z));
	} 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 <= -2.8e+49:
		tmp = t_1
	elif y <= 7.6e-5:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	elif y <= 3.2e+69:
		tmp = (x / (b / (y * y))) + (y / (b / z))
	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 <= -2.8e+49)
		tmp = t_1;
	elseif (y <= 7.6e-5)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	elseif (y <= 3.2e+69)
		tmp = Float64(Float64(x / Float64(b / Float64(y * y))) + Float64(y / Float64(b / z)));
	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 <= -2.8e+49)
		tmp = t_1;
	elseif (y <= 7.6e-5)
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	elseif (y <= 3.2e+69)
		tmp = (x / (b / (y * y))) + (y / (b / z));
	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, -2.8e+49], t$95$1, If[LessEqual[y, 7.6e-5], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+69], N[(N[(x / N[(b / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999998e49 or 3.19999999999999985e69 < y

   1. Initial program 2.6%

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

   2. Taylor expanded in y around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. associate-/l* 77.2%

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

   4. Simplified 77.2%

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

   if -2.7999999999999998e49 < y < 7.6000000000000004e-5

   1. Initial program 98.5%

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

   2. Taylor expanded in y around 0 85.4%

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

      1. *-commutative 66.4%

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

   4. Simplified 85.4%

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

   if 7.6000000000000004e-5 < y < 3.19999999999999985e69

   1. Initial program 54.5%

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

   2. Taylor expanded in b around inf 48.3%

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

      1. unpow2 48.3%

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

   4. Simplified 48.3%

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

   5. Taylor expanded in y around inf 35.4%

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

      1. *-commutative 35.4%

         \[\leadsto \frac{\color{blue}{{y}^{2} \cdot x}}{b} + \frac{y \cdot z}{b} \]

      2. unpow2 35.4%

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

      3. associate-/l* 35.4%

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

   7. Simplified 35.4%

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

   8. Taylor expanded in y around 0 35.4%

      \[\leadsto \color{blue}{\frac{x \cdot {y}^{2}}{b}} + \frac{y}{\frac{b}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 41.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{b}{{y}^{2}}}} + \frac{y}{\frac{b}{z}} \]

      2. unpow2 41.7%

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

   10. Simplified 41.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{b}{y \cdot y}}} + \frac{y}{\frac{b}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+49}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y}} + \frac{y}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 10: 70.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-59}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-11}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y}} + \frac{y}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -2.15e+18)
     t_1
     (if (<= y 1.75e-59)
       (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i (* y c)))
       (if (<= y 9e-11)
         (/ (+ t (* y 230661.510616)) (+ i (* b (* y y))))
         (if (<= y 3.5e-8)
           (/ t (* y c))
           (if (<= y 3.2e+69) (+ (/ x (/ b (* y y))) (/ y (/ b z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -2.15e+18) {
		tmp = t_1;
	} else if (y <= 1.75e-59) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c));
	} else if (y <= 9e-11) {
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	} else if (y <= 3.5e-8) {
		tmp = t / (y * c);
	} else if (y <= 3.2e+69) {
		tmp = (x / (b / (y * y))) + (y / (b / z));
	} 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 <= (-2.15d+18)) then
        tmp = t_1
    else if (y <= 1.75d-59) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * c))
    else if (y <= 9d-11) then
        tmp = (t + (y * 230661.510616d0)) / (i + (b * (y * y)))
    else if (y <= 3.5d-8) then
        tmp = t / (y * c)
    else if (y <= 3.2d+69) then
        tmp = (x / (b / (y * y))) + (y / (b / z))
    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 <= -2.15e+18) {
		tmp = t_1;
	} else if (y <= 1.75e-59) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c));
	} else if (y <= 9e-11) {
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	} else if (y <= 3.5e-8) {
		tmp = t / (y * c);
	} else if (y <= 3.2e+69) {
		tmp = (x / (b / (y * y))) + (y / (b / z));
	} 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 <= -2.15e+18:
		tmp = t_1
	elif y <= 1.75e-59:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c))
	elif y <= 9e-11:
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)))
	elif y <= 3.5e-8:
		tmp = t / (y * c)
	elif y <= 3.2e+69:
		tmp = (x / (b / (y * y))) + (y / (b / z))
	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 <= -2.15e+18)
		tmp = t_1;
	elseif (y <= 1.75e-59)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * c)));
	elseif (y <= 9e-11)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(b * Float64(y * y))));
	elseif (y <= 3.5e-8)
		tmp = Float64(t / Float64(y * c));
	elseif (y <= 3.2e+69)
		tmp = Float64(Float64(x / Float64(b / Float64(y * y))) + Float64(y / Float64(b / z)));
	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 <= -2.15e+18)
		tmp = t_1;
	elseif (y <= 1.75e-59)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * c));
	elseif (y <= 9e-11)
		tmp = (t + (y * 230661.510616)) / (i + (b * (y * y)));
	elseif (y <= 3.5e-8)
		tmp = t / (y * c);
	elseif (y <= 3.2e+69)
		tmp = (x / (b / (y * y))) + (y / (b / z));
	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, -2.15e+18], t$95$1, If[LessEqual[y, 1.75e-59], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-11], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(b * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-8], N[(t / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+69], N[(N[(x / N[(b / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.15e18 or 3.19999999999999985e69 < y

   1. Initial program 8.0%

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

   2. Taylor expanded in y around inf 68.1%

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

      1. associate--l+ 68.1%

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

      2. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

   if -2.15e18 < y < 1.75e-59

   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 91.8%

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

      1. *-commutative 91.8%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in y around 0 82.6%

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

      1. *-commutative 82.6%

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

   7. Simplified 82.6%

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

   if 1.75e-59 < y < 8.9999999999999999e-11

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 85.5%

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

      1. unpow2 85.5%

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

   4. Simplified 85.5%

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

   5. Taylor expanded in y around 0 56.0%

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

      1. *-commutative 56.0%

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

   7. Simplified 56.0%

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

   if 8.9999999999999999e-11 < y < 3.50000000000000024e-8

   1. Initial program 98.4%

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

   2. Taylor expanded in t around inf 98.4%

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

   3. Taylor expanded in c around inf 98.4%

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

      1. *-commutative 98.4%

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

   5. Simplified 98.4%

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

   if 3.50000000000000024e-8 < y < 3.19999999999999985e69

   1. Initial program 54.5%

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

   2. Taylor expanded in b around inf 48.3%

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

      1. unpow2 48.3%

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

   4. Simplified 48.3%

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

   5. Taylor expanded in y around inf 35.4%

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

      1. *-commutative 35.4%

         \[\leadsto \frac{\color{blue}{{y}^{2} \cdot x}}{b} + \frac{y \cdot z}{b} \]

      2. unpow2 35.4%

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

      3. associate-/l* 35.4%

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

   7. Simplified 35.4%

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

   8. Taylor expanded in y around 0 35.4%

      \[\leadsto \color{blue}{\frac{x \cdot {y}^{2}}{b}} + \frac{y}{\frac{b}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 41.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{b}{{y}^{2}}}} + \frac{y}{\frac{b}{z}} \]

      2. unpow2 41.7%

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

   10. Simplified 41.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{b}{y \cdot y}}} + \frac{y}{\frac{b}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-59}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-11}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + b \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{y \cdot c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y}} + \frac{y}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 11: 67.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y}} + \frac{y}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (/ a (/ y x))))))
   (if (<= y -8.2e+17)
     t_1
     (if (<= y 7.6e-5)
       (/ t (+ i (* y (+ c (* y b)))))
       (if (<= y 3.2e+69) (+ (/ x (/ b (* y y))) (/ y (/ b z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a / (y / x)));
	double tmp;
	if (y <= -8.2e+17) {
		tmp = t_1;
	} else if (y <= 7.6e-5) {
		tmp = t / (i + (y * (c + (y * b))));
	} else if (y <= 3.2e+69) {
		tmp = (x / (b / (y * y))) + (y / (b / z));
	} 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 <= (-8.2d+17)) then
        tmp = t_1
    else if (y <= 7.6d-5) then
        tmp = t / (i + (y * (c + (y * b))))
    else if (y <= 3.2d+69) then
        tmp = (x / (b / (y * y))) + (y / (b / z))
    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 <= -8.2e+17) {
		tmp = t_1;
	} else if (y <= 7.6e-5) {
		tmp = t / (i + (y * (c + (y * b))));
	} else if (y <= 3.2e+69) {
		tmp = (x / (b / (y * y))) + (y / (b / z));
	} 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 <= -8.2e+17:
		tmp = t_1
	elif y <= 7.6e-5:
		tmp = t / (i + (y * (c + (y * b))))
	elif y <= 3.2e+69:
		tmp = (x / (b / (y * y))) + (y / (b / z))
	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 <= -8.2e+17)
		tmp = t_1;
	elseif (y <= 7.6e-5)
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 3.2e+69)
		tmp = Float64(Float64(x / Float64(b / Float64(y * y))) + Float64(y / Float64(b / z)));
	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 <= -8.2e+17)
		tmp = t_1;
	elseif (y <= 7.6e-5)
		tmp = t / (i + (y * (c + (y * b))));
	elseif (y <= 3.2e+69)
		tmp = (x / (b / (y * y))) + (y / (b / z));
	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, -8.2e+17], t$95$1, If[LessEqual[y, 7.6e-5], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+69], N[(N[(x / N[(b / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.2e17 or 3.19999999999999985e69 < y

   1. Initial program 8.0%

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

   2. Taylor expanded in y around inf 68.1%

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

      1. associate--l+ 68.1%

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

      2. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

   if -8.2e17 < y < 7.6000000000000004e-5

   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 t around inf 77.8%

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

   3. Taylor expanded in y around 0 76.1%

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

      1. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   if 7.6000000000000004e-5 < y < 3.19999999999999985e69

   1. Initial program 54.5%

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

   2. Taylor expanded in b around inf 48.3%

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

      1. unpow2 48.3%

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

   4. Simplified 48.3%

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

   5. Taylor expanded in y around inf 35.4%

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

      1. *-commutative 35.4%

         \[\leadsto \frac{\color{blue}{{y}^{2} \cdot x}}{b} + \frac{y \cdot z}{b} \]

      2. unpow2 35.4%

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

      3. associate-/l* 35.4%

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

   7. Simplified 35.4%

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

   8. Taylor expanded in y around 0 35.4%

      \[\leadsto \color{blue}{\frac{x \cdot {y}^{2}}{b}} + \frac{y}{\frac{b}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 41.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{b}{{y}^{2}}}} + \frac{y}{\frac{b}{z}} \]

      2. unpow2 41.7%

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

   10. Simplified 41.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{b}{y \cdot y}}} + \frac{y}{\frac{b}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+17}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{b}{y \cdot y}} + \frac{y}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \end{array} \]

Alternative 12: 65.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+18} \lor \neg \left(y \leq 3.25 \cdot 10^{+40}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6e+18) (not (<= y 3.25e+40)))
   (+ x (- (/ z y) (/ a (/ y x))))
   (/ t (+ i (* y c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6e+18) || !(y <= 3.25e+40)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-6d+18)) .or. (.not. (y <= 3.25d+40))) then
        tmp = x + ((z / y) - (a / (y / x)))
    else
        tmp = t / (i + (y * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6e+18) || !(y <= 3.25e+40)) {
		tmp = x + ((z / y) - (a / (y / x)));
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6e+18) or not (y <= 3.25e+40):
		tmp = x + ((z / y) - (a / (y / x)))
	else:
		tmp = t / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6e+18) || !(y <= 3.25e+40))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a / Float64(y / x))));
	else
		tmp = Float64(t / Float64(i + Float64(y * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -6e+18) || ~((y <= 3.25e+40)))
		tmp = x + ((z / y) - (a / (y / x)));
	else
		tmp = t / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6e+18], N[Not[LessEqual[y, 3.25e+40]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6e18 or 3.2500000000000001e40 < y

   1. Initial program 9.6%

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

   2. Taylor expanded in y around inf 64.4%

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

      1. associate--l+ 64.4%

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

      2. associate-/l* 68.5%

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

   4. Simplified 68.5%

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

   if -6e18 < y < 3.2500000000000001e40

   1. Initial program 98.6%

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

   2. Taylor expanded in t around inf 74.1%

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

   3. Taylor expanded in y around 0 65.7%

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

      1. *-commutative 65.7%

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

   5. Simplified 65.7%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+18} \lor \neg \left(y \leq 3.25 \cdot 10^{+40}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]

Alternative 13: 67.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+19} \lor \neg \left(y \leq 3.25 \cdot 10^{+40}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.4e+19) (not (<= y 3.25e+40)))
   (+ 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 <= -5.4e+19) || !(y <= 3.25e+40)) {
		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 <= (-5.4d+19)) .or. (.not. (y <= 3.25d+40))) 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 <= -5.4e+19) || !(y <= 3.25e+40)) {
		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 <= -5.4e+19) or not (y <= 3.25e+40):
		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 <= -5.4e+19) || !(y <= 3.25e+40))
		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 <= -5.4e+19) || ~((y <= 3.25e+40)))
		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, -5.4e+19], N[Not[LessEqual[y, 3.25e+40]], $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 < -5.4e19 or 3.2500000000000001e40 < y

   1. Initial program 9.6%

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

   2. Taylor expanded in y around inf 64.4%

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

      1. associate--l+ 64.4%

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

      2. associate-/l* 68.5%

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

   4. Simplified 68.5%

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

   if -5.4e19 < y < 3.2500000000000001e40

   1. Initial program 98.6%

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

   2. Taylor expanded in t around inf 74.1%

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

   3. Taylor expanded in y around 0 72.6%

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

      1. *-commutative 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+19} \lor \neg \left(y \leq 3.25 \cdot 10^{+40}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - \frac{a}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]

Alternative 14: 58.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -50000000000000:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -50000000000000.0)
   (- x (/ a (/ y x)))
   (if (<= y 1.5e+43) (/ t (+ i (* y c))) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -50000000000000.0) {
		tmp = x - (a / (y / x));
	} else if (y <= 1.5e+43) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-50000000000000.0d0)) then
        tmp = x - (a / (y / x))
    else if (y <= 1.5d+43) then
        tmp = t / (i + (y * c))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -50000000000000.0) {
		tmp = x - (a / (y / x));
	} else if (y <= 1.5e+43) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -50000000000000.0:
		tmp = x - (a / (y / x))
	elif y <= 1.5e+43:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -50000000000000.0)
		tmp = Float64(x - Float64(a / Float64(y / x)));
	elseif (y <= 1.5e+43)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -50000000000000.0)
		tmp = x - (a / (y / x));
	elseif (y <= 1.5e+43)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -50000000000000.0], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+43], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < -5e13

   1. Initial program 14.7%

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

      1. add-cube-cbrt 14.6%

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

      2. pow3 14.6%

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

      3. *-commutative 14.6%

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

      4. *-commutative 14.6%

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

      5. fma-def 14.6%

         \[\leadsto \frac{\left({\left(\sqrt[3]{y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}}\right)}^{3} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. fma-def 14.6%

         \[\leadsto \frac{\left({\left(\sqrt[3]{y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)}\right)}^{3} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 14.6%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in z around 0 11.8%

      \[\leadsto \frac{\left(\color{blue}{{1}^{0.3333333333333333} \cdot \left(y \cdot \left(27464.7644705 + x \cdot {y}^{2}\right)\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. pow-base-1 11.8%

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

      2. *-lft-identity 11.8%

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

      3. *-commutative 11.8%

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

      4. unpow2 11.8%

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

   6. Simplified 11.8%

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

   7. Taylor expanded in y around inf 42.6%

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

      1. mul-1-neg 42.6%

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

      2. unsub-neg 42.6%

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

      3. associate-/l* 48.8%

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

   9. Simplified 48.8%

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

   if -5e13 < y < 1.50000000000000008e43

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 74.4%

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

   3. Taylor expanded in y around 0 66.4%

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

      1. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   if 1.50000000000000008e43 < y

   1. Initial program 8.5%

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

   2. Taylor expanded in y around inf 52.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -50000000000000:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 50.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -860000:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -860000.0) (- x (/ a (/ y x))) (if (<= y 9.6e+42) (/ 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 <= -860000.0) {
		tmp = x - (a / (y / x));
	} else if (y <= 9.6e+42) {
		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 <= (-860000.0d0)) then
        tmp = x - (a / (y / x))
    else if (y <= 9.6d+42) 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 <= -860000.0) {
		tmp = x - (a / (y / x));
	} else if (y <= 9.6e+42) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -860000.0:
		tmp = x - (a / (y / x))
	elif y <= 9.6e+42:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -860000.0)
		tmp = Float64(x - Float64(a / Float64(y / x)));
	elseif (y <= 9.6e+42)
		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 <= -860000.0)
		tmp = x - (a / (y / x));
	elseif (y <= 9.6e+42)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -860000.0], N[(x - N[(a / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e+42], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < -8.6e5

   1. Initial program 14.7%

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

      1. add-cube-cbrt 14.6%

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

      2. pow3 14.6%

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

      3. *-commutative 14.6%

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

      4. *-commutative 14.6%

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

      5. fma-def 14.6%

         \[\leadsto \frac{\left({\left(\sqrt[3]{y \cdot \color{blue}{\mathsf{fma}\left(y, x \cdot y + z, 27464.7644705\right)}}\right)}^{3} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. fma-def 14.6%

         \[\leadsto \frac{\left({\left(\sqrt[3]{y \cdot \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(x, y, z\right)}, 27464.7644705\right)}\right)}^{3} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied egg-rr 14.6%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right)}\right)}^{3}} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Taylor expanded in z around 0 11.8%

      \[\leadsto \frac{\left(\color{blue}{{1}^{0.3333333333333333} \cdot \left(y \cdot \left(27464.7644705 + x \cdot {y}^{2}\right)\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. pow-base-1 11.8%

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

      2. *-lft-identity 11.8%

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

      3. *-commutative 11.8%

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

      4. unpow2 11.8%

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

   6. Simplified 11.8%

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

   7. Taylor expanded in y around inf 42.6%

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

      1. mul-1-neg 42.6%

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

      2. unsub-neg 42.6%

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

      3. associate-/l* 48.8%

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

   9. Simplified 48.8%

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

   if -8.6e5 < y < 9.5999999999999994e42

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0 52.9%

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

   if 9.5999999999999994e42 < y

   1. Initial program 8.5%

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

   2. Taylor expanded in y around inf 52.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -860000:\\ \;\;\;\;x - \frac{a}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 50.6% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.3e+17) x (if (<= y 9.6e+42) (/ 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 <= -3.3e+17) {
		tmp = x;
	} else if (y <= 9.6e+42) {
		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 <= (-3.3d+17)) then
        tmp = x
    else if (y <= 9.6d+42) 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 <= -3.3e+17) {
		tmp = x;
	} else if (y <= 9.6e+42) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.3e+17:
		tmp = x
	elif y <= 9.6e+42:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.3e+17)
		tmp = x;
	elseif (y <= 9.6e+42)
		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 <= -3.3e+17)
		tmp = x;
	elseif (y <= 9.6e+42)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.3e+17], x, If[LessEqual[y, 9.6e+42], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e17 or 9.5999999999999994e42 < y

   1. Initial program 9.7%

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

   2. Taylor expanded in y around inf 51.4%

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

   if -3.3e17 < y < 9.5999999999999994e42

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0 51.9%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 25.7% 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 65.2%

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

2. Taylor expanded in y around inf 21.5%

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

3. Final simplification 21.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(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)))