Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.9% → 82.8%

Time: 27.0s

Alternatives: 14

Speedup: 1.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.9% 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: 82.8% accurate, 0.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / (i + (y * (c + (y * ((y * (y + a)) + b)))))) <= ((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)) - ((x * a) / y);
	}
	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(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))))) <= 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(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	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[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $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 91.4%

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

      1. fma-define 91.4%

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

      2. fma-define 91.4%

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

      3. fma-define 91.4%

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

      4. fma-define 91.4%

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

      5. fma-define 91.4%

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

      6. fma-define 91.4%

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

      7. fma-define 91.4%

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

   3. Simplified 91.4%

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

   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. Add Preprocessing

   3. Taylor expanded in y around inf 81.2%

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

4. Final simplification 88.2%

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

Alternative 2: 82.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))) + t) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	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) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x + (z / y)) - ((x * a) / y);
	}
	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) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (x + (z / y)) - ((x * a) / y)
	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(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(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[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $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 91.4%

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

   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. Add Preprocessing

   3. Taylor expanded in y around inf 81.2%

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

4. Final simplification 88.2%

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

Alternative 3: 59.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot 230661.510616}{i}\\ t_2 := c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\\ t_3 := \frac{\frac{t}{y}}{t\_2}\\ t_4 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.66 \cdot 10^{+49}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-36}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{y \cdot t\_2}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+59}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (+ t (* y 230661.510616)) i))
        (t_2 (+ c (* y (+ (* y (+ y a)) b))))
        (t_3 (/ (/ t y) t_2))
        (t_4 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.66e+49)
     t_4
     (if (<= y -5.6e-36)
       t_3
       (if (<= y 4.8e-142)
         t_1
         (if (<= y 4.2e-102)
           (/ t (* y t_2))
           (if (<= y 7.2e-42) t_1 (if (<= y 6e+59) t_3 t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double t_2 = c + (y * ((y * (y + a)) + b));
	double t_3 = (t / y) / t_2;
	double t_4 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.66e+49) {
		tmp = t_4;
	} else if (y <= -5.6e-36) {
		tmp = t_3;
	} else if (y <= 4.8e-142) {
		tmp = t_1;
	} else if (y <= 4.2e-102) {
		tmp = t / (y * t_2);
	} else if (y <= 7.2e-42) {
		tmp = t_1;
	} else if (y <= 6e+59) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (t + (y * 230661.510616d0)) / i
    t_2 = c + (y * ((y * (y + a)) + b))
    t_3 = (t / y) / t_2
    t_4 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.66d+49)) then
        tmp = t_4
    else if (y <= (-5.6d-36)) then
        tmp = t_3
    else if (y <= 4.8d-142) then
        tmp = t_1
    else if (y <= 4.2d-102) then
        tmp = t / (y * t_2)
    else if (y <= 7.2d-42) then
        tmp = t_1
    else if (y <= 6d+59) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double t_2 = c + (y * ((y * (y + a)) + b));
	double t_3 = (t / y) / t_2;
	double t_4 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.66e+49) {
		tmp = t_4;
	} else if (y <= -5.6e-36) {
		tmp = t_3;
	} else if (y <= 4.8e-142) {
		tmp = t_1;
	} else if (y <= 4.2e-102) {
		tmp = t / (y * t_2);
	} else if (y <= 7.2e-42) {
		tmp = t_1;
	} else if (y <= 6e+59) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * 230661.510616)) / i
	t_2 = c + (y * ((y * (y + a)) + b))
	t_3 = (t / y) / t_2
	t_4 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.66e+49:
		tmp = t_4
	elif y <= -5.6e-36:
		tmp = t_3
	elif y <= 4.8e-142:
		tmp = t_1
	elif y <= 4.2e-102:
		tmp = t / (y * t_2)
	elif y <= 7.2e-42:
		tmp = t_1
	elif y <= 6e+59:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * 230661.510616)) / i)
	t_2 = Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))
	t_3 = Float64(Float64(t / y) / t_2)
	t_4 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.66e+49)
		tmp = t_4;
	elseif (y <= -5.6e-36)
		tmp = t_3;
	elseif (y <= 4.8e-142)
		tmp = t_1;
	elseif (y <= 4.2e-102)
		tmp = Float64(t / Float64(y * t_2));
	elseif (y <= 7.2e-42)
		tmp = t_1;
	elseif (y <= 6e+59)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * 230661.510616)) / i;
	t_2 = c + (y * ((y * (y + a)) + b));
	t_3 = (t / y) / t_2;
	t_4 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.66e+49)
		tmp = t_4;
	elseif (y <= -5.6e-36)
		tmp = t_3;
	elseif (y <= 4.8e-142)
		tmp = t_1;
	elseif (y <= 4.2e-102)
		tmp = t / (y * t_2);
	elseif (y <= 7.2e-42)
		tmp = t_1;
	elseif (y <= 6e+59)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t / y), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.66e+49], t$95$4, If[LessEqual[y, -5.6e-36], t$95$3, If[LessEqual[y, 4.8e-142], t$95$1, If[LessEqual[y, 4.2e-102], N[(t / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-42], t$95$1, If[LessEqual[y, 6e+59], t$95$3, t$95$4]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.65999999999999999e49 or 6.0000000000000001e59 < y

   1. Initial program 5.8%

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

   3. Taylor expanded in y around inf 74.8%

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

   if -1.65999999999999999e49 < y < -5.6000000000000002e-36 or 7.2000000000000004e-42 < y < 6.0000000000000001e59

   1. Initial program 80.2%

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

   3. Taylor expanded in i around 0 67.6%

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

   4. Taylor expanded in t around inf 35.5%

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

      1. associate-/r* 37.6%

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

      2. +-commutative 37.6%

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

      3. fma-undefine 37.6%

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

      4. +-commutative 37.6%

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

      5. +-commutative 37.6%

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

      6. fma-undefine 37.6%

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

   6. Simplified 37.6%

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

   7. Taylor expanded in c around 0 37.6%

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

   if -5.6000000000000002e-36 < y < 4.79999999999999976e-142 or 4.2e-102 < y < 7.2000000000000004e-42

   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. Add Preprocessing

   3. Taylor expanded in y around 0 55.0%

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

      1. fma-define 55.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

      2. associate-*r/ 55.0%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616 \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      3. metadata-eval 55.0%

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{230661.510616}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. associate-/l* 59.0%

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i} - \color{blue}{c \cdot \frac{t}{{i}^{2}}}, \frac{t}{i}\right) \]

   5. Simplified 59.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{230661.510616}{i} - c \cdot \frac{t}{{i}^{2}}, \frac{t}{i}\right)} \]

   6. Taylor expanded in i around inf 66.7%

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

      1. *-commutative 66.7%

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

   8. Simplified 66.7%

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

   if 4.79999999999999976e-142 < y < 4.2e-102

   1. Initial program 99.9%

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

   3. Taylor expanded in i around 0 67.5%

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

   4. Taylor expanded in t around inf 67.7%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.66 \cdot 10^{+49}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-36}:\\ \;\;\;\;\frac{\frac{t}{y}}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-142}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+59}:\\ \;\;\;\;\frac{\frac{t}{y}}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot 230661.510616}{i}\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_3 := y \cdot \left(y \cdot \left(y + a\right) + b\right)\\ t_4 := \frac{t}{y \cdot \left(c + t\_3\right)}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-31}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-102}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+59}:\\ \;\;\;\;\frac{\frac{t}{y}}{t\_3}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (+ t (* y 230661.510616)) i))
        (t_2 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_3 (* y (+ (* y (+ y a)) b)))
        (t_4 (/ t (* y (+ c t_3)))))
   (if (<= y -1.25e+50)
     t_2
     (if (<= y -5e-31)
       t_4
       (if (<= y 4.8e-142)
         t_1
         (if (<= y 2.55e-102)
           t_4
           (if (<= y 1.04e-41) t_1 (if (<= y 6e+59) (/ (/ t y) t_3) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double t_2 = (x + (z / y)) - ((x * a) / y);
	double t_3 = y * ((y * (y + a)) + b);
	double t_4 = t / (y * (c + t_3));
	double tmp;
	if (y <= -1.25e+50) {
		tmp = t_2;
	} else if (y <= -5e-31) {
		tmp = t_4;
	} else if (y <= 4.8e-142) {
		tmp = t_1;
	} else if (y <= 2.55e-102) {
		tmp = t_4;
	} else if (y <= 1.04e-41) {
		tmp = t_1;
	} else if (y <= 6e+59) {
		tmp = (t / y) / t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (t + (y * 230661.510616d0)) / i
    t_2 = (x + (z / y)) - ((x * a) / y)
    t_3 = y * ((y * (y + a)) + b)
    t_4 = t / (y * (c + t_3))
    if (y <= (-1.25d+50)) then
        tmp = t_2
    else if (y <= (-5d-31)) then
        tmp = t_4
    else if (y <= 4.8d-142) then
        tmp = t_1
    else if (y <= 2.55d-102) then
        tmp = t_4
    else if (y <= 1.04d-41) then
        tmp = t_1
    else if (y <= 6d+59) then
        tmp = (t / y) / t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / i;
	double t_2 = (x + (z / y)) - ((x * a) / y);
	double t_3 = y * ((y * (y + a)) + b);
	double t_4 = t / (y * (c + t_3));
	double tmp;
	if (y <= -1.25e+50) {
		tmp = t_2;
	} else if (y <= -5e-31) {
		tmp = t_4;
	} else if (y <= 4.8e-142) {
		tmp = t_1;
	} else if (y <= 2.55e-102) {
		tmp = t_4;
	} else if (y <= 1.04e-41) {
		tmp = t_1;
	} else if (y <= 6e+59) {
		tmp = (t / y) / t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * 230661.510616)) / i
	t_2 = (x + (z / y)) - ((x * a) / y)
	t_3 = y * ((y * (y + a)) + b)
	t_4 = t / (y * (c + t_3))
	tmp = 0
	if y <= -1.25e+50:
		tmp = t_2
	elif y <= -5e-31:
		tmp = t_4
	elif y <= 4.8e-142:
		tmp = t_1
	elif y <= 2.55e-102:
		tmp = t_4
	elif y <= 1.04e-41:
		tmp = t_1
	elif y <= 6e+59:
		tmp = (t / y) / t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * 230661.510616)) / i)
	t_2 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_3 = Float64(y * Float64(Float64(y * Float64(y + a)) + b))
	t_4 = Float64(t / Float64(y * Float64(c + t_3)))
	tmp = 0.0
	if (y <= -1.25e+50)
		tmp = t_2;
	elseif (y <= -5e-31)
		tmp = t_4;
	elseif (y <= 4.8e-142)
		tmp = t_1;
	elseif (y <= 2.55e-102)
		tmp = t_4;
	elseif (y <= 1.04e-41)
		tmp = t_1;
	elseif (y <= 6e+59)
		tmp = Float64(Float64(t / y) / t_3);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * 230661.510616)) / i;
	t_2 = (x + (z / y)) - ((x * a) / y);
	t_3 = y * ((y * (y + a)) + b);
	t_4 = t / (y * (c + t_3));
	tmp = 0.0;
	if (y <= -1.25e+50)
		tmp = t_2;
	elseif (y <= -5e-31)
		tmp = t_4;
	elseif (y <= 4.8e-142)
		tmp = t_1;
	elseif (y <= 2.55e-102)
		tmp = t_4;
	elseif (y <= 1.04e-41)
		tmp = t_1;
	elseif (y <= 6e+59)
		tmp = (t / y) / t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t / N[(y * N[(c + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+50], t$95$2, If[LessEqual[y, -5e-31], t$95$4, If[LessEqual[y, 4.8e-142], t$95$1, If[LessEqual[y, 2.55e-102], t$95$4, If[LessEqual[y, 1.04e-41], t$95$1, If[LessEqual[y, 6e+59], N[(N[(t / y), $MachinePrecision] / t$95$3), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.25e50 or 6.0000000000000001e59 < y

   1. Initial program 5.8%

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

   3. Taylor expanded in y around inf 74.8%

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

   if -1.25e50 < y < -5e-31 or 4.79999999999999976e-142 < y < 2.55e-102

   1. Initial program 92.3%

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

   3. Taylor expanded in i around 0 69.3%

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

   4. Taylor expanded in t around inf 46.6%

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

   if -5e-31 < y < 4.79999999999999976e-142 or 2.55e-102 < y < 1.04e-41

   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. Add Preprocessing

   3. Taylor expanded in y around 0 55.0%

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

      1. fma-define 55.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

      2. associate-*r/ 55.0%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616 \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      3. metadata-eval 55.0%

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{230661.510616}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. associate-/l* 59.0%

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i} - \color{blue}{c \cdot \frac{t}{{i}^{2}}}, \frac{t}{i}\right) \]

   5. Simplified 59.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{230661.510616}{i} - c \cdot \frac{t}{{i}^{2}}, \frac{t}{i}\right)} \]

   6. Taylor expanded in i around inf 66.7%

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

      1. *-commutative 66.7%

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

   8. Simplified 66.7%

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

   if 1.04e-41 < y < 6.0000000000000001e59

   1. Initial program 69.0%

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

   3. Taylor expanded in i around 0 63.8%

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

   4. Taylor expanded in t around inf 36.4%

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

      1. associate-/r* 41.2%

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

      2. +-commutative 41.2%

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

      3. fma-undefine 41.2%

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

      4. +-commutative 41.2%

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

      5. +-commutative 41.2%

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

      6. fma-undefine 41.2%

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

   6. Simplified 41.2%

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

   7. Taylor expanded in c around 0 39.8%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-142}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{-41}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+59}:\\ \;\;\;\;\frac{\frac{t}{y}}{y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_2 := c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\\ \mathbf{if}\;y \leq -2.22 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t\_2}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+76}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_2 (+ c (* y (+ (* y (+ y a)) b)))))
   (if (<= y -2.22e+49)
     t_1
     (if (<= y 6.1e+49)
       (/ (+ t (* y 230661.510616)) (+ i (* y t_2)))
       (if (<= y 4.1e+76)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))) t_2)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double t_2 = c + (y * ((y * (y + a)) + b));
	double tmp;
	if (y <= -2.22e+49) {
		tmp = t_1;
	} else if (y <= 6.1e+49) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 4.1e+76) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    t_2 = c + (y * ((y * (y + a)) + b))
    if (y <= (-2.22d+49)) then
        tmp = t_1
    else if (y <= 6.1d+49) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_2))
    else if (y <= 4.1d+76) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))) / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double t_2 = c + (y * ((y * (y + a)) + b));
	double tmp;
	if (y <= -2.22e+49) {
		tmp = t_1;
	} else if (y <= 6.1e+49) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 4.1e+76) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	t_2 = c + (y * ((y * (y + a)) + b))
	tmp = 0
	if y <= -2.22e+49:
		tmp = t_1
	elif y <= 6.1e+49:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2))
	elif y <= 4.1e+76:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_2 = Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))
	tmp = 0.0
	if (y <= -2.22e+49)
		tmp = t_1;
	elseif (y <= 6.1e+49)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_2)));
	elseif (y <= 4.1e+76)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	t_2 = c + (y * ((y * (y + a)) + b));
	tmp = 0.0;
	if (y <= -2.22e+49)
		tmp = t_1;
	elseif (y <= 6.1e+49)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	elseif (y <= 4.1e+76)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.22e+49], t$95$1, If[LessEqual[y, 6.1e+49], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+76], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.21999999999999995e49 or 4.0999999999999998e76 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 79.1%

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

   if -2.21999999999999995e49 < y < 6.09999999999999963e49

   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. Add Preprocessing

   3. Taylor expanded in y around 0 82.3%

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

      1. *-commutative 82.3%

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

   5. Simplified 82.3%

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

   if 6.09999999999999963e49 < y < 4.0999999999999998e76

   1. Initial program 40.5%

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

   3. Taylor expanded in i around 0 29.5%

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

   4. Taylor expanded in t around 0 65.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.22 \cdot 10^{+49}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+76}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+51} \lor \neg \left(y \leq 1.52 \cdot 10^{+68}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.9e+51) (not (<= y 1.52e+68)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.9e+51) || !(y <= 1.52e+68)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * ((y * (y + a)) + 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 <= (-5.9d+51)) .or. (.not. (y <= 1.52d+68))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * ((y * (y + a)) + 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 <= -5.9e+51) || !(y <= 1.52e+68)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5.9e+51) or not (y <= 1.52e+68):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5.9e+51) || !(y <= 1.52e+68))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5.9e+51) || ~((y <= 1.52e+68)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5.9e+51], N[Not[LessEqual[y, 1.52e+68]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.89999999999999983e51 or 1.52000000000000008e68 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 77.9%

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

   if -5.89999999999999983e51 < y < 1.52000000000000008e68

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0 88.0%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+51} \lor \neg \left(y \leq 1.52 \cdot 10^{+68}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.55 \cdot 10^{+49} \lor \neg \left(y \leq 1.52 \cdot 10^{+68}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.55e+49) (not (<= y 1.52e+68)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.55e+49) || !(y <= 1.52e+68)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + 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 <= (-4.55d+49)) .or. (.not. (y <= 1.52d+68))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * ((y * (y + a)) + 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 <= -4.55e+49) || !(y <= 1.52e+68)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.55e+49) or not (y <= 1.52e+68):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.55e+49) || !(y <= 1.52e+68))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.55e+49) || ~((y <= 1.52e+68)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.55e+49], N[Not[LessEqual[y, 1.52e+68]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.54999999999999993e49 or 1.52000000000000008e68 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 77.9%

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

   if -4.54999999999999993e49 < y < 1.52000000000000008e68

   1. Initial program 93.9%

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

   3. Taylor expanded in y around 0 80.7%

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

      1. *-commutative 80.7%

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

   5. Simplified 80.7%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.55 \cdot 10^{+49} \lor \neg \left(y \leq 1.52 \cdot 10^{+68}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{t}{y}}{y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-42}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (/ t y) (* y (+ (* y (+ y a)) b))))
        (t_2 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.32e+49)
     t_2
     (if (<= y -2.5e-35)
       t_1
       (if (<= y 8.6e-42)
         (/ (+ t (* y 230661.510616)) i)
         (if (<= y 6e+59) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t / y) / (y * ((y * (y + a)) + b));
	double t_2 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.32e+49) {
		tmp = t_2;
	} else if (y <= -2.5e-35) {
		tmp = t_1;
	} else if (y <= 8.6e-42) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 6e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t / y) / (y * ((y * (y + a)) + b))
    t_2 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.32d+49)) then
        tmp = t_2
    else if (y <= (-2.5d-35)) then
        tmp = t_1
    else if (y <= 8.6d-42) then
        tmp = (t + (y * 230661.510616d0)) / i
    else if (y <= 6d+59) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t / y) / (y * ((y * (y + a)) + b));
	double t_2 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.32e+49) {
		tmp = t_2;
	} else if (y <= -2.5e-35) {
		tmp = t_1;
	} else if (y <= 8.6e-42) {
		tmp = (t + (y * 230661.510616)) / i;
	} else if (y <= 6e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t / y) / (y * ((y * (y + a)) + b))
	t_2 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.32e+49:
		tmp = t_2
	elif y <= -2.5e-35:
		tmp = t_1
	elif y <= 8.6e-42:
		tmp = (t + (y * 230661.510616)) / i
	elif y <= 6e+59:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t / y) / Float64(y * Float64(Float64(y * Float64(y + a)) + b)))
	t_2 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.32e+49)
		tmp = t_2;
	elseif (y <= -2.5e-35)
		tmp = t_1;
	elseif (y <= 8.6e-42)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	elseif (y <= 6e+59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t / y) / (y * ((y * (y + a)) + b));
	t_2 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.32e+49)
		tmp = t_2;
	elseif (y <= -2.5e-35)
		tmp = t_1;
	elseif (y <= 8.6e-42)
		tmp = (t + (y * 230661.510616)) / i;
	elseif (y <= 6e+59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t / y), $MachinePrecision] / N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.32e+49], t$95$2, If[LessEqual[y, -2.5e-35], t$95$1, If[LessEqual[y, 8.6e-42], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 6e+59], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.32000000000000009e49 or 6.0000000000000001e59 < y

   1. Initial program 5.8%

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

   3. Taylor expanded in y around inf 74.8%

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

   if -1.32000000000000009e49 < y < -2.49999999999999982e-35 or 8.6000000000000002e-42 < y < 6.0000000000000001e59

   1. Initial program 80.2%

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

   3. Taylor expanded in i around 0 67.6%

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

   4. Taylor expanded in t around inf 35.5%

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

      1. associate-/r* 37.6%

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

      2. +-commutative 37.6%

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

      3. fma-undefine 37.6%

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

      4. +-commutative 37.6%

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

      5. +-commutative 37.6%

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

      6. fma-undefine 37.6%

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

   6. Simplified 37.6%

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

   7. Taylor expanded in c around 0 34.7%

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

   if -2.49999999999999982e-35 < y < 8.6000000000000002e-42

   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. Add Preprocessing

   3. Taylor expanded in y around 0 52.3%

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

      1. fma-define 52.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

      2. associate-*r/ 52.4%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616 \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      3. metadata-eval 52.4%

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{230661.510616}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. associate-/l* 55.8%

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i} - \color{blue}{c \cdot \frac{t}{{i}^{2}}}, \frac{t}{i}\right) \]

   5. Simplified 55.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{230661.510616}{i} - c \cdot \frac{t}{{i}^{2}}, \frac{t}{i}\right)} \]

   6. Taylor expanded in i around inf 63.4%

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

      1. *-commutative 63.4%

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

   8. Simplified 63.4%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+49}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{t}{y}}{y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-42}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+59}:\\ \;\;\;\;\frac{\frac{t}{y}}{y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+49} \lor \neg \left(y \leq 2.05 \cdot 10^{+52}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.1e+49) (not (<= y 2.05e+52)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.1e+49) || !(y <= 2.05e+52)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.1d+49)) .or. (.not. (y <= 2.05d+52))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.1e+49) || !(y <= 2.05e+52)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.1e+49) or not (y <= 2.05e+52):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.1e+49) || !(y <= 2.05e+52))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.1e+49) || ~((y <= 2.05e+52)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.1e+49], N[Not[LessEqual[y, 2.05e+52]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e49 or 2.05e52 < y

   1. Initial program 5.8%

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

   3. Taylor expanded in y around inf 74.1%

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

   if -1.1e49 < y < 2.05e52

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 81.9%

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

      1. *-commutative 81.9%

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

   5. Simplified 81.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+49} \lor \neg \left(y \leq 2.05 \cdot 10^{+52}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+49} \lor \neg \left(y \leq 2.6 \cdot 10^{+52}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.2e+49) (not (<= y 2.6e+52)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/ t (+ i (* y (+ c (* y (+ (* y (+ y a)) b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.2e+49) || !(y <= 2.6e+52)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + 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 <= (-5.2d+49)) .or. (.not. (y <= 2.6d+52))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = t / (i + (y * (c + (y * ((y * (y + a)) + 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 <= -5.2e+49) || !(y <= 2.6e+52)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5.2e+49) or not (y <= 2.6e+52):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5.2e+49) || !(y <= 2.6e+52))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5.2e+49) || ~((y <= 2.6e+52)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = t / (i + (y * (c + (y * ((y * (y + a)) + b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5.2e+49], N[Not[LessEqual[y, 2.6e+52]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999977e49 or 2.6e52 < y

   1. Initial program 5.8%

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

   3. Taylor expanded in y around inf 74.1%

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

   if -5.19999999999999977e49 < y < 2.6e52

   1. Initial program 94.9%

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

   3. Taylor expanded in t around inf 68.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+49} \lor \neg \left(y \leq 2.6 \cdot 10^{+52}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+35} \lor \neg \left(y \leq 1.6 \cdot 10^{+52}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8.6e+35) (not (<= y 1.6e+52)))
   (- (+ x (/ z y)) (/ (* x a) y))
   (/ (+ t (* y 230661.510616)) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.6e+35) || !(y <= 1.6e+52)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / 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 <= (-8.6d+35)) .or. (.not. (y <= 1.6d+52))) then
        tmp = (x + (z / y)) - ((x * a) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / 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 <= -8.6e+35) || !(y <= 1.6e+52)) {
		tmp = (x + (z / y)) - ((x * a) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -8.6e+35) or not (y <= 1.6e+52):
		tmp = (x + (z / y)) - ((x * a) / y)
	else:
		tmp = (t + (y * 230661.510616)) / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -8.6e+35) || !(y <= 1.6e+52))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -8.6e+35) || ~((y <= 1.6e+52)))
		tmp = (x + (z / y)) - ((x * a) / y);
	else
		tmp = (t + (y * 230661.510616)) / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -8.6e+35], N[Not[LessEqual[y, 1.6e+52]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5999999999999995e35 or 1.6e52 < y

   1. Initial program 7.6%

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

   3. Taylor expanded in y around inf 71.8%

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

   if -8.5999999999999995e35 < y < 1.6e52

   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. Add Preprocessing

   3. Taylor expanded in y around 0 40.1%

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

      1. fma-define 40.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

      2. associate-*r/ 40.1%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616 \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      3. metadata-eval 40.1%

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{230661.510616}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. associate-/l* 42.7%

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i} - \color{blue}{c \cdot \frac{t}{{i}^{2}}}, \frac{t}{i}\right) \]

   5. Simplified 42.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{230661.510616}{i} - c \cdot \frac{t}{{i}^{2}}, \frac{t}{i}\right)} \]

   6. Taylor expanded in i around inf 48.5%

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

      1. *-commutative 48.5%

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

   8. Simplified 48.5%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+35} \lor \neg \left(y \leq 1.6 \cdot 10^{+52}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+20}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.4e+41) x (if (<= y 1.18e+20) (/ (+ t (* y 230661.510616)) i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.4e+41) {
		tmp = x;
	} else if (y <= 1.18e+20) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.4d+41)) then
        tmp = x
    else if (y <= 1.18d+20) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.4e+41) {
		tmp = x;
	} else if (y <= 1.18e+20) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.4e+41:
		tmp = x
	elif y <= 1.18e+20:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.4e+41)
		tmp = x;
	elseif (y <= 1.18e+20)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.4e+41)
		tmp = x;
	elseif (y <= 1.18e+20)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.4e+41], x, If[LessEqual[y, 1.18e+20], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4000000000000002e41 or 1.18e20 < y

   1. Initial program 10.1%

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

   3. Taylor expanded in y around inf 52.3%

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

   if -2.4000000000000002e41 < y < 1.18e20

   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. Add Preprocessing

   3. Taylor expanded in y around 0 42.1%

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

      1. fma-define 42.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

      2. associate-*r/ 42.1%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616 \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      3. metadata-eval 42.1%

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{230661.510616}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. associate-/l* 44.8%

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i} - \color{blue}{c \cdot \frac{t}{{i}^{2}}}, \frac{t}{i}\right) \]

   5. Simplified 44.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{230661.510616}{i} - c \cdot \frac{t}{{i}^{2}}, \frac{t}{i}\right)} \]

   6. Taylor expanded in i around inf 50.9%

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

      1. *-commutative 50.9%

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

   8. Simplified 50.9%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+20}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.4e+36) x (if (<= y 6.8e+20) (/ 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 <= -2.4e+36) {
		tmp = x;
	} else if (y <= 6.8e+20) {
		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 <= (-2.4d+36)) then
        tmp = x
    else if (y <= 6.8d+20) 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 <= -2.4e+36) {
		tmp = x;
	} else if (y <= 6.8e+20) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.4e+36:
		tmp = x
	elif y <= 6.8e+20:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.4e+36)
		tmp = x;
	elseif (y <= 6.8e+20)
		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 <= -2.4e+36)
		tmp = x;
	elseif (y <= 6.8e+20)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.4e+36], x, If[LessEqual[y, 6.8e+20], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999992e36 or 6.8e20 < y

   1. Initial program 10.1%

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

   3. Taylor expanded in y around inf 52.3%

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

   if -2.39999999999999992e36 < y < 6.8e20

   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. Add Preprocessing

   3. Taylor expanded in y around 0 43.6%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.6% accurate, 33.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return x;
}

Python

def code(x, y, z, t, a, b, c, i):
	return x

Julia

function code(x, y, z, t, a, b, c, i)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := x

Derivation

1. Initial program 62.5%

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

3. Taylor expanded in y around inf 23.6%

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

4. Final simplification 23.6%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(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)))