Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.0% → 84.4%

Time: 29.7s

Alternatives: 14

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ t_2 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{\frac{t}{t\_2} + y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t\_2}}{x} + \frac{{y}^{4}}{t\_2}\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
           t)
          (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c)))))
        (t_2 (fma y (fma y (fma y (+ y a) b) c) i)))
   (if (<= t_1 (- INFINITY))
     (*
      x
      (+
       (/
        (+
         (/ t t_2)
         (* y (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) t_2)))
        x)
       (/ (pow y 4.0) t_2)))
     (if (<= t_1 INFINITY) t_1 (+ x (- (/ z y) (* a (/ x 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 * ((y * ((y * (y + a)) + b)) + c)));
	double t_2 = fma(y, fma(y, fma(y, (y + a), b), c), i);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x * ((((t / t_2) + (y * ((230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2))) / x) + (pow(y, 4.0) / t_2));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a * (x / 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(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))))
	t_2 = fma(y, fma(y, fma(y, Float64(y + a), b), c), i)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(Float64(Float64(t / t_2) + Float64(y * Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / t_2))) / x) + Float64((y ^ 4.0) / t_2)));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	end
	return 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[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x * N[(N[(N[(N[(t / t$95$2), $MachinePrecision] + N[(y * N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + N[(N[Power[y, 4.0], $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < -inf.0

   1. Initial program 34.1%

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

   3. Taylor expanded in x around -inf 61.8%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}}{x} + -1 \cdot \frac{{y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right)} \]

   5. Simplified 80.3%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \left(-1 \cdot \left(\frac{\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)} + y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}}{x} + \frac{{y}^{4}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 92.6%

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

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) 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 61.4%

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

      1. associate--l+ 61.4%

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

      2. associate-/l* 65.7%

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

   5. Simplified 65.7%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)} + y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}}{x} + \frac{{y}^{4}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\\ \mathbf{elif}\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)} \leq \infty:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
           t)
          (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))))
   (if (<= t_1 INFINITY) t_1 (+ x (- (/ z y) (* a (/ x 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 * ((y * ((y * (y + a)) + b)) + c)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a * (x / 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 * ((y * ((y * (y + a)) + b)) + c)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x + ((z / y) - (a * (x / 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 * ((y * ((y * (y + a)) + b)) + c)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = x + ((z / y) - (a * (x / 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(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / 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 * ((y * ((y * (y + a)) + b)) + c)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x + ((z / y) - (a * (x / 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[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 89.1%

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

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) 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 61.4%

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

      1. associate--l+ 61.4%

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

      2. associate-/l* 65.7%

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

   5. Simplified 65.7%

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

4. Final simplification 81.3%

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

Alternative 3: 55.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot 230661.510616}{y \cdot c}\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-120}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+38}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (+ t (* y 230661.510616)) (* y c)))
        (t_2 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.85e-20)
     t_2
     (if (<= y -1.2e-152)
       t_1
       (if (<= y 3.5e-120)
         (/ t i)
         (if (<= y 8e-112)
           t_1
           (if (<= y 1.95e+38)
             (/
              (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))
              c)
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / (y * c);
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.85e-20) {
		tmp = t_2;
	} else if (y <= -1.2e-152) {
		tmp = t_1;
	} else if (y <= 3.5e-120) {
		tmp = t / i;
	} else if (y <= 8e-112) {
		tmp = t_1;
	} else if (y <= 1.95e+38) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t + (y * 230661.510616d0)) / (y * c)
    t_2 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.85d-20)) then
        tmp = t_2
    else if (y <= (-1.2d-152)) then
        tmp = t_1
    else if (y <= 3.5d-120) then
        tmp = t / i
    else if (y <= 8d-112) then
        tmp = t_1
    else if (y <= 1.95d+38) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))) / c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / (y * c);
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.85e-20) {
		tmp = t_2;
	} else if (y <= -1.2e-152) {
		tmp = t_1;
	} else if (y <= 3.5e-120) {
		tmp = t / i;
	} else if (y <= 8e-112) {
		tmp = t_1;
	} else if (y <= 1.95e+38) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * 230661.510616)) / (y * c)
	t_2 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.85e-20:
		tmp = t_2
	elif y <= -1.2e-152:
		tmp = t_1
	elif y <= 3.5e-120:
		tmp = t / i
	elif y <= 8e-112:
		tmp = t_1
	elif y <= 1.95e+38:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / c
	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)) / Float64(y * c))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.85e-20)
		tmp = t_2;
	elseif (y <= -1.2e-152)
		tmp = t_1;
	elseif (y <= 3.5e-120)
		tmp = Float64(t / i);
	elseif (y <= 8e-112)
		tmp = t_1;
	elseif (y <= 1.95e+38)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))) / c);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * 230661.510616)) / (y * c);
	t_2 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.85e-20)
		tmp = t_2;
	elseif (y <= -1.2e-152)
		tmp = t_1;
	elseif (y <= 3.5e-120)
		tmp = t / i;
	elseif (y <= 8e-112)
		tmp = t_1;
	elseif (y <= 1.95e+38)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(y * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e-20], t$95$2, If[LessEqual[y, -1.2e-152], t$95$1, If[LessEqual[y, 3.5e-120], N[(t / i), $MachinePrecision], If[LessEqual[y, 8e-112], t$95$1, If[LessEqual[y, 1.95e+38], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.85e-20 or 1.95000000000000012e38 < y

   1. Initial program 12.8%

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

   3. Taylor expanded in y around inf 50.3%

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

      1. associate--l+ 50.3%

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

      2. associate-/l* 53.5%

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

   5. Simplified 53.5%

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

   if -1.85e-20 < y < -1.2e-152 or 3.5e-120 < y < 7.9999999999999996e-112

   1. Initial program 99.5%

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

   3. Taylor expanded in c around inf 50.8%

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

   4. Taylor expanded in y around 0 43.9%

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

   if -1.2e-152 < y < 3.5e-120

   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 y around 0 80.3%

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

   if 7.9999999999999996e-112 < y < 1.95000000000000012e38

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 57.2%

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

   4. Taylor expanded in c around inf 24.4%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-20}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-152}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-120}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-112}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+38}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ t_2 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t\_2}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+88}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y)))))
        (t_2 (+ (* y (+ (* y (+ y a)) b)) c)))
   (if (<= y -5.6e+103)
     t_1
     (if (<= y 2.05e-27)
       (/ (+ t (* y 230661.510616)) (+ i (* y t_2)))
       (if (<= y 5.4e+88)
         (/ (+ 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) - (a * (x / y)));
	double t_2 = (y * ((y * (y + a)) + b)) + c;
	double tmp;
	if (y <= -5.6e+103) {
		tmp = t_1;
	} else if (y <= 2.05e-27) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 5.4e+88) {
		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) - (a * (x / y)))
    t_2 = (y * ((y * (y + a)) + b)) + c
    if (y <= (-5.6d+103)) then
        tmp = t_1
    else if (y <= 2.05d-27) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_2))
    else if (y <= 5.4d+88) 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) - (a * (x / y)));
	double t_2 = (y * ((y * (y + a)) + b)) + c;
	double tmp;
	if (y <= -5.6e+103) {
		tmp = t_1;
	} else if (y <= 2.05e-27) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 5.4e+88) {
		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) - (a * (x / y)))
	t_2 = (y * ((y * (y + a)) + b)) + c
	tmp = 0
	if y <= -5.6e+103:
		tmp = t_1
	elif y <= 2.05e-27:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2))
	elif y <= 5.4e+88:
		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(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	t_2 = Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)
	tmp = 0.0
	if (y <= -5.6e+103)
		tmp = t_1;
	elseif (y <= 2.05e-27)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_2)));
	elseif (y <= 5.4e+88)
		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) - (a * (x / y)));
	t_2 = (y * ((y * (y + a)) + b)) + c;
	tmp = 0.0;
	if (y <= -5.6e+103)
		tmp = t_1;
	elseif (y <= 2.05e-27)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	elseif (y <= 5.4e+88)
		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[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, If[LessEqual[y, -5.6e+103], t$95$1, If[LessEqual[y, 2.05e-27], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+88], 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 < -5.60000000000000017e103 or 5.40000000000000031e88 < y

   1. Initial program 0.2%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. associate--l+ 66.4%

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

      2. associate-/l* 70.9%

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

   5. Simplified 70.9%

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

   if -5.60000000000000017e103 < y < 2.0499999999999999e-27

   1. Initial program 91.9%

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

   3. Taylor expanded in y around 0 82.4%

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

      1. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   if 2.0499999999999999e-27 < y < 5.40000000000000031e88

   1. Initial program 55.5%

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

   3. Taylor expanded in t around 0 40.6%

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

   4. Taylor expanded in i around 0 46.1%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+88}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot t\_1}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+83}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ y a)) b)) c))
        (t_2 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -5.6e+103)
     t_2
     (if (<= y 2e-27)
       (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) (+ i (* y t_1)))
       (if (<= y 1.08e+83)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))) 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 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.6e+103) {
		tmp = t_2;
	} else if (y <= 2e-27) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 1.08e+83) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / 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 = (y * ((y * (y + a)) + b)) + c
    t_2 = x + ((z / y) - (a * (x / y)))
    if (y <= (-5.6d+103)) then
        tmp = t_2
    else if (y <= 2d-27) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * t_1))
    else if (y <= 1.08d+83) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))) / 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 = (y * ((y * (y + a)) + b)) + c;
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.6e+103) {
		tmp = t_2;
	} else if (y <= 2e-27) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	} else if (y <= 1.08e+83) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * ((y * (y + a)) + b)) + c
	t_2 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -5.6e+103:
		tmp = t_2
	elif y <= 2e-27:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1))
	elif y <= 1.08e+83:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -5.6e+103)
		tmp = t_2;
	elseif (y <= 2e-27)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * t_1)));
	elseif (y <= 1.08e+83)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))) / 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 = (y * ((y * (y + a)) + b)) + c;
	t_2 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -5.6e+103)
		tmp = t_2;
	elseif (y <= 2e-27)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * t_1));
	elseif (y <= 1.08e+83)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / 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[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e+103], t$95$2, If[LessEqual[y, 2e-27], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e+83], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.60000000000000017e103 or 1.08e83 < y

   1. Initial program 0.2%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. associate--l+ 66.4%

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

      2. associate-/l* 70.9%

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

   5. Simplified 70.9%

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

   if -5.60000000000000017e103 < y < 2.0000000000000001e-27

   1. Initial program 91.9%

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

   3. Taylor expanded in y around 0 83.0%

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

      1. *-commutative 83.0%

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

   5. Simplified 83.0%

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

   if 2.0000000000000001e-27 < y < 1.08e83

   1. Initial program 55.5%

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

   3. Taylor expanded in t around 0 40.6%

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

   4. Taylor expanded in i around 0 46.1%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+83}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+89} \lor \neg \left(y \leq 2.65 \cdot 10^{+47}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.15e+89) (not (<= y 2.65e+47)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.15e+89) || !(y <= 2.65e+47)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-2.15d+89)) .or. (.not. (y <= 2.65d+47))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -2.15e+89) || !(y <= 2.65e+47)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.15e+89) or not (y <= 2.65e+47):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.15e+89) || !(y <= 2.65e+47))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -2.15e+89) || ~((y <= 2.65e+47)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.15e+89], N[Not[LessEqual[y, 2.65e+47]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1500000000000001e89 or 2.65e47 < y

   1. Initial program 1.6%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. associate--l+ 62.5%

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

      2. associate-/l* 66.7%

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

   5. Simplified 66.7%

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

   if -2.1500000000000001e89 < y < 2.65e47

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 85.3%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+89} \lor \neg \left(y \leq 2.65 \cdot 10^{+47}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+82}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{c + y \cdot \left(b + y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -5.6e+103)
     t_1
     (if (<= y 2.1e-27)
       (/
        (+ t (* y 230661.510616))
        (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))
       (if (<= y 2.25e+82)
         (/
          (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))
          (+ c (* y (+ b (* y a)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.6e+103) {
		tmp = t_1;
	} else if (y <= 2.1e-27) {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	} else if (y <= 2.25e+82) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / (c + (y * (b + (y * a))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    if (y <= (-5.6d+103)) then
        tmp = t_1
    else if (y <= 2.1d-27) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    else if (y <= 2.25d+82) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))) / (c + (y * (b + (y * a))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -5.6e+103) {
		tmp = t_1;
	} else if (y <= 2.1e-27) {
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	} else if (y <= 2.25e+82) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / (c + (y * (b + (y * a))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -5.6e+103:
		tmp = t_1
	elif y <= 2.1e-27:
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	elif y <= 2.25e+82:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / (c + (y * (b + (y * a))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -5.6e+103)
		tmp = t_1;
	elseif (y <= 2.1e-27)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	elseif (y <= 2.25e+82)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))) / Float64(c + Float64(y * Float64(b + Float64(y * a)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -5.6e+103)
		tmp = t_1;
	elseif (y <= 2.1e-27)
		tmp = (t + (y * 230661.510616)) / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	elseif (y <= 2.25e+82)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))) / (c + (y * (b + (y * a))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e+103], t$95$1, If[LessEqual[y, 2.1e-27], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+82], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.60000000000000017e103 or 2.2499999999999998e82 < y

   1. Initial program 0.2%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. associate--l+ 66.4%

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

      2. associate-/l* 70.9%

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

   5. Simplified 70.9%

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

   if -5.60000000000000017e103 < y < 2.10000000000000015e-27

   1. Initial program 91.9%

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

   3. Taylor expanded in y around 0 82.4%

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

      1. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   if 2.10000000000000015e-27 < y < 2.2499999999999998e82

   1. Initial program 55.5%

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

   3. Taylor expanded in t around 0 40.6%

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

   4. Taylor expanded in i around 0 46.1%

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

   5. Taylor expanded in y around 0 45.3%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+82}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{c + y \cdot \left(b + y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ t_2 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot t\_2}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t\_2}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+67}:\\ \;\;\;\;\frac{27464.7644705 + \left(y \cdot \left(x \cdot y + z\right) + 230661.510616 \cdot \frac{1}{y}\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y)))))
        (t_2 (+ (* y (+ (* y (+ y a)) b)) c)))
   (if (<= y -5.6e+103)
     t_1
     (if (<= y 2.1e-27)
       (/ (+ t (* y 230661.510616)) (+ i (* y t_2)))
       (if (<= y 2.9e+46)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* y z)))) t_2)
         (if (<= y 1.1e+67)
           (/
            (+
             27464.7644705
             (+ (* y (+ (* x y) z)) (* 230661.510616 (/ 1.0 y))))
            b)
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double t_2 = (y * ((y * (y + a)) + b)) + c;
	double tmp;
	if (y <= -5.6e+103) {
		tmp = t_1;
	} else if (y <= 2.1e-27) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 2.9e+46) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	} else if (y <= 1.1e+67) {
		tmp = (27464.7644705 + ((y * ((x * y) + z)) + (230661.510616 * (1.0 / y)))) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z / y) - (a * (x / y)))
    t_2 = (y * ((y * (y + a)) + b)) + c
    if (y <= (-5.6d+103)) then
        tmp = t_1
    else if (y <= 2.1d-27) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * t_2))
    else if (y <= 2.9d+46) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))) / t_2
    else if (y <= 1.1d+67) then
        tmp = (27464.7644705d0 + ((y * ((x * y) + z)) + (230661.510616d0 * (1.0d0 / y)))) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z / y) - (a * (x / y)));
	double t_2 = (y * ((y * (y + a)) + b)) + c;
	double tmp;
	if (y <= -5.6e+103) {
		tmp = t_1;
	} else if (y <= 2.1e-27) {
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	} else if (y <= 2.9e+46) {
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	} else if (y <= 1.1e+67) {
		tmp = (27464.7644705 + ((y * ((x * y) + z)) + (230661.510616 * (1.0 / y)))) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z / y) - (a * (x / y)))
	t_2 = (y * ((y * (y + a)) + b)) + c
	tmp = 0
	if y <= -5.6e+103:
		tmp = t_1
	elif y <= 2.1e-27:
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2))
	elif y <= 2.9e+46:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2
	elif y <= 1.1e+67:
		tmp = (27464.7644705 + ((y * ((x * y) + z)) + (230661.510616 * (1.0 / y)))) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	t_2 = Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)
	tmp = 0.0
	if (y <= -5.6e+103)
		tmp = t_1;
	elseif (y <= 2.1e-27)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * t_2)));
	elseif (y <= 2.9e+46)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))) / t_2);
	elseif (y <= 1.1e+67)
		tmp = Float64(Float64(27464.7644705 + Float64(Float64(y * Float64(Float64(x * y) + z)) + Float64(230661.510616 * Float64(1.0 / y)))) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z / y) - (a * (x / y)));
	t_2 = (y * ((y * (y + a)) + b)) + c;
	tmp = 0.0;
	if (y <= -5.6e+103)
		tmp = t_1;
	elseif (y <= 2.1e-27)
		tmp = (t + (y * 230661.510616)) / (i + (y * t_2));
	elseif (y <= 2.9e+46)
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2;
	elseif (y <= 1.1e+67)
		tmp = (27464.7644705 + ((y * ((x * y) + z)) + (230661.510616 * (1.0 / y)))) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, If[LessEqual[y, -5.6e+103], t$95$1, If[LessEqual[y, 2.1e-27], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+46], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 1.1e+67], N[(N[(27464.7644705 + N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + N[(230661.510616 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.60000000000000017e103 or 1.1e67 < y

   1. Initial program 0.3%

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

   3. Taylor expanded in y around inf 65.6%

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

      1. associate--l+ 65.6%

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

      2. associate-/l* 70.1%

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

   5. Simplified 70.1%

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

   if -5.60000000000000017e103 < y < 2.10000000000000015e-27

   1. Initial program 91.9%

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

   3. Taylor expanded in y around 0 82.4%

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

      1. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   if 2.10000000000000015e-27 < y < 2.9000000000000002e46

   1. Initial program 67.6%

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

   3. Taylor expanded in t around 0 51.4%

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

   4. Taylor expanded in i around 0 53.5%

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

   5. Taylor expanded in x around 0 48.2%

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

   if 2.9000000000000002e46 < y < 1.1e67

   1. Initial program 31.7%

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

   3. Taylor expanded in t around 0 18.2%

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

   4. Taylor expanded in b around inf 0.2%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{\left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right)\right) \cdot \left(i + y \cdot \left(c + {y}^{2} \cdot \left(a + y\right)\right)\right)}{b \cdot {y}^{3}} + \left(\left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right) + 230661.510616 \cdot \frac{1}{y}\right)}{b}} \]
   5. Step-by-step derivation

      1. fma-define 0.2%

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

      2. associate-/l* 14.5%

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

      3. associate-+l+ 14.5%

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

      4. associate-*r/ 14.5%

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

      5. metadata-eval 14.5%

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

   6. Simplified 14.5%

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

   7. Taylor expanded in b around inf 46.1%

      \[\leadsto \frac{\color{blue}{27464.7644705 + \left(230661.510616 \cdot \frac{1}{y} + y \cdot \left(z + x \cdot y\right)\right)}}{b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+67}:\\ \;\;\;\;\frac{27464.7644705 + \left(y \cdot \left(x \cdot y + z\right) + 230661.510616 \cdot \frac{1}{y}\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot 230661.510616}{y \cdot c}\\ t_2 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ (+ t (* y 230661.510616)) (* y c)))
        (t_2 (+ x (- (/ z y) (* a (/ x y))))))
   (if (<= y -1.85e-20)
     t_2
     (if (<= y -1.1e-149)
       t_1
       (if (<= y 3.2e-120)
         (/ t i)
         (if (<= y 1.45e-115) t_1 (if (<= y 5.4e+34) (/ t i) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / (y * c);
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.85e-20) {
		tmp = t_2;
	} else if (y <= -1.1e-149) {
		tmp = t_1;
	} else if (y <= 3.2e-120) {
		tmp = t / i;
	} else if (y <= 1.45e-115) {
		tmp = t_1;
	} else if (y <= 5.4e+34) {
		tmp = t / i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t + (y * 230661.510616d0)) / (y * c)
    t_2 = x + ((z / y) - (a * (x / y)))
    if (y <= (-1.85d-20)) then
        tmp = t_2
    else if (y <= (-1.1d-149)) then
        tmp = t_1
    else if (y <= 3.2d-120) then
        tmp = t / i
    else if (y <= 1.45d-115) then
        tmp = t_1
    else if (y <= 5.4d+34) then
        tmp = t / i
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * 230661.510616)) / (y * c);
	double t_2 = x + ((z / y) - (a * (x / y)));
	double tmp;
	if (y <= -1.85e-20) {
		tmp = t_2;
	} else if (y <= -1.1e-149) {
		tmp = t_1;
	} else if (y <= 3.2e-120) {
		tmp = t / i;
	} else if (y <= 1.45e-115) {
		tmp = t_1;
	} else if (y <= 5.4e+34) {
		tmp = t / i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * 230661.510616)) / (y * c)
	t_2 = x + ((z / y) - (a * (x / y)))
	tmp = 0
	if y <= -1.85e-20:
		tmp = t_2
	elif y <= -1.1e-149:
		tmp = t_1
	elif y <= 3.2e-120:
		tmp = t / i
	elif y <= 1.45e-115:
		tmp = t_1
	elif y <= 5.4e+34:
		tmp = t / i
	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)) / Float64(y * c))
	t_2 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	tmp = 0.0
	if (y <= -1.85e-20)
		tmp = t_2;
	elseif (y <= -1.1e-149)
		tmp = t_1;
	elseif (y <= 3.2e-120)
		tmp = Float64(t / i);
	elseif (y <= 1.45e-115)
		tmp = t_1;
	elseif (y <= 5.4e+34)
		tmp = Float64(t / i);
	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)) / (y * c);
	t_2 = x + ((z / y) - (a * (x / y)));
	tmp = 0.0;
	if (y <= -1.85e-20)
		tmp = t_2;
	elseif (y <= -1.1e-149)
		tmp = t_1;
	elseif (y <= 3.2e-120)
		tmp = t / i;
	elseif (y <= 1.45e-115)
		tmp = t_1;
	elseif (y <= 5.4e+34)
		tmp = t / i;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(y * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e-20], t$95$2, If[LessEqual[y, -1.1e-149], t$95$1, If[LessEqual[y, 3.2e-120], N[(t / i), $MachinePrecision], If[LessEqual[y, 1.45e-115], t$95$1, If[LessEqual[y, 5.4e+34], N[(t / i), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85e-20 or 5.4000000000000001e34 < y

   1. Initial program 13.6%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. associate-/l* 53.1%

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

   5. Simplified 53.1%

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

   if -1.85e-20 < y < -1.0999999999999999e-149 or 3.1999999999999999e-120 < y < 1.4499999999999999e-115

   1. Initial program 99.5%

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

   3. Taylor expanded in c around inf 50.8%

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

   4. Taylor expanded in y around 0 43.9%

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

   if -1.0999999999999999e-149 < y < 3.1999999999999999e-120 or 1.4499999999999999e-115 < y < 5.4000000000000001e34

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0 60.7%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-20}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-149}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-115}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ t_2 := y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{t}{i + y \cdot t\_2}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+70}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (- (/ z y) (* a (/ x y)))))
        (t_2 (+ (* y (+ (* y (+ y a)) b)) c)))
   (if (<= y -5.6e+103)
     t_1
     (if (<= y 2.1e-27)
       (/ t (+ i (* y t_2)))
       (if (<= y 1.26e+70)
         (/ (+ 230661.510616 (* y (+ 27464.7644705 (* 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) - (a * (x / y)));
	double t_2 = (y * ((y * (y + a)) + b)) + c;
	double tmp;
	if (y <= -5.6e+103) {
		tmp = t_1;
	} else if (y <= 2.1e-27) {
		tmp = t / (i + (y * t_2));
	} else if (y <= 1.26e+70) {
		tmp = (230661.510616 + (y * (27464.7644705 + (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) - (a * (x / y)))
    t_2 = (y * ((y * (y + a)) + b)) + c
    if (y <= (-5.6d+103)) then
        tmp = t_1
    else if (y <= 2.1d-27) then
        tmp = t / (i + (y * t_2))
    else if (y <= 1.26d+70) then
        tmp = (230661.510616d0 + (y * (27464.7644705d0 + (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) - (a * (x / y)));
	double t_2 = (y * ((y * (y + a)) + b)) + c;
	double tmp;
	if (y <= -5.6e+103) {
		tmp = t_1;
	} else if (y <= 2.1e-27) {
		tmp = t / (i + (y * t_2));
	} else if (y <= 1.26e+70) {
		tmp = (230661.510616 + (y * (27464.7644705 + (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) - (a * (x / y)))
	t_2 = (y * ((y * (y + a)) + b)) + c
	tmp = 0
	if y <= -5.6e+103:
		tmp = t_1
	elif y <= 2.1e-27:
		tmp = t / (i + (y * t_2))
	elif y <= 1.26e+70:
		tmp = (230661.510616 + (y * (27464.7644705 + (y * z)))) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))))
	t_2 = Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)
	tmp = 0.0
	if (y <= -5.6e+103)
		tmp = t_1;
	elseif (y <= 2.1e-27)
		tmp = Float64(t / Float64(i + Float64(y * t_2)));
	elseif (y <= 1.26e+70)
		tmp = Float64(Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(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) - (a * (x / y)));
	t_2 = (y * ((y * (y + a)) + b)) + c;
	tmp = 0.0;
	if (y <= -5.6e+103)
		tmp = t_1;
	elseif (y <= 2.1e-27)
		tmp = t / (i + (y * t_2));
	elseif (y <= 1.26e+70)
		tmp = (230661.510616 + (y * (27464.7644705 + (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[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, If[LessEqual[y, -5.6e+103], t$95$1, If[LessEqual[y, 2.1e-27], N[(t / N[(i + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+70], N[(N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.60000000000000017e103 or 1.26000000000000001e70 < y

   1. Initial program 0.2%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. associate--l+ 66.4%

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

      2. associate-/l* 70.9%

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

   5. Simplified 70.9%

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

   if -5.60000000000000017e103 < y < 2.10000000000000015e-27

   1. Initial program 91.9%

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

   3. Taylor expanded in t around inf 66.7%

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

   if 2.10000000000000015e-27 < y < 1.26000000000000001e70

   1. Initial program 55.5%

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

   3. Taylor expanded in t around 0 40.6%

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

   4. Taylor expanded in i around 0 46.1%

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

   5. Taylor expanded in x around 0 38.5%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+70}:\\ \;\;\;\;\frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+103} \lor \neg \left(y \leq 2.45 \cdot 10^{+47}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.6e+103) (not (<= y 2.45e+47)))
   (+ x (- (/ z y) (* a (/ x y))))
   (/ t (+ i (* y (+ (* y (+ (* y (+ y a)) b)) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.6e+103) || !(y <= 2.45e+47)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-5.6d+103)) .or. (.not. (y <= 2.45d+47))) then
        tmp = x + ((z / y) - (a * (x / y)))
    else
        tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.6e+103) || !(y <= 2.45e+47)) {
		tmp = x + ((z / y) - (a * (x / y)));
	} else {
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5.6e+103) or not (y <= 2.45e+47):
		tmp = x + ((z / y) - (a * (x / y)))
	else:
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5.6e+103) || !(y <= 2.45e+47))
		tmp = Float64(x + Float64(Float64(z / y) - Float64(a * Float64(x / y))));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5.6e+103) || ~((y <= 2.45e+47)))
		tmp = x + ((z / y) - (a * (x / y)));
	else
		tmp = t / (i + (y * ((y * ((y * (y + a)) + b)) + c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5.6e+103], N[Not[LessEqual[y, 2.45e+47]], $MachinePrecision]], N[(x + N[(N[(z / y), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.60000000000000017e103 or 2.4500000000000001e47 < y

   1. Initial program 1.6%

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

   3. Taylor expanded in y around inf 63.2%

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

      1. associate--l+ 63.2%

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

      2. associate-/l* 67.4%

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

   5. Simplified 67.4%

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

   if -5.60000000000000017e103 < y < 2.4500000000000001e47

   1. Initial program 88.8%

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

   3. Taylor expanded in t around inf 61.5%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+103} \lor \neg \left(y \leq 2.45 \cdot 10^{+47}\right):\\ \;\;\;\;x + \left(\frac{z}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-120}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-113}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.6e+103)
   x
   (if (<= y 3.6e-120)
     (/ t i)
     (if (<= y 1.4e-113)
       (/ (+ t (* y 230661.510616)) (* y c))
       (if (<= y 1.8e+34) (/ 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 <= -5.6e+103) {
		tmp = x;
	} else if (y <= 3.6e-120) {
		tmp = t / i;
	} else if (y <= 1.4e-113) {
		tmp = (t + (y * 230661.510616)) / (y * c);
	} else if (y <= 1.8e+34) {
		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 <= (-5.6d+103)) then
        tmp = x
    else if (y <= 3.6d-120) then
        tmp = t / i
    else if (y <= 1.4d-113) then
        tmp = (t + (y * 230661.510616d0)) / (y * c)
    else if (y <= 1.8d+34) 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 <= -5.6e+103) {
		tmp = x;
	} else if (y <= 3.6e-120) {
		tmp = t / i;
	} else if (y <= 1.4e-113) {
		tmp = (t + (y * 230661.510616)) / (y * c);
	} else if (y <= 1.8e+34) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.6e+103:
		tmp = x
	elif y <= 3.6e-120:
		tmp = t / i
	elif y <= 1.4e-113:
		tmp = (t + (y * 230661.510616)) / (y * c)
	elif y <= 1.8e+34:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.6e+103)
		tmp = x;
	elseif (y <= 3.6e-120)
		tmp = Float64(t / i);
	elseif (y <= 1.4e-113)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(y * c));
	elseif (y <= 1.8e+34)
		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 <= -5.6e+103)
		tmp = x;
	elseif (y <= 3.6e-120)
		tmp = t / i;
	elseif (y <= 1.4e-113)
		tmp = (t + (y * 230661.510616)) / (y * c);
	elseif (y <= 1.8e+34)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.6e+103], x, If[LessEqual[y, 3.6e-120], N[(t / i), $MachinePrecision], If[LessEqual[y, 1.4e-113], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+34], N[(t / i), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.60000000000000017e103 or 1.8e34 < y

   1. Initial program 3.9%

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

   3. Taylor expanded in y around inf 50.7%

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

   if -5.60000000000000017e103 < y < 3.6000000000000003e-120 or 1.4e-113 < y < 1.8e34

   1. Initial program 90.5%

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

   3. Taylor expanded in y around 0 43.6%

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

   if 3.6000000000000003e-120 < y < 1.4e-113

   1. Initial program 99.4%

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

   3. Taylor expanded in c around inf 99.4%

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

   4. Taylor expanded in y around 0 99.4%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-120}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-113}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.6e+103) x (if (<= y 2.5e+34) (/ 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 <= -5.6e+103) {
		tmp = x;
	} else if (y <= 2.5e+34) {
		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 <= (-5.6d+103)) then
        tmp = x
    else if (y <= 2.5d+34) 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 <= -5.6e+103) {
		tmp = x;
	} else if (y <= 2.5e+34) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.6e+103:
		tmp = x
	elif y <= 2.5e+34:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.6e+103)
		tmp = x;
	elseif (y <= 2.5e+34)
		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 <= -5.6e+103)
		tmp = x;
	elseif (y <= 2.5e+34)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.6e+103], x, If[LessEqual[y, 2.5e+34], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.60000000000000017e103 or 2.4999999999999999e34 < y

   1. Initial program 3.9%

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

   3. Taylor expanded in y around inf 50.7%

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

   if -5.60000000000000017e103 < y < 2.4999999999999999e34

   1. Initial program 90.8%

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

   3. Taylor expanded in y around 0 42.3%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 26.1% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.2%

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

3. Taylor expanded in y around inf 20.8%

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

4. Final simplification 20.8%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024066 
(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)))