Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.8% → 83.9%

Time: 19.5s

Alternatives: 14

Speedup: 1.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
           t)
          (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))
   (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) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	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) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x + (z / y)) - (a * (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) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	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(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + 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) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	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[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $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 88.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   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 74.9%

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

      1. associate-/l* 79.1%

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

   5. Simplified 79.1%

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

4. Final simplification 85.1%

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

Alternative 2: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\\ t_2 := \left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{t\_1}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;\frac{y \cdot t\_1 + t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))
        (t_2 (- (+ x (/ z y)) (* a (/ x y)))))
   (if (<= y -1.75e+68)
     t_2
     (if (<= y -3.4e-13)
       (* y (/ t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
       (if (<= y 3.3e+38)
         (/ (+ (* y t_1) t) (+ i (* y (+ c (* y b)))))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))));
	double t_2 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -1.75e+68) {
		tmp = t_2;
	} else if (y <= -3.4e-13) {
		tmp = y * (t_1 / ((y * ((y * ((y * (y + a)) + b)) + c)) + i));
	} else if (y <= 3.3e+38) {
		tmp = ((y * t_1) + t) / (i + (y * (c + (y * b))));
	} 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 = 230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z))))
    t_2 = (x + (z / y)) - (a * (x / y))
    if (y <= (-1.75d+68)) then
        tmp = t_2
    else if (y <= (-3.4d-13)) then
        tmp = y * (t_1 / ((y * ((y * ((y * (y + a)) + b)) + c)) + i))
    else if (y <= 3.3d+38) then
        tmp = ((y * t_1) + t) / (i + (y * (c + (y * b))))
    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 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))));
	double t_2 = (x + (z / y)) - (a * (x / y));
	double tmp;
	if (y <= -1.75e+68) {
		tmp = t_2;
	} else if (y <= -3.4e-13) {
		tmp = y * (t_1 / ((y * ((y * ((y * (y + a)) + b)) + c)) + i));
	} else if (y <= 3.3e+38) {
		tmp = ((y * t_1) + t) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))
	t_2 = (x + (z / y)) - (a * (x / y))
	tmp = 0
	if y <= -1.75e+68:
		tmp = t_2
	elif y <= -3.4e-13:
		tmp = y * (t_1 / ((y * ((y * ((y * (y + a)) + b)) + c)) + i))
	elif y <= 3.3e+38:
		tmp = ((y * t_1) + t) / (i + (y * (c + (y * b))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))
	t_2 = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)))
	tmp = 0.0
	if (y <= -1.75e+68)
		tmp = t_2;
	elseif (y <= -3.4e-13)
		tmp = Float64(y * Float64(t_1 / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)));
	elseif (y <= 3.3e+38)
		tmp = Float64(Float64(Float64(y * t_1) + t) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))));
	t_2 = (x + (z / y)) - (a * (x / y));
	tmp = 0.0;
	if (y <= -1.75e+68)
		tmp = t_2;
	elseif (y <= -3.4e-13)
		tmp = y * (t_1 / ((y * ((y * ((y * (y + a)) + b)) + c)) + i));
	elseif (y <= 3.3e+38)
		tmp = ((y * t_1) + t) / (i + (y * (c + (y * b))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e+68], t$95$2, If[LessEqual[y, -3.4e-13], N[(y * N[(t$95$1 / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+38], N[(N[(N[(y * t$95$1), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.74999999999999989e68 or 3.2999999999999999e38 < y

   1. Initial program 2.1%

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

   3. Taylor expanded in y around inf 71.4%

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

      1. associate-/l* 75.3%

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

   5. Simplified 75.3%

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

   if -1.74999999999999989e68 < y < -3.40000000000000015e-13

   1. Initial program 56.3%

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

   3. Taylor expanded in t around inf 51.4%

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

   4. Taylor expanded in t around 0 47.7%

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

      1. associate-/l* 65.0%

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

   6. Simplified 65.0%

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

   if -3.40000000000000015e-13 < y < 3.2999999999999999e38

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 93.3%

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

      1. *-commutative 93.3%

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

   5. Simplified 93.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+68}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;\frac{y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right) + t}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+65} \lor \neg \left(y \leq 1.46 \cdot 10^{+47}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.4e+65) (not (<= y 1.46e+47)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.4e+65) || !(y <= 1.46e+47)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-4.4d+65)) .or. (.not. (y <= 1.46d+47))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.4e+65) || !(y <= 1.46e+47)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.4e+65) or not (y <= 1.46e+47):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.4e+65) || !(y <= 1.46e+47))
		tmp = Float64(Float64(x + 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(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.4e+65) || ~((y <= 1.46e+47)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.4e+65], N[Not[LessEqual[y, 1.46e+47]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $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[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999997e65 or 1.46000000000000006e47 < y

   1. Initial program 2.1%

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

   3. Taylor expanded in y around inf 71.6%

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

      1. associate-/l* 75.5%

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

   5. Simplified 75.5%

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

   if -4.3999999999999997e65 < y < 1.46000000000000006e47

   1. Initial program 92.9%

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

   3. Taylor expanded in x around 0 86.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+65} \lor \neg \left(y \leq 1.46 \cdot 10^{+47}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+37} \lor \neg \left(y \leq 5.3 \cdot 10^{+41}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4e+37) (not (<= y 5.3e+41)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y (+ b (* y a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4e+37) || !(y <= 5.3e+41)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	}
	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 <= (-4d+37)) .or. (.not. (y <= 5.3d+41))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
    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 <= -4e+37) || !(y <= 5.3e+41)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4e+37) or not (y <= 5.3e+41):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4e+37) || !(y <= 5.3e+41))
		tmp = Float64(Float64(x + 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(c + Float64(y * Float64(b + Float64(y * a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4e+37) || ~((y <= 5.3e+41)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4e+37], N[Not[LessEqual[y, 5.3e+41]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $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[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999982e37 or 5.2999999999999997e41 < y

   1. Initial program 5.7%

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

   3. Taylor expanded in y around inf 68.2%

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

      1. associate-/l* 71.7%

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

   5. Simplified 71.7%

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

   if -3.99999999999999982e37 < y < 5.2999999999999997e41

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 89.2%

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

   4. Taylor expanded in y around 0 89.2%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+37} \lor \neg \left(y \leq 5.3 \cdot 10^{+41}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+33} \lor \neg \left(y \leq 4.5 \cdot 10^{+35}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8.6e+33) (not (<= y 4.5e+35)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.6e+33) || !(y <= 4.5e+35)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-8.6d+33)) .or. (.not. (y <= 4.5d+35))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.6e+33) || !(y <= 4.5e+35)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -8.6e+33) or not (y <= 4.5e+35):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -8.6e+33) || !(y <= 4.5e+35))
		tmp = Float64(Float64(x + 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(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -8.6e+33) || ~((y <= 4.5e+35)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -8.6e+33], N[Not[LessEqual[y, 4.5e+35]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $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[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.60000000000000057e33 or 4.4999999999999997e35 < y

   1. Initial program 5.7%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. associate-/l* 71.1%

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

   5. Simplified 71.1%

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

   if -8.60000000000000057e33 < y < 4.4999999999999997e35

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0 89.8%

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

   4. Taylor expanded in y around 0 84.4%

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

      1. *-commutative 89.1%

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

   6. Simplified 84.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+33} \lor \neg \left(y \leq 4.5 \cdot 10^{+35}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+37} \lor \neg \left(y \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.15e+37) (not (<= y 1.45e-6)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ i (* y (+ c (* y (+ b (* y a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.15e+37) || !(y <= 1.45e-6)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.15d+37)) .or. (.not. (y <= 1.45d-6))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * (b + (y * a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.15e+37) || !(y <= 1.45e-6)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.15e+37) or not (y <= 1.45e-6):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.15e+37) || !(y <= 1.45e-6))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.15e+37) || ~((y <= 1.45e-6)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * (b + (y * a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.15e+37], N[Not[LessEqual[y, 1.45e-6]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000001e37 or 1.4500000000000001e-6 < y

   1. Initial program 9.6%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. associate-/l* 67.7%

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

   5. Simplified 67.7%

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

   if -1.15000000000000001e37 < y < 1.4500000000000001e-6

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 86.7%

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

      1. *-commutative 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in y around 0 86.7%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+37} \lor \neg \left(y \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+36} \lor \neg \left(y \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.9e+36) (not (<= y 1.45e-6)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/ (+ t (* y 230661.510616)) (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.9e+36) || !(y <= 1.45e-6)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-4.9d+36)) .or. (.not. (y <= 1.45d-6))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.9e+36) || !(y <= 1.45e-6)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.9e+36) or not (y <= 1.45e-6):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.9e+36) || !(y <= 1.45e-6))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.9e+36) || ~((y <= 1.45e-6)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.9e+36], N[Not[LessEqual[y, 1.45e-6]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.89999999999999981e36 or 1.4500000000000001e-6 < y

   1. Initial program 9.6%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. associate-/l* 67.7%

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

   5. Simplified 67.7%

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

   if -4.89999999999999981e36 < y < 1.4500000000000001e-6

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 84.6%

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

      1. *-commutative 84.6%

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

   5. Simplified 84.6%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+36} \lor \neg \left(y \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+37} \lor \neg \left(y \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6.4e+37) (not (<= y 1.45e-6)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/
    (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.4e+37) || !(y <= 1.45e-6)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-6.4d+37)) .or. (.not. (y <= 1.45d-6))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.4e+37) || !(y <= 1.45e-6)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6.4e+37) or not (y <= 1.45e-6):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6.4e+37) || !(y <= 1.45e-6))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -6.4e+37) || ~((y <= 1.45e-6)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6.4e+37], N[Not[LessEqual[y, 1.45e-6]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.40000000000000027e37 or 1.4500000000000001e-6 < y

   1. Initial program 9.6%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. associate-/l* 67.7%

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

   5. Simplified 67.7%

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

   if -6.40000000000000027e37 < y < 1.4500000000000001e-6

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 86.7%

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

      1. *-commutative 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in y around 0 82.6%

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

      1. *-commutative 90.0%

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

   8. Simplified 82.6%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+37} \lor \neg \left(y \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+36} \lor \neg \left(y \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.6e+36) (not (<= y 1.45e-6)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.6e+36) || !(y <= 1.45e-6)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.6d+36)) .or. (.not. (y <= 1.45d-6))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.6e+36) || !(y <= 1.45e-6)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.6e+36) or not (y <= 1.45e-6):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.6e+36) || !(y <= 1.45e-6))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.6e+36) || ~((y <= 1.45e-6)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.6e+36], N[Not[LessEqual[y, 1.45e-6]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999997e36 or 1.4500000000000001e-6 < y

   1. Initial program 9.6%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. associate-/l* 67.7%

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

   5. Simplified 67.7%

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

   if -3.5999999999999997e36 < y < 1.4500000000000001e-6

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 86.7%

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

      1. *-commutative 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in y around 0 82.6%

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

      1. *-commutative 90.0%

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

   8. Simplified 82.6%

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

   9. Taylor expanded in y around 0 81.1%

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

       1. *-commutative 81.1%

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

   11. Simplified 81.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+36} \lor \neg \left(y \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+36} \lor \neg \left(y \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -6.5e+36) (not (<= y 1.45e-6)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/ t (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.5e+36) || !(y <= 1.45e-6)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-6.5d+36)) .or. (.not. (y <= 1.45d-6))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = t / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -6.5e+36) || !(y <= 1.45e-6)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -6.5e+36) or not (y <= 1.45e-6):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -6.5e+36) || !(y <= 1.45e-6))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -6.5e+36) || ~((y <= 1.45e-6)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -6.5e+36], N[Not[LessEqual[y, 1.45e-6]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999998e36 or 1.4500000000000001e-6 < y

   1. Initial program 9.6%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. associate-/l* 67.7%

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

   5. Simplified 67.7%

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

   if -6.4999999999999998e36 < y < 1.4500000000000001e-6

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 86.7%

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

      1. *-commutative 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in y around 0 82.6%

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

      1. *-commutative 90.0%

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

   8. Simplified 82.6%

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

   9. Taylor expanded in t around inf 68.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+36} \lor \neg \left(y \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -40000000000000 \lor \neg \left(y \leq 3.2 \cdot 10^{-16}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -40000000000000.0) (not (<= y 3.2e-16)))
   (- (+ x (/ z y)) (* a (/ x y)))
   (/ (+ t (* y 230661.510616)) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -40000000000000.0) || !(y <= 3.2e-16)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-40000000000000.0d0)) .or. (.not. (y <= 3.2d-16))) then
        tmp = (x + (z / y)) - (a * (x / y))
    else
        tmp = (t + (y * 230661.510616d0)) / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -40000000000000.0) || !(y <= 3.2e-16)) {
		tmp = (x + (z / y)) - (a * (x / y));
	} else {
		tmp = (t + (y * 230661.510616)) / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -40000000000000.0) or not (y <= 3.2e-16):
		tmp = (x + (z / y)) - (a * (x / y))
	else:
		tmp = (t + (y * 230661.510616)) / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -40000000000000.0) || !(y <= 3.2e-16))
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -40000000000000.0) || ~((y <= 3.2e-16)))
		tmp = (x + (z / y)) - (a * (x / y));
	else
		tmp = (t + (y * 230661.510616)) / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -40000000000000.0], N[Not[LessEqual[y, 3.2e-16]], $MachinePrecision]], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e13 or 3.20000000000000023e-16 < y

   1. Initial program 12.4%

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

   3. Taylor expanded in y around inf 61.0%

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

      1. associate-/l* 64.2%

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

   5. Simplified 64.2%

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

   if -4e13 < y < 3.20000000000000023e-16

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 48.1%

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

   4. Taylor expanded in i around inf 59.7%

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

      1. +-commutative 59.7%

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

      2. *-commutative 59.7%

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

   6. Simplified 59.7%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -40000000000000 \lor \neg \left(y \leq 3.2 \cdot 10^{-16}\right):\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.085:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -0.085) x (if (<= y 3.8e-16) (/ (+ t (* y 230661.510616)) i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -0.085) {
		tmp = x;
	} else if (y <= 3.8e-16) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-0.085d0)) then
        tmp = x
    else if (y <= 3.8d-16) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -0.085) {
		tmp = x;
	} else if (y <= 3.8e-16) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -0.085:
		tmp = x
	elif y <= 3.8e-16:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -0.085)
		tmp = x;
	elseif (y <= 3.8e-16)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -0.085)
		tmp = x;
	elseif (y <= 3.8e-16)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -0.085], x, If[LessEqual[y, 3.8e-16], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0850000000000000061 or 3.80000000000000012e-16 < y

   1. Initial program 14.3%

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

   3. Taylor expanded in y around inf 49.3%

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

   if -0.0850000000000000061 < y < 3.80000000000000012e-16

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 49.5%

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

   4. Taylor expanded in i around inf 61.5%

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

      1. +-commutative 61.5%

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

      2. *-commutative 61.5%

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

   6. Simplified 61.5%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.085:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -2.35e+38) x (if (<= y 5.5e+14) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.35e+38) {
		tmp = x;
	} else if (y <= 5.5e+14) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-2.35d+38)) then
        tmp = x
    else if (y <= 5.5d+14) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -2.35e+38) {
		tmp = x;
	} else if (y <= 5.5e+14) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -2.35e+38:
		tmp = x
	elif y <= 5.5e+14:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -2.35e+38)
		tmp = x;
	elseif (y <= 5.5e+14)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -2.35e+38)
		tmp = x;
	elseif (y <= 5.5e+14)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -2.35e+38], x, If[LessEqual[y, 5.5e+14], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.35e38 or 5.5e14 < y

   1. Initial program 5.7%

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

   3. Taylor expanded in y around inf 55.7%

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

   if -2.35e38 < y < 5.5e14

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0 49.4%

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

Alternative 14: 25.4% 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 56.4%

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

3. Taylor expanded in y around inf 26.8%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024177 
(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)))