Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2

Average Error: 0.1 → 0.3

Time: 5.4s

Precision: binary64

Cost: 712

Math

\[\left(x \cdot y\right) \cdot \left(1 - y\right) \]

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+160}:\\ \;\;\;\;\frac{y \cdot x}{\frac{-1}{y}}\\ \mathbf{elif}\;y \leq 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{-1}{y}}{x}}\\ \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* x y) (- 1.0 y)))

↓

(FPCore (x y)
 :precision binary64
 (if (<= y -1e+160)
   (/ (* y x) (/ -1.0 y))
   (if (<= y 1e+65) (* x (* y (- 1.0 y))) (/ y (/ (/ -1.0 y) x)))))

C

double code(double x, double y) {
	return (x * y) * (1.0 - y);
}

↓

double code(double x, double y) {
	double tmp;
	if (y <= -1e+160) {
		tmp = (y * x) / (-1.0 / y);
	} else if (y <= 1e+65) {
		tmp = x * (y * (1.0 - y));
	} else {
		tmp = y / ((-1.0 / y) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * y) * (1.0d0 - y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1d+160)) then
        tmp = (y * x) / ((-1.0d0) / y)
    else if (y <= 1d+65) then
        tmp = x * (y * (1.0d0 - y))
    else
        tmp = y / (((-1.0d0) / y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	return (x * y) * (1.0 - y);
}

↓

public static double code(double x, double y) {
	double tmp;
	if (y <= -1e+160) {
		tmp = (y * x) / (-1.0 / y);
	} else if (y <= 1e+65) {
		tmp = x * (y * (1.0 - y));
	} else {
		tmp = y / ((-1.0 / y) / x);
	}
	return tmp;
}

Python

def code(x, y):
	return (x * y) * (1.0 - y)

↓

def code(x, y):
	tmp = 0
	if y <= -1e+160:
		tmp = (y * x) / (-1.0 / y)
	elif y <= 1e+65:
		tmp = x * (y * (1.0 - y))
	else:
		tmp = y / ((-1.0 / y) / x)
	return tmp

Julia

function code(x, y)
	return Float64(Float64(x * y) * Float64(1.0 - y))
end

↓

function code(x, y)
	tmp = 0.0
	if (y <= -1e+160)
		tmp = Float64(Float64(y * x) / Float64(-1.0 / y));
	elseif (y <= 1e+65)
		tmp = Float64(x * Float64(y * Float64(1.0 - y)));
	else
		tmp = Float64(y / Float64(Float64(-1.0 / y) / x));
	end
	return tmp
end

MATLAB

function tmp = code(x, y)
	tmp = (x * y) * (1.0 - y);
end

↓

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1e+160)
		tmp = (y * x) / (-1.0 / y);
	elseif (y <= 1e+65)
		tmp = x * (y * (1.0 - y));
	else
		tmp = y / ((-1.0 / y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := N[(N[(x * y), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := If[LessEqual[y, -1e+160], N[(N[(y * x), $MachinePrecision] / N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+65], N[(x * N[(y * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(-1.0 / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000001e160

   1. Initial program 0.3

      \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]

   2. Applied egg-rr 64.0

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

   3. Applied egg-rr 0.4

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{\frac{1}{1 - y}}} \]

   4. Applied egg-rr 0.4

      \[\leadsto \color{blue}{\frac{x \cdot y}{\frac{1}{1 - y}}} \]

   5. Taylor expanded in y around inf 0.4

      \[\leadsto \frac{x \cdot y}{\color{blue}{\frac{-1}{y}}} \]

   if -1.00000000000000001e160 < y < 9.9999999999999999e64

   1. Initial program 0.1

      \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]

   2. Applied egg-rr 26.5

      \[\leadsto \color{blue}{{\left(\sqrt{\left(x \cdot y\right) \cdot \left(1 - y\right)}\right)}^{2}} \]

   3. Applied egg-rr 0.2

      \[\leadsto \color{blue}{\left(y \cdot \left(1 - y\right)\right) \cdot x} \]

   if 9.9999999999999999e64 < y

   1. Initial program 0.3

      \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]

   2. Applied egg-rr 35.7

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

   3. Applied egg-rr 0.4

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{\frac{1}{1 - y}}} \]

   4. Applied egg-rr 0.4

      \[\leadsto \color{blue}{\frac{y}{\frac{\frac{1}{1 - y}}{x}}} \]

   5. Taylor expanded in y around inf 0.4

      \[\leadsto \frac{y}{\frac{\color{blue}{\frac{-1}{y}}}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+160}:\\ \;\;\;\;\frac{y \cdot x}{\frac{-1}{y}}\\ \mathbf{elif}\;y \leq 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{-1}{y}}{x}}\\ \end{array} \]

Alternatives

Alternative 1
Error	2.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -5.838124845251465 \cdot 10^{+20}:\\ \;\;\;\;\frac{y \cdot x}{\frac{-1}{y}}\\ \mathbf{elif}\;y \leq 0.0003676134116460638:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{-1}{y}}{x}}\\ \end{array} \]

Alternative 2
Error	7.8
Cost	648

\[\begin{array}{l} t_0 := x \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{if}\;y \leq -5.838124845251465 \cdot 10^{+20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0003676134116460638:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	2.8
Cost	648

\[\begin{array}{l} t_0 := y \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{if}\;y \leq -5.838124845251465 \cdot 10^{+20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0003676134116460638:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	2.8
Cost	648

\[\begin{array}{l} \mathbf{if}\;y \leq -5.838124845251465 \cdot 10^{+20}:\\ \;\;\;\;\frac{y \cdot x}{\frac{-1}{y}}\\ \mathbf{elif}\;y \leq 0.0003676134116460638:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 5
Error	0.1
Cost	448

\[y \cdot \left(x - y \cdot x\right) \]

Alternative 6
Error	21.4
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2022216 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1.0 y)))