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

Average Error: 0.1 → 0.1

Time: 6.1s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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
    code = y * ((1.0d0 - y) * x)
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) {
	return y * ((1.0 - y) * x);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

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

2. Taylor expanded in x around 0 0.1

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

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	7.0
Cost	648

\[\begin{array}{l} t_0 := x \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{if}\;y \leq -1.331863686544641:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.6951948352754024:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	1.8
Cost	648

\[\begin{array}{l} t_0 := \left(y \cdot x\right) \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.331863686544641:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.6951948352754024:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	21.3
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2022317 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1.0 y)))