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

Average Accuracy: 99.8% → 99.8%

Time: 7.0s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (1.0d0 - y) * (x * y)
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 (1.0 - y) * (x * y);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternatives

Alternative 1
Accuracy	99.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+124} \lor \neg \left(y \leq 2.35 \cdot 10^{+145}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	97.0%
Cost	649

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3
Accuracy	99.8%
Cost	448

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

Alternative 4
Accuracy	66.5%
Cost	192

\[x \cdot y \]

Reproduce

herbie shell --seed 2023151 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1.0 y)))