System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2

Average Error: 0.0 → 0.0

Time: 2.4s

Precision: binary64

Cost: 448

Math

\[0.5 \cdot \left(x \cdot x - y\right) \]

↓

\[0.5 \cdot \left(x \cdot x - y\right) \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (- (* x x) y)))

↓

(FPCore (x y) :precision binary64 (* 0.5 (- (* x x) y)))

C

double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

↓

double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * ((x * x) - y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * ((x * x) - y)
end function

Java

public static double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

↓

public static double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Python

def code(x, y):
	return 0.5 * ((x * x) - y)

↓

def code(x, y):
	return 0.5 * ((x * x) - y)

Julia

function code(x, y)
	return Float64(0.5 * Float64(Float64(x * x) - y))
end

↓

function code(x, y)
	return Float64(0.5 * Float64(Float64(x * x) - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * ((x * x) - y);
end

↓

function tmp = code(x, y)
	tmp = 0.5 * ((x * x) - y);
end

Wolfram

code[x_, y_] := N[(0.5 * N[(N[(x * x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(0.5 * N[(N[(x * x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[0.5 \cdot \left(x \cdot x - y\right) \]

2. Final simplification 0.0

   \[\leadsto 0.5 \cdot \left(x \cdot x - y\right) \]

Alternatives

Alternative 1
Error	10.6
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(0.5 \cdot x\right)\\ \mathbf{if}\;x \leq -431912211370920500:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.969774585051767 \cdot 10^{-30}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	20.8
Cost	192

\[y \cdot -0.5 \]

Reproduce

herbie shell --seed 2022317 
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  :precision binary64
  (* 0.5 (- (* x x) y)))