sqrt C

Average Error: 30.5 → 0.4

Time: 1.8s

Precision: binary64

Math

\[\sqrt{2 \cdot \left(x \cdot x\right)} \]

↓

\[\left|x \cdot \sqrt{2}\right| \]

FPCore

(FPCore (x) :precision binary64 (sqrt (* 2.0 (* x x))))

↓

(FPCore (x) :precision binary64 (fabs (* x (sqrt 2.0))))

C

double code(double x) {
	return sqrt((2.0 * (x * x)));
}

↓

double code(double x) {
	return fabs((x * sqrt(2.0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt((2.0d0 * (x * x)))
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = abs((x * sqrt(2.0d0)))
end function

Java

public static double code(double x) {
	return Math.sqrt((2.0 * (x * x)));
}

↓

public static double code(double x) {
	return Math.abs((x * Math.sqrt(2.0)));
}

Python

def code(x):
	return math.sqrt((2.0 * (x * x)))

↓

def code(x):
	return math.fabs((x * math.sqrt(2.0)))

Julia

function code(x)
	return sqrt(Float64(2.0 * Float64(x * x)))
end

↓

function code(x)
	return abs(Float64(x * sqrt(2.0)))
end

MATLAB

function tmp = code(x)
	tmp = sqrt((2.0 * (x * x)));
end

↓

function tmp = code(x)
	tmp = abs((x * sqrt(2.0)));
end

Wolfram

code[x_] := N[Sqrt[N[(2.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

↓

code[x_] := N[Abs[N[(x * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Error

Bits error versus x

Derivation

1. Initial program 30.5

   \[\sqrt{2 \cdot \left(x \cdot x\right)} \]

2. Applied egg-rr 0.4

   \[\leadsto \color{blue}{\left|x \cdot \sqrt{2}\right|} \]

3. Final simplification 0.4

   \[\leadsto \left|x \cdot \sqrt{2}\right| \]

Reproduce

herbie shell --seed 2022151 
(FPCore (x)
  :name "sqrt C"
  :precision binary64
  (sqrt (* 2.0 (* x x))))