Average Error: 31.0 → 0.1
Time: 2.7s
Precision: binary64
\[\sqrt{2 \cdot {x}^{2}} \]
↓
\[\mathsf{hypot}\left(x, x\right) \]
(FPCore (x) :precision binary64 (sqrt (* 2.0 (pow x 2.0))))
↓
(FPCore (x) :precision binary64 (hypot x x))
double code(double x) {
	return sqrt((2.0 * pow(x, 2.0)));
}
↓
double code(double x) {
	return hypot(x, x);
}

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

def code(x):
	return math.sqrt((2.0 * math.pow(x, 2.0)))
↓
def code(x):
	return math.hypot(x, x)

function code(x)
	return sqrt(Float64(2.0 * (x ^ 2.0)))
end
↓
function code(x)
	return hypot(x, x)
end

function tmp = code(x)
	tmp = sqrt((2.0 * (x ^ 2.0)));
end
↓
function tmp = code(x)
	tmp = hypot(x, x);
end

code[x_] := N[Sqrt[N[(2.0 * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
↓
code[x_] := N[Sqrt[x ^ 2 + x ^ 2], $MachinePrecision]

\sqrt{2 \cdot {x}^{2}}
↓
\mathsf{hypot}\left(x, x\right)

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 31.0

    \[\sqrt{2 \cdot {x}^{2}} \]

  2. Applied add-sqr-sqrt_binary6431.2

    \[\leadsto \color{blue}{\sqrt{\sqrt{2 \cdot {x}^{2}}} \cdot \sqrt{\sqrt{2 \cdot {x}^{2}}}} \]

  3. Simplified31.2

    \[\leadsto \color{blue}{\sqrt{\mathsf{hypot}\left(x, x\right)}} \cdot \sqrt{\sqrt{2 \cdot {x}^{2}}} \]

  4. Simplified0.5

    \[\leadsto \sqrt{\mathsf{hypot}\left(x, x\right)} \cdot \color{blue}{\sqrt{\mathsf{hypot}\left(x, x\right)}} \]

  5. Applied rem-square-sqrt_binary640.1

    \[\leadsto \color{blue}{\mathsf{hypot}\left(x, x\right)} \]

  6. Final simplification0.1

    \[\leadsto \mathsf{hypot}\left(x, x\right) \]

Reproduce

herbie shell --seed 2022137 
(FPCore (x)
  :name "sqrt D"
  :precision binary64
  (sqrt (* 2.0 (pow x 2.0))))