?

Average Error: 47% → 0.02%

Time: 3.6s

Precision: binary64

Cost: 6528

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

↓

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

(FPCore (x) :precision binary64 (sqrt (+ (pow x 2.0) (pow x 2.0))))

↓

(FPCore (x) :precision binary64 (hypot x x))

double code(double x) {
	return sqrt((pow(x, 2.0) + pow(x, 2.0)));
}

↓

double code(double x) {
	return hypot(x, x);
}

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

↓

public static double code(double x) {
	return Math.hypot(x, x);
}

def code(x):
	return math.sqrt((math.pow(x, 2.0) + math.pow(x, 2.0)))

↓

def code(x):
	return math.hypot(x, x)

function code(x)
	return sqrt(Float64((x ^ 2.0) + (x ^ 2.0)))
end

↓

function code(x)
	return hypot(x, x)
end

function tmp = code(x)
	tmp = sqrt(((x ^ 2.0) + (x ^ 2.0)));
end

↓

function tmp = code(x)
	tmp = hypot(x, x);
end

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

↓

code[x_] := N[Sqrt[x ^ 2 + x ^ 2], $MachinePrecision]

\sqrt{{x}^{2} + {x}^{2}}

↓

\mathsf{hypot}\left(x, x\right)

Try it out?

In
Out

Enter valid numbers for all inputs

Simplified0.02

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

Proof

[Start]47	\[ \sqrt{{x}^{2} + {x}^{2}} \]
unpow2 [=>]47	\[ \sqrt{\color{blue}{x \cdot x} + {x}^{2}} \]
unpow2 [=>]47	\[ \sqrt{x \cdot x + \color{blue}{x \cdot x}} \]
hypot-def [=>]0.02	\[ \color{blue}{\mathsf{hypot}\left(x, x\right)} \]

Alternative 1
Error	87.09%
Cost	452

\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;4 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]

Alternative 2
Error	93.54%
Cost	192

\[x + -2 \]

Alternative 3
Error	88.55%
Cost	192

\[x + x \]

Alternative 4
Error	98.32%
Cost	64

\[-2 \]

herbie shell --seed 2023115 
(FPCore (x)
  :name "sqrt E (should all be same)"
  :precision binary64
  (sqrt (+ (pow x 2.0) (pow x 2.0))))