?

Average Error: 12.7 → 0.0
Time: 7.8s
Precision: binary64
Cost: 6528

?

\[\left(0 \leq x \land x \leq 10^{+18}\right) \land \left(0 \leq y \land y \leq 10^{+18}\right)\]
\[\sqrt{{x}^{2} + {y}^{2}} \]
\[\mathsf{hypot}\left(x, y\right) \]
(FPCore (x y) :precision binary64 (sqrt (+ (pow x 2.0) (pow y 2.0))))
(FPCore (x y) :precision binary64 (hypot x y))
double code(double x, double y) {
	return sqrt((pow(x, 2.0) + pow(y, 2.0)));
}
double code(double x, double y) {
	return hypot(x, y);
}
public static double code(double x, double y) {
	return Math.sqrt((Math.pow(x, 2.0) + Math.pow(y, 2.0)));
}
public static double code(double x, double y) {
	return Math.hypot(x, y);
}
def code(x, y):
	return math.sqrt((math.pow(x, 2.0) + math.pow(y, 2.0)))
def code(x, y):
	return math.hypot(x, y)
function code(x, y)
	return sqrt(Float64((x ^ 2.0) + (y ^ 2.0)))
end
function code(x, y)
	return hypot(x, y)
end
function tmp = code(x, y)
	tmp = sqrt(((x ^ 2.0) + (y ^ 2.0)));
end
function tmp = code(x, y)
	tmp = hypot(x, y);
end
code[x_, y_] := N[Sqrt[N[(N[Power[x, 2.0], $MachinePrecision] + N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
code[x_, y_] := N[Sqrt[x ^ 2 + y ^ 2], $MachinePrecision]
\sqrt{{x}^{2} + {y}^{2}}
\mathsf{hypot}\left(x, y\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 12.7

    \[\sqrt{{x}^{2} + {y}^{2}} \]
  2. Simplified0.0

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

    [Start]12.7

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

    unpow2 [=>]12.7

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

    unpow2 [=>]12.7

    \[ \sqrt{x \cdot x + \color{blue}{y \cdot y}} \]

    hypot-def [=>]0.0

    \[ \color{blue}{\mathsf{hypot}\left(x, y\right)} \]
  3. Final simplification0.0

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

Alternatives

Alternative 1
Error30.3
Cost576
\[y + 0.5 \cdot \left(x \cdot \frac{x}{y}\right) \]
Alternative 2
Error30.6
Cost64
\[y \]

Error

Reproduce?

herbie shell --seed 1 
(FPCore (x y)
  :name "sqrt(x^2+y^2)"
  :precision binary64
  :pre (and (and (<= 0.0 x) (<= x 1e+18)) (and (<= 0.0 y) (<= y 1e+18)))
  (sqrt (+ (pow x 2.0) (pow y 2.0))))