Average Error: 31.0 → 0.1
Time: 4.8s
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)

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 31.0

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{hypot}\left(x, x\right)} \]
    Proof
    (hypot.f64 x x): 0 points increase in error, 0 points decrease in error
    (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))): 132 points increase in error, 0 points decrease in error
    (sqrt.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 x 2)) (*.f64 x x))): 0 points increase in error, 0 points decrease in error
    (sqrt.f64 (+.f64 (pow.f64 x 2) (Rewrite<= unpow2_binary64 (pow.f64 x 2)))): 0 points increase in error, 0 points decrease in error

  3. Final simplification0.1

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

Alternatives

Alternative 1
Error56.7
Cost192
\[x + x \]

Error

Reproduce

herbie shell --seed 2022291 
(FPCore (x)
  :name "sqrt E"
  :precision binary64
  (sqrt (+ (pow x 2.0) (pow x 2.0))))