?

Average Error: 31.5 → 0
Time: 1.0s
Precision: binary64
Cost: 6528

?

\[\sqrt{x \cdot x + y \cdot y} \]
↓
\[\mathsf{hypot}\left(x, y\right) \]
(FPCore (x y) :precision binary64 (sqrt (+ (* x x) (* y y))))
↓
(FPCore (x y) :precision binary64 (hypot x y))
double code(double x, double y) {
	return sqrt(((x * x) + (y * y)));
}
↓
double code(double x, double y) {
	return hypot(x, y);
}

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

def code(x, y):
	return math.sqrt(((x * x) + (y * y)))
↓
def code(x, y):
	return math.hypot(x, y)

function code(x, y)
	return sqrt(Float64(Float64(x * x) + Float64(y * y)))
end
↓
function code(x, y)
	return hypot(x, y)
end

function tmp = code(x, y)
	tmp = sqrt(((x * x) + (y * y)));
end
↓
function tmp = code(x, y)
	tmp = hypot(x, y);
end

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

\sqrt{x \cdot x + y \cdot y}
↓
\mathsf{hypot}\left(x, y\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.5
Target17.4
Herbie0
\[\begin{array}{l} \mathbf{if}\;x < -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x < 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Derivation?

  1. Initial program 31.5

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

  2. Simplified0

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

    [Start]31.5

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

    hypot-def [=>]0

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

  3. Final simplification0

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

Reproduce?

herbie shell --seed 2023077 
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"
  :precision binary64

  :herbie-target
  (if (< x -1.1236950826599826e+145) (- x) (if (< x 1.116557621183362e+93) (sqrt (+ (* x x) (* y y))) x))

  (sqrt (+ (* x x) (* y y))))