sqrt B (should all be same)

Average Error: 46.96% → 0.02%

Time: 2.2s

Precision: binary64

Cost: 6528

Math

\[\sqrt{\left(2 \cdot x\right) \cdot x} \]

↓

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

FPCore

(FPCore (x) :precision binary64 (sqrt (* (* 2.0 x) x)))

↓

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

C

double code(double x) {
	return sqrt(((2.0 * x) * x));
}

↓

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

Java

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

↓

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

Python

def code(x):
	return math.sqrt(((2.0 * x) * x))

↓

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

Julia

function code(x)
	return sqrt(Float64(Float64(2.0 * x) * x))
end

↓

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

MATLAB

function tmp = code(x)
	tmp = sqrt(((2.0 * x) * x));
end

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 46.96

   \[\sqrt{\left(2 \cdot x\right) \cdot x} \]

2. Applied egg-rr 47

   \[\leadsto \color{blue}{{\left(2 \cdot \left(x \cdot x\right)\right)}^{0.5}} \]

3. Applied egg-rr 47

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

4. Simplified 0.02

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

   [Start] 47	\[ \sqrt{2 \cdot \left(x \cdot x\right)} \]
   associate-*r* [=>] 46.96	\[ \sqrt{\color{blue}{\left(2 \cdot x\right) \cdot x}} \]
   *-commutative [=>] 46.96	\[ \sqrt{\color{blue}{x \cdot \left(2 \cdot x\right)}} \]
   count-2 [<=] 46.96	\[ \sqrt{x \cdot \color{blue}{\left(x + x\right)}} \]
   distribute-lft-out [<=] 47	\[ \sqrt{\color{blue}{x \cdot x + x \cdot x}} \]
   hypot-def [=>] 0.02	\[ \color{blue}{\mathsf{hypot}\left(x, x\right)} \]

5. Final simplification 0.02

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

Reproduce

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