sqrt E (should all be same)

Average Error: 30.4 → 0.0

Time: 2.7s

Precision: binary64

Cost: 6528

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Java

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);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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]

Derivation

1. Initial program 30.4

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

2. Simplified 0.0

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

   [Start] 30.4	\[ \sqrt{{x}^{2} + {x}^{2}} \]
   unpow2 [=>] 30.4	\[ \sqrt{\color{blue}{x \cdot x} + {x}^{2}} \]
   unpow2 [=>] 30.4	\[ \sqrt{x \cdot x + \color{blue}{x \cdot x}} \]
   hypot-def [=>] 0.0	\[ \color{blue}{\mathsf{hypot}\left(x, x\right)} \]

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2023054 
(FPCore (x)
  :name "sqrt E (should all be same)"
  :precision binary64
  (sqrt (+ (pow x 2.0) (pow x 2.0))))