sqrt A (should all be same)

Average Accuracy: 51.8% → 100.0%

Time: 2.3s

Precision: binary64

Cost: 6528

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 57.4%

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

2. Simplified 100.0%

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

   [Start] 57.4	\[ \sqrt{x \cdot x + x \cdot x} \]
   hypot-def [=>] 100.0	\[ \color{blue}{\mathsf{hypot}\left(x, x\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	12.7%
Cost	452

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\left(x \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]

Alternative 2
Accuracy	12.7%
Cost	324

\[\begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-310}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]

Alternative 3
Accuracy	5.1%
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2023157 
(FPCore (x)
  :name "sqrt A (should all be same)"
  :precision binary64
  (sqrt (+ (* x x) (* x x))))