Data.Octree.Internal:octantDistance from Octree-0.5.4.2

Average Error: 31.2 → 0.0

Time: 2.1s

Precision: binary64

Cost: 6528

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Java

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);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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]

Target

Original	31.2
Target	17.6
Herbie	0.0

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

Derivation

1. Initial program 31.2

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

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{hypot}\left(x, y\right)} \]
   Proof
   (hypot.f64 x y): 0 points increase in error, 0 points decrease in error
   (Rewrite<= hypot-def_binary64 (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))): 143 points increase in error, 1 points decrease in error

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	36.6
Cost	788

\[\begin{array}{l} \mathbf{if}\;x \leq -1.0005096622161097 \cdot 10^{-35}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -3.295502009220733 \cdot 10^{-49}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -5.962936472060393 \cdot 10^{-101}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -3.4550455850610005 \cdot 10^{-177}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.618986003622812 \cdot 10^{-205}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 2
Error	36.7
Cost	788

\[\begin{array}{l} \mathbf{if}\;x \leq -1.0005096622161097 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{\frac{x}{y}} \cdot -0.5 - x\\ \mathbf{elif}\;x \leq -3.295502009220733 \cdot 10^{-49}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -5.962936472060393 \cdot 10^{-101}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -3.4550455850610005 \cdot 10^{-177}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.618986003622812 \cdot 10^{-205}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3
Error	46.7
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022300 
(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))))