AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B

Average Error: 0.0 → 0.0

Time: 1.4s

Precision: binary64

Cost: 320

Math

\[\frac{x}{y + x} \]

↓

\[\frac{x}{x + y} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (+ y x)))

↓

(FPCore (x y) :precision binary64 (/ x (+ x y)))

C

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

↓

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (y + x)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (x + y)
end function

Java

public static double code(double x, double y) {
	return x / (y + x);
}

↓

public static double code(double x, double y) {
	return x / (x + y);
}

Python

def code(x, y):
	return x / (y + x)

↓

def code(x, y):
	return x / (x + y)

Julia

function code(x, y)
	return Float64(x / Float64(y + x))
end

↓

function code(x, y)
	return Float64(x / Float64(x + y))
end

MATLAB

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

↓

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

Wolfram

code[x_, y_] := N[(x / N[(y + x), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\frac{x}{y + x} \]

2. Simplified 0.0

   \[\leadsto \color{blue}{\frac{x}{x + y}} \]

3. Final simplification 0.0

   \[\leadsto \frac{x}{x + y} \]

Alternatives

Alternative 1
Error	16.8
Cost	584

\[\begin{array}{l} t_0 := 1 - \frac{y}{x}\\ \mathbf{if}\;x \leq -9.33757743399206 \cdot 10^{-77}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 358013177552034100:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	16.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -9.33757743399206 \cdot 10^{-77}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9616111207.270092:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	31.7
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022225 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))