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

Average Error: 0.0 → 0.0

Time: 2.5s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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 / (x + y)
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 / (x + y);
}

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	17.2
Cost	1113

\[\begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+57}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-24}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-158} \lor \neg \left(x \leq 7.2 \cdot 10^{-133}\right) \land x \leq 8.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]

Alternative 2
Error	17.0
Cost	984

\[\begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+57}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-24}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-133}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 16000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	31.6
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022365 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))