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

Average Accuracy: 100.0% → 100.0%

Time: 5.1s

Precision: binary64

Cost: 832

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = ((y - x) / (y + x)) * (x / (y - x))
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

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

2. Applied egg-rr 55.5%

   \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(y, y, -x \cdot x\right)} \cdot \left(y - x\right)} \]
   Step-by-step derivation

   [Start] 100.0	\[ \frac{x}{y + x} \]
   flip-+ [=>] 58.5	\[ \frac{x}{\color{blue}{\frac{y \cdot y - x \cdot x}{y - x}}} \]
   associate-/r/ [=>] 55.3	\[ \color{blue}{\frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)} \]
   fma-neg [=>] 55.5	\[ \frac{x}{\color{blue}{\mathsf{fma}\left(y, y, -x \cdot x\right)}} \cdot \left(y - x\right) \]

3. Simplified 54.6%

   \[\leadsto \color{blue}{\frac{x \cdot \left(y - x\right)}{y \cdot y - x \cdot x}} \]
   Step-by-step derivation

   [Start] 55.5	\[ \frac{x}{\mathsf{fma}\left(y, y, -x \cdot x\right)} \cdot \left(y - x\right) \]
   associate-*l/ [=>] 54.6	\[ \color{blue}{\frac{x \cdot \left(y - x\right)}{\mathsf{fma}\left(y, y, -x \cdot x\right)}} \]
   unpow2 [<=] 54.6	\[ \frac{x \cdot \left(y - x\right)}{\mathsf{fma}\left(y, y, -\color{blue}{{x}^{2}}\right)} \]
   fma-neg [<=] 54.6	\[ \frac{x \cdot \left(y - x\right)}{\color{blue}{y \cdot y - {x}^{2}}} \]
   unpow2 [=>] 54.6	\[ \frac{x \cdot \left(y - x\right)}{y \cdot y - \color{blue}{x \cdot x}} \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{y - x}{x + y} \cdot \frac{x}{y - x}} \]
   Step-by-step derivation

   [Start] 54.6	\[ \frac{x \cdot \left(y - x\right)}{y \cdot y - x \cdot x} \]
   *-commutative [=>] 54.6	\[ \frac{\color{blue}{\left(y - x\right) \cdot x}}{y \cdot y - x \cdot x} \]
   difference-of-squares [=>] 54.6	\[ \frac{\left(y - x\right) \cdot x}{\color{blue}{\left(y + x\right) \cdot \left(y - x\right)}} \]
   times-frac [=>] 100.0	\[ \color{blue}{\frac{y - x}{y + x} \cdot \frac{x}{y - x}} \]
   +-commutative [=>] 100.0	\[ \frac{y - x}{\color{blue}{x + y}} \cdot \frac{x}{y - x} \]

5. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	74.1%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+22}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Accuracy	100.0%
Cost	320

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

Alternative 3
Accuracy	50.9%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023157 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))