Average Error: 0.0 → 0.0
Time: 3.0s
Precision: binary64
\[\frac{x - y}{x + y} \]
↓
\[\frac{x}{x + y} - \log \log \left(1 + \mathsf{expm1}\left(e^{\frac{y}{x + y}}\right)\right) \]
(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
↓
(FPCore (x y)
 :precision binary64
 (- (/ x (+ x y)) (log (log (+ 1.0 (expm1 (exp (/ y (+ x y)))))))))
double code(double x, double y) {
	return (x - y) / (x + y);
}
↓
double code(double x, double y) {
	return (x / (x + y)) - log(log((1.0 + expm1(exp((y / (x + y)))))));
}

public static double code(double x, double y) {
	return (x - y) / (x + y);
}
↓
public static double code(double x, double y) {
	return (x / (x + y)) - Math.log(Math.log((1.0 + Math.expm1(Math.exp((y / (x + y)))))));
}

def code(x, y):
	return (x - y) / (x + y)
↓
def code(x, y):
	return (x / (x + y)) - math.log(math.log((1.0 + math.expm1(math.exp((y / (x + y)))))))

function code(x, y)
	return Float64(Float64(x - y) / Float64(x + y))
end
↓
function code(x, y)
	return Float64(Float64(x / Float64(x + y)) - log(log(Float64(1.0 + expm1(exp(Float64(y / Float64(x + y))))))))
end

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] - N[Log[N[Log[N[(1.0 + N[(Exp[N[Exp[N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \log \log \left(1 + \mathsf{expm1}\left(e^{\frac{y}{x + y}}\right)\right)

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{x + y} - \frac{y}{x + y} \]

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Applied egg-rr0.0

    \[\leadsto \frac{x}{x + y} - \color{blue}{\log \left(e^{\frac{y}{x + y}}\right)} \]

  4. Applied egg-rr0.0

    \[\leadsto \frac{x}{x + y} - \log \color{blue}{\log \left(1 + \mathsf{expm1}\left(e^{\frac{y}{y + x}}\right)\right)} \]

  5. Final simplification0.0

    \[\leadsto \frac{x}{x + y} - \log \log \left(1 + \mathsf{expm1}\left(e^{\frac{y}{x + y}}\right)\right) \]

Reproduce

herbie shell --seed 2022133 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))