Average Error: 0.0 → 0.0
Time: 2.2s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n} \]
↓
\[\log \left(1 + \mathsf{fma}\left(1, e^{\frac{f + n}{n - f}}, -1\right)\right) \]
(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))
↓
(FPCore (f n)
 :precision binary64
 (log (+ 1.0 (fma 1.0 (exp (/ (+ f n) (- n f))) -1.0))))
double code(double f, double n) {
	return -(f + n) / (f - n);
}
↓
double code(double f, double n) {
	return log((1.0 + fma(1.0, exp(((f + n) / (n - f))), -1.0)));
}

function code(f, n)
	return Float64(Float64(-Float64(f + n)) / Float64(f - n))
end
↓
function code(f, n)
	return log(Float64(1.0 + fma(1.0, exp(Float64(Float64(f + n) / Float64(n - f))), -1.0)))
end

code[f_, n_] := N[((-N[(f + n), $MachinePrecision]) / N[(f - n), $MachinePrecision]), $MachinePrecision]
↓
code[f_, n_] := N[Log[N[(1.0 + N[(1.0 * N[Exp[N[(N[(f + n), $MachinePrecision] / N[(n - f), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

\frac{-\left(f + n\right)}{f - n}
↓
\log \left(1 + \mathsf{fma}\left(1, e^{\frac{f + n}{n - f}}, -1\right)\right)

Error

Bits error versus f

Bits error versus n

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n} \]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{f + n}{n - f}} \]

  3. Applied egg-rr0.0

    \[\leadsto \color{blue}{\log \left(1 + \mathsf{expm1}\left(\frac{f + n}{n - f}\right)\right)} \]

  4. Applied egg-rr0.0

    \[\leadsto \log \left(1 + \color{blue}{\mathsf{fma}\left(1, e^{\frac{f + n}{n - f}}, -1\right)}\right) \]

  5. Final simplification0.0

    \[\leadsto \log \left(1 + \mathsf{fma}\left(1, e^{\frac{f + n}{n - f}}, -1\right)\right) \]

Reproduce

herbie shell --seed 2022159 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))