Floating-point numbers are an essential part of modern software, recently gaining particular prominence \r\non the web where floating- point numbers are the exclusive numeric format in Javascript. To use floating point numbers, we require a way to convert the binary machine representations into decimal human readable outputs. Existing conversion algorithm make trade-offs between completeness and performance. The classic Dragon4 algorithm by Steele and White and its later refinements achieve completeness – i.e. produce correct and optimal outputs on all inputs – by using arbitrary precision integer (bignum) arithmetic which leads to a high performance cost. On the other hand, the recent Grisu algorithm by Loitsch shows how to recover performance by using native integer arithmetic but sacrifices optimality for 0.5% of all inputs. We present Errol, a new complete algorithm that is guaranteed to produce correct and optimal results for all inputs, while simultaneously being 2x faster than Grisu and 8x faster than previous complete methods. We formalize and describe Errol and present an implementation and experimental evaluation of our method against the state-of-the-art.