Ancient Greek had a rule that if anything was prefixed to a word starting with r-, the r- was doubled. That did not involve just compounds, but also prepositions put in front of verbs, alpha privative (the equivalent of un-), and even augments, the prefix indicating past tense:
- μέλι “honey” + ῥυτός “flowing” > μελίρρυτος “flowing with honey”
- ῥέω “to flow” > ἁνα-ρρέω “to flow back”
- ῥευστός “in flux” > ἄ-ρρευστος “static”
- ῥύω ” I cleanse” > ἔ-ρρυα “I cleansed”
The rule had broken down in spelling by Byzantine Greek, and the rule has no application in either pronunciation or spelling in Standard Modern Greek. But of course scientific use of Greek took Classical Greek as its model.
So when new compounds were made up in scientific Greek in the West, they (usually) applied the rules of Classical Greek phonology to their coinages. After all, Classical Greek had a -rrhiza compound already: γλυκύ-ρριζα “sweet-root” = “liquorice”. Liquorice, scientific name: Glycyrrhiza glabra.