This compares the binary radix tree's proof to Ethereum tree. The proofs where encoded in cbor and compressed with gzip. Etherum's proof where encoded using rlp. The compressed results for Ethereum where not recoded since they where larger then the uncompressed proofs

10000 keys

Binary Radix Tree

cbor 660 bytes
compressed size 572

Ethereum

rlp 1649 bytes

Diff 65%

20000 keys

Binary Radix Tree

cbor 705 bytes
compressed size 607

Ethereum

rlp 1772 bytes

Diff 66%

30000 keys

Binary Radix Tree

cbor 731 bytes
compressed 628 size

Ethereum

rlp 1829 bytes

Diff 66%

40000 keys

Binary Radix Tree

cbor 749 bytes
compressed 643 size

Ethereum

rlp 1876 bytes

Diff 66%

50000 keys

Binary Radix Tree

cbor 764 bytes
compressed 654 size

Ethereum

rlp 1917 bytes

Diff 66%

60000 keys

Binary Radix Tree

cbor 776 bytes
compressed 663 size

Ethereum

rlp 1956 bytes

70000 keys

Binary Radix Tree

cbor 786 bytes
compressed 671 size

Ethereum

rlp 1990 bytes

Diff 66%

80000 keys

Binary Radix Tree

cbor 795 bytes
compressed 679 size

Ethereum

rlp 2021 bytes

Diff 66%

90000 keys

Binary Radix Tree

cbor 803 bytes
compressed 685 size

Ethereum

rlp 2050 bytes

Diff 67%

100000 keys

Binary Radix Tree

cbor 810 bytes
compressed 691 size

Ethereum

rlp 2075 bytes

Diff 67%

multikey

The following show that multikey are more compact the single key proofs . Each tree was populated with 10000 keys

Two Keys Proofs

cbor 1088
compressed 916

Three Keys Proofs

cbor 1675
compressed 1381

Four Keys Proofs

cbor 2221
compressed 1801