Estimate the world population, at 5 different levels of accuracy code-challenge

Your goal is, given a year between 1951 and 2020 to output the world population in that year. However, you must write 5 different expressions. Each program must contain the previous as a substring.

Your first program is 5 bytes, the second 10, then 20, 40 finally a program or function with a maximums size of 80 bytes. Each expression must contain the previous expression as a substring.

For the purpose of this challenge, snippets that take input from global variables are allowed, for all programs except the last. which must be either a complete program or a function.

Scoring

For each year, your score is the product of the proportional square error. In other words:

$$\frac{(X_0 - V)^2 \cdot (X_1 - V)^2 \cdot (X_2 - V)^2 \cdot(X_3 - V)^2 \cdot (X_4 - V)^2}{V^{10}}$$

Where X_n is the estimate your nth program outputs and V is the true population at that year. Your total score is sum of the score of each year.

Lower score is better.

Example

Python, Score \$7.503\cdot10^{59}\$

5 byte solution:

413e7

10 byte solution

413e9+x**2

20 byte solution

413e9+x**2.46*4.321

40 byte solution

0*413e9+x**2.46*4.321+x**3.718232*8.3e9

80 byte solution

lambda x:0.010*413e9+x**2.46*4.321+x**3.718232*8.3e9+__import__("math").sin(x/2)

Data

In JSON format:

{2020: 7794798739, 2019: 7713468100, 2018: 7631091040, 2017: 7547858925, 2016: 7464022049, 2015: 7379797139, 2014: 7295290765, 2013: 7210581976, 2012: 7125828059, 2011: 7041194301, 2010: 6956823603, 2009: 6872767093, 2008: 6789088686, 2007: 6705946610, 2006: 6623517833, 2005: 6541907027, 2004: 6461159389, 2003: 6381185114, 2002: 6301773188, 2001: 6222626606, 2000: 6143493823, 1999: 6064239055, 1998: 5984793942, 1997: 5905045788, 1996: 5824891951, 1995: 5744212979, 1994: 5663150427, 1993: 5581597546, 1992: 5498919809, 1991: 5414289444, 1990: 5327231061, 1989: 5237441558, 1988: 5145426008, 1987: 5052522147, 1986: 4960567912, 1985: 4870921740, 1984: 4784011621, 1983: 4699569304, 1982: 4617386542, 1981: 4536996762, 1980: 4458003514, 1979: 4380506100, 1978: 4304533501, 1977: 4229506060, 1976: 4154666864, 1975: 4079480606, 1974: 4003794172, 1973: 3927780238, 1972: 3851650245, 1971: 3775759617, 1970: 3700437046, 1969: 3625680627, 1968: 3551599127, 1967: 3478769962, 1966: 3407922630, 1965: 3339583597, 1964: 3273978338, 1963: 3211001009, 1962: 3150420795, 1961: 3091843507, 1960: 3034949748, 1959: 2979576185, 1958: 2925686705, 1957: 2873306090, 1956: 2822443282, 1955: 2773019936, 1954: 2724846741, 1953: 2677608960, 1952: 2630861562}