Estimate the world population, at 5 different levels of accuracy code-challenge
Your goal is, given a year between 1952 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 Xn 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}\$
Note the numbers here are absolute nonsense, I hope most submissions will have a score that can be written in the title without needing scientific notation
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
Year | Population |
---|---|
2020 | 7,794,798,739 |
2019 | 7,713,468,100 |
2018 | 7,631,091,040 |
2017 | 7,547,858,925 |
2016 | 7,464,022,049 |
2015 | 7,379,797,139 |
2014 | 7,295,290,765 |
2013 | 7,210,581,976 |
2012 | 7,125,828,059 |
2011 | 7,041,194,301 |
2010 | 6,956,823,603 |
2009 | 6,872,767,093 |
2008 | 6,789,088,686 |
2007 | 6,705,946,610 |
2006 | 6,623,517,833 |
2005 | 6,541,907,027 |
2004 | 6,461,159,389 |
2003 | 6,381,185,114 |
2002 | 6,301,773,188 |
2001 | 6,222,626,606 |
2000 | 6,143,493,823 |
1999 | 6,064,239,055 |
1998 | 5,984,793,942 |
1997 | 5,905,045,788 |
1996 | 5,824,891,951 |
1995 | 5,744,212,979 |
1994 | 5,663,150,427 |
1993 | 5,581,597,546 |
1992 | 5,498,919,809 |
1991 | 5,414,289,444 |
1990 | 5,327,231,061 |
1989 | 5,237,441,558 |
1988 | 5,145,426,008 |
1987 | 5,052,522,147 |
1986 | 4,960,567,912 |
1985 | 4,870,921,740 |
1984 | 4,784,011,621 |
1983 | 4,699,569,304 |
1982 | 4,617,386,542 |
1981 | 4,536,996,762 |
1980 | 4,458,003,514 |
1979 | 4,380,506,100 |
1978 | 4,304,533,501 |
1977 | 4,229,506,060 |
1976 | 4,154,666,864 |
1975 | 4,079,480,606 |
1974 | 4,003,794,172 |
1973 | 3,927,780,238 |
1972 | 3,851,650,245 |
1971 | 3,775,759,617 |
1970 | 3,700,437,046 |
1969 | 3,625,680,627 |
1968 | 3,551,599,127 |
1967 | 3,478,769,962 |
1966 | 3,407,922,630 |
1965 | 3,339,583,597 |
1964 | 3,273,978,338 |
1963 | 3,211,001,009 |
1962 | 3,150,420,795 |
1961 | 3,091,843,507 |
1960 | 3,034,949,748 |
1959 | 2,979,576,185 |
1958 | 2,925,686,705 |
1957 | 2,873,306,090 |
1956 | 2,822,443,282 |
1955 | 2,773,019,936 |
1954 | 2,724,846,741 |
1953 | 2,677,608,960 |
1952 | 2,630,861,562 |
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}