Look at a chart of sin(x) + sin(x/2) + sin(x/3) + sin(x/5) + sin(x/7) + sin(x/11) + sin(x/13) + sin(x/17) + sin(x/19) + sin(x/23) + sin(x/29) + sin(x/31) + sin(x/37) + sin(x/43), you can find a local peak close to practically any number; the chart is effectively entirely composed of peaks.
It's extremely unsurprising that you would find peaks near mathematically relevant numbers, since there are peaks near any number whatsoever. You could pick ten random numbers out of a hat and fine tune those to 99.999%+ accuracy as well using the same scaling procedure.
# Target constants CONSTANTS = { 'fine_structure': 131.11, 'phi': 1.9, 'pi': 3.6, 'e': 2.4, 'sqrt_2': 1.1, 'sqrt_3': 1.2, 'sqrt_5': 2.5,
Best results: L = 3017.391610 s = 0.042000 Average: 94.848564% Minimum: 82.509479%
Constants:
sqrt_2 : 100.00000000%
sqrt_3 : 99.99236291%
phi : 99.93928922%
pi : 99.89806320%
e : 99.88623436%
sqrt_5 : 99.85340314%