Genetic programming: imprecise length of sin(x) curve

Input table (tab-delim text)

Software: Eureqa 0.99.0 Pro Edition

Round 1. Initial solutions

Target expression: y = f(x)
Building-blocks: Constant, Input Variable, Addition, Subtraction, Multiplication, Sine
Generations: 50 000
Error metric: Mean Absolute Error

Solutions

y = 1.21600701553692*x + 0.103235897404127*sin(2.00004390670861*x)
Maximum Error: 0.0023092174
Mean Absolute Error: 0.0014074521
Complexity: 12

y = 0.0103244082922343 + 1.21544966385314*x
Maximum Error: 0.11215953
Mean Absolute Error: 0.065622238
Complexity: 5

y = 1.21594279290912*x
Maximum Error: 0.104953
Mean Absolute Error: 0.065925093
Complexity: 3

Round-best residual error:

Round 2. Common fractions

Target expression: y = f0()*x + f1()*sin(2*x)
Building-blocks: Integer Constant, Input Variable, Addition, Multiplication, Division
Generations: 50 000
Error metric: Mean Absolute Error

Solutions

y = 45/37*x + 3/29*sin(2*x)
Maximum Error: 0.008487667
Mean Absolute Error: 0.0035314589
Complexity: 8

y = 91/75*x
Maximum Error: 0.18083608
Mean Absolute Error: 0.072710567
Complexity: 5

Round-best residual error:

Round 3. Fix Residual Error

Target expression: y = 45/37*x + 3/29*sin(2*x) + f()*x
Building-blocks: Integer Constant, Addition, Multiplication, Division
Generations: 50 000
Error metric: Mean Absolute Error

Solutions

y = 45/37*x + 3/29*sin(2*x) - x/4796
Maximum Error: 0.0023955584
Mean Absolute Error: 0.001415
Complexity: 1

Final residual error: