expression : exp(iπ) + 1
terms used : 28
computed real part of exp(iπ) : -1.000000000000000
computed imaginary part of exp(iπ) : 0.000000000000000
residual magnitude : 3.767e-16
within tolerance : true
The example approximates exp(iπ) by a finite Taylor series over complex numbers.
The resulting residual is not claimed to be mathematically exact zero; it is checked against the explicit tolerance from JSON.
The computed real part is effectively -1 and the imaginary part is near 0 at the chosen precision.
That gives a reproducible finite certificate for the familiar Euler-identity witness.