# Python Math Domain Error (How to Fix This Stupid Bug)

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You may encounter a special `ValueError` when working with Python’s `math` module.

`ValueError: math domain error`

Python raises this error when you try to do something that is not mathematically possible or mathematically defined.

To understand this error, have a look at the definition of the domain:

The domain of a function is the complete set of possible values of the independent variable. Roughly speaking, the domain is the set of all possible (input) x-values which result in a valid (output) y-value.” (source)

The domain of a function is the set of all possible input values. If Python throws the `ValueError: math domain error`, you’ve passed an undefined input into the `math` function. Fix the error by passing a valid input for which the function is able to calculate a numerical output.

Here are a few examples:

## Python Math Domain Error Sqrt

The math domain error appears if you pass a negative argument into the `math.sqrt()` function. It’s mathematically impossible to calculate the square root of a negative number without using complex numbers. Python doesn’t get that and throws a `ValueError: math domain error`.

Here’s a minimal example:

```from math import sqrt
print(sqrt(-1))
'''
Traceback (most recent call last):
File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 2, in <module>
print(sqrt(-1))
ValueError: math domain error
'''```

You can fix the math domain error by using the `cmath` package that allows the creation of complex numbers:

```from cmath import sqrt
print(sqrt(-1))
# 1j```

## Python Math Domain Error Log

The `math domain error` for the `math.log()` function appears if you pass a zero value into it—the logarithm is not defined for value 0.

Here’s the code on an input value outside the domain of the logarithm function:

```from math import log
print(log(0))```

The output is the math domain error:

```Traceback (most recent call last):
File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module>
print(log(0))
ValueError: math domain error```

You can fix this error by passing a valid input value into the `math.log()` function:

```from math import log
print(log(0.000001))
# -13.815510557964274```

This error can sometimes appear if you pass a very small number into it—Python’s float type cannot express all numbers. To pass a value “close to 0”, use the `Decimal` module with higher precision, or pass a very small input argument such as:

`math.log(sys.float_info.min)`

## Python Math Domain Error Acos

The `math domain error` for the `math.acos()` function appears if you pass a value into it for which it is not defined—arccos is only defined for values between -1 and 1.

Here’s the wrong code:

```import math
print(math.acos(2))```

The output is the math domain error:

```Traceback (most recent call last):
File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module>
print(math.acos(2))
ValueError: math domain error```

You can fix this error by passing a valid input value between [-1,1] into the `math.acos()` function:

```import math
print(math.acos(0.5))
# 1.0471975511965979```

## Python Math Domain Error Asin

The `math domain error` for the `math.asin()` function appears if you pass a value into it for which it is not defined—arcsin is only defined for values between -1 and 1.

Here’s the erroneous code:

```import math
print(math.asin(2))```

The output is the math domain error:

```Traceback (most recent call last):
File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module>
print(math.asin(2))
ValueError: math domain error```

You can fix this error by passing a valid input value between [-1,1] into the `math.asin()` function:

```import math
print(math.asin(0.5))
# 0.5235987755982989```

## Python Math Domain Error Pow

The `math domain error` for the `math.pow(a,b)` function to calculate a**b appears if you pass a negative base value into it and try to calculate a negative power of it. The reason it is not defined is that any negative number to the power of 0.5 would be the square number—and thus, a complex number. But complex numbers are not defined by default in Python!

```import math
print(math.pow(-2, 0.5))```

The output is the math domain error:

```Traceback (most recent call last):
File "C:\Users\xcent\Desktop\Finxter\Blog\code.py", line 3, in <module>
print(math.pow(-2, 0.5))
ValueError: math domain error```

If you need a complex number, ab must be rewritten into eb ln a. For example:

```import cmath
print(cmath.exp(0.5 * cmath.log(-2)))
# (8.659560562354932e-17+1.414213562373095j)```

You see, it’s a complex number!

## NumPy Math Domain Error — np.log(x)

```import numpy as np
import matplotlib.pyplot as plt

# Plotting y = log(x)
fig, ax = plt.subplots()
ax.set(xlim=(-5, 20), ylim=(-4, 4), title='log(x)', ylabel='y', xlabel='x')
x = np.linspace(-10, 20, num=1000)
y = np.log(x)

plt.plot(x, y)```

This is the graph of `log(x)`. Don’t worry if you don’t understand the code, what’s more important is the following point. You can see that log(x) tends to negative infinity as x tends to 0. Thus, it is mathematically meaningless to calculate the log of a negative number. If you try to do so, Python raises a math domain error.

```>>> math.log(-10)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ValueError: math domain error```

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