Refactor random test:
1.) move input and output inside the function
2.) show input in test information

For example:

@test.describe("Random Tests")
def tests():
    input, output = generate_test_array()
    for i in range(0,100):
        @test.it(f"input: {input[i]}")
        def test_tnt_order():
                d = uniform(0.1,384400000)
                test.assert_approx_equals(necessary_tons_of_tnt(input[i]),output[i], margin=1e-6)

It's not stated what to do with indices pointing at non-existing words.

Sample and fixed tests should use exact expected values instead of rounded to 5 decimal places ones.

The current precision requirement (1e-2) is so lenient that a simple approximation based on the two given test cases passes all tests. I suggest increasing the required precision to 1e-6, which should be easily reached with any solution based on the correctly derived closed-form solution.

Division seems to not be tested.

Since inputs seem to be simple polynomials, this kata seems to be a close duplicate of Differentiate a polynomial, with some additional mess in input strings.

• Saying "basic operators" doesn't really explain anything, x**x**x also consists of "basic operators" but calculating its derivative is far more involved than for, say, "x * 2"
• "t" is not a mathematical operator
• Initial solution is wrong
• No sample tests
• No random tests
• The result should be tested for approximate equality instead

With the current tests, this kata is practically a simple regex-replacement task which isn't really a novel idea.