<system>
You are an experienced Python developer. You will be provided with an incorrect code snippet from a Python program. The task this program is supposed to perform is described in the following user prompt.
Your task is to rewrite the program so that it performs the task as expected without any errors. You will be rewarded based on the number of test cases your code passes.
</system>

<user>
## Description

The environment aims to increase the number of independent state and control
variables as compared to the classic control environments. The swimmers
consist of three or more segments ('***links***') and one less articulation
joints ('***rotors***') - one rotor joint connecting exactly two links to
form a linear chain. The swimmer is suspended in a two dimensional pool and
always starts in the same position (subject to some deviation drawn from an
uniform distribution), and the goal is to move as fast as possible towards
the right by applying torque on the rotors and using the fluids friction.

## Action Space
The action space is a `Box(-1, 1, (2,), float32)`. An action represents the torques applied between *links*

| Num | Action                             | Control Min | Control Max | Name (in corresponding XML file) | Joint | Unit         |
|-----|------------------------------------|-------------|-------------|----------------------------------|-------|--------------|
| 0   | Torque applied on the first rotor  | -1          | 1           | motor1_rot                       | hinge | torque (N m) |
| 1   | Torque applied on the second rotor | -1          | 1           | motor2_rot                       | hinge | torque (N m) |

## Observation Space
By default, observations consists of:
* θ<sub>i</sub>: angle of part *i* with respect to the *x* axis
* θ<sub>i</sub>': its derivative with respect to time (angular velocity)

In the default case, observations do not include the x- and y-coordinates of the front tip. These may
be included by passing `exclude_current_positions_from_observation=False` during construction.
Then, the observation space will be `Box(-Inf, Inf, (10,), float64)` where the first two observations
represent the x- and y-coordinates of the front tip.
Regardless of whether `exclude_current_positions_from_observation` was set to true or false, the x- and y-coordinates
will be returned in `info` with keys `"x_position"` and `"y_position"`, respectively.

By default, the observation is a `Box(-Inf, Inf, (8,), float64)` where the elements correspond to the following:

| Num | Observation                          | Min  | Max | Name (in corresponding XML file) | Joint | Unit                     |
| --- | ------------------------------------ | ---- | --- | -------------------------------- | ----- | ------------------------ |
| 0   | angle of the front tip               | -Inf | Inf | free_body_rot                    | hinge | angle (rad)              |
| 1   | angle of the first rotor             | -Inf | Inf | motor1_rot                       | hinge | angle (rad)              |
| 2   | angle of the second rotor            | -Inf | Inf | motor2_rot                       | hinge | angle (rad)              |
| 3   | velocity of the tip along the x-axis | -Inf | Inf | slider1                          | slide | velocity (m/s)           |
| 4   | velocity of the tip along the y-axis | -Inf | Inf | slider2                          | slide | velocity (m/s)           |
| 5   | angular velocity of front tip        | -Inf | Inf | free_body_rot                    | hinge | angular velocity (rad/s) |
| 6   | angular velocity of first rotor      | -Inf | Inf | motor1_rot                       | hinge | angular velocity (rad/s) |
| 7   | angular velocity of second rotor     | -Inf | Inf | motor2_rot                       | hinge | angular velocity (rad/s) |
| excluded | position of the tip along the x-axis | -Inf | Inf | slider1                          | slide | position (m)           |
| excluded | position of the tip along the y-axis | -Inf | Inf | slider2                          | slide | position (m)           |

## Rewards
The reward consists of two parts:
- *forward_reward*: A reward of moving forward which is measured
as *`forward_reward_weight` * (x-coordinate before action - x-coordinate after action)/dt*. *dt* is
the time between actions and is dependent on the frame_skip parameter
(default is 4), where the frametime is 0.01 - making the
default *dt = 4 * 0.01 = 0.04*. This reward would be positive if the swimmer
swims right as desired.
- *ctrl_cost*: A cost for penalising the swimmer if it takes
actions that are too large. It is measured as *`ctrl_cost_weight` *
sum(action<sup>2</sup>)* where *`ctrl_cost_weight`* is a parameter set for the
control and has a default value of 1e-4

The total reward returned is ***reward*** *=* *forward_reward - ctrl_cost* and `info` will also contain the individual reward terms

## Starting State
All observations start in state (0,0,0,0,0,0,0,0) with a Uniform noise in the range of [-`reset_noise_scale`, `reset_noise_scale`] is added to the initial state for stochasticity.

## Episode End
The episode truncates when the episode length is greater than 1000.

## Class Definition
The class should be called "Environment". It should have at least:

- an __init__ function to set up the Environment, which defines all the variables described in the above documentation, plus any additional variables needed to maintain the environment state or to implement its functionality.
- a set_state function to set a custom value for the environment and its internal representation (you can assume that when "set_state" is used, the task is not done and internal variables should be set as a consequence). set_state takes a single argument as input: a state observation from the observation space defined above.
- a step function to predict a step in the environment. The input parameters for the step function are:
    - An action, which must be contained in the action space described above.
  
    The outputs required by the step function are:
    - An observation, which must be contained in the observation space described above.
    - The reward for taking the action, as described in the reward definition above.
    - A boolean variable indicating if the episode is done.

## Important Notes
Only produce the environment class, containing the __init__, set_state and step functions and any additional functions you may need to complete this task. Do not write an example of how to use the class or anything else.
Be careful about edge cases.
Make sure to write all the required functions and that they have the exact names as specified in the task description. Missing or incorrectly named functions will not pass the tests and will result in a score of 0.
It is of VITAL importance that you do not leave undefined any function, but implement each of them completely.

First, write an explanation of the difference between the ground-truth transition and the step function's outputs in the example provided.
Second, point out the part of the code responsible for the incorrect prediction and why its logic is erroneous.
Third, suggest a concrete, actionable fix for it. 
Finally, fix the program in its entirety following the suggestion. The expected output is in the format:
## Error explanation
[your explanation of the error]
    
## Error location and wrong logic
[where the error comes from and why]
    
## Fix suggestion
[how to fix the error]
    
## Correct code
[your code]

## Incorrect code
You are provided with the following code snippet to fix.
```python
{CODE}
```
The code's step function additionally makes a wrong prediction about this transition.
## Step function inputs
{TRANSITION_INPUTS}
    
## Ground-truth transition
{GT_PREDICTION}
    
## Step function's incorrect outputs
{PREDICTION}
</user>