I think you are looking at the speed graph rather than the value graph. The speed graph is nearly useless in Time remapping. It's the slope of the value graph that lets you know what's going on with your video. The value graph represents time. Time remapping is a bit tricky to figure out because it requires you to visualize time in a whole new way. It's like Einstein said, "Time is relative." Try showing a reference graph and editing the value graph.
Assuming that is the speed graph I can see that the video is speeding up when it gets to the first keyframe, then playing at nearly a constant speed between keyframe 1 and 2, then it quickly speeds up and then plays as an ever so slowly increase in speed and so on. There are also rough spots in the graph that indicate that speed is rapidly changing. The problem is that I cannot tell anything at all about the speed of the clip using this view. Take a look at this example.
Between points KF 1 and KF 2 the video is playing back at normal speed so Time is real time. At KF 2 Time starts to go backwards because the value line is going down hill. Between KF 3 and KF 4 time is now back in the normal direction and because the slope is the same as between KF 1 and KF 2 time is again running in the right direction. Here's the catch, and the thing that is hard to visualize. Time went forward to in real time until 6:17 then time runs backwards until we get to 16:11 but the time, or frame number, of the video at 16:22 is 2.5 seconds. We have shifted the time of the video to 2.5 seconds after watching the video for 16:11. Did you follow that. See, it's hard to visualize on the graph.
Now between KF 4 and KF 5 the fun really starts. You have work at it to think of the value graph as time and the speed graph as rate of change, not speed of playback. As you can see the time starts to increase after KF 4 and then reaches a fairly steep speed for a few frames, then time starts to slow down until at KF 5, time stops. The speed graph shows time speeding up and then slowing down.
So how do you solve the problem with your time remapping? First, edit the Speed Graph. Second, press the G key and hold down the Alt/Option key to change the pen tool to the Convert Point tool (the little sideways V) and click on each of the keyframes to remove the bezier handles that are causing the spikes in your value graph. If you want to put some easing in the time remapping the standard ease in and ease out will not work most of the time because they are designed for spatial relationships not temporal relationships. This means you'll have to very carefully edit the bezier handles in the speed graph to get the effect you want.
Thank you kind sir it did help alot. very much appreciated.