Removing the Springboard animations from your iPhone (with iOS 9) will speed it way up. The animations are the brief things you see when you open and close apps. Seems like a fraction of a second and it wouldn’t be noticeable to remove, but it is.
Here’s how you do it without jailbreaking:
Step 1: Open Settings → General → Accessibility → Assistive Touch and enable the Assistive Touch switch.
Step 2: Go to the Home screen and drag the Assistive Touch nub to the bottom right-hand corner of the screen.
Step 3: Invoke Spotlight search by swiping down on the Home screen. When the Assistive Touch nub rests above the keyboard, tap the screen to dismiss Spotlight. If you time Spotlight to dismiss as soon as the nub goes above the keyboard, you’ll notice Spotlight’s interface speed up, indicating that the glitch is now active.
Step 4: Try launching any app to see if the animations are gone. If not, repeat Step 3 until it works. Some suggest that you should try ~20 times, but I was able to make it work almost immediately.
Step 5: Disable the Assistive Touch switch enabled in Step 1.
Here’s a video as well in case you are struggling.