"leaping up" is a grammatically correct and usable phrase in written English.
It is typically used to talk about someone rapidly rising to a standing position. For example, "The cat startled us by leaping up from the chair."
Stephen Hawking must be mentally leaping up and down.
Orgyen keeps leaping up, blocking the view of other fans.
On the replay, an Eagles fan was visible in the background leaping up in exultation.
And as Mr. McAdams explained, many people hearing it performed cannot resist "leaping up and applauding".
"Mayor Mitchel himself, leaping up in the automobile, drew a revolver," The New York Times reported.
Plumes of light are leaping up like pale, green-tinged flames.
"Mine!" said a man in the audience, leaping up with his program.
Jordan, perhaps making contact as he was leaping up, slammed the ball through the basket.
It's freezing outside, so she keeps leaping up to cling to a radiator.
"Let's go to the locker room," he says, leaping up from his seat.
The London delegates in the hall reacted ecstatically, leaping up and hugging one another.
