Raising to the power leads to 10x performance slowdown in double-nested loop

test1.py

from numba import njit, prange
import numpy as np
import math
from time import time

SOFTENING_SQ = 0.001
G = 1.0


@njit(parallel=True)
def foo(m, pos, vel, acc):
    mass = m
    velocity = vel
    acceleration = acc

    dt = 0.01

    for i in prange(len(m)):
        velocity[i] += acceleration[i] * dt * 0.5  # Perform half-step with old acceleration
        pos[i] += velocity[i] * dt  # Update position with old velocity

    for i in prange(len(m)):
        x1 = pos[i]

        ax = 0.0
        for j in range(len(m)):
            x2 = pos[j]

            dx = x2 - x1
            dx2 = dx * dx
            r2 = dx2 + 0.1
            inv_r3 = r2
            # 3.626232147216797
            # 2.376734972000122
            # inv_r3 = math.pow(r2, -1.5)
            # 38.593775510787964
            # 37.70081043243408
            # inv_r3 = r2 ** (-1.5)
            # 38.75098156929016
            # 37.54234862327576
            # inv_r3 = np.power(r2, -1.5)
            # 40.880536794662476
            # 39.159523248672485

            ax += G * dx * inv_r3 * mass[j]

        acceleration[i] = ax
        velocity[i] += acceleration[i] * dt * 0.5  # Perform half-step with new acceleration
    return pos, velocity, acceleration


N = 100000
m = np.random.uniform(10, 100, N)
pos = np.zeros(N)
vel = np.zeros(N)
acc = np.zeros(N)
t1 = time()
pos, vel, acc = foo(m, pos, vel, acc)
t2 = time()
print(t2-t1)
t1 = time()
pos, vel, acc = foo(m, pos, vel, acc)
t2 = time()
print(t2-t1)