# approximate pi by integrating 1/(1+x²) from 0 to 1,
# doing so in parallel with threading for a speed-up.

f ← ˜÷1+1ⁿ2
# create interval [a, b) with n values
# interval ? a b n
ι ← ⍜-×⊙⊙(÷⟜⇡)
# integrate f on given interval
# integral ? f a b n
i! ← ÷⊃⧻/+ ^0 ι
# time a unary function
# ? f
t! ← ⊙(&p" ms"&pf×1e3⌵-)⊙now^0⊙now
# partition into n subintervals
# [subintervals a_b] ? a b n
p ← ⊂⟜(\+↯⤙(˜÷⌵-))

p 0 1 4 # n=4 threads
⊃(&p $ sequential:
  t!(⧈₂/(i!f⊙⊙1e7))
| &p $ parallel:
  t!(wait⧈₂/pool(i!f⊙⊙1e7))
)
&p $ error:
&p ⌵-π×4÷⊃⧻/+ ◌