Arithmetic in prose is generated, not computed. A multi-step total can be wrong in a middle step while the final line stays confident.
The calc block below recomputes a five-step chain exactly. Each power is shown, so any line can be checked by hand.
chain success, per-step 0.9 over 5 steps (stated example values)
0.9^2 = 0.81
0.9^3 = 0.81 x 0.9 = 0.729
0.9^4 = 0.729 x 0.9 = 0.6561
0.9^5 = 0.6561 x 0.9 = 0.59049
cost: assume 1 million input tokens cost 3 units (labelled EXAMPLE parameter)
cost = 250000 / 1000000 x 3 = 0.25 x 3 = 0.75 units
token budget split: 50% + 30% + 20% = 100%Training data ends at some point, so prices, tool options and standard revisions go stale. A reply may quote last cycle facts in this cycle tone.
Stale quoting | Why it looks right | What replaces it |
|---|---|---|
A price from an old table | Exact figures carry authority | A repricing under the current stated rate. |
A removed tool option | It existed when the data was written | The current option list from the tool reference. |
A superseded standard clause | Clause numbers change slowly | The current revision of the standard. |
Recompute every quoted total from its stated inputs. The program below rechecks the chain product and the cost figure from this lesson.
import sys
def main():
p = 0.9
got = 1.0
for _ in range(5):
got = got * p
if abs(got - 0.59049) > 1e-12:
print("FAIL: chain gave " + str(got))
sys.exit(1)
units_per_million = 3.0
tokens = 250000
cost = tokens / 1000000.0 * units_per_million
if abs(cost - 0.75) > 1e-12:
print("FAIL: cost gave " + str(cost))
sys.exit(1)
print("PASS: chain 0.59049 and cost 0.75 units confirmed")
main()Five multiplications give 0.59049, and 250000 tokens at 3 units per million give 0.75 units. Both lines match the calc block above.
Recomputation: 0.9^5 is 0.59049, so 0.62 is wrong. The recomputation decides, not the confident tone.
Reprice with the current table under the stated example rate. Old numbers stay stale no matter how neatly they are shown.