FI SYSTEMS / DEVICE DESIGN EXAMPLES
Explore the sensor model’s battery-life and size choices, then the separate software and solar comparisons.
SENSOR DESIGN MODEL
What eight selected sensing cases mean for one modeled device.
The starting device: a 10 W sensor with 100 Wh of usable battery energy, 1 kg weight and 1 L volume. The model includes its full energy use at the same reporting rate.
longer battery life per charge
10 hours
→ 10.34–12.99 hours
For remote sensors and portable instruments.
less average input
10 W
→ 9.68–7.7 W
For a sensor with limited available power.
less heat to remove
10 W heat load
→ 9.68–7.7 W
A heat-flow comparison for sealed instruments.
lighter example design
1,000 g
→ 987–907.83 g
Battery and cooling resize at the original runtime.
less example device volume
1,000 cm³
→ 985.38–896.31 cm³
Fixed packing and clearances in the example layout.
readings in the best case
48 readings; equal allocation
→ 23 readings; same modeled quality limit
25 readings avoided. Extra planning uses 3% of the original job energy, included in these net savings.
Two choices: keep the 100 Wh battery and run for 10.34–12.99 hours, or use 96.75–76.96 Wh and keep the original 10 hours. The size and weight figures use the second choice, with a smaller battery and cooling assembly.
WHAT WE PAY FOR
Extra planning uses 0.30 W in the 10 W example at the same work rate. In the best case, taking fewer readings saves 2.60 W before planning, leaving 2.30 W saved overall. With these inputs, the saving starts when readings fall by more than 6%.
In three cases with equal noise across channels, the plan skips no readings. Power rises to 10.30 W and the same battery lasts 9.71 hours instead of 10—2.91% less battery life per charge. One other case saves only 1.17% energy. The linked technical reference includes all 12 cases.
WHERE FI FITS
This approach fits instruments whose repeated readings have different noise levels and a defined quality target. Fewer unnecessary readings could help the battery last longer or allow a lighter design.
Exact conventional planning methods reach the same reading counts. FI brings the plan, result checks and device-energy calculation together.
If sensing uses 20% of the device’s total energy, the 3.25–23.04% sensing saving becomes 0.65–4.61% less whole-device energy, assuming the other 80% stays fixed and no further costs are added. That means 0.65–4.83% longer battery life per charge on the same usable battery.
Saved plan: net energy reduction = 50% × fraction of readings avoided − 3%. The model keeps energy per reading, required answer quality and useful work rate fixed. Readings skipped by the plan are assumed not to be taken. Eight cases span 3.25–23.0416667%, one saves 1.1666667%, and three use 3% more. The calculation covers selected model cases.
Battery life per charge = usable battery Wh ÷ average W. Battery-life increase = saving ÷ (1 − saving). Same usable capacity, conversion efficiency, cutoff and operating profile are assumed. Battery downsizing keeps energy density and packing unchanged.
Size/weight budget: 250 g and 300 cm³ of scalable battery; 150 g and 150 cm³ of scalable cooling; all remaining parts fixed; no added physical parts. At each energy endpoint, mass saved = 400 g × saving and volume saved = 450 cm³ × saving. The cooling calculation assumes the thermal design load falls by that same fraction, with unchanged ambient, surface temperature and heat transfer per area. The modeled mass and volume assume peak loads, structural limits and packing allow those part sizes; fixed parts retain their original size.
The heat comparison uses the same energy leaving the unit in forms other than heat and the same stored-energy change over the same interval. Its starting heat load is 10 W.
RECORDED AND MODELED RESULTS
Sensing, exact calculation and solar prediction have separate comparisons and costs.
Calculation speed
3.54% overallAgainst the earlier FI implementation, a normalized 100-second aggregate becomes 96.46 seconds overall. The matching-input family becomes 68.12 seconds. Required exact answers stay unchanged. If active power stayed at 1 W, those times would use 96.46 J or 68.12 J instead of 100 J.
In the late-mismatch family, a normalized 100-second aggregate becomes 106.92 seconds. Six of ten groups slowed.
H22 compared square_direction_factored with the earlier internal factored_hybrid across 2,500 cases. Energy and heat were projected at unchanged active power and were not measured. In a separate 15 October independent AI accounting review, FI was slower than capable ordinary gmpy2 in all 26 preserved first-call and warm timing groups.
Solar prediction
37.83%The retained T026 summary reports this reduction in pooled low-light prediction error. The original execution record has not been recovered, leaving the reported improvement without independent verification. Low-light prediction remains a possible engineering application.
The retained summary reports worse results in two temperature cases and a failed overall no-regression check.
Source: retained T026 prediction-model summary. The original execution record remains unrecovered; no new run or independently verified solar result accompanies it.
The sensing calculation covers 12 selected cases. Readings consume 50% of the original job energy, and added processing costs 3%. Net energy reduction = half the reading-count reduction, minus 3 percentage points. Eight cases fall in the stated saving range. Three equal-noise cases use more energy after processing costs.
An earlier heat-management approach spread work over more time. Peak temperature fell, but completion time doubled or tripled and energy use rose, so the approach was rejected.
H22 used 2,500 prospectively selected requests and eight timed rounds per method. Summing the case medians gave a 3.542337% reduction against the prior FI hybrid; the exact-direction family alone gave 31.883441%. Late-mismatch was 6.923998% slower. These observations came from the original host and exclude startup, imports and later verification and logging. The separate 15 October independent AI accounting review found FI slower than capable ordinary gmpy2 in all 26 preserved first-call and warm timing groups.
Saved results and source recordREPORT CALCULATIONS / DESIGN COMPARISON
fewer expression evaluations
3,194,940 before
→ 2,457,660 after
Reusing exact intermediate values removes 737,280 repeated expression evaluations from this report design.
separate checker retained
The calculation and checker each keep their own saved intermediate values. They repeat less arithmetic while the checker remains independent.
additional FI arithmetic reduction
Caching means keeping intermediate answers in memory for reuse.
A conventional implementation using the same cache reaches the same arithmetic count.
These figures compare the arithmetic used to build the reports.
The count covers five reports, three jobs, two states and 4,096 sample pairs: 122,880 pairs per calculation path. The original calculation and checker use 26 rational-expression operations per pair; with caching they use 20. Both counts include 60 final divisions: 3,194,940 → 2,457,660. The reduction is 737,280 ÷ 3,194,940 = 23.0764897%.
The report-arithmetic count falls by 23.08%.
Technical reference: exact arithmetic count
