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Get Started Free →Deterministic router for math cognitive stack - maps user intent to exact CLI commands
.claude/skills/math-router/SKILL.md| Test case | Without → With | Effect | Δ tokens | Δ turns |
|---|---|---|---|---|
| case-18 | ✗→✓ | ▲ Improved | -65% | 0% |
| case-19 | ✗→✓ | ▲ Improved | -39% | 0% |
| case-21 | ✓→✗ | ▼ Worse | -6% | 0% |
| case-22 | ✓→✓ | ＝ Same ✓ | 1% | 0% |
| case-23 | ✓→✓ | ＝ Same ✓ | 12% | 0% |
ALWAYS use this router first for math requests.
Instead of reading individual skill documentation, call the router to get the exact command:
bash# Route any math intent to get the CLI command uv run python scripts/cc_math/math_router.py route "<user's math request>"
uv run python scripts/cc_math/math_router.py route "integrate sin(x) from 0 to pi"json { "command": "uv run python scripts/cc_math/sympy_compute.py integrate \"sin(x)\" --var x --lower 0 --upper pi", "confidence": 0.95 }
| Category | Commands | |----------|----------| | sympy | integrate, diff, solve, simplify, limit, det, eigenvalues, inv, expand, factor, series, laplace, fourier | | pint | convert, check | | shapely | create, measure, pred, op | | z3 | prove, sat, optimize | | scratchpad | verify, explain | | tutor | hint, steps, generate | | plot | plot2d, plot3d, latex |
bash# List all available routes uv run python scripts/cc_math/math_router.py list # List routes by category uv run python scripts/cc_math/math_router.py list --category sympy
If the router returns {"command": null}, the intent wasn't recognized. Then:
| Case | Status | Duration (ms) | Turns | Tokens | Tool calls | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Without | With | Δ | Without | With | Δ | Without | With | Δ | Without | With | Δ | ||
case-01 | fail→fail | 4,808 | 4,127 | -14% | 1 | 1 | 0% | 1,024 | 670 | -35% | 0 | 0 | — |
case-02 | fail→fail | 5,324 | 3,885 | -27% | 1 | 1 | 0% | 1,120 | 654 | -42% | 0 | 0 | — |
case-03 | fail→fail | 8,848 | 4,548 | -49% | 1 | 1 | 0% | 1,891 | 674 | -64% | 0 | 0 | — |
case-04 | fail→fail | 7,242 | 4,878 | -33% | 1 | 1 | 0% | 1,694 | 655 | -61% | 0 | 0 | — |
case-05 | fail→fail | 8,126 | 9,866 | +21% | 1 | 1 | 0% | 2,164 | 2,311 | +7% | 0 | 0 | — |
case-06 | fail→fail | 7,184 | 4,179 | -42% | 1 | 1 | 0% | 1,713 | 656 | -62% | 0 | 0 | — |
case-07 | fail→fail | 7,264 | 4,136 | -43% | 1 | 1 | 0% | 1,598 | 687 | -57% | 0 | 0 | — |
case-08 | fail→fail | 3,677 | 4,265 | +16% | 1 | 1 | 0% | 804 | 676 | -16% | 0 | 0 | — |
case-14 | fail→fail | 8,916 | 4,057 | -54% | 1 | 1 | 0% | 1,891 | 686 | -64% | 0 | 0 | — |
case-09 | fail→fail | 8,158 | 4,785 | -41% | 1 | 1 | 0% | 1,771 | 743 | -58% | 0 | 0 | — |
case-10 | fail→fail | 5,666 | 4,577 | -19% | 1 | 1 | 0% | 1,213 | 718 | -41% | 0 | 0 | — |
case-11 | fail→fail | 6,604 | 3,896 | -41% | 1 | 1 | 0% | 1,614 | 679 | -58% | 0 | 0 | — |
case-12 | fail→fail | 6,017 | 4,713 | -22% | 1 | 1 | 0% | 1,430 | 638 | -55% | 0 | 0 | — |
case-13 | fail→fail | 8,381 | 3,961 | -53% | 1 | 1 | 0% | 1,751 | 670 | -62% | 0 | 0 | — |
case-15 | fail→fail | 6,454 | 4,711 | -27% | 1 | 1 | 0% | 1,480 | 698 | -53% | 0 | 0 | — |
case-16 | fail→fail | 17,910 | 3,492 | -81% | 1 | 1 | 0% | 3,830 | 607 | -84% | 0 | 0 | — |
case-17 | fail→fail | 4,987 | 6,719 | +35% | 1 | 1 | 0% | 778 | 1,119 | +44% | 0 | 0 | — |
case-18 | fail→pass | 10,100 | 1,293 | -87% | 1 | 1 | 0% | 1,843 | 637 | -65% | 0 | 0 | — |
case-19 | fail→pass | 9,557 | 2,332 | -76% | 1 | 1 | 0% | 1,437 | 881 | -39% | 0 | 0 | — |
case-20 | fail→fail | 6,758 | 4,261 | -37% | 1 | 1 | 0% | 1,590 | 665 | -58% | 0 | 0 | — |
case-21 | pass→fail | 5,129 | 7,310 | +43% | 1 | 1 | 0% | 921 | 869 | -6% | 0 | 0 | — |
case-22 | pass→pass | 31,917 | 15,149 | -53% | 1 | 1 | 0% | 2,404 | 2,434 | +1% | 0 | 0 | — |
case-23 | pass→pass | 5,068 | 3,483 | -31% | 1 | 1 | 0% | 933 | 1,048 | +12% | 0 | 0 | — |
DecimalAI ran this skill against gemini-3.6-flash twice over the same eval suite — once with the skill loaded and once without — and compared the two runs case by case. 23 cases were attempted, and 6 counted toward the lift figure. The other 17 produced results that are not comparable between the two arms, so they are excluded from the headline rather than averaged into it. The headline lift of +4 percentage points is the difference between those two pass rates over the 6 comparable cases. 1 case got worse with the skill loaded, and it is included in that figure.
Without the skill loaded, the model failed this case. With it loaded, the same prompt on the same model passed. This is one improved case from the latest verified run; every case, including any that regressed, is in the table above.
| Model | Method | Date | Lift |
|---|---|---|---|
| gemini-3.6-flash | verified | 7/31/2026 | — |
Other measured skills in the registry, with their headline benchmark lift.