Improve solve_for_outer_interval for max/min comparisons#9162
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alexreinking wants to merge 1 commit into
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Improve solve_for_outer_interval for max/min comparisons#9162alexreinking wants to merge 1 commit into
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Two related improvements to SolveForInterval:
1. SolveExpression::visit(Sub): add f(x)*a - f(x) → f(x)*(a-1) and the
symmetric f(x) - f(x)*a → f(x)*(1-a) reduction rules. Without these,
expressions like 2*x - x couldn't be simplified, blocking the solver
from rearranging comparisons such as 2*x <= x into x <= 0.
2. SolveForInterval::visit(LE/GE): when solve_expression fails to fully
isolate the variable, try a direct max/min decomposition on the LHS
before falling back to fail(). The rules applied are:
max(a, b) <= c ⟺ a <= c && b <= c
min(a, b) <= c ⟺ a <= c || b <= c
max(a, b) * pos_c <= rhs ⟺ a*pos_c <= rhs && b*pos_c <= rhs
min(a, b) * pos_c <= rhs ⟺ a*pos_c <= rhs || b*pos_c <= rhs
(and symmetric >= variants)
Together these enable two previously unhandled cases:
- max(x, 1) * 2 <= x → Interval::nothing() (always false)
- max(abs(select(x < 0, f(x-1), 5)), 2) <= x → [2, +∞)
(the constant branch forces x >= 2 even when f is opaque)
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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abadams
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May 29, 2026
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lgtm provided the fuzzer accepts it
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The fuzz failure in CI is not related to this change. It's in |
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Two related improvements to SolveForInterval:
SolveExpression::visit(Sub): add
f(x)*a - f(x) → f(x)*(a-1)and the symmetricf(x) - f(x)*a → f(x)*(1-a)reduction rules. Without these, expressions like2*x - xcouldn't be simplified, blocking the solver from rearranging comparisons such as2*x <= xintox <= 0.SolveForInterval::visit(LE/GE): when solve_expression fails to fully isolate the variable, try a direct max/min decomposition on the LHS before falling back to fail(). The rules applied are:
max(a, b) <= c ⟺ a <= c && b <= c min(a, b) <= c ⟺ a <= c || b <= c max(a, b) * pos_c <= rhs ⟺ a*pos_c <= rhs && b*pos_c <= rhs min(a, b) * pos_c <= rhs ⟺ a*pos_c <= rhs || b*pos_c <= rhs(and symmetric >= variants)Together these enable two previously unhandled cases:
max(x, 1) * 2 <= x→Interval::nothing()(always false)max(abs(select(x < 0, f(x-1), 5)), 2) <= x→[2, +∞)(the constant branch forces x >= 2 even when f is opaque)These limitations were found by @stevenraphael
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