[ { "api_error_status": null, "duration_api_ms": 48597, "duration_ms": 48649, "fast_mode_disabled_reason": "sdk_opt_in_required", "fast_mode_state": "off", "first_content_frame_ms": 1441, "is_error": false, "modelUsage": { "claude-opus-5": { "cacheCreationInputTokens": 5091, "cacheReadInputTokens": 0, "canonicalModel": "claude-opus-5", "contextWindow": 1000000, "costBasis": "list", "costUSD": 0.14182, "inputTokens": 2, "maxOutputTokens": 64000, "outputTokens": 3636, "provider": "firstParty", "thinkingTokens": 735, "webSearchRequests": 0 } }, "num_turns": 1, "permission_denials": [], "queued_turn_count": 0, "result": "## Preconditions\n\n1. Every emitted program is a single top-level `module { ... }` whose body consists only of a possibly empty sequence of callable definitions, with no other top-level operations, no symbol-table attributes, and no terminator written for the module itself.\n2. Each callable is either an `llvm.func` (forms named `plain_*`, `blocked_*`, `resolved_*`, and the inner `inner_*`) or a `func.func` (form named `native_*`), never a declaration without a body: every callable emitted carries a full `{ ... }` region.\n3. Every symbol name in a program is unique, because each callable name is suffixed with the position index of the function within the module, and the nested inner callable reuses that same index under a distinct prefix.\n4. Every SSA value name is unique within its enclosing region, achieved by embedding the function index (and, for chained intrinsics, the intrinsic index) in the name.\n5. Every operand is defined before its use: the only intra-body data dependence emitted is `arith.addf %q, %z`, which consumes the result of the immediately preceding `arith.mulf` in the same block.\n6. `llvm.intr.fmuladd` always appears with exactly three operands of one common type and a result of that same type, written in the full functional form `(T, T, T) -> T`.\n7. The three operands of every `llvm.intr.fmuladd` are the block arguments `%x`, `%y`, `%z` of the callable that owns the operation, so the intrinsic never reads a value produced by another operation.\n8. Every callable that owns an `llvm.intr.fmuladd` has a three-argument signature `(%x: T, %y: T, %z: T) -> T` in which the argument types, the result type, and the intrinsic's operand/result type are all the same single type.\n9. Every `llvm.func` body terminates with `llvm.return %x : T` whose operand type equals the declared result type, and the `func.func` body terminates with `return %a : T` likewise matching its declared result type; no other terminators are used.\n10. The results of the emitted `llvm.intr.fmuladd`, `llvm.fmul`, `math.fma`, `arith.mulf`, and `arith.addf` operations are dead \u2014 no emitted return or later operation consumes an intrinsic or residual result except the `arith.mulf` \u2192 `arith.addf` pair.\n11. When a fast-math contract is present, it is written as the discrete attribute `{fastmathFlags = #llvm.fastmath<...>}` attached directly to the `llvm.intr.fmuladd` operation, between the operand list and the `:` type signature.\n12. Function-level attributes, when present, are written as an `attributes { ... }` clause placed after the signature and before the opening brace of the body, and they never appear on the same callable as an operation-level fast-math attribute.\n13. The nested form places its `llvm.intr.fmuladd` inside an `llvm.func` that is itself inside a `builtin.module` region nested in a `func.func` body, so the intrinsic's nearest enclosing callable is the inner `llvm.func` and not the outer `func.func`; the outer `func.func` region contains no floating-point operation of its own.\n14. The nested inner `llvm.func` has its own complete body with its own three block arguments and its own `llvm.return`, independent of the outer function's single argument `%a`.\n15. Location information, when emitted, is a trailing `loc(\"...\")` on the intrinsic operation with a string unique to that operation within the program; operations without a `loc` are left with the default unknown location.\n16. All floating-point types used in a single callable are one uniform type drawn from the scalar types `f32`, `f64`, `f16` or the vector type `vector<4xf32>`; type mixing within one callable never occurs.\n17. The alternative \"resolved\" shape contains no `llvm.intr.fmuladd` at all: it uses only `math.fma`, `arith.mulf`, and `arith.addf` on the block arguments, and thus an emitted program need not contain any intrinsic.\n18. An emitted program may legally contain zero callables, so the empty module is a valid input.\n\n## Sampling conventions\n\n1. The number of top-level callables is chosen uniformly from the integer range 0 through 3 inclusive, so no program has more than three top-level functions.\n2. Functions are emitted in index order starting at 0, with the index recorded in state and incremented once per function; the index is textually reused in every symbol, SSA name, and location string of that function.\n3. Each function independently selects one of exactly four shapes from a six-element menu in which the `plain` shape occurs three times and `blocked`, `nested`, and `resolved` once each, so the plain shape is over-represented but all four remain reachable.\n4. The `plain` shape draws its uniform type from exactly the four choices `f32`, `f64`, `f16`, `vector<4xf32>`; no other element type, bit width, vector shape, or scalable vector is ever emitted.\n5. The `blocked`, `nested`, and `resolved` shapes restrict their type to `f32` or `f64` only, so vector and half-precision types appear exclusively in the plain shape.\n6. A plain function emits between 1 and 2 `llvm.intr.fmuladd` operations, chosen uniformly, generated by a state-counted right recursion that stops exactly when the counter equals the chosen count; three or more intrinsics in one plain function are never emitted.\n7. The result names of the plain chain are `%r_` with `k` running from 0, and the matching location strings are `\"fmuladd__\"`.\n8. Each intrinsic in a plain chain independently draws its fast-math contract from exactly four options: no attribute at all, ``, ``, or ``; no other flag names, combinations, or orderings are produced, and two intrinsics in the same function may differ.\n9. A plain function optionally prefixes its intrinsic chain with exactly one residual operation `%m = llvm.fmul %x, %y : T`, chosen by a binary coin; when omitted nothing is emitted in its place, and never more than one residual operation is produced.\n10. The residual `llvm.fmul` is always emitted before the intrinsic chain and never after or between intrinsics.\n11. The `blocked` shape emits exactly one intrinsic, named `%b` with location `\"fmuladd_blocked_\"`, and never carries a fast-math attribute on that intrinsic.\n12. The `blocked` shape's function attribute is drawn from exactly three fixed alternatives \u2014 `reciprocal_estimates = \"all\"`, `passthrough = [\"strictfp\"]`, and `no_signed_zeros_fp_math = true` \u2014 each emitted alone, never combined and never on any other shape.\n13. The `nested` shape is a fixed skeleton with a single `builtin.module` nesting level containing exactly one inner `llvm.func` with exactly one intrinsic `%n` and location `\"fmuladd_nested_\"`; the nesting depth, inner function count, and intrinsic count are never varied.\n14. The nested intrinsic's fast-math attribute is fixed to `{fastmathFlags = #llvm.fastmath}` and is never absent or varied.\n15. The outer `func.func` of the nested shape always has exactly one argument `%a` of the same type as the inner function's type and returns it unchanged.\n16. The `resolved` shape is a fixed three-operation skeleton \u2014 `%p = math.fma`, `%q = arith.mulf`, `%s = arith.addf` \u2014 always in that order, always on `%x`, `%y`, `%z`, with no attributes and no `loc` on any of them.\n17. Symbol names follow the fixed scheme `@plain_`, `@blocked_`, `@native_`, `@inner_`, `@resolved_`, and SSA value prefixes are fixed per shape (`%r`, `%m`, `%b`, `%n`, `%p`, `%q`, `%s`).\n18. Every callable returns its first argument (`%x`, or `%a` for the outer native function) rather than any computed value, a fixed skeleton choice that keeps all computed results dead.\n19. Formatting is fixed: two-space indentation inside `llvm.func` bodies, deeper indentation for the nested module and inner function, one blank line after each top-level callable, and the module's closing brace on its own final line.\n20. 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