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// breakeven.go — break-even analysis for proxy-mediated tool discovery

// (Spec 083 US1, FR-003/FR-004, research D8).

package bench

import "fmt"

// ComputeBreakEven computes the number of retrieve_tools calls at which the

// proxy's cumulative context cost (proxy menu + N discovery responses) equals

// the naive full-menu cost:

//

// break_even_calls = (naive_full_menu_tokens − proxy_menu_tokens) / mean_response_tokens

//

// Below break_even_calls discovery calls the proxy is strictly cheaper; each

// call beyond it spends part of the menu savings. All three inputs are echoed

// in the result (FR-004) so a reader can recompute the number from the row

// alone. Both menu inputs MUST come from the same canonical full-definition

// renderer (research D7b) or the numerator compares different token shapes.

//

// When the numerator is ≤ 0 the proxy menu is already at least as expensive

// as the naive menu — there are no savings to amortize — and the result is a

// NoBreakEven row (BreakEvenCalls stays 0), whatever the response cost.

// Otherwise meanResponseTokens must be positive: a zero mean means no

// responses were measured, and dividing by it is undefined, so that is an

// error rather than a fabricated verdict.

func ComputeBreakEven(naiveFullMenuTokens, proxyMenuTokens int, meanResponseTokens float64) (*BreakEvenAnalysis, error) {

b := &BreakEvenAnalysis{

NaiveFullMenuTokens: naiveFullMenuTokens,

ProxyMenuTokens: proxyMenuTokens,

MeanResponseTokens: meanResponseTokens,

}

numerator := naiveFullMenuTokens - proxyMenuTokens

if numerator <= 0 {

b.NoBreakEven = true

return b, nil

}

if meanResponseTokens <= 0 {

return nil, fmt.Errorf("break-even undefined: mean response tokens must be > 0, got %v (no measured responses?)", meanResponseTokens)

}

b.BreakEvenCalls = float64(numerator) / meanResponseTokens

return b, nil

}