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A logarithm of a perfect power takes the exponent out, so related logarithms collect - #1217
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…arithms collect ln(4/3) + ln(16/9) / 2 was left as written; it is 2 ln(4/3), which the metric then prefers as the single literal ln(16/9). The rule that reads log(a, b^n) as n log(a, b) could not see a rational literal that is a power without saying so, and 16/9 is (4/3)^2. A logarithm of a positive rational literal that is a perfect power is offered as the exponent times the logarithm of the root -- the largest exponent that fits, read exactly on numerators and denominators that fit 64 bits. A positive root only: -8 is (-2)^3, but ln(-8) is ln 8 + i pi where 3 ln(-2) is 3 ln 2 + 3 i pi, so nothing is assumed by refusing it. The form is longer on its own and the metric keeps the literal; it is what lets two logarithms of related literals collect. Both spellings of the rule, Sound and Expands; the census moves by one. Question I.5 of #1212's presentation: the integral answers ln(16/9). BREAKING-CHANGES.md has the rows, measured on both builds. Part of #1212. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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Part of #1212 — the first of the small items in my comment there: question I.5's presentation.
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ln(4/3) + ln(16/9) / 2was left as written; it is2 ln(4/3), which the metric then prefers as the single literalln(16/9). The rule that readslog(a, b^n)asn log(a, b)could not see a rational literal that is a power without saying so.A new rule in
Power, in both spellings: a logarithm of a positive rational literal that is a perfect power is offered as the exponent times the logarithm of the root —ln(16/9)as2 ln(4/3),ln(64)as6 ln(2),ln(1/8)as3 ln(1/2). The largest exponent that fits is read exactly, on numerators and denominators within 64 bits (TreeAnalyzer.TryPerfectPower). A positive root only:-8is(-2)^3, butln(-8)isln 8 + iπwhere3 ln(-2)is3 ln 2 + 3iπ, so a negative root is refused rather than assumed.Sound,Expands(+2 nodes), so it is offered to the metric and never taken on its own.integral((2x^2+x+1)/(x^3+x^2+x+1), x, 3/4, 4/3)— question I.5ln(4/3) + ln(16/9) / 2ln(16/9)ln(4/3) + ln(16/9) / 2ln(4/3) + ln(16/9) / 22 * ln(4/3)ln(8) - 3 ln(2),log(3, 81) / 40,1ln(16/9),ln(64)aloneChecks
LogarithmOfAPerfectPowerTest: five perfect powers read, five non-powers refused (including-8,1,0), the sheet's integral, three collections, two literals left alone. The rule census moves by one (WritingARule.md, the guide tests,ReversibleRuleTest, theSaturationremark). Full suite in two chunks: 9,715 passed, 0 failed (Calculus 1,355, the rest 8,360).🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura