SQLite

            pExpr->iTable = exprProbability(pList->a[1].pExpr);
            if( pExpr->iTable<0 ){
              sqlite3ErrorMsg(pParse, "second parameter to unlikely() must be "
                                      "between 0.0 and 1.0");
              pNC->nErr++;
            }
          }else{
            pExpr->iTable = 62;  /* TUNING:  Default 2nd arg to unlikely() is 0.0625 */
          }             
        }
      }
#ifndef SQLITE_OMIT_AUTHORIZATION
      if( pDef ){
        auth = sqlite3AuthCheck(pParse, SQLITE_FUNCTION, 0, pDef->zName, 0);
        if( auth!=SQLITE_OK ){

  WhereLoopBuilder *pBuilder,
  WhereTerm *pLower,   /* Lower bound on the range. ex: "x>123" Might be NULL */
  WhereTerm *pUpper,   /* Upper bound on the range. ex: "x<455" Might be NULL */
  WhereCost *pnOut     /* IN/OUT: Number of rows visited */
){
  int rc = SQLITE_OK;
  int nOut = (int)*pnOut;
  WhereCost nNew;

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  Index *p = pBuilder->pNew->u.btree.pIndex;
  int nEq = pBuilder->pNew->u.btree.nEq;

  if( p->nSample>0
   && nEq==pBuilder->nRecValid

      assert( (pLower->eOperator & (WO_GT|WO_GE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
      if( rc==SQLITE_OK && bOk ){
        tRowcnt iNew;
        whereKeyStats(pParse, p, pRec, 0, a);
        iNew = a[0] + ((pLower->eOperator & WO_GT) ? a[1] : 0);
        if( iNew>iLower ) iLower = iNew;
        nOut--;
      }
    }

    /* If possible, improve on the iUpper estimate using ($P:$U). */
    if( pUpper ){
      int bOk;                    /* True if value is extracted from pExpr */
      Expr *pExpr = pUpper->pExpr->pRight;
      assert( (pUpper->eOperator & (WO_LT|WO_LE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
      if( rc==SQLITE_OK && bOk ){
        tRowcnt iNew;
        whereKeyStats(pParse, p, pRec, 1, a);
        iNew = a[0] + ((pUpper->eOperator & WO_LE) ? a[1] : 0);
        if( iNew<iUpper ) iUpper = iNew;
        nOut--;
      }
    }

    pBuilder->pRec = pRec;
    if( rc==SQLITE_OK ){

      if( iUpper>iLower ){
        nNew = whereCost(iUpper - iLower);
      }else{
        nNew = 10;        assert( 10==whereCost(2) );
      }
      if( nNew<nOut ){
        nOut = nNew;

#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(pBuilder);
#endif
  assert( pLower || pUpper );
  /* TUNING:  Each inequality constraint reduces the search space 4-fold.
  ** A BETWEEN operator, therefore, reduces the search space 16-fold */
  nNew = nOut;
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ){
    nNew -= 20;        assert( 20==whereCost(4) );
    nOut--;
  }
  if( pUpper ){
    nNew -= 20;        assert( 20==whereCost(4) );
    nOut--;
  }
  if( nNew<10 ) nNew = 10;
  if( nNew<nOut ) nOut = nNew;
  *pnOut = (WhereCost)nOut;
  return rc;
}

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
/*
** Estimate the number of rows that will be returned based on

      ** all of (1) dependencies (2) setup-cost, (3) run-cost, and
      ** (4) number of output rows. */
      assert( p->rSetup==pTemplate->rSetup );
      if( p->prereq==pTemplate->prereq
       && p->nLTerm<pTemplate->nLTerm
       && (p->wsFlags & pTemplate->wsFlags & WHERE_INDEXED)!=0
       && (p->u.btree.pIndex==pTemplate->u.btree.pIndex
          || pTemplate->rRun+p->nLTerm<=p->rRun+pTemplate->nLTerm)
      ){
        /* Overwrite an existing WhereLoop with an similar one that uses
        ** more terms of the index */
        pNext = p->pNextLoop;
        break;
      }else{
        /* pTemplate is not helpful.

  reset_db
  execsql {
    CREATE TABLE t1(a, UNIQUE(a));
    INSERT INTO t1 VALUES($two);
    ANALYZE;
  }
  set nByte2 [lindex [sqlite3_db_status db SCHEMA_USED 0] 1]


  expr {$nByte2 > $nByte+900 && $nByte2 < $nByte+1050}
} {1}

#-------------------------------------------------------------------------
# Test that stat4 data may be used with partial indexes.
#

  SELECT * FROM t1 WHERE d IS NOT NULL AND a=0 AND b=10 AND c=10;
} {/USING INDEX i1/}
do_eqp_test 17.3 {
  SELECT * FROM t1 WHERE d IS NOT NULL AND a=0 AND b=0 AND c=10;
} {/USING INDEX i1/}

do_execsql_test 17.4 {
  CREATE INDEX i2 ON t1(c, d);
  ANALYZE main.i2;
}
do_eqp_test 17.5 {
  SELECT * FROM t1 WHERE d IS NOT NULL AND a=0 AND b=10 AND c=10;
} {/USING INDEX i1/}
do_eqp_test 17.6 {
  SELECT * FROM t1 WHERE d IS NOT NULL AND a=0 AND b=0 AND c=10;