Details

sample26.0ms

Algorithm

intervals

Results

12.0ms	95×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize6.0ms

Local error

Found 1 expressions with local error:

0.7b	(- (atan (+ N 1.0)) (atan N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `diff-atan` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 15

Calls

1 calls:

5.0ms

(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

(- (atan (+ N 1.0)) (atan N))

simplify70.0ms

Counts

18 → 18

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	72	123
1	142	114
2	286	112
3	678	111
4	2488	111
5	5001	111
done	5001	111

prune35.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.8b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
3×	`associate-r`
2×	`associate-*l/` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 28

Calls

2 calls:

19.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series48.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify51.0ms

Counts

34 → 34

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	121	151
1	432	127
2	2321	127
3	5002	127
done	5002	127

prune62.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.8b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
17.1b	(cbrt (* (+ N 1.0) N))
17.1b	(cbrt (* (+ N 1.0) N))
17.1b	(cbrt (* (+ N 1.0) N))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*l/`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))

series293.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
99.0ms	(cbrt (* (+ N 1.0) N))
95.0ms	(cbrt (* (+ N 1.0) N))
93.0ms	(cbrt (* (+ N 1.0) N))

simplify64.0ms

Counts

52 → 52

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	208	572
1	609	524
2	2244	482
3	5002	474
done	5002	474

prune181.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 4 expressions with local error:

17.1b	(cbrt (* (+ N 1.0) N))
17.1b	(cbrt (* (+ N 1.0) N))
17.1b	(cbrt (* (+ N 1.0) N))
17.1b	(cbrt (* (+ N 1.0) N))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cbrt-div` `associate-*l/`
4×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))

series388.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (* (+ N 1.0) N))
95.0ms	(cbrt (* (+ N 1.0) N))
102.0ms	(cbrt (* (+ N 1.0) N))
96.0ms	(cbrt (* (+ N 1.0) N))

simplify63.0ms

Counts

56 → 56

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	190	556
1	580	528
2	2211	472
3	5001	472
done	5001	472

prune233.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.7b

regimes51.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4
done	12	4

end0.0ms

sample725.0ms

Algorithm

intervals

Results

366.0ms	2830×	body	1280	valid
125.0ms	4115×	body	80	valid
64.0ms	605×	body	640	valid
26.0ms	308×	body	320	valid
9.0ms	142×	body	160	valid