Details

sample28.0ms

Algorithm

intervals

Results

13.0ms	92×	body	1280	valid
4.0ms	122×	body	80	valid
2.0ms	21×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 16.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.3b	(- (atan (+ N 1.0)) (atan N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 22

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
6.0ms	(- (atan (+ N 1.0)) (atan N))

series14.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
12.0ms	(- (atan (+ N 1.0)) (atan N))

simplify79.0ms

Counts

28 → 28

Iterations

Useful iterations: 3 (12.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2491	142
5	5001	142
done	5001	142

prune57.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite25.0ms

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:

23.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series46.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify57.0ms

Counts

34 → 34

Iterations

Useful iterations: 1 (5.0ms)

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

prune64.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
15.8b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.8b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
13.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series38.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
4.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify103.0ms

Counts

94 → 94

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	110	649
1	391	565
2	2248	539
3	5001	520
done	5001	520

prune144.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
15.8b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.8b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 40

Calls

4 calls:

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify73.0ms

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	49	332
1	79	294
2	159	294
3	330	292
4	1202	292
5	5002	292
done	5002	292

prune130.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.4b

regimes55.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b 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

sample724.0ms

Algorithm

intervals

Results

373.0ms	2880×	body	1280	valid
118.0ms	4067×	body	80	valid
66.0ms	600×	body	640	valid
26.0ms	309×	body	320	valid
9.0ms	144×	body	160	valid