Details

sample50.0ms

Algorithm

intervals

Results

23.0ms	92×	body	1280	valid
7.0ms	122×	body	80	valid
4.0ms	21×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	6×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

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))

series15.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
13.0ms	(- (atan (+ N 1.0)) (atan N))

simplify1.7s

Counts

28 → 28

Iterations

Useful iterations: 4 (128.0ms)

Iter	Nodes	Cost
0	40	271
1	76	259
2	145	245
3	270	241
4	534	239
5	1497	239
done	5000	239

prune107.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

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:

39.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series77.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(* (+ N 1.0) N)
6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify3.7s

Counts

34 → 34

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	55	317
1	120	312
2	356	264
3	1001	264
4	4336	264
done	5002	264

prune88.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize17.0ms

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))))

rewrite34.0ms

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)))
23.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
5.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
2.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
7.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
24.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify4.4s

Counts

94 → 94

Iterations

Useful iterations: 5 (2.6s)

Iter	Nodes	Cost
0	64	1843
1	104	1267
2	216	1115
3	409	1064
4	838	1028
5	4762	998
done	5000	998

prune172.0ms

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))))

rewrite6.0ms

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:

3.0ms	(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))))

series39.0ms

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)))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify1.1s

Counts

52 → 52

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	32	698
1	50	646
2	72	570
3	99	570
4	143	570
5	251	570
6	549	570
7	1704	570
done	5000	570

prune150.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.4b

regimes54.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	12	9
done	12	9

end0.0ms

sample778.0ms

Algorithm

intervals

Results

387.0ms	2880×	body	1280	valid
132.0ms	4067×	body	80	valid
65.0ms	600×	body	640	valid
27.0ms	309×	body	320	valid
9.0ms	144×	body	160	valid