Details

sample27.0ms

Algorithm

intervals

Results

13.0ms	96×	body	1280	valid
4.0ms	124×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	5×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.3b	(- (atan (+ N 1.0)) (atan N))

rewrite3.0ms

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:

0.0ms	(atan (+ N 1.0))
2.0ms	(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
11.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.6s

Counts

28 → 28

Iterations

Useful iterations: 4 (90.0ms)

Iter	Nodes	Cost
0	40	271
1	76	259
2	144	245
3	238	241
4	457	239
5	1155	239
6	4316	239
done	5000	239

prune52.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.4b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite11.0ms

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:

10.0ms	(* (+ 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)))

simplify4.1s

Counts

34 → 34

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	55	317
1	120	312
2	347	264
3	1180	264
4	3589	264
done	5000	264

prune69.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
16.0b	(cbrt (* (+ N 1.0) N))
16.0b	(cbrt (* (+ N 1.0) N))
16.0b	(cbrt (* (+ N 1.0) N))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*l/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`associate-*r/` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

9.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
3.0ms	(cbrt (* (+ N 1.0) N))
3.0ms	(cbrt (* (+ N 1.0) N))
3.0ms	(cbrt (* (+ N 1.0) N))

series373.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
87.0ms	(cbrt (* (+ N 1.0) N))
87.0ms	(cbrt (* (+ N 1.0) N))
90.0ms	(cbrt (* (+ N 1.0) N))

simplify1.3s

Counts

84 → 84

Iterations

Useful iterations: 3 (510.0ms)

Iter	Nodes	Cost
0	152	1527
1	354	1427
2	1057	1328
3	3688	1135
done	5000	1135

prune242.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (+ N 1.0))
0.4b	(cbrt (+ N 1.0))
0.4b	(cbrt (+ N 1.0))
0.4b	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 49

Calls

4 calls:

2.0ms	(cbrt (+ N 1.0))
2.0ms	(cbrt (+ N 1.0))
2.0ms	(cbrt (+ N 1.0))
0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(cbrt (+ N 1.0))
78.0ms	(cbrt (+ N 1.0))
79.0ms	(cbrt (+ N 1.0))
3.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify2.3s

Counts

61 → 61

Iterations

Useful iterations: 4 (1.0s)

Iter	Nodes	Cost
0	92	906
1	201	876
2	478	733
3	1211	631
4	4184	604
done	5000	604

prune154.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.3b

regimes56.0ms

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	7	9
1	12	9
done	12	9

end0.0ms

sample692.0ms

Algorithm

intervals

Results

369.0ms	2863×	body	1280	valid
118.0ms	3981×	body	80	valid
67.0ms	644×	body	640	valid
28.0ms	337×	body	320	valid
11.0ms	175×	body	160	valid