Details

sample27.0ms

Algorithm

intervals

Results

12.0ms	89×	body	1280	valid
4.0ms	121×	body	80	valid
3.0ms	26×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	6×	body	160	valid

simplify3.0ms

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

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.2b	(- (atan (+ N 1.0)) (atan N))

rewrite4.0ms

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))
3.0ms	(- (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))

simplify2.3s

Counts

28 → 28

Iterations

Useful iterations: 4 (86.0ms)

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

prune57.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.2b	(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)))

series48.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify2.9s

Counts

34 → 34

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	55	317
1	120	312
2	347	264
3	1178	264
4	3491	264
done	5000	264

prune72.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
16.5b	(cbrt (* (+ N 1.0) N))
16.5b	(cbrt (* (+ N 1.0) N))
16.5b	(cbrt (* (+ N 1.0) N))

rewrite22.0ms

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))

series387.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
90.0ms	(cbrt (* (+ N 1.0) N))
90.0ms	(cbrt (* (+ N 1.0) N))
90.0ms	(cbrt (* (+ N 1.0) N))

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: 3 (483.0ms)

Iter	Nodes	Cost
0	152	1527
1	354	1427
2	1066	1328
3	3708	1135
done	5000	1135

prune250.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
0.6b	(cbrt N)
16.5b	(cbrt (* (+ N 1.0) N))
16.5b	(cbrt (* (+ N 1.0) N))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*l/`
16×	`cbrt-div`
11×	`pow1` `add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity` `pow1/3`
8×	`flip3-+` `flip-+`
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)))
0.0ms	(cbrt N)
3.0ms	(cbrt (* (+ N 1.0) N))
3.0ms	(cbrt (* (+ N 1.0) N))

series468.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
165.0ms	(cbrt N)
97.0ms	(cbrt (* (+ N 1.0) N))
92.0ms	(cbrt (* (+ N 1.0) N))

simplify1.3s

Counts

84 → 84

Iterations

Useful iterations: 3 (611.0ms)

Iter	Nodes	Cost
0	167	1345
1	379	1245
2	1115	1152
3	3881	994
done	5000	994

prune270.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes23.0ms

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	7	9
1	12	9
done	12	9

end0.0ms

sample693.0ms

Algorithm

intervals

Results

365.0ms	2833×	body	1280	valid
122.0ms	4034×	body	80	valid
65.0ms	624×	body	640	valid
28.0ms	347×	body	320	valid
12.0ms	162×	body	160	valid