Details

sample55.0ms

Algorithm

intervals

Results

22.0ms	78×	body	1280	valid
9.0ms	134×	body	80	valid
6.0ms	26×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	5×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
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))
4.0ms	(- (atan (+ N 1.0)) (atan N))

series17.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
14.0ms	(- (atan (+ N 1.0)) (atan N))

simplify1.6s

Counts

28 → 28

Iterations

Iter	Nodes
done	5000
5	1579
4	611
3	284
2	150
1	76
0	40

prune112.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.2b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
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:

16.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series64.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify1.4s

Counts

34 → 34

Iterations

Iter	Nodes
done	5001
3	1156
2	337
1	126
0	55

prune119.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.5b	(cbrt N)
0.5b	(cbrt N)
0.5b	(cbrt N)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

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

series1.0s

Counts

4 → 12

Calls

4 calls:

252.0ms	(* (cbrt N) (cbrt N))
268.0ms	(cbrt N)
242.0ms	(cbrt N)
251.0ms	(cbrt N)

simplify2.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5007
4	3735
3	1034
2	377
1	136
0	61

prune350.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt N)
0.5b	(cbrt N)
0.5b	(cbrt N)
0.5b	(cbrt N)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series997.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(cbrt N)
225.0ms	(cbrt N)
269.0ms	(cbrt N)
227.0ms	(cbrt N)

simplify3.0s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
6	4494
5	1126
4	390
3	175
2	94
1	44
0	24

prune284.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes36.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	7

end0.0ms

sample1.5s

Algorithm

intervals

Results

973.0ms	2867×	body	1280	valid
163.0ms	4027×	body	80	valid
95.0ms	630×	body	640	valid
87.0ms	319×	body	320	valid
13.0ms	157×	body	160	valid