Details

sample54.0ms

Algorithm

intervals

Results

24.0ms	90×	body	1280	valid
8.0ms	125×	body	80	valid
5.0ms	24×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	7×	body	160	valid

simplify8.0ms

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: 16.5b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

5.0ms

(- (atan (+ N 1.0)) (atan N))

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

(- (atan (+ N 1.0)) (atan N))

simplify2.1s

Counts

18 → 18

Iterations

Iter	Nodes
done	5000
5	1546
4	605
3	281
2	147
1	73
0	36

prune109.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite21.0ms

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:

20.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series70.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify1.7s

Counts

34 → 34

Iterations

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

prune159.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
14.8b	(cbrt (* (+ N 1.0) N))
14.8b	(cbrt (* (+ N 1.0) N))
14.8b	(cbrt (* (+ N 1.0) N))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

34.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
12.0ms	(cbrt (* (+ N 1.0) N))
11.0ms	(cbrt (* (+ N 1.0) N))
19.0ms	(cbrt (* (+ N 1.0) N))

series636.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
147.0ms	(cbrt (* (+ N 1.0) N))
144.0ms	(cbrt (* (+ N 1.0) N))
146.0ms	(cbrt (* (+ N 1.0) N))

simplify2.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
3	2865
2	991
1	378
0	152

prune451.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

14.8b	(cbrt (* (+ N 1.0) N))
14.8b	(cbrt (* (+ N 1.0) N))
14.8b	(cbrt (* (+ N 1.0) N))
14.8b	(cbrt (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

86×	`cbrt-div`
74×	`associate-*l/`
30×	`flip3-+` `flip-+`
28×	`frac-times`
8×	`associate-*r/`
4×	`cbrt-prod` `add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `pow1/3` `add-exp-log` `add-cube-cbrt` `add-log-exp`
1×	`pow3` `rem-cbrt-cube`

Counts

4 → 69

Calls

4 calls:

6.0ms	(cbrt (* (+ N 1.0) N))
6.0ms	(cbrt (* (+ N 1.0) N))
8.0ms	(cbrt (* (+ N 1.0) N))
63.0ms	(cbrt (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (* (+ N 1.0) N))
112.0ms	(cbrt (* (+ N 1.0) N))
122.0ms	(cbrt (* (+ N 1.0) N))
112.0ms	(cbrt (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))))

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	5003
3	1679
2	637
1	323
0	177

prune582.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

regimes43.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	7

end0.0ms

sample1.7s

Algorithm

intervals

Results

696.0ms	2811×	body	1280	valid
579.0ms	4101×	body	80	valid
118.0ms	626×	body	640	valid
82.0ms	315×	body	320	valid
15.0ms	147×	body	160	valid