Details

sample38.0ms

Algorithm

intervals

Results

20.0ms	88×	body	1280	valid
6.0ms	136×	body	80	valid
2.0ms	12×	body	640	valid
2.0ms	15×	body	320	valid
0.0ms	5×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	28
2	28
1	23
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
1.3b	(- (atan (+ N 1)) (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` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

1.0ms	(atan (+ N 1))
4.0ms	(- (atan (+ N 1)) (atan N))

series28.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
26.0ms	(- (atan (+ N 1)) (atan N))

simplify2.0s

Counts

30 → 30

Iterations

Iter	Nodes
6	4612
5	1681
4	747
3	417
2	245
1	149
0	41

prune263.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1) N)
0.4b	(atan2 1 (+ 1 (* (+ N 1) 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/` `insert-posit16` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

14.0ms	(* (+ N 1) N)
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series57.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(* (+ N 1) N)
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.3s

Counts

36 → 36

Iterations

Iter	Nodes
4	2111
3	810
2	416
1	213
0	55

prune254.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
14.3b	(cbrt (* (+ N 1) N))
14.3b	(cbrt (* (+ N 1) N))
14.3b	(cbrt (* (+ N 1) N))

rewrite36.0ms

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` `insert-posit16` `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 → 76

Calls

4 calls:

20.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
5.0ms	(cbrt (* (+ N 1) N))
5.0ms	(cbrt (* (+ N 1) N))
5.0ms	(cbrt (* (+ N 1) N))

series221.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
48.0ms	(cbrt (* (+ N 1) N))
54.0ms	(cbrt (* (+ N 1) N))
58.0ms	(cbrt (* (+ N 1) N))

simplify977.0ms

Counts

88 → 88

Iterations

Iter	Nodes
3	2548
2	1202
1	578
0	138

prune759.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
0.6b	(cbrt N)
14.3b	(cbrt (* (+ N 1) N))
14.3b	(cbrt (* (+ N 1) N))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*l/`
16×	`cbrt-div`
11×	`add-sqr-sqrt` `pow1`
9×	`cbrt-prod` `*-un-lft-identity` `pow1/3` `add-cube-cbrt`
8×	`flip3-+` `flip-+`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `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 → 76

Calls

4 calls:

20.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
1.0ms	(cbrt N)
5.0ms	(cbrt (* (+ N 1) N))
5.0ms	(cbrt (* (+ N 1) N))

series407.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
214.0ms	(cbrt N)
71.0ms	(cbrt (* (+ N 1) N))
51.0ms	(cbrt (* (+ N 1) N))

simplify941.0ms

Counts

88 → 88

Iterations

Iter	Nodes
3	2721
2	1310
1	634
0	154

prune913.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes27.0ms

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
2	11
1	11
0	6

end0.0ms

sample1.3s

Algorithm

intervals

Results

729.0ms	2784×	body	1280	valid
282.0ms	4123×	body	80	valid
117.0ms	641×	body	640	valid
42.0ms	305×	body	320	valid
14.0ms	147×	body	160	valid