Details

sample47.0ms

Algorithm

intervals

Results

21.0ms	86×	body	1280	valid
8.0ms	134×	body	80	valid
6.0ms	27×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize23.0ms

Local error

Found 1 expressions with local error:

1.0b	(- (atan (+ N 1)) (atan N))

rewrite9.0ms

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` `insert-posit16` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 16

Calls

1 calls:

9.0ms

(- (atan (+ N 1)) (atan N))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(- (atan (+ N 1)) (atan N))

simplify999.0ms

Counts

19 → 19

Iterations

Iter	Nodes
done	2000
5	1968
4	692
3	307
2	147
1	73
0	36

prune60.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1) N)
0.5b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite33.0ms

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:

32.0ms	(* (+ N 1) N)
1.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series76.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify564.0ms

Counts

36 → 36

Iterations

Iter	Nodes
done	2001
3	706
2	266
1	121
0	55

prune119.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ N 1))
0.2b	(cbrt (+ N 1))
0.3b	(* (cbrt (+ N 1)) (cbrt (+ N 1)))
0.5b	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 92

Calls

4 calls:

2.0ms	(cbrt (+ N 1))
2.0ms	(cbrt (+ N 1))
26.0ms	(* (cbrt (+ N 1)) (cbrt (+ N 1)))
0.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))

series128.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(cbrt (+ N 1))
44.0ms	(cbrt (+ N 1))
37.0ms	(* (cbrt (+ N 1)) (cbrt (+ N 1)))
3.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))

simplify1.1s

Counts

104 → 104

Iterations

Iter	Nodes
done	2001
3	1688
2	752
1	307
0	138

prune459.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ N 1))
0.3b	(cbrt (- N 1))
0.5b	(atan2 1 (+ 1 (* (/ (* (cbrt (* (+ N 1) (- N 1))) (cbrt (+ N 1))) (cbrt (- N 1))) (* (cbrt (+ N 1)) N))))
15.4b	(cbrt (* (+ N 1) (- N 1)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `cbrt-div`
11×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
4×	`frac-times` `pow1` `flip3-+` `flip3--` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `flip--` `add-log-exp`
3×	`pow1/3`
2×	`associate-l/` `associate-r/` `difference-of-squares`
1×	`difference-of-sqr-1` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 59

Calls

4 calls:

3.0ms	(cbrt (+ N 1))
3.0ms	(cbrt (- N 1))
0.0ms	(atan2 1 (+ 1 (* (/ (* (cbrt (* (+ N 1) (- N 1))) (cbrt (+ N 1))) (cbrt (- N 1))) (* (cbrt (+ N 1)) N))))
8.0ms	(cbrt (* (+ N 1) (- N 1)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(cbrt (+ N 1))
52.0ms	(cbrt (- N 1))
3.0ms	(atan2 1 (+ 1 (* (/ (* (cbrt (* (+ N 1) (- N 1))) (cbrt (+ N 1))) (cbrt (- N 1))) (* (cbrt (+ N 1)) N))))
194.0ms	(cbrt (* (+ N 1) (- N 1)))

simplify748.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	2000
2	1207
1	433
0	195

prune505.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

regimes50.0ms

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	11
1	11
0	6

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.2s	2896×	body	1280	valid
324.0ms	4033×	body	80	valid
173.0ms	642×	body	640	valid
90.0ms	269×	body	320	valid
25.0ms	160×	body	160	valid