Details

sample59.0ms

Algorithm

intervals

Results

36.0ms	98×	body	1280	valid
8.0ms	123×	body	80	valid
5.0ms	20×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
2.0b	(- (atan (+ N 1)) (atan N))

rewrite11.0ms

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:

2.0ms	(atan (+ N 1))
9.0ms	(- (atan (+ N 1)) (atan N))

series23.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1))
20.0ms	(- (atan (+ N 1)) (atan N))

simplify917.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	2000
5	2000
4	719
3	313
2	151
1	77
0	41

prune251.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1) N)
0.4b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite22.0ms

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:

21.0ms	(* (+ N 1) N)
1.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series77.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(* (+ N 1) N)
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.3s

Counts

36 → 36

Iterations

Iter	Nodes
done	2002
4	2002
3	706
2	266
1	121
0	55

prune271.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(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` `insert-posit16` `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 → 77

Calls

4 calls:

8.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
3.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.2s

Counts

4 → 12

Calls

4 calls:

337.0ms	(* (cbrt N) (cbrt N))
346.0ms	(cbrt N)
252.0ms	(cbrt N)
313.0ms	(cbrt N)

simplify1.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	2007
4	2007
3	1045
2	380
1	138
0	63

prune771.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
0.4b	(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))
0.6b	(cbrt N)
32.6b	(cbrt (* N N))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log`
7×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `associate-r`
4×	`associate-*l/` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow1/3`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

4 → 54

Calls

4 calls:

38.0ms	(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
0.0ms	(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))
1.0ms	(cbrt N)
3.0ms	(cbrt (* N N))

series517.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
8.0ms	(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))
220.0ms	(cbrt N)
208.0ms	(cbrt (* N N))

simplify1.0s

Counts

66 → 66

Iterations

Iter	Nodes
done	2005
3	2005
2	747
1	245
0	103

prune672.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes50.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	6

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.2s	2890×	body	1280	valid
258.0ms	3991×	body	80	valid
137.0ms	644×	body	640	valid
95.0ms	298×	body	320	valid
20.0ms	177×	body	160	valid