Details

sample38.0ms

Algorithm

intervals

Results

17.0ms	79×	body	1280	valid
7.0ms	135×	body	80	valid
4.0ms	22×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	6×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
1.8b	(- (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))

series14.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
12.0ms	(- (atan (+ N 1)) (atan N))

simplify1.8s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
5	2018
4	719
3	313
2	151
1	77
0	41

prune106.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1) N)
0.2b	(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:

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

series72.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(* (+ N 1) N)
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.7s

Counts

36 → 36

Iterations

Iter	Nodes
done	5008
4	2728
3	706
2	266
1	121
0	55

prune146.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-log-exp`
3×	`*-un-lft-identity`
2×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`+-commutative` `sum-log` `flip3-+` `distribute-rgt-out` `distribute-rgt1-in` `flip-+`

Counts

2 → 22

Calls

2 calls:

6.0ms	(+ N (* N N))
0.0ms	(atan2 1 (+ 1 (+ N (* N N))))

series53.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(+ N (* N N))
3.0ms	(atan2 1 (+ 1 (+ N (* N N))))

simplify1.1s

Counts

28 → 28

Iterations

Iter	Nodes
done	5000
3	1310
2	322
1	101
0	43

prune89.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1 (+ 1 (+ N (* N N))))
0.6b	(* (sqrt (atan2 1 (+ 1 (+ N (* N N))))) (sqrt (atan2 1 (+ 1 (+ N (* N N))))))
12.5b	(sqrt (atan2 1 (+ 1 (+ N (* N N)))))
12.5b	(sqrt (atan2 1 (+ 1 (+ N (* N N)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

0.0ms	(atan2 1 (+ 1 (+ N (* N N))))
9.0ms	(* (sqrt (atan2 1 (+ 1 (+ N (* N N))))) (sqrt (atan2 1 (+ 1 (+ N (* N N))))))
1.0ms	(sqrt (atan2 1 (+ 1 (+ N (* N N)))))
1.0ms	(sqrt (atan2 1 (+ 1 (+ N (* N N)))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1 (+ 1 (+ N (* N N))))
3.0ms	(* (sqrt (atan2 1 (+ 1 (+ N (* N N))))) (sqrt (atan2 1 (+ 1 (+ N (* N N))))))
14.0ms	(sqrt (atan2 1 (+ 1 (+ N (* N N)))))
22.0ms	(sqrt (atan2 1 (+ 1 (+ N (* N N)))))

simplify3.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
5	4086
4	1034
3	482
2	243
1	128
0	65

prune221.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes66.0ms

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	10
1	10
0	6

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.0s	2805×	body	1280	valid
255.0ms	4054×	body	80	valid
146.0ms	652×	body	640	valid
46.0ms	336×	body	320	valid
15.0ms	153×	body	160	valid