Details

sample61.0ms

Algorithm

intervals

Results

24.0ms	85×	body	1280	valid
9.0ms	148×	body	80	valid
3.0ms	14×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize28.0ms

Local error

Found 1 expressions with local error:

1.2b	(- (atan (+ N 1.0)) (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:

8.0ms

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

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

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

simplify7.6s

Counts

19 → 19

Iterations

Iter	Nodes
done	5002
6	4790
5	1528
4	605
3	270
2	148
1	74
0	37

prune120.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite31.0ms

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:

29.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series64.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(* (+ N 1.0) N)
9.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify2.4s

Counts

36 → 36

Iterations

Iter	Nodes
done	5000
3	1277
2	340
1	128
0	57

prune249.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1.0 N) (+ (* N N) 1))
0.5b	(atan2 1.0 (+ (* 1.0 N) (+ (* N N) 1)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
3×	`sum-log`
2×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+`

Counts

2 → 22

Calls

2 calls:

25.0ms	(+ (* 1.0 N) (+ (* N N) 1))
1.0ms	(atan2 1.0 (+ (* 1.0 N) (+ (* N N) 1)))

series36.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* 1.0 N) (+ (* N N) 1))
10.0ms	(atan2 1.0 (+ (* 1.0 N) (+ (* N N) 1)))

simplify2.8s

Counts

28 → 28

Iterations

Iter	Nodes
done	5013
3	2384
2	545
1	156
0	48

prune192.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.7b	(cbrt N)
0.7b	(cbrt N)
0.7b	(cbrt N)

rewrite24.0ms

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:

15.0ms	(* (cbrt N) (cbrt N))
2.0ms	(cbrt N)
2.0ms	(cbrt N)
2.0ms	(cbrt N)

series917.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(* (cbrt N) (cbrt N))
224.0ms	(cbrt N)
221.0ms	(cbrt N)
225.0ms	(cbrt N)

simplify5.3s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
4	3734
3	1049
2	353
1	137
0	63

prune521.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes80.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	8

end0.0ms

sample1.3s

Algorithm

intervals

Results

528.0ms	4022×	body	80	valid
501.0ms	2867×	body	1280	valid
114.0ms	613×	body	640	valid
35.0ms	339×	body	320	valid
12.0ms	159×	body	160	valid