Details

sample42.0ms

Algorithm

intervals

Results

22.0ms	92×	body	1280	valid
7.0ms	126×	body	80	valid
4.0ms	22×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	8×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
2.3b	(- (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))
5.0ms	(- (atan (+ N 1)) (atan N))

series14.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
13.0ms	(- (atan (+ N 1)) (atan N))

simplify2.1s

Counts

30 → 30

Iterations

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

prune95.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1) N)
0.3b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite21.0ms

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:

20.0ms	(* (+ N 1) N)
1.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series62.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(* (+ N 1) N)
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify3.1s

Counts

36 → 36

Iterations

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

prune167.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(* N (+ N 1))
0.3b	(atan2 1 (+ 1 (* N (+ N 1))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

14.0ms	(* N (+ N 1))
0.0ms	(atan2 1 (+ 1 (* N (+ N 1))))

series57.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify1.9s

Counts

38 → 38

Iterations

Iter	Nodes
done	5733
3	2512
2	504
1	149
0	56

prune168.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
17.0b	(cbrt (* (+ N 1) N))
17.0b	(cbrt (* (+ N 1) N))
17.0b	(cbrt (* (+ N 1) N))

rewrite68.0ms

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:

36.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
10.0ms	(cbrt (* (+ N 1) N))
11.0ms	(cbrt (* (+ N 1) N))
9.0ms	(cbrt (* (+ N 1) N))

series250.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
55.0ms	(cbrt (* (+ N 1) N))
67.0ms	(cbrt (* (+ N 1) N))
64.0ms	(cbrt (* (+ N 1) N))

simplify2.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5006
3	2993
2	952
1	345
0	138

prune346.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes32.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
1	11
0	6

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.0s	2732×	body	1280	valid
254.0ms	4134×	body	80	valid
154.0ms	648×	body	640	valid
59.0ms	318×	body	320	valid
22.0ms	168×	body	160	valid