Details

sample34.0ms

Algorithm

intervals

Results

16.0ms	90×	body	1280	valid
6.0ms	136×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	3×	body	160	valid

simplify1.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.9b	(- (atan (+ N 1.0)) (atan N))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 22

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
11.0ms	(- (atan (+ N 1.0)) (atan N))

series15.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
13.0ms	(- (atan (+ N 1.0)) (atan N))

simplify47.0ms

Counts: 28 → 28

prune117.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.1b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

48.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series89.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(* (+ N 1.0) N)
6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify44.0ms

Counts: 34 → 34

prune113.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `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 → 73

Calls

4 calls:

19.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.2s

Counts

4 → 12

Calls

4 calls:

338.0ms	(* (cbrt N) (cbrt N))
309.0ms	(cbrt N)
236.0ms	(cbrt N)
276.0ms	(cbrt N)

simplify57.0ms

Counts: 85 → 85

prune373.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

44.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
4.0ms	(cbrt (+ N 1.0))
4.0ms	(cbrt (+ N 1.0))
4.0ms	(cbrt (+ N 1.0))

series526.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
160.0ms	(cbrt (+ N 1.0))
108.0ms	(cbrt (+ N 1.0))
96.0ms	(cbrt (+ N 1.0))

simplify91.0ms

Counts: 107 → 107

prune515.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes20.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

819.0ms	2822×	body	1280	valid
243.0ms	4091×	body	80	valid
205.0ms	612×	body	640	valid
48.0ms	323×	body	320	valid
17.0ms	152×	body	160	valid