Details

sample50.0ms

Algorithm

intervals

Results

18.0ms	84×	body	1280	valid
11.0ms	18×	body	320	valid
6.0ms	128×	body	80	valid
4.0ms	20×	body	640	valid
1.0ms	6×	body	160	valid

simplify15.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.5b	(- (atan (+ N 1.0)) (atan N))

rewrite15.0ms

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))

series24.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(atan (+ N 1.0))
20.0ms	(- (atan (+ N 1.0)) (atan N))

simplify1.2s

Counts: 28 → 28

prune60.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (* (+ N 1.0) N))
0.0b	(* (+ N 1.0) N)
0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

7.0ms	(+ 1 (* (+ N 1.0) N))
22.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series88.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ 1 (* (+ N 1.0) N))
62.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify1.3s

Counts: 48 → 48

prune125.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
13.6b	(cbrt (* (+ N 1.0) N))
13.6b	(cbrt (* (+ N 1.0) N))
13.6b	(cbrt (* (+ N 1.0) N))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

23.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
12.0ms	(cbrt (* (+ N 1.0) N))
8.0ms	(cbrt (* (+ N 1.0) N))
15.0ms	(cbrt (* (+ N 1.0) N))

series528.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
128.0ms	(cbrt (* (+ N 1.0) N))
130.0ms	(cbrt (* (+ N 1.0) N))
118.0ms	(cbrt (* (+ N 1.0) N))

simplify622.0ms

Counts: 84 → 84

prune344.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
12.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
12.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
14.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
3.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
3.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
6.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
17.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
22.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify5.1s

Counts: 94 → 94

prune163.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.3b

regimes26.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify31.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

677.0ms	2840×	body	1280	valid
218.0ms	4052×	body	80	valid
137.0ms	651×	body	640	valid
36.0ms	295×	body	320	valid
14.0ms	162×	body	160	valid