Details

sample27.0ms

Algorithm

intervals

Results

12.0ms	86×	body	1280	valid
4.0ms	132×	body	80	valid
3.0ms	26×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	6×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.7b	(- (atan (+ N 1.0)) (atan N))

rewrite7.0ms

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:

1.0ms	(atan (+ N 1.0))
5.0ms	(- (atan (+ N 1.0)) (atan N))

series14.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
12.0ms	(- (atan (+ N 1.0)) (atan N))

simplify74.0ms

Counts

28 → 28

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2491	142
5	5001	142
done	5001	142

prune52.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (* (+ N 1.0) N))
0.0b	(* (+ N 1.0) N)
0.4b	(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:

9.0ms	(+ 1 (* (+ N 1.0) N))
20.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series64.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ 1 (* (+ N 1.0) N))
42.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify111.0ms

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	177	222
1	766	193
2	4572	193
3	5001	193
done	5001	193

prune88.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.3b	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.4b	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `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 → 88

Calls

4 calls:

4.0ms	(cbrt (+ N 1.0))
4.0ms	(cbrt (+ N 1.0))
39.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

series272.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (+ N 1.0))
85.0ms	(cbrt (+ N 1.0))
97.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
4.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify157.0ms

Counts

100 → 100

Iterations

Useful iterations: 3 (149.0ms)

Iter	Nodes	Cost
0	330	806
1	1079	745
2	4794	696
3	5001	692
done	5001	692

prune256.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0)))
0.3b	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.4b	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0))) N))))
14.7b	(cbrt (- (* N N) (* 1.0 1.0)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

104×	`cbrt-prod`
77×	`*-un-lft-identity`
71×	`add-sqr-sqrt`
56×	`times-frac`
47×	`add-cube-cbrt`
18×	`cbrt-div` `difference-of-squares`
11×	`pow1`
9×	`swap-sqr`
8×	`add-exp-log` `associate-/r*` `distribute-lft-out--`
7×	`pow1/3` `associate-r` `associate-l` `associate-/l*`
6×	`flip3-+` `flip-+` `distribute-lft-out`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

23.0ms	(/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0)))
38.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0))) N))))
6.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0)))
98.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
9.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0))) N))))
187.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

simplify78.0ms

Counts

173 → 173

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	655	2009
1	2435	1922
2	5002	1848
done	5002	1848

prune519.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

regimes22.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4
done	12	4

end0.0ms

sample780.0ms

Algorithm

intervals

Results

395.0ms	2871×	body	1280	valid
130.0ms	3990×	body	80	valid
73.0ms	649×	body	640	valid
29.0ms	324×	body	320	valid
11.0ms	166×	body	160	valid