Details

sample56.0ms

Algorithm

intervals

Results

25.0ms	84×	body	1280	valid
9.0ms	128×	body	80	valid
5.0ms	20×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	6×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize22.0ms

Local error

Found 2 expressions with local error:

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

series25.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
22.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.0s

Counts

28 → 28

Iterations

Useful iterations: 4 (257.0ms)

Iter	Nodes	Cost
0	40	271
1	76	259
2	145	245
3	270	241
4	534	239
5	1497	239
done	5000	239

prune68.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize8.0ms

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)))

rewrite42.0ms

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:

15.0ms	(+ 1 (* (+ N 1.0) N))
25.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series119.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ 1 (* (+ N 1.0) N))
78.0ms	(* (+ N 1.0) N)
12.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify2.0s

Counts

48 → 48

Iterations

Useful iterations: 2 (169.0ms)

Iter	Nodes	Cost
0	73	489
1	175	461
2	517	403
3	1850	403
done	5001	403

prune141.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize20.0ms

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))

rewrite61.0ms

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:

32.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
8.0ms	(cbrt (* (+ N 1.0) N))
8.0ms	(cbrt (* (+ N 1.0) N))
8.0ms	(cbrt (* (+ N 1.0) N))

series659.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
139.0ms	(cbrt (* (+ N 1.0) N))
139.0ms	(cbrt (* (+ N 1.0) N))
183.0ms	(cbrt (* (+ N 1.0) N))

simplify1.8s

Counts

84 → 84

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	152	1527
1	354	1427
2	973	1328
3	2854	1135
done	5001	1091

prune296.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize12.0ms

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))))

rewrite23.0ms

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)))
16.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
7.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
22.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
18.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify4.9s

Counts

94 → 94

Iterations

Useful iterations: 5 (2.8s)

Iter	Nodes	Cost
0	64	1843
1	104	1267
2	216	1115
3	409	1064
4	838	1028
5	4762	998
done	5000	998

prune160.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.3b

regimes27.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	12	9
done	12	9

end0.0ms

sample1.4s

Algorithm

intervals

Results

876.0ms	2840×	body	1280	valid
257.0ms	4052×	body	80	valid
94.0ms	651×	body	640	valid
32.0ms	295×	body	320	valid
13.0ms	162×	body	160	valid