Details

sample68.0ms

Algorithm

intervals

Results

34.0ms	77×	body	1280	valid
10.0ms	137×	body	80	valid
8.0ms	28×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

11.0ms

(- (atan (+ N 1.0)) (atan N))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(- (atan (+ N 1.0)) (atan N))

simplify1.8s

Counts

18 → 18

Iterations

Useful iterations: 4 (187.0ms)

Iter	Nodes	Cost
0	36	209
1	73	205
2	143	191
3	267	187
4	533	185
5	1495	185
done	5000	185

prune32.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite47.0ms

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:

45.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series64.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(* (+ N 1.0) N)
6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify4.0s

Counts

34 → 34

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	55	317
1	120	312
2	356	264
3	1001	264
4	4336	264
done	5002	264

prune76.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
13.9b	(cbrt (* (+ N 1.0) N))
13.9b	(cbrt (* (+ N 1.0) N))
13.9b	(cbrt (* (+ N 1.0) N))

rewrite48.0ms

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:

24.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))

series530.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
119.0ms	(cbrt (* (+ N 1.0) N))
114.0ms	(cbrt (* (+ N 1.0) N))
134.0ms	(cbrt (* (+ N 1.0) N))

simplify1.7s

Counts

84 → 84

Iterations

Useful iterations: done (1.7s)

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

prune328.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

13.9b	(cbrt (* (+ N 1.0) N))
13.9b	(cbrt (* (+ N 1.0) N))
13.9b	(cbrt (* (+ N 1.0) N))
13.9b	(cbrt (* (+ N 1.0) N))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cbrt-div` `associate-*l/`
4×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))

series493.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (* (+ N 1.0) N))
132.0ms	(cbrt (* (+ N 1.0) N))
127.0ms	(cbrt (* (+ N 1.0) N))
121.0ms	(cbrt (* (+ N 1.0) N))

simplify2.6s

Counts

56 → 56

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	82	988
1	192	972
2	460	924
3	1259	784
4	4444	696
done	5000	696

prune336.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes24.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.7s

Algorithm

intervals

Results

734.0ms	2902×	body	1280	valid
340.0ms	313×	body	320	valid
288.0ms	4008×	body	80	valid
164.0ms	632×	body	640	valid
14.0ms	145×	body	160	valid