Details

sample27.0ms

Algorithm

intervals

Results

13.0ms	93×	body	1280	valid
4.0ms	130×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.2b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

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

series12.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify79.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (14.0ms)

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

prune40.0ms

Filtered

28 candidates to 19 candidates (67.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	2	29

Merged error: 0.4b

Counts

29 → 2

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)))

rewrite10.0ms

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:

3.0ms	(+ 1 (* (+ N 1.0) N))
6.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series70.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ 1 (* (+ N 1.0) N))
48.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify112.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	177	223
1	766	193
2	4572	193
3	5001	193

prune74.0ms

Filtered

48 candidates to 32 candidates (66.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	44	6	50

Merged error: 0.3b

Counts

50 → 6

localize9.0ms

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))))

rewrite24.0ms

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:

3.0ms	(cbrt (+ N 1.0))
3.0ms	(cbrt (+ N 1.0))
14.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
1.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (+ N 1.0))
92.0ms	(cbrt (+ N 1.0))
107.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
3.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify158.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (148.0ms)

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

prune218.0ms

Filtered

100 candidates to 69 candidates (69.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	100	6	106

Merged error: 0.3b

Counts

106 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
18×	`flip3-+` `flip-+`
12×	`frac-times`
6×	`associate-r/` `associate-l/`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow1/3`

Counts

4 → 58

Calls

4 calls:

8.0ms	(cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))
8.0ms	(cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))
8.0ms	(cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))
1.0ms	(atan2 1.0 (+ 1 (* (* (* (cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))) (cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))) (cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))) (* (cbrt (+ N 1.0)) N))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))
106.0ms	(cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))
107.0ms	(cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))
4.0ms	(atan2 1.0 (+ 1 (* (* (* (cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))) (cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))) (cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))) (* (cbrt (+ N 1.0)) N))))

simplify56.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	206	1032
1	488	934
2	1436	925
3	5001	925

prune226.0ms

Filtered

70 candidates to 56 candidates (80.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	70	6	76

Merged error: 0.3b

Counts

76 → 6

regimes26.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample735.0ms

Algorithm

intervals

Results

391.0ms	2809×	body	1280	valid
132.0ms	4089×	body	80	valid
69.0ms	610×	body	640	valid
29.0ms	330×	body	320	valid
10.0ms	162×	body	160	valid