Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	88×	body	1280	valid
7.0ms	130×	body	80	valid
4.0ms	28×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify4.0ms

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

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: 15.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

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

series7.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
5.0ms	(- (atan (+ N 1.0)) (atan N))

simplify79.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (15.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2447	142
5	5001	142

prune36.0ms

Filtered

19 candidates to 28 candidates (-47.4%)

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: 0.3b

Counts

29 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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:

5.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series7.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify53.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	121	151
1	432	127
2	2321	127
3	5002	127

prune55.0ms

Filtered

22 candidates to 34 candidates (-54.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	30	6	36

Merged error: 0.2b

Counts

36 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
15.2b	(cbrt (* (+ N 1.0) N))
15.2b	(cbrt (* (+ N 1.0) N))
15.2b	(cbrt (* (+ N 1.0) N))

rewrite21.0ms

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:

6.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
4.0ms	(cbrt (* (+ N 1.0) N))
4.0ms	(cbrt (* (+ N 1.0) N))
4.0ms	(cbrt (* (+ N 1.0) N))

series43.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
9.0ms	(cbrt (* (+ N 1.0) N))
9.0ms	(cbrt (* (+ N 1.0) N))
10.0ms	(cbrt (* (+ N 1.0) N))

simplify43.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	362	890
1	1236	832
2	5001	754

prune223.0ms

Filtered

67 candidates to 84 candidates (-25.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	83	7	90

Merged error: 0.2b

Counts

90 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series90.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (cbrt N) (cbrt N))
21.0ms	(cbrt N)
23.0ms	(cbrt N)
22.0ms	(cbrt N)

simplify73.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	148	349
1	471	322
2	2276	265
3	5002	252

prune82.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	84	8	92

Merged error: 0.2b

Counts

92 → 8

regimes45.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample914.0ms

Algorithm

intervals

Results

475.0ms	2882×	body	1280	valid
152.0ms	4020×	body	80	valid
83.0ms	615×	body	640	valid
33.0ms	314×	body	320	valid
13.0ms	169×	body	160	valid

Details

sample34.0ms

simplify4.0ms

prune2.0ms

localize6.0ms

rewrite5.0ms

series7.0ms

simplify79.0ms

prune36.0ms

localize5.0ms

rewrite7.0ms

series7.0ms

simplify53.0ms

prune55.0ms

localize10.0ms

rewrite21.0ms

series43.0ms

simplify43.0ms

prune223.0ms

localize9.0ms

rewrite10.0ms

series90.0ms

simplify73.0ms

prune82.0ms

regimes45.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample914.0ms

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