Details

sample54.0ms

Algorithm

intervals

Results

21.0ms	46×	body	2560	valid
11.0ms	34×	body	1280	valid
7.0ms	41×	body	640	valid
4.0ms	38×	body	320	valid
3.0ms	82×	body	80	valid
1.0ms	15×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	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: 28.3b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.2b	(- 1.0 (cos x))
13.8b	(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
48.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify62.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune110.0ms

Filtered

48 candidates to 34 candidates (70.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	36	12	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	12	49

Merged error: 0.2b

Counts

49 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
2.2b	(- 1.0 (cos x))
2.2b	(- 1.0 (cos x))
2.2b	(- 1.0 (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
28×	`cbrt-prod`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1`
10×	`swap-sqr` `add-log-exp`
9×	`flip3--` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log` `pow1/3`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 98

Calls

4 calls:

10.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series191.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
22.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify108.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	224	813
1	704	768
2	3166	698
3	5001	681

prune226.0ms

Filtered

110 candidates to 70 candidates (63.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	107	15	122

Merged error: 0.1b

Counts

122 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 (cos x)))
0.3b	(pow (- 1.0 (cos x)) 2/3)
2.2b	(- 1.0 (cos x))
2.2b	(- 1.0 (cos x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `add-exp-log` `cbrt-prod` `unpow-prod-down`
4×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`pow-unpow` `flip3--` `flip--`
2×	`sub-neg` `cbrt-div` `diff-log`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 62

Calls

4 calls:

3.0ms	(cbrt (- 1.0 (cos x)))
4.0ms	(pow (- 1.0 (cos x)) 2/3)
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series287.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (- 1.0 (cos x)))
120.0ms	(pow (- 1.0 (cos x)) 2/3)
18.0ms	(- 1.0 (cos x))
23.0ms	(- 1.0 (cos x))

simplify99.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	238	403
1	742	367
2	2847	352
3	5001	352

prune182.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	74	15	89

Merged error: 0.1b

Counts

89 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (log (exp (- 1.0 (cos x)))) 2/3)
2.2b	(- 1.0 (cos x))
2.2b	(- 1.0 (cos x))
2.4b	(log (exp (- 1.0 (cos x))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`log-pow`
10×	`exp-prod`
9×	`add-cube-cbrt` `unpow-prod-down`
8×	`add-log-exp`
7×	`pow1`
5×	`add-exp-log` `log-prod`
4×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `pow-unpow`
2×	`flip3--` `diff-log` `exp-sum` `flip--`
1×	`pow-to-exp` `log-div` `pow-pow` `exp-diff` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

4 → 71

Calls

4 calls:

6.0ms	(pow (log (exp (- 1.0 (cos x)))) 2/3)
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(pow (log (exp (- 1.0 (cos x)))) 2/3)
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))

simplify87.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	238	413
1	716	353
2	2524	347
3	5001	346

prune177.0ms

Filtered

83 candidates to 56 candidates (67.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	82	16	98

Merged error: 0.1b

Counts

98 → 16

regimes75.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.8b

bsearch68.0ms

Steps

Iters	Range		Point
10	2.7173623733142798e-14	0.17152303280385153	0.029118134313232017
6	-0.06221852409423964	-0.011085094476318487	-0.03270467354047881

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	33
1	49	33

end0.0ms

sample1.7s

Algorithm

intervals

Results

785.0ms	1622×	body	2560	valid
293.0ms	1220×	body	1280	valid
236.0ms	1535×	body	640	valid
115.0ms	946×	body	320	valid
79.0ms	2197×	body	80	valid
37.0ms	480×	body	160	valid

Details

sample54.0ms

simplify7.0ms

prune2.0ms

localize7.0ms

rewrite11.0ms

series66.0ms

simplify62.0ms

prune110.0ms

localize10.0ms

rewrite24.0ms

series191.0ms

simplify108.0ms

prune226.0ms

localize12.0ms

rewrite16.0ms

series287.0ms

simplify99.0ms

prune182.0ms

localize19.0ms

rewrite20.0ms

series178.0ms

simplify87.0ms

prune177.0ms

regimes75.0ms

bsearch68.0ms

simplify6.0ms

end0.0ms

sample1.7s

Profiling