Details

sample67.0ms

Algorithm

intervals

Results

41.0ms	230×	body	10240	exit
6.0ms	185×	body	80	valid
3.0ms	35×	body	320	valid
3.0ms	19×	body	640	valid
1.0ms	18×	body	160	valid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	20	9
1	48	9
2	107	9
3	224	8
4	1514	8
5	5001	8

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 16.9b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ x (+ wj 1))
0.2b	(/ (/ x (+ wj 1)) (exp wj))
6.2b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
118×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
24×	`associate-/l*`
21×	`distribute-lft-out`
13×	`add-cbrt-cube`
12×	`associate-/r/`
11×	`add-exp-log` `associate-/r*`
9×	`add-log-exp`
7×	`flip3-+` `flip-+` `div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`diff-log` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

5.0ms	(/ wj (+ wj 1))
5.0ms	(/ x (+ wj 1))
9.0ms	(/ (/ x (+ wj 1)) (exp wj))
29.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ wj (+ wj 1))
25.0ms	(/ x (+ wj 1))
60.0ms	(/ (/ x (+ wj 1)) (exp wj))
77.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify78.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	721	1524
1	3303	1471
2	5001	1469

prune347.0ms

Filtered

188 candidates to 138 candidates (73.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	184	4	188
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	186	4	190

Merged error: 0.1b

Counts

190 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (pow wj 2))
0.0b	(* 2 (* wj x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `distribute-lft-out`

Counts

2 → 30

Calls

2 calls:

4.0ms	(+ x (pow wj 2))
5.0ms	(* 2 (* wj x))

series50.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ x (pow wj 2))
22.0ms	(* 2 (* wj x))

simplify63.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	149	128
1	550	109
2	2327	108
3	5001	108

prune54.0ms

Filtered

36 candidates to 21 candidates (58.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	34	2	36
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	34	6	40

Merged error: 0.1b

Counts

40 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x (pow wj 2)))
0.5b	(cbrt (+ x (pow wj 2)))
0.5b	(cbrt (+ x (pow wj 2)))
0.5b	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `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 → 95

Calls

4 calls:

4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))
12.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

308.0ms	(cbrt (+ x (pow wj 2)))
307.0ms	(cbrt (+ x (pow wj 2)))
317.0ms	(cbrt (+ x (pow wj 2)))
262.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))

simplify161.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (152.0ms)

Iter	Nodes	Cost
0	252	878
1	951	827
2	4722	760
3	5002	749

prune240.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	106	7	113

Merged error: 0.1b

Counts

113 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
0.5b	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
0.5b	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
0.5b	(* (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))) (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

420×	`cbrt-div`
148×	`frac-times`
126×	`flip3-+` `flip-+`
50×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
11×	`pow1` `cbrt-prod`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `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 → 165

Calls

4 calls:

11.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
11.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
14.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
11.0ms	(* (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))) (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
262.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
266.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
287.0ms	(* (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))) (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))))

simplify160.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	370	4751
1	1003	4616
2	4113	4534
3	5002	4524

prune424.0ms

Filtered

177 candidates to 93 candidates (52.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	176	8	184

Merged error: 0.1b

Counts

184 → 8

regimes76.0ms

Accuracy

68.8% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 2.0b

bsearch36.0ms

Steps

Iters	Range		Point
9	1.2261953182377537e-15	1.3201210546183864e-08	4.794595763324104e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	27	14

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.4s	7538×	body	10240	exit
189.0ms	6294×	body	80	valid
75.0ms	738×	body	320	valid
68.0ms	467×	body	640	valid
38.0ms	566×	body	160	valid