Details

sample111.0ms

Algorithm

intervals

Results

44.0ms	100×	body	1280	valid
23.0ms	76×	body	640	valid
13.0ms	224×	body	80	valid
8.0ms	48×	body	320	valid
3.0ms	23×	body	160	valid

simplify381.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	9
1	41	9
2	83	9
3	173	9
4	271	9
5	533	9
6	1023	9
7	1395	9
8	4369	9
9	5002	9

prune3.0ms

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: 18.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.0b	(- (exp l) (exp (- l)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`associate-l`
22×	`*-un-lft-identity`
13×	`associate-r`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`unswap-sqr`
4×	`associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `flip3--` `*-commutative` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 89

Calls

4 calls:

20.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
8.0ms	(* J (- (exp l) (exp (- l))))
14.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (- l)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
60.0ms	(* J (- (exp l) (exp (- l))))
95.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
41.0ms	(- (exp l) (exp (- l)))

simplify48.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	384	928
1	1462	833
2	5002	826

prune309.0ms

Filtered

101 candidates to 71 candidates (70.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	3	102

Merged error: 0.1b

Counts

102 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.1b	(* 1/60 (pow l 5))
0.1b	(* 1/3 (pow l 3))
0.1b	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
60×	`associate-l`
48×	`associate-r`
38×	`add-sqr-sqrt`
36×	`distribute-lft-out`
21×	`add-exp-log`
17×	`add-cube-cbrt`
15×	`pow1` `add-cbrt-cube`
12×	`unswap-sqr`
10×	`prod-exp`
8×	`unpow-prod-down`
6×	`pow-prod-down` `cbrt-unprod`
5×	`*-commutative`
4×	`+-commutative` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `cube-prod` `associate-*r/` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `associate-*l/` `pow-exp` `flip-+`
1×	`cube-mult` `unpow3`

Counts

4 → 139

Calls

4 calls:

37.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
7.0ms	(* 1/60 (pow l 5))
11.0ms	(* 1/3 (pow l 3))
43.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
47.0ms	(* 1/60 (pow l 5))
41.0ms	(* 1/3 (pow l 3))
165.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	506	1137
1	2566	1021
2	5002	1021

prune446.0ms

Filtered

151 candidates to 84 candidates (55.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	145	6	151
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	145	9	154

Merged error: 0b

Counts

154 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/60 (pow l 5))
0.1b	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
0.1b	(* 1/3 (pow l 3))
0.2b	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
61×	`associate-l`
47×	`associate-r`
38×	`add-sqr-sqrt`
36×	`distribute-lft-out`
21×	`add-exp-log`
17×	`add-cube-cbrt`
15×	`pow1` `add-cbrt-cube`
12×	`unswap-sqr`
10×	`prod-exp`
8×	`unpow-prod-down`
6×	`pow-prod-down` `cbrt-unprod`
5×	`*-commutative`
4×	`cube-prod` `associate-*l/` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `flip-+`
1×	`cube-mult` `unpow3`

Counts

4 → 131

Calls

4 calls:

6.0ms	(* 1/60 (pow l 5))
44.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
10.0ms	(* 1/3 (pow l 3))
38.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* 1/60 (pow l 5))
165.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
41.0ms	(* 1/3 (pow l 3))
89.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	479	1129
1	2369	1004
2	5001	1004

prune424.0ms

Filtered

143 candidates to 78 candidates (54.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	143	9	152

Merged error: 0b

Counts

152 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt J) (cbrt J))
0.5b	(cbrt J)
0.5b	(cbrt J)
0.5b	(cbrt J)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

6.0ms	(* (cbrt J) (cbrt J))
1.0ms	(cbrt J)
1.0ms	(cbrt J)
1.0ms	(cbrt J)

series746.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (cbrt J) (cbrt J))
179.0ms	(cbrt J)
185.0ms	(cbrt J)
177.0ms	(cbrt J)

simplify93.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	124	311
1	521	267
2	3258	241
3	5001	238

prune367.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	89	8	97

Merged error: 0b

Counts

97 → 8

regimes283.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	30	12

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	2706×	body	1280	valid
663.0ms	2533×	body	640	valid
463.0ms	8216×	body	80	valid
252.0ms	1439×	body	320	valid
87.0ms	743×	body	160	valid