Details

sample126.0ms

Algorithm

intervals

Results

46.0ms	88×	body	1280	valid
18.0ms	279×	body	80	valid
17.0ms	60×	body	640	valid
10.0ms	47×	body	320	valid
4.0ms	29×	body	160	valid

simplify184.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	9
1	41	9
2	83	9
3	173	9
4	284	9
5	556	9
6	919	9
7	1220	9
8	3918	9
9	5002	9

prune6.0ms

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: 18.5b

Counts

2 → 1

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
0.2b	(* J (- (exp l) (exp (neg l))))
4.4b	(- (exp l) (exp (neg l)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

9.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
7.0ms	(* J (- (exp l) (exp (neg l))))
5.0ms	(- (exp l) (exp (neg l)))

series182.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
58.0ms	(* J (- (exp l) (exp (neg l))))
32.0ms	(- (exp l) (exp (neg l)))

simplify36.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	265	566
1	1128	479
2	5001	473

prune299.0ms

Filtered

69 candidates to 47 candidates (68.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 0.3b

Counts

70 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `prod-exp`
8×	`unpow-prod-down`
7×	`associate-l` `unswap-sqr`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`pow-prod-down` `*-commutative`
2×	`pow-to-exp` `flip3-+` `associate-r/` `associate-l/` `pow-exp` `flip-+`
1×	`+-commutative` `cube-mult` `unpow3` `sum-log`

Counts

4 → 87

Calls

4 calls:

11.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
8.0ms	(* 1/60 (pow l 5))
11.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))

series586.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
54.0ms	(* 1/60 (pow l 5))
166.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
38.0ms	(* 1/3 (pow l 3))

simplify65.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	465	784
1	2234	701
2	5003	701

prune480.0ms

Filtered

99 candidates to 65 candidates (65.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Merged error: 0.2b

Counts

102 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`associate-r`
21×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-l`
11×	`pow1`
10×	`prod-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`cbrt-unprod`
4×	`cube-prod` `pow-prod-down` `associate-l/` `-commutative` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `flip-+`
1×	`cube-mult` `unpow3`

Counts

4 → 96

Calls

4 calls:

5.0ms	(* 1/60 (pow l 5))
11.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
10.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))

series353.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 1/60 (pow l 5))
163.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
92.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
42.0ms	(* 1/3 (pow l 3))

simplify70.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	444	867
1	2076	737
2	5001	737

prune496.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	108	7	115

Merged error: 0.2b

Counts

115 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))

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`
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 (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))

series620.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
146.0ms	(cbrt (cos (/ K 2.0)))
139.0ms	(cbrt (cos (/ K 2.0)))
146.0ms	(cbrt (cos (/ K 2.0)))

simplify149.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (141.0ms)

Iter	Nodes	Cost
0	188	731
1	706	652
2	4250	602
3	5001	597

prune520.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	85	7	92

Merged error: 0.2b

Counts

92 → 7

regimes530.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	30	12

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	2604×	body	1280	valid
770.0ms	2611×	body	640	valid
534.0ms	8467×	body	80	valid
302.0ms	1496×	body	320	valid
102.0ms	767×	body	160	valid

Details

sample126.0ms

simplify184.0ms

prune6.0ms

localize17.0ms

rewrite23.0ms

series182.0ms

simplify36.0ms

prune299.0ms

localize17.0ms

rewrite39.0ms

series586.0ms

simplify65.0ms

prune480.0ms

localize18.0ms

rewrite35.0ms

series353.0ms

simplify70.0ms

prune496.0ms

localize21.0ms

rewrite11.0ms

series620.0ms

simplify149.0ms

prune520.0ms

regimes530.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.7s

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