Details

sample122.0ms

Algorithm

intervals

Results

38.0ms	79×	body	1280	valid
26.0ms	88×	body	640	valid
19.0ms	305×	body	80	valid
7.0ms	37×	body	320	valid
4.0ms	26×	body	160	valid

simplify185.0ms

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

prune4.0ms

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: 16.5b

Counts

2 → 1

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (neg l))))
0.0b	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
9.2b	(- (exp l) (exp (neg l)))

rewrite24.0ms

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:

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

series37.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(* J (- (exp l) (exp (neg l))))
21.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (neg l)))

simplify37.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (31.0ms)

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

prune103.0ms

Filtered

47 candidates to 69 candidates (-46.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	2	70

Merged error: 0.1b

Counts

70 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
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))

rewrite36.0ms

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` `add-log-exp`
8×	`unpow-prod-down`
7×	`associate-l` `unswap-sqr`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`pow-prod-down` `sum-log` `*-commutative`
2×	`pow-to-exp` `flip3-+` `associate-r/` `associate-l/` `pow-exp` `flip-+`
1×	`+-commutative` `cube-mult` `associate-+r+` `unpow3`

Counts

4 → 89

Calls

4 calls:

8.0ms	(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
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)))
9.0ms	(* 1/3 (pow l 3))

series54.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
4.0ms	(* 1/60 (pow l 5))
40.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
4.0ms	(* 1/3 (pow l 3))

simplify69.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	443	717
1	2193	619
2	5001	619

prune227.0ms

Filtered

64 candidates to 101 candidates (-57.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	97	6	103

Merged error: 0.0b

Counts

103 → 6

localize20.0ms

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

rewrite33.0ms

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))
10.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
9.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))

series61.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* 1/60 (pow l 5))
36.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
14.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
4.0ms	(* 1/3 (pow l 3))

simplify64.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	444	856
1	2079	731
2	5001	731

prune205.0ms

Filtered

69 candidates to 108 candidates (-56.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	108	6	114

Merged error: 0.0b

Counts

114 → 6

localize23.0ms

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)))

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 (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)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
18.0ms	(cbrt (cos (/ K 2.0)))
17.0ms	(cbrt (cos (/ K 2.0)))
18.0ms	(cbrt (cos (/ K 2.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	134	575
1	452	524
2	2183	487
3	5002	482

prune242.0ms

Filtered

60 candidates to 85 candidates (-41.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	3	3
Picked	0	1	1
Done	1	1	2
Total	84	7	91

Merged error: 0.0b

Counts

91 → 7

regimes603.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

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

1.3s	2716×	body	1280	valid
779.0ms	2558×	body	640	valid
551.0ms	8428×	body	80	valid
282.0ms	1364×	body	320	valid
107.0ms	805×	body	160	valid

Details

sample122.0ms

simplify185.0ms

prune4.0ms

localize17.0ms

rewrite24.0ms

series37.0ms

simplify37.0ms

prune103.0ms

localize21.0ms

rewrite36.0ms

series54.0ms

simplify69.0ms

prune227.0ms

localize20.0ms

rewrite33.0ms

series61.0ms

simplify64.0ms

prune205.0ms

localize23.0ms

rewrite10.0ms

series83.0ms

simplify74.0ms

prune242.0ms

regimes603.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.7s

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