Details

sample130.0ms

Algorithm

intervals

Results

39.0ms	90×	body	1280	valid
28.0ms	81×	body	640	valid
18.0ms	274×	body	80	valid
10.0ms	53×	body	320	valid
3.0ms	21×	body	160	valid

simplify187.0ms

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

Filtered

1 candidates to 0 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: 17.2b

Counts

2 → 1

localize13.0ms

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)))
5.4b	(- (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))))
10.0ms	(* (* 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

prune93.0ms

Filtered

69 candidates to 47 candidates (31.9%)

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

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)
0.1b	(* 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))

rewrite37.0ms

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)
5.0ms	(* 1/60 (pow l 5))
12.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))

series113.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
4.0ms	(* 1/60 (pow l 5))
36.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
4.0ms	(* 1/3 (pow l 3))

simplify67.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (13.0ms)

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

prune223.0ms

Filtered

99 candidates to 65 candidates (34.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Merged error: 0.0b

Counts

101 → 8

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))

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))

series61.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/60 (pow l 5))
39.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
13.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
4.0ms	(* 1/3 (pow l 3))

simplify68.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (14.0ms)

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

prune234.0ms

Filtered

108 candidates to 69 candidates (36.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	108	8	116

Merged error: 0.0b

Counts

116 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (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)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
17.0ms	(cbrt (cos (/ K 2.0)))
17.0ms	(cbrt (cos (/ K 2.0)))
19.0ms	(cbrt (cos (/ K 2.0)))

simplify76.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (69.0ms)

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

prune239.0ms

Filtered

85 candidates to 60 candidates (29.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	85	8	93

Merged error: 0.0b

Counts

93 → 8

regimes545.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	30	12

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.2s	2678×	body	1280	valid
885.0ms	2522×	body	640	valid
541.0ms	8489×	body	80	valid
288.0ms	1435×	body	320	valid
100.0ms	749×	body	160	valid

Details

sample130.0ms

simplify187.0ms

prune4.0ms

localize13.0ms

rewrite24.0ms

series37.0ms

simplify37.0ms

prune93.0ms

localize17.0ms

rewrite37.0ms

series113.0ms

simplify67.0ms

prune223.0ms

localize20.0ms

rewrite35.0ms

series61.0ms

simplify68.0ms

prune234.0ms

localize21.0ms

rewrite11.0ms

series78.0ms

simplify76.0ms

prune239.0ms

regimes545.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.8s

Profiling