Details

sample2.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 12.402344%

Guaranteed chance to sample good point: 56.96767%

Results

28.0ms	43×	body	1280	valid
16.0ms	48×	body	640	valid
12.0ms	31×	body	1280	invalid
9.0ms	125×	body	80	valid
8.0ms	29×	body	640	invalid
6.0ms	91×	body	80	invalid
6.0ms	24×	body	320	valid
3.0ms	13×	body	320	invalid
2.0ms	16×	body	160	valid
1.0ms	5×	body	160	invalid

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: 22.2b

Counts

2 → 1

localize13.0ms

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))))
7.5b	(- (exp l) (exp (neg l)))

rewrite22.0ms

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)))

series40.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
11.0ms	(* J (- (exp l) (exp (neg l))))
5.0ms	(- (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

prune96.0ms

Filtered

47 candidates to 69 candidates (-46.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.3b

Counts

70 → 1

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)))
0.2b	(* 1/3 (pow l 3))

rewrite35.0ms

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))
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))

series118.0ms

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))
41.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
4.0ms	(* 1/3 (pow l 3))

simplify70.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (14.0ms)

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

prune224.0ms

Filtered

65 candidates to 99 candidates (-52.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Merged error: 0.3b

Counts

100 → 7

localize17.0ms

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)))
0.2b	(* 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))

series59.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/60 (pow l 5))
38.0ms	(* 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))

simplify65.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

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

prune239.0ms

Filtered

69 candidates to 108 candidates (-56.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	106	9	115

Merged error: 0.3b

Counts

115 → 9

localize22.0ms

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)))

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)))

series75.0ms

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)))
16.0ms	(cbrt (cos (/ K 2.0)))
17.0ms	(cbrt (cos (/ K 2.0)))

simplify76.0ms

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

prune250.0ms

Filtered

60 candidates to 85 candidates (-41.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	84	10	94

Merged error: 0.2b

Counts

94 → 10

regimes624.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	30	12

end0.0ms

sample6.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 12.402344%

Guaranteed chance to sample good point: 56.96767%

Results

654.0ms	1135×	body	1280	valid
544.0ms	1359×	body	1280	invalid
451.0ms	1338×	body	640	valid
318.0ms	1133×	body	640	invalid
297.0ms	4175×	body	80	valid
212.0ms	2800×	body	80	invalid
199.0ms	877×	body	320	valid
113.0ms	551×	body	320	invalid
73.0ms	475×	body	160	valid
35.0ms	256×	body	160	invalid

Details

sample2.5s

simplify185.0ms

prune4.0ms

localize13.0ms

rewrite22.0ms

series40.0ms

simplify36.0ms

prune96.0ms

localize17.0ms

rewrite35.0ms

series118.0ms

simplify70.0ms

prune224.0ms

localize17.0ms

rewrite33.0ms

series59.0ms

simplify65.0ms

prune239.0ms

localize22.0ms

rewrite10.0ms

series75.0ms

simplify76.0ms

prune250.0ms

regimes624.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.0s

Profiling