Details

sample1.4s

Algorithm

intervals

sampling

Space saved by range analysis: 9.551872%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 0%

Results

24.0ms	60×	body	1280	invalid
21.0ms	35×	body	1280	valid
18.0ms	53×	body	640	valid
11.0ms	116×	body	80	valid
11.0ms	42×	body	640	invalid
9.0ms	37×	body	320	valid
5.0ms	78×	body	80	invalid
3.0ms	17×	body	320	invalid
2.0ms	15×	body	160	valid
1.0ms	8×	body	160	invalid

simplify181.0ms

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

prune5.0ms

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: 18.6b

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)))
5.6b	(- (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:

8.0ms	(* 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)))

series42.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(* J (- (exp l) (exp (neg l))))
25.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
6.0ms	(- (exp l) (exp (neg l)))

simplify35.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (29.0ms)

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

prune100.0ms

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: 0.1b

Counts

70 → 1

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)))) (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))
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))

series119.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (* (* 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))
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))

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

prune224.0ms

Filtered

65 candidates to 99 candidates (-52.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	6	100

Merged error: 0.0b

Counts

100 → 6

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)) (+ (* 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)))
7.0ms	(* 1/3 (pow l 3))

series63.0ms

Counts

4 → 12

Calls

4 calls:

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))))
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))

simplify65.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (12.0ms)

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

prune247.0ms

Filtered

69 candidates to 108 candidates (-56.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	107	7	114

Merged error: 0.0b

Counts

114 → 7

localize24.0ms

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:

6.0ms	(* (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)))

series84.0ms

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)))
18.0ms	(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

prune253.0ms

Filtered

60 candidates to 85 candidates (-41.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	8	92

Merged error: 0.0b

Counts

92 → 8

regimes577.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b 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

sample4.9s

Algorithm

intervals

sampling

Space saved by range analysis: 9.551872%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 0%

Results

773.0ms	1290×	body	1280	valid
610.0ms	1528×	body	1280	invalid
479.0ms	1378×	body	640	valid
376.0ms	1300×	body	640	invalid
286.0ms	4105×	body	80	valid
197.0ms	2840×	body	80	invalid
192.0ms	809×	body	320	valid
126.0ms	618×	body	320	invalid
62.0ms	418×	body	160	valid
49.0ms	331×	body	160	invalid

Details

sample1.4s

simplify181.0ms

prune5.0ms

localize13.0ms

rewrite24.0ms

series42.0ms

simplify35.0ms

prune100.0ms

localize18.0ms

rewrite37.0ms

series119.0ms

simplify65.0ms

prune224.0ms

localize18.0ms

rewrite35.0ms

series63.0ms

simplify65.0ms

prune247.0ms

localize24.0ms

rewrite11.0ms

series84.0ms

simplify74.0ms

prune253.0ms

regimes577.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.9s

Profiling