Details

sample1.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 9.375%

Guaranteed chance to sample good point: 76.885776%

Results

19.0ms	33×	body	1280	valid
19.0ms	49×	body	1280	invalid
15.0ms	43×	body	640	valid
14.0ms	49×	body	640	invalid
9.0ms	131×	body	80	valid
7.0ms	103×	body	80	invalid
7.0ms	33×	body	320	valid
3.0ms	15×	body	320	invalid
2.0ms	17×	body	160	invalid
2.0ms	16×	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: 16.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0))) U)
0.0b	(* J (- (exp l) (exp (neg l))))
0.0b	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
5.7b	(- (exp l) (exp (neg l)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`associate-r` `add-log-exp`
7×	`add-cube-cbrt`
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×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

9.0ms	(+ (* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0))) U)
7.0ms	(* J (- (exp l) (exp (neg l))))
8.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (neg l)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0))) U)
13.0ms	(* J (- (exp l) (exp (neg l))))
20.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (neg l)))

simplify44.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	354	755
1	1430	660
2	5001	652

prune137.0ms

Filtered

58 candidates to 83 candidates (-43.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	3	84

Merged error: 0.1b

Counts

84 → 3

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	(* 1/3 (pow l 3))
0.2b	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

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

series116.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (* (* 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))
4.0ms	(* 1/3 (pow l 3))
39.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

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

prune208.0ms

Filtered

65 candidates to 99 candidates (-52.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	96	6	102

Merged error: 0.0b

Counts

102 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/60 (pow l 5))
0.1b	(* 1/3 (pow l 3))
0.1b	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
0.2b	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))

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

series60.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/60 (pow l 5))
4.0ms	(* 1/3 (pow l 3))
13.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
38.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))

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

prune215.0ms

Filtered

69 candidates to 108 candidates (-56.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

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

Merged error: 0b

Counts

114 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/3 (pow l 3))
0.1b	(* 1/3 (pow l 3))
7.8b	(* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
13.9b	(/ (* (* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l))))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
28×	`associate-r`
25×	`add-exp-log`
19×	`add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
10×	`prod-exp`
9×	`associate-l` `unswap-sqr`
8×	`unpow-prod-down` `cube-prod`
6×	`pow1` `cbrt-unprod`
4×	`associate-*r/` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `flip3--` `times-frac` `div-exp` `associate-/r` `-commutative` `flip--`
2×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `distribute-lft-in` `unpow3` `associate-*l/` `pow-exp` `associate-/r/` `associate-/l/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

6.0ms	(* 1/3 (pow l 3))
6.0ms	(* 1/3 (pow l 3))
11.0ms	(* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
21.0ms	(/ (* (* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l))))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

series160.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/3 (pow l 3))
4.0ms	(* 1/3 (pow l 3))
62.0ms	(* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
90.0ms	(/ (* (* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l))))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

simplify104.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	551	1783
1	3116	1455
2	5002	1454

prune463.0ms

Filtered

84 candidates to 126 candidates (-50.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	126	7	133

Merged error: 0b

Counts

133 → 7

regimes762.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b 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

sample4.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 9.375%

Guaranteed chance to sample good point: 76.885776%

Results

676.0ms	1165×	body	1280	valid
577.0ms	1448×	body	1280	invalid
451.0ms	1327×	body	640	valid
351.0ms	1268×	body	640	invalid
295.0ms	4221×	body	80	valid
196.0ms	2756×	body	80	invalid
189.0ms	836×	body	320	valid
118.0ms	605×	body	320	invalid
62.0ms	451×	body	160	valid
46.0ms	339×	body	160	invalid

Details

sample1.4s

simplify185.0ms

prune4.0ms

localize12.0ms

rewrite31.0ms

series82.0ms

simplify44.0ms

prune137.0ms

localize18.0ms

rewrite36.0ms

series116.0ms

simplify70.0ms

prune208.0ms

localize17.0ms

rewrite33.0ms

series60.0ms

simplify65.0ms

prune215.0ms

localize22.0ms

rewrite46.0ms

series160.0ms

simplify104.0ms

prune463.0ms

regimes762.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample4.9s

Profiling