Details

sample115.0ms

Algorithm

intervals

Results

48.0ms	96×	body	1280	valid
22.0ms	72×	body	640	valid
14.0ms	236×	body	80	valid
9.0ms	49×	body	320	valid
3.0ms	21×	body	160	valid

simplify366.0ms

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	271	9
5	533	9
6	1023	9
7	1395	9
8	4369	9
9	5002	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 20.8b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.6b	(- (exp l) (exp (- l)))

rewrite23.0ms

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

series181.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* J (- (exp l) (exp (- l))))
89.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
35.0ms	(- (exp l) (exp (- l)))

simplify36.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	264	566
1	1116	481
2	5002	475

prune172.0ms

Filtered

69 candidates to 47 candidates (68.1%)

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

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` `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))
6.0ms	(* 1/3 (pow l 3))
15.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
55.0ms	(* 1/60 (pow l 5))
36.0ms	(* 1/3 (pow l 3))
162.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify209.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (14.0ms)

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

prune271.0ms

Filtered

101 candidates to 64 candidates (63.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	96	5	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	6	102

Merged error: 0.0b

Counts

102 → 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))
0.2b	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

rewrite40.0ms

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))
16.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
6.0ms	(* 1/3 (pow l 3))
10.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/60 (pow l 5))
168.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
36.0ms	(* 1/3 (pow l 3))
89.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

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

prune286.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	108	6	114

Merged error: 0.0b

Counts

114 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/3 (pow l 3))
0.1b	(* 1/3 (pow l 3))
0.1b	(* 1/3 (pow l 3))
29.3b	(/ (* (- (* (* 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))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
36×	`associate-r`
24×	`add-exp-log`
18×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-cbrt-cube`
12×	`unpow-prod-down` `cube-prod` `unswap-sqr`
10×	`prod-exp`
9×	`associate-l`
6×	`sqr-pow`
4×	`pow1` `cbrt-unprod` `add-log-exp`
3×	`cube-mult` `pow-to-exp` `times-frac` `unpow3` `pow-exp` `associate-/r` `-commutative`
2×	`cbrt-undiv` `flip3--` `div-exp` `associate-*l/` `associate-/r/` `flip--` `associate-/l/`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 118

Calls

4 calls:

6.0ms	(* 1/3 (pow l 3))
6.0ms	(* 1/3 (pow l 3))
6.0ms	(* 1/3 (pow l 3))
18.0ms	(/ (* (- (* (* 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))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* 1/3 (pow l 3))
41.0ms	(* 1/3 (pow l 3))
34.0ms	(* 1/3 (pow l 3))
175.0ms	(/ (* (- (* (* 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))))

simplify69.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	367	1217
1	2016	1033
2	5001	991

prune386.0ms

Filtered

130 candidates to 83 candidates (63.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	130	6	136

Merged error: 0.0b

Counts

136 → 6

regimes221.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b 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

sample3.4s

Algorithm

intervals

Results

1.3s	2703×	body	1280	valid
744.0ms	2502×	body	640	valid
555.0ms	8476×	body	80	valid
286.0ms	1433×	body	320	valid
91.0ms	706×	body	160	valid