Details

sample103.0ms

Algorithm

intervals

Results

30.0ms	64×	body	1280	valid
25.0ms	83×	body	640	valid
16.0ms	249×	body	80	valid
10.0ms	48×	body	320	valid
3.0ms	20×	body	160	valid

simplify370.0ms

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: 18.3b

Counts

2 → 1

localize17.0ms

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)))
5.7b	(- (exp l) (exp (- 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 (- l))))
9.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (- l)))

series196.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* J (- (exp l) (exp (- l))))
97.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
37.0ms	(- (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

prune183.0ms

Filtered

69 candidates to 47 candidates (68.1%)

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

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
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))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`associate-r`
21×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
10×	`associate-l` `prod-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`cbrt-unprod`
4×	`cube-prod` `associate-r/` `pow-prod-down` `-commutative` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `associate-*l/` `pow-exp` `flip-+`
1×	`distribute-rgt-in` `cube-mult` `distribute-lft-in` `unpow3`

Counts

4 → 98

Calls

4 calls:

10.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
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)))
7.0ms	(* 1/3 (pow l 3))

series413.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
50.0ms	(* 1/60 (pow l 5))
179.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
39.0ms	(* 1/3 (pow l 3))

simplify71.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	464	817
1	2375	697
2	5001	697

prune327.0ms

Filtered

110 candidates to 70 candidates (63.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	106	6	112

Merged error: 0.0b

Counts

112 → 6

localize17.0ms

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))
11.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
7.0ms	(* 1/3 (pow l 3))
10.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* 1/60 (pow l 5))
177.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
39.0ms	(* 1/3 (pow l 3))
95.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

simplify73.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

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

prune319.0ms

Filtered

108 candidates to 69 candidates (63.9%)

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: 0.0b

Counts

114 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/3 (pow l 3))
0.1b	(* 1/3 (pow l 3))
7.1b	(* 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)))))
15.5b	(/ (* (* 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))))

rewrite49.0ms

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:

7.0ms	(* 1/3 (pow l 3))
6.0ms	(* 1/3 (pow l 3))
12.0ms	(* 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))))

series1.0s

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 1/3 (pow l 3))
38.0ms	(* 1/3 (pow l 3))
427.0ms	(* 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)))))
514.0ms	(/ (* (* 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))))

simplify101.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (83.0ms)

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

prune431.0ms

Filtered

126 candidates to 84 candidates (66.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	125	8	133

Merged error: 0.0b

Counts

133 → 8

regimes281.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b 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

sample3.5s

Algorithm

intervals

Results

1.2s	2603×	body	1280	valid
797.0ms	2643×	body	640	valid
564.0ms	8505×	body	80	valid
294.0ms	1433×	body	320	valid
99.0ms	739×	body	160	valid