Details

sample132.0ms

Algorithm

intervals

Results

44.0ms	92×	body	1280	valid
28.0ms	97×	body	640	valid
24.0ms	282×	body	80	valid
11.0ms	50×	body	320	valid
3.0ms	19×	body	160	valid

simplify369.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize12.0ms

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)))
5.0b	(- (exp l) (exp (- l)))

rewrite248.0ms

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:

19.0ms	(* J (- (exp l) (exp (- l))))
222.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.0ms	(- (exp l) (exp (- l)))

series180.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* J (- (exp l) (exp (- l))))
89.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
35.0ms	(- (exp l) (exp (- l)))

simplify39.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (33.0ms)

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

prune197.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* 2 (* J l)) (cos (/ K 2.0))) U)
0.0b	(* 2 (* J l))
0.1b	(* (* 2 (* J l)) (cos (/ K 2.0)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`associate-r` `associate-l`
2×	`*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 50

Calls

3 calls:

18.0ms	(+ (* (* 2 (* J l)) (cos (/ K 2.0))) U)
6.0ms	(* 2 (* J l))
17.0ms	(* (* 2 (* J l)) (cos (/ K 2.0)))

series167.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(+ (* (* 2 (* J l)) (cos (/ K 2.0))) U)
18.0ms	(* 2 (* J l))
58.0ms	(* (* 2 (* J l)) (cos (/ K 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	244	365
1	1034	314
2	5002	314

prune120.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 2 (* J (* (cos (* 0.5 K)) l))) U)
0.0b	(* 2 (* J (* (cos (* 0.5 K)) l)))
0.1b	(* J (* (cos (* 0.5 K)) l))
0.1b	(* (cos (* 0.5 K)) l)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-l`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`associate-r`
3×	`*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

20.0ms	(+ (* 2 (* J (* (cos (* 0.5 K)) l))) U)
20.0ms	(* 2 (* J (* (cos (* 0.5 K)) l)))
9.0ms	(* J (* (cos (* 0.5 K)) l))
5.0ms	(* (cos (* 0.5 K)) l)

series254.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(+ (* 2 (* J (* (cos (* 0.5 K)) l))) U)
61.0ms	(* 2 (* J (* (cos (* 0.5 K)) l)))
54.0ms	(* J (* (cos (* 0.5 K)) l))
45.0ms	(* (cos (* 0.5 K)) l)

simplify42.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	265	514
1	1044	433
2	5002	433

prune166.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* J (* (cos (* 0.5 K)) l))
0.1b	(* (cos (* 0.5 K)) l)
0.3b	(* (sqrt 2) (* (sqrt 2) (* J (* (cos (* 0.5 K)) l))))
0.3b	(* (sqrt 2) (* J (* (cos (* 0.5 K)) l)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1` `add-exp-log` `add-cbrt-cube`
20×	`pow-prod-down` `prod-exp` `cbrt-unprod`
18×	`associate-l`
13×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `sqrt-prod`
4×	`*-commutative` `add-log-exp`
1×	`unswap-sqr`

Counts

4 → 87

Calls

4 calls:

9.0ms	(* J (* (cos (* 0.5 K)) l))
5.0ms	(* (cos (* 0.5 K)) l)
58.0ms	(* (sqrt 2) (* (sqrt 2) (* J (* (cos (* 0.5 K)) l))))
22.0ms	(* (sqrt 2) (* J (* (cos (* 0.5 K)) l)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* J (* (cos (* 0.5 K)) l))
44.0ms	(* (cos (* 0.5 K)) l)
142.0ms	(* (sqrt 2) (* (sqrt 2) (* J (* (cos (* 0.5 K)) l))))
97.0ms	(* (sqrt 2) (* J (* (cos (* 0.5 K)) l)))

simplify48.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	286	706
1	1382	545
2	5002	545

prune208.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes165.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	6
1	16	6

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	2667×	body	1280	valid
791.0ms	2612×	body	640	valid
765.0ms	8591×	body	80	valid
306.0ms	1403×	body	320	valid
115.0ms	748×	body	160	valid