Details

sample113.0ms

Algorithm

intervals

Results

44.0ms	110×	body	1280	valid
23.0ms	95×	body	640	valid
15.0ms	277×	body	80	valid
6.0ms	37×	body	320	valid
3.0ms	30×	body	160	valid

simplify367.0ms

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: 17.8b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.9b	(- (exp l) (exp (- l)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-cube-cbrt` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-r/` `associate-l/` `flip--`
1×	`sub-neg` `diff-log` `associate-l` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 34

Calls

2 calls:

26.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.0ms	(- (exp l) (exp (- l)))

series126.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
36.0ms	(- (exp l) (exp (- l)))

simplify136.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	226	370
1	853	307
2	4646	306
3	5002	306

prune125.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

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)
0.0b	(* 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)))

rewrite92.0ms

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:

37.0ms	(+ (* (* 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))
7.0ms	(* 1/3 (pow l 3))
41.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series587.0ms

Counts

4 → 12

Calls

4 calls:

336.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
47.0ms	(* 1/60 (pow l 5))
42.0ms	(* 1/3 (pow l 3))
162.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	465	784
1	2234	701
2	5003	701

prune335.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 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))

rewrite82.0ms

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))
31.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
36.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
7.0ms	(* 1/3 (pow l 3))

series342.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* 1/60 (pow l 5))
164.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
90.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
41.0ms	(* 1/3 (pow l 3))

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

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

prune366.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt J) (cbrt J))
0.6b	(cbrt J)
0.6b	(cbrt J)
0.6b	(cbrt J)

rewrite9.0ms

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 J) (cbrt J))
0.0ms	(cbrt J)
0.0ms	(cbrt J)
1.0ms	(cbrt J)

series741.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (cbrt J) (cbrt J))
179.0ms	(cbrt J)
176.0ms	(cbrt J)
181.0ms	(cbrt J)

simplify88.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune369.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0b

regimes602.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	30	12

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	2635×	body	1280	valid
676.0ms	2571×	body	640	valid
475.0ms	8452×	body	80	valid
247.0ms	1436×	body	320	valid
93.0ms	796×	body	160	valid