Details

sample108.0ms

Algorithm

intervals

Results

32.0ms	64×	body	1280	valid
27.0ms	83×	body	640	valid
17.0ms	249×	body	80	valid
10.0ms	48×	body	320	valid
3.0ms	20×	body	160	valid

simplify372.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	44	8
2	91	8
3	195	8
4	332	8
5	652	8
6	1279	8
7	1694	8
8	4980	8
9	5001	8

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 18.3b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`prod-diff`
24×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
5×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `associate-l` `log1p-expm1-u`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

8.0ms	(* J (- (exp l) (exp (- l))))
1.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
6.0ms	(- (exp l) (exp (- l)))

series261.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* J (- (exp l) (exp (- l))))
168.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
36.0ms	(- (exp l) (exp (- l)))

simplify43.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	318	1176
1	1096	780
2	5001	725

prune239.0ms

Filtered

93 candidates to 56 candidates (60.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	2	94

Merged error: 0.1b

Counts

94 → 2

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0b	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.1b	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`fma-udef`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 42

Calls

3 calls:

1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
4.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

series433.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
133.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
243.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify106.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	176	451
1	760	390
2	4095	382
3	5001	382

prune209.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	46	7	53

Merged error: 0.0b

Counts

53 → 7

localize20.0ms

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)

rewrite11.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 81

Calls

4 calls:

6.0ms	(* (cbrt J) (cbrt J))
1.0ms	(cbrt J)
1.0ms	(cbrt J)
1.0ms	(cbrt J)

series737.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (cbrt J) (cbrt J))
179.0ms	(cbrt J)
179.0ms	(cbrt J)
177.0ms	(cbrt J)

simplify89.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255

prune432.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	92	8	100

Merged error: 0.0b

Counts

100 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt J)
0.6b	(cbrt (cbrt J))
0.6b	(cbrt (cbrt J))
0.6b	(cbrt (cbrt J))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 61

Calls

4 calls:

1.0ms	(cbrt J)
2.0ms	(cbrt (cbrt J))
2.0ms	(cbrt (cbrt J))
2.0ms	(cbrt (cbrt J))

series927.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt J)
246.0ms	(cbrt (cbrt J))
248.0ms	(cbrt (cbrt J))
246.0ms	(cbrt (cbrt J))

simplify50.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	75	283
1	145	265
2	361	257
3	1382	257
4	5002	257

prune431.0ms

Filtered

73 candidates to 70 candidates (95.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	72	9	81

Merged error: 0.0b

Counts

81 → 9

regimes350.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	2603×	body	1280	valid
829.0ms	2643×	body	640	valid
596.0ms	8505×	body	80	valid
316.0ms	1433×	body	320	valid
103.0ms	739×	body	160	valid