Details

sample100.0ms

Algorithm

intervals

Results

35.0ms	83×	body	1280	valid
21.0ms	82×	body	640	valid
13.0ms	240×	body	80	valid
9.0ms	53×	body	320	valid
3.0ms	24×	body	160	valid

simplify379.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize18.0ms

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)
4.2b	(- (exp l) (exp (- l)))

rewrite35.0ms

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:

24.0ms	(* J (- (exp l) (exp (- l))))
0.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
8.0ms	(- (exp l) (exp (- l)))

series263.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* J (- (exp l) (exp (- l))))
168.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
37.0ms	(- (exp l) (exp (- l)))

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (33.0ms)

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

prune247.0ms

Filtered

93 candidates to 56 candidates (60.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

6.0ms	(* 2 (* J l))
0.0ms	(fma (* 2 (* J l)) (cos (/ K 2.0)) U)

series112.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(* 2 (* J l))
92.0ms	(fma (* 2 (* J l)) (cos (/ K 2.0)) U)

simplify125.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	127	162
1	414	140
2	1545	140
3	4868	140
4	5001	140

prune90.0ms

Filtered

36 candidates to 25 candidates (69.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* J (* (cos (* 0.5 K)) l))
0.1b	(* (cos (* 0.5 K)) l)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`associate-l`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
1×	`unswap-sqr`

Counts

2 → 40

Calls

2 calls:

9.0ms	(* J (* (cos (* 0.5 K)) l))
5.0ms	(* (cos (* 0.5 K)) l)

series102.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(* J (* (cos (* 0.5 K)) l))
50.0ms	(* (cos (* 0.5 K)) l)

simplify71.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	138	240
1	534	199
2	2487	199
3	5001	199

prune118.0ms

Filtered

46 candidates to 30 candidates (65.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (* J (cos (* 0.5 K))) l)
0.2b	(* J (cos (* 0.5 K)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`associate-r`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
1×	`unswap-sqr`

Counts

2 → 40

Calls

2 calls:

10.0ms	(* (* J (cos (* 0.5 K))) l)
5.0ms	(* J (cos (* 0.5 K)))

series98.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(* (* J (cos (* 0.5 K))) l)
42.0ms	(* J (cos (* 0.5 K)))

simplify64.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	130	237
1	627	196
2	2603	196
3	5001	196

prune105.0ms

Filtered

46 candidates to 30 candidates (65.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes215.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	5
1	14	5

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	2627×	body	1280	valid
645.0ms	2478×	body	640	valid
456.0ms	8328×	body	80	valid
248.0ms	1375×	body	320	valid
84.0ms	737×	body	160	valid