Details

sample89.0ms

Algorithm

intervals

Results

27.0ms	66×	body	1280	valid
18.0ms	69×	body	640	valid
14.0ms	265×	body	80	valid
7.0ms	40×	body	320	valid
4.0ms	34×	body	160	valid

simplify375.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
0.0b	(* J (- (exp l) (exp (- l))))
6.0b	(- (exp l) (exp (- l)))

rewrite17.0ms

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:

1.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
8.0ms	(* J (- (exp l) (exp (- l))))
5.0ms	(- (exp l) (exp (- l)))

series262.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
58.0ms	(* J (- (exp l) (exp (- l))))
35.0ms	(- (exp l) (exp (- l)))

simplify41.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (32.0ms)

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

prune255.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

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)

series374.0ms

Counts

2 → 6

Calls

2 calls:

131.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
242.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify87.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	166	362
1	654	312
2	3194	304
3	5002	304

prune161.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l))))
0.0b	(fma (+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
0.1b	(* 1/3 (pow l 3))
5.8b	(* J (* 1/3 (pow l 3)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
13×	`associate-r`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`fma-udef`
2×	`pow-to-exp` `associate-+r+` `pow-exp` `*-commutative` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `fma-def` `distribute-lft-in` `flip3-+` `unpow3` `pow-prod-down` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

6.0ms	(+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(fma (+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
6.0ms	(* 1/3 (pow l 3))
6.0ms	(* J (* 1/3 (pow l 3)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l))))
250.0ms	(fma (+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
35.0ms	(* 1/3 (pow l 3))
61.0ms	(* J (* 1/3 (pow l 3)))

simplify59.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	359	599
1	1580	520
2	5002	508

prune357.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize212.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

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)

series727.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(* (cbrt J) (cbrt J))
183.0ms	(cbrt J)
179.0ms	(cbrt J)
171.0ms	(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

prune420.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes249.0ms

Accuracy

0% (0.3b 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	26	11
1	26	11

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	2667×	body	1280	valid
660.0ms	2520×	body	640	valid
451.0ms	8358×	body	80	valid
256.0ms	1481×	body	320	valid
88.0ms	784×	body	160	valid