Details

sample106.0ms

Algorithm

intervals

Results

33.0ms	79×	body	1280	valid
25.0ms	79×	body	640	valid
15.0ms	265×	body	80	valid
8.0ms	49×	body	320	valid
3.0ms	25×	body	160	valid

simplify376.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize13.0ms

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))))
6.1b	(- (exp l) (exp (- l)))

rewrite74.0ms

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:

0.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
54.0ms	(* J (- (exp l) (exp (- l))))
17.0ms	(- (exp l) (exp (- l)))

series236.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
52.0ms	(* J (- (exp l) (exp (- l))))
33.0ms	(- (exp l) (exp (- l)))

simplify43.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (34.0ms)

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

prune342.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0b	(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)

rewrite9.0ms

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:

7.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

series391.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
49.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
219.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify110.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	176	451
1	760	390
2	4093	382
3	5001	382

prune305.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
0.6b	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.6b	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.6b	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))

rewrite16.0ms

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:

12.0ms	(* (cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
1.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))

series563.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
134.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
137.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
138.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))

simplify146.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (132.0ms)

Iter	Nodes	Cost
0	306	1320
1	970	1218
2	4372	1056
3	5001	1030

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0b	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0b	(fma (* J (* (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))) (cos (/ K 2.0)) U)
0.3b	(* (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr` `fma-udef`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

0.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0ms	(fma (* J (* (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))) (cos (/ K 2.0)) U)
17.0ms	(* (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
50.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
228.0ms	(fma (* J (* (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))) (cos (/ K 2.0)) U)
52.0ms	(* (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (sqrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	186	893
1	737	758
2	5001	718

prune558.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes401.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	2713×	body	1280	valid
684.0ms	2546×	body	640	valid
505.0ms	8396×	body	80	valid
268.0ms	1461×	body	320	valid
88.0ms	763×	body	160	valid