Details

sample105.0ms

Algorithm

intervals

Results

39.0ms	99×	body	1280	valid
18.0ms	74×	body	640	valid
14.0ms	270×	body	80	valid
8.0ms	46×	body	320	valid
2.0ms	23×	body	160	valid

simplify374.0ms

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: 18.5b

localize17.0ms

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)
5.9b	(- (exp l) (exp (- l)))

rewrite33.0ms

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:

23.0ms	(* J (- (exp l) (exp (- l))))
0.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
7.0ms	(- (exp l) (exp (- l)))

series253.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* J (- (exp l) (exp (- l))))
163.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
35.0ms	(- (exp l) (exp (- l)))

simplify39.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (31.0ms)

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

prune248.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite4.0ms

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:

0.0ms	(fma 1/60 (pow l 5) (* 2 l))
3.0ms	(* J (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)

series493.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(fma 1/60 (pow l 5) (* 2 l))
131.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
238.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify94.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	178	421
1	700	364
2	3483	356
3	5001	356

prune214.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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)
0.2b	(* 1/3 (pow l 3))
5.4b	(* J (* 1/3 (pow l 3)))

rewrite25.0ms

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:

8.0ms	(+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l))))
0.0ms	(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))
8.0ms	(* J (* 1/3 (pow l 3)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l))))
245.0ms	(fma (+ (* J (* 1/3 (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
36.0ms	(* 1/3 (pow l 3))
59.0ms	(* J (* 1/3 (pow l 3)))

simplify57.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (49.0ms)

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

prune356.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

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)))))
0.7b	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.7b	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.7b	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))

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×	`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:

5.0ms	(* (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)))))
0.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0ms	(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))))

series599.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (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)))))
147.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
142.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
149.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))

simplify140.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (127.0ms)

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

prune456.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes245.0ms

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

sample3.0s

Algorithm

intervals

Results

1.1s	2666×	body	1280	valid
665.0ms	2611×	body	640	valid
443.0ms	8434×	body	80	valid
250.0ms	1454×	body	320	valid
83.0ms	738×	body	160	valid