Details

sample117.0ms

Algorithm

intervals

Results

44.0ms	110×	body	1280	valid
27.0ms	95×	body	640	valid
15.0ms	277×	body	80	valid
6.0ms	37×	body	320	valid
3.0ms	30×	body	160	valid

simplify365.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
5.9b	(- (exp l) (exp (- l)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

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

series200.0ms

Counts

2 → 6

Calls

2 calls:

162.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
38.0ms	(- (exp l) (exp (- l)))

simplify151.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (146.0ms)

Iter	Nodes	Cost
0	229	499
1	610	347
2	3424	343
3	5001	329

prune137.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(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)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

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)

series285.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
230.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify41.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	101	245
1	302	214
2	1331	206
3	5003	206

prune115.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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))))

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))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (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)))))
152.0ms	(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))))
138.0ms	(cbrt (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))

simplify139.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (125.0ms)

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

prune446.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)) (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)))
0.6b	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
0.6b	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
0.6b	(cbrt (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

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 (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)) (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)))
0.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
0.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
1.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))

series2.0s

Counts

4 → 12

Calls

4 calls:

790.0ms	(* (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)) (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)))
390.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
393.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
409.0ms	(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))

simplify156.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	294	1835
1	989	1685
2	4974	1549
3	5001	1549

prune430.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes305.0ms

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

sample3.0s

Algorithm

intervals

Results

1.1s	2635×	body	1280	valid
661.0ms	2571×	body	640	valid
457.0ms	8452×	body	80	valid
246.0ms	1436×	body	320	valid
97.0ms	796×	body	160	valid