Details

sample477.0ms

Algorithm

intervals

Results

71.0ms	22×	body	2560	valid
46.0ms	55×	body	1280	valid
31.0ms	151×	body	80	valid
8.0ms	24×	body	640	valid
3.0ms	14×	body	320	valid
2.0ms	10×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	41	7
2	82	7
3	122	7
4	147	7
5	157	7
6	159	7
7	159	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.4b	(/ 1.0 (* F F))
3.5b	(* (/ 1.0 (* F F)) (tan (* PI l)))
29.0b	(tan (* PI l))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
8×	`pow1`
7×	`times-frac`
6×	`associate-r` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `associate-/l*` `unswap-sqr`
2×	`pow-prod-down` `*-commutative` `div-inv`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r*`

Counts

4 → 85

Calls

4 calls:

7.0ms	(* PI l)
8.0ms	(/ 1.0 (* F F))
48.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series258.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* PI l)
25.0ms	(/ 1.0 (* F F))
132.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
77.0ms	(tan (* PI l))

simplify43.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	334	468
1	1442	399
2	5001	398

prune251.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ 1.0 F) (tan (* PI l)))
29.0b	(tan (* PI l))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`associate-l`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `times-frac`
9×	`associate-r`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`tan-quot` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `div-inv`

Counts

4 → 86

Calls

4 calls:

7.0ms	(* PI l)
6.0ms	(* PI l)
31.0ms	(* (/ 1.0 F) (tan (* PI l)))
10.0ms	(tan (* PI l))

series232.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
23.0ms	(* PI l)
124.0ms	(* (/ 1.0 F) (tan (* PI l)))
64.0ms	(tan (* PI l))

simplify88.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	286	403
1	1032	363
2	3928	361
3	5001	360

prune279.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(/ (sin (* PI l)) (* (cos (* PI l)) F))
28.7b	(sin (* PI l))
28.8b	(cos (* PI l))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

7.0ms	(* PI l)
21.0ms	(/ (sin (* PI l)) (* (cos (* PI l)) F))
7.0ms	(sin (* PI l))
8.0ms	(cos (* PI l))

series171.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* PI l)
107.0ms	(/ (sin (* PI l)) (* (cos (* PI l)) F))
22.0ms	(sin (* PI l))
18.0ms	(cos (* PI l))

simplify33.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	278	386
1	1050	331
2	5002	329

prune251.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt l)
0.6b	(cbrt l)
0.6b	(cbrt l)
28.9b	(tan (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`tan-quot`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt l)
1.0ms	(cbrt l)
1.0ms	(cbrt l)
50.0ms	(tan (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt l)
175.0ms	(cbrt l)
176.0ms	(cbrt l)
83.0ms	(tan (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

simplify202.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	111	258
1	276	234
2	926	218
3	4988	218
4	5001	218

prune198.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.8b

regimes440.0ms

Accuracy

73.6% (1.3b remaining)

Error of 9.2b against oracle of 7.9b and baseline of 12.9b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	47
1	65	47

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	829×	body	2560	valid
1.2s	1684×	body	1280	valid
330.0ms	950×	body	640	valid
297.0ms	4502×	body	80	valid
97.0ms	379×	body	320	valid
70.0ms	3×	body	10240	exit
40.0ms	234×	body	160	valid