Details

sample441.0ms

Algorithm

intervals

Results

109.0ms	35×	body	2560	valid
50.0ms	65×	body	1280	valid
12.0ms	124×	body	80	valid
11.0ms	30×	body	640	valid
2.0ms	7×	body	320	valid
2.0ms	9×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	39	7
2	76	7
3	114	7
4	137	7
5	144	7
6	144	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.4b	(/ 1.0 (* F F))
2.8b	(* (/ 1.0 (* F F)) (tan (* PI l)))
33.9b	(tan (* PI l))

rewrite39.0ms

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` `div-exp` `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 → 77

Calls

4 calls:

3.0ms	(* PI l)
3.0ms	(/ 1.0 (* F F))
16.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
3.0ms	(tan (* PI l))

series254.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
24.0ms	(/ 1.0 (* F F))
137.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
73.0ms	(tan (* PI l))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	323	443
1	1416	374
2	5001	374

prune242.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 17.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ (sqrt 1.0) F) (tan (* PI l)))
33.9b	(tan (* PI l))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
28×	`associate-l`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `sqrt-prod`
9×	`associate-r`
5×	`unswap-sqr`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`tan-quot` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `div-inv`

Counts

4 → 88

Calls

4 calls:

3.0ms	(* PI l)
3.0ms	(* PI l)
15.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series269.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
19.0ms	(* PI l)
164.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
66.0ms	(tan (* PI l))

simplify102.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	297	498
1	1061	455
2	4012	454
3	5002	454

prune326.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 16.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ (* (sin (* PI l)) (sqrt 1.0)) (* (cos (* PI l)) F))
33.1b	(cos (* PI l))
33.7b	(sin (* PI l))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

3.0ms	(* PI l)
8.0ms	(/ (* (sin (* PI l)) (sqrt 1.0)) (* (cos (* PI l)) F))
2.0ms	(cos (* PI l))
2.0ms	(sin (* PI l))

series259.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
196.0ms	(/ (* (sin (* PI l)) (sqrt 1.0)) (* (cos (* PI l)) F))
20.0ms	(cos (* PI l))
23.0ms	(sin (* PI l))

simplify43.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	339	429
1	1657	342
2	5001	342

prune258.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 11.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (cos (* PI l)) F) (* (sin (* PI l)) (sqrt 1.0)))
0.8b	(/ 1 (/ (* (cos (* PI l)) F) (* (sin (* PI l)) (sqrt 1.0))))
33.1b	(cos (* PI l))
33.7b	(sin (* PI l))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-exp-log`
34×	`add-cbrt-cube`
26×	`div-exp`
20×	`times-frac`
16×	`prod-exp`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`cbrt-undiv`
8×	`cbrt-unprod`
6×	`associate-/r*` `div-inv`
5×	`pow1` `rec-exp` `1-exp`
4×	`associate-/l*` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

4 → 91

Calls

4 calls:

8.0ms	(/ (* (cos (* PI l)) F) (* (sin (* PI l)) (sqrt 1.0)))
11.0ms	(/ 1 (/ (* (cos (* PI l)) F) (* (sin (* PI l)) (sqrt 1.0))))
2.0ms	(cos (* PI l))
2.0ms	(sin (* PI l))

series443.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ (* (cos (* PI l)) F) (* (sin (* PI l)) (sqrt 1.0)))
205.0ms	(/ 1 (/ (* (cos (* PI l)) F) (* (sin (* PI l)) (sqrt 1.0))))
17.0ms	(cos (* PI l))
24.0ms	(sin (* PI l))

simplify65.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	468	1143
1	2437	951
2	5001	920

prune240.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.7b

regimes482.0ms

Accuracy

81% (0.7b remaining)

Error of 5.2b against oracle of 4.5b and baseline of 8.1b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	39
1	62	39

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	811×	body	2560	valid
1.3s	1721×	body	1280	valid
425.0ms	4478×	body	80	valid
372.0ms	966×	body	640	valid
110.0ms	415×	body	320	valid
41.0ms	197×	body	160	valid
24.0ms	1×	body	10240	exit