Details

sample395.0ms

Algorithm

intervals

Results

56.0ms	17×	body	2560	valid
45.0ms	54×	body	1280	valid
15.0ms	143×	body	80	valid
12.0ms	28×	body	640	valid
4.0ms	13×	body	320	valid
2.0ms	11×	body	160	valid

simplify17.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ 1.0 (* F F))
6.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
28.4b	(tan (* PI l))

rewrite41.0ms

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:

4.0ms	(* 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)))
72.0ms	(tan (* PI l))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

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

prune221.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.1b

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)))
28.4b	(tan (* PI l))

rewrite21.0ms

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×	`prod-exp` `cbrt-unprod` `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 → 78

Calls

4 calls:

3.0ms	(* PI l)
3.0ms	(* PI l)
11.0ms	(* (/ 1.0 F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series230.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* PI l)
20.0ms	(* PI l)
122.0ms	(* (/ 1.0 F) (tan (* PI l)))
65.0ms	(tan (* PI l))

simplify85.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	277	382
1	1009	342
2	3834	341
3	5001	341

prune254.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ (sin (* PI l)) (* (cos (* PI l)) F))
27.8b	(cos (* PI l))
28.5b	(sin (* PI l))

rewrite15.0ms

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×	`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 → 53

Calls

4 calls:

5.0ms	(* PI l)
5.0ms	(/ (sin (* PI l)) (* (cos (* PI l)) F))
2.0ms	(cos (* PI l))
2.0ms	(sin (* PI l))

series167.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
107.0ms	(/ (sin (* PI l)) (* (cos (* PI l)) F))
17.0ms	(cos (* PI l))
23.0ms	(sin (* PI l))

simplify36.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	267	357
1	1024	304
2	5001	304

prune215.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (cos (* PI l)) F) (sin (* PI l)))
0.5b	(/ 1 (/ (* (cos (* PI l)) F) (sin (* PI l))))
27.8b	(cos (* PI l))
28.5b	(sin (* PI l))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
30×	`add-exp-log`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`add-cbrt-cube`
14×	`div-exp`
10×	`associate-/r*`
7×	`cbrt-undiv`
6×	`div-inv`
5×	`pow1`
4×	`prod-exp` `associate-/l*` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num` `cbrt-unprod`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

4 → 91

Calls

4 calls:

5.0ms	(/ (* (cos (* PI l)) F) (sin (* PI l)))
7.0ms	(/ 1 (/ (* (cos (* PI l)) F) (sin (* PI l))))
4.0ms	(cos (* PI l))
2.0ms	(sin (* PI l))

series256.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (* (cos (* PI l)) F) (sin (* PI l)))
107.0ms	(/ 1 (/ (* (cos (* PI l)) F) (sin (* PI l))))
17.0ms	(cos (* PI l))
23.0ms	(sin (* PI l))

simplify49.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	406	947
1	1941	821
2	5001	784

prune222.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.9b

regimes364.0ms

Accuracy

31.6% (2.5b remaining)

Error of 7.0b 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	65	42
1	65	42

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.6s	810×	body	2560	valid
1.4s	1715×	body	1280	valid
431.0ms	4494×	body	80	valid
431.0ms	980×	body	640	valid
116.0ms	391×	body	320	valid
47.0ms	2×	body	10240	exit
41.0ms	203×	body	160	valid