Details

sample435.0ms

Algorithm

intervals

Results

87.0ms	27×	body	2560	valid
39.0ms	47×	body	1280	valid
17.0ms	156×	body	80	valid
12.0ms	29×	body	640	valid
6.0ms	18×	body	320	valid
1.0ms	4×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 13.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
1.5b	(/ 1.0 (* F F))
3.7b	(* (/ 1.0 (* F F)) (tan (* PI l)))
29.3b	(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` `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:

12.0ms	(* PI l)
3.0ms	(/ 1.0 (* F F))
17.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
3.0ms	(tan (* PI l))

series248.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
24.0ms	(/ 1.0 (* F F))
133.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
71.0ms	(tan (* PI l))

simplify49.0ms

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

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ (cbrt 1.0) F) (tan (* PI l)))
29.3b	(tan (* PI l))

rewrite30.0ms

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`
12×	`add-cbrt-cube`
10×	`pow1` `cbrt-prod`
9×	`associate-r`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 96

Calls

4 calls:

6.0ms	(* PI l)
3.0ms	(* PI l)
15.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series272.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
24.0ms	(* PI l)
168.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
60.0ms	(tan (* PI l))

simplify98.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	303	519
1	1044	478
2	4000	476
3	5001	475

prune371.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ (* (sin (* PI l)) (cbrt 1.0)) (* (cos (* PI l)) F))
28.5b	(cos (* PI l))
28.8b	(sin (* PI l))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
16×	`add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `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 → 61

Calls

4 calls:

3.0ms	(* PI l)
7.0ms	(/ (* (sin (* PI l)) (cbrt 1.0)) (* (cos (* PI l)) F))
2.0ms	(cos (* PI l))
2.0ms	(sin (* PI l))

series263.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* PI l)
199.0ms	(/ (* (sin (* PI l)) (cbrt 1.0)) (* (cos (* PI l)) F))
17.0ms	(cos (* PI l))
23.0ms	(sin (* PI l))

simplify45.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	347	463
1	1605	372
2	5001	371

prune281.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* (cos (* PI l)) F) (* (sin (* PI l)) (cbrt 1.0))))
0.3b	(/ (* (cos (* PI l)) F) (* (sin (* PI l)) (cbrt 1.0)))
28.5b	(cos (* PI l))
28.8b	(sin (* PI l))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-exp-log`
30×	`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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

4 → 99

Calls

4 calls:

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

series443.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ 1 (/ (* (cos (* PI l)) F) (* (sin (* PI l)) (cbrt 1.0))))
198.0ms	(/ (* (cos (* PI l)) F) (* (sin (* PI l)) (cbrt 1.0)))
17.0ms	(cos (* PI l))
22.0ms	(sin (* PI l))

simplify66.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	476	1195
1	2401	997
2	5003	968

prune278.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.5b

regimes317.0ms

Accuracy

80.4% (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	60	42
1	60	42

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.6s	806×	body	2560	valid
1.4s	1719×	body	1280	valid
443.0ms	4519×	body	80	valid
424.0ms	941×	body	640	valid
117.0ms	5×	body	10240	exit
116.0ms	366×	body	320	valid
49.0ms	211×	body	160	valid