Details

sample428.0ms

Algorithm

intervals

Results

83.0ms	25×	body	2560	valid
51.0ms	62×	body	1280	valid
11.0ms	144×	body	80	valid
9.0ms	23×	body	640	valid
5.0ms	18×	body	320	valid
2.0ms	8×	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: 17.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.5b	(/ 1.0 (* F F))
4.8b	(* (/ 1.0 (* F F)) (tan (* PI l)))
31.7b	(tan (* PI l))

rewrite79.0ms

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))
51.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series240.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
23.0ms	(/ 1.0 (* F F))
125.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
73.0ms	(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

prune364.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.4b	(* (/ 1.0 F) (tan (* PI l)))
31.7b	(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:

6.0ms	(* PI l)
6.0ms	(* PI l)
31.0ms	(* (/ 1.0 F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series215.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* PI l)
19.0ms	(* PI l)
120.0ms	(* (/ 1.0 F) (tan (* PI l)))
58.0ms	(tan (* PI l))

simplify88.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (82.0ms)

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

prune436.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
30.3b	(cos (* PI l))
31.1b	(sin (* PI l))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

7.0ms	(* PI l)
7.0ms	(* PI l)
10.0ms	(cos (* PI l))
7.0ms	(sin (* PI l))

series80.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* PI l)
18.0ms	(* PI l)
16.0ms	(cos (* PI l))
22.0ms	(sin (* PI l))

simplify112.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	162	201
1	606	181
2	3058	180
3	5002	180

prune367.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 6.4b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
30.6b	(cos (* (sqrt PI) (* (sqrt PI) l)))
31.1b	(sin (* PI l))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 48

Calls

4 calls:

1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
20.0ms	(cos (* (sqrt PI) (* (sqrt PI) l)))
7.0ms	(sin (* PI l))

series44.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
18.0ms	(cos (* (sqrt PI) (* (sqrt PI) l)))
26.0ms	(sin (* PI l))

simplify76.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	135	203
1	448	182
2	1999	182
3	5002	178

prune262.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 6.4b

regimes805.0ms

Accuracy

77.4% (1.1b remaining)

Error of 8.5b against oracle of 7.4b and baseline of 12.3b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	43
1	64	43

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	785×	body	2560	valid
1.4s	1701×	body	1280	valid
393.0ms	969×	body	640	valid
361.0ms	4514×	body	80	valid
107.0ms	405×	body	320	valid
48.0ms	2×	body	10240	exit
38.0ms	209×	body	160	valid