Details

sample387.0ms

Algorithm

intervals

Results

80.0ms	25×	body	2560	valid
32.0ms	60×	body	1280	valid
7.0ms	29×	body	640	valid
6.0ms	147×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	9×	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: 17.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.6b	(/ 1.0 (* F F))
4.6b	(* (/ 1.0 (* F F)) (tan (* PI l)))
32.0b	(tan (* PI l))

rewrite22.0ms

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)
4.0ms	(/ 1.0 (* F F))
9.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
3.0ms	(tan (* PI l))

series265.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
24.0ms	(/ 1.0 (* F F))
138.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
83.0ms	(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

prune235.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.3b	(* (/ (cbrt 1.0) F) (tan (* PI l)))
32.0b	(tan (* PI l))

rewrite21.0ms

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×	`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)
9.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series276.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
20.0ms	(* PI l)
169.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
68.0ms	(tan (* PI l))

simplify96.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	294	496
1	1023	455
2	3911	454
3	5001	451

prune346.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cbrt 1.0) F) (tan (* (sqrt PI) (* (sqrt PI) l))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
31.9b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`associate-l`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
10×	`cbrt-prod`
9×	`add-exp-log`
8×	`pow1` `add-cbrt-cube`
6×	`sqrt-prod`
4×	`add-log-exp`
3×	`tan-quot` `associate-r` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `*-commutative` `div-inv`

Counts

4 → 78

Calls

4 calls:

10.0ms	(* (/ (cbrt 1.0) F) (tan (* (sqrt PI) (* (sqrt PI) l))))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
3.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series241.0ms

Counts

4 → 8

Calls

4 calls:

172.0ms	(* (/ (cbrt 1.0) F) (tan (* (sqrt PI) (* (sqrt PI) l))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
69.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify86.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	275	648
1	864	588
2	3374	585
3	5002	582

prune362.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 12.4b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
31.7b	(cos (* (sqrt PI) (* (sqrt PI) l)))
31.9b	(sin (* PI l))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

2.0ms	(sqrt PI)
2.0ms	(sqrt PI)
3.0ms	(cos (* (sqrt PI) (* (sqrt PI) l)))
2.0ms	(sin (* PI l))

series45.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
19.0ms	(cos (* (sqrt PI) (* (sqrt PI) l)))
27.0ms	(sin (* PI l))

simplify82.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	150	209
1	507	184
2	2295	184
3	5001	180

prune213.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.6b

regimes515.0ms

Accuracy

76.8% (1.1b remaining)

Error of 8.9b against oracle of 7.9b and baseline of 12.4b

bsearch3.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	64
1	69	64

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.4s	817×	body	2560	valid
941.0ms	1713×	body	1280	valid
219.0ms	879×	body	640	valid
194.0ms	4585×	body	80	valid
61.0ms	394×	body	320	valid
23.0ms	220×	body	160	valid