Details

sample492.0ms

Algorithm

intervals

Results

97.0ms	30×	body	2560	valid
40.0ms	57×	body	1280	valid
31.0ms	34×	body	640	valid
11.0ms	142×	body	80	valid
3.0ms	13×	body	320	valid
1.0ms	7×	body	160	valid

simplify21.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(/ 1.0 (* F F))
3.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
33.4b	(tan (* PI l))

rewrite74.0ms

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)
7.0ms	(/ 1.0 (* F F))
47.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series246.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* PI l)
23.0ms	(/ 1.0 (* F F))
125.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
74.0ms	(tan (* PI l))

simplify42.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	334	468
1	1442	399
2	5001	398

prune253.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

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)))
33.4b	(tan (* PI l))

rewrite60.0ms

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)
6.0ms	(* PI l)
34.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
10.0ms	(tan (* PI l))

series256.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
18.0ms	(* PI l)
157.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
62.0ms	(tan (* PI l))

simplify94.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (87.0ms)

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

prune387.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(/ (* (cbrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
32.4b	(cos (* PI l))
32.6b	(sin (* PI l))

rewrite49.0ms

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:

7.0ms	(* PI l)
27.0ms	(/ (* (cbrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
7.0ms	(cos (* PI l))
7.0ms	(sin (* PI l))

series250.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* PI l)
188.0ms	(/ (* (cbrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
16.0ms	(cos (* PI l))
22.0ms	(sin (* PI l))

simplify45.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	353	462
1	1667	371
2	5002	370

prune295.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt l)
0.6b	(cbrt l)
32.5b	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
32.6b	(sin (* PI l))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt l)
1.0ms	(cbrt l)
40.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
7.0ms	(sin (* PI l))

series400.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt l)
174.0ms	(cbrt l)
26.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
23.0ms	(sin (* PI l))

simplify84.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	156	247
1	513	219
2	2269	215
3	5001	210

prune241.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.2b

regimes547.0ms

Accuracy

87.5% (0.6b remaining)

Error of 8.3b against oracle of 7.8b and baseline of 12.2b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	52
1	62	52

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	826×	body	2560	valid
1.2s	1722×	body	1280	valid
340.0ms	930×	body	640	valid
295.0ms	4471×	body	80	valid
116.0ms	5×	body	10240	exit
101.0ms	437×	body	320	valid
32.0ms	207×	body	160	valid