Details

sample499.0ms

Algorithm

intervals

Results

110.0ms	29×	body	2560	valid
50.0ms	68×	body	1280	valid
11.0ms	34×	body	640	valid
9.0ms	129×	body	80	valid
1.0ms	6×	body	320	valid
1.0ms	8×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.7b	(/ 1.0 (* F F))
3.7b	(* (/ 1.0 (* F F)) (tan (* PI l)))
33.4b	(tan (* PI l))

rewrite75.0ms

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

series260.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
29.0ms	(/ 1.0 (* F F))
134.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
77.0ms	(tan (* PI l))

simplify41.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (35.0ms)

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

prune261.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.3b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

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:

7.0ms	(* PI l)
7.0ms	(* PI l)
31.0ms	(* (/ 1.0 F) (tan (* PI l)))
10.0ms	(tan (* PI l))

series238.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
26.0ms	(* PI l)
127.0ms	(* (/ 1.0 F) (tan (* PI l)))
64.0ms	(tan (* PI l))

simplify85.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (80.0ms)

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

prune299.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(/ (* 1.0 (sin (* PI l))) (* F (cos (* PI l))))
33.1b	(sin (* PI l))
33.1b	(cos (* PI l))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `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	(/ (* 1.0 (sin (* PI l))) (* F (cos (* PI l))))
7.0ms	(sin (* PI l))
7.0ms	(cos (* PI l))

series183.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
122.0ms	(/ (* 1.0 (sin (* PI l))) (* F (cos (* PI l))))
23.0ms	(sin (* PI l))
18.0ms	(cos (* PI l))

simplify43.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	347	433
1	1687	342
2	5001	341

prune259.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt l)
0.6b	(cbrt l)
33.1b	(sin (* PI l))
33.4b	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

rewrite51.0ms

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)
7.0ms	(sin (* PI l))
42.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt l)
183.0ms	(cbrt l)
27.0ms	(sin (* PI l))
29.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

simplify82.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (79.0ms)

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

prune225.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.2b

regimes497.0ms

Accuracy

83.4% (0.8b remaining)

Error of 8.9b against oracle of 8.0b and baseline of 13.1b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	44
1	60	44

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.7s	875×	body	2560	valid
1.2s	1695×	body	1280	valid
346.0ms	972×	body	640	valid
291.0ms	4449×	body	80	valid
117.0ms	5×	body	10240	exit
95.0ms	396×	body	320	valid
32.0ms	212×	body	160	valid