Details

sample389.0ms

Algorithm

intervals

Results

88.0ms	29×	body	2560	valid
30.0ms	55×	body	1280	valid
8.0ms	26×	body	640	valid
6.0ms	145×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	6×	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

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))
4.1b	(* (/ 1.0 (* F F)) (tan (* PI l)))
30.9b	(tan (* PI l))

rewrite24.0ms

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:

3.0ms	(* PI l)
4.0ms	(/ 1.0 (* F F))
10.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
3.0ms	(tan (* PI l))

series257.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
24.0ms	(/ 1.0 (* F F))
133.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
80.0ms	(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

prune251.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.2b

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)))
30.9b	(tan (* PI l))

rewrite18.0ms

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:

3.0ms	(* PI l)
3.0ms	(* PI l)
7.0ms	(* (/ 1.0 F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series225.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
19.0ms	(* PI l)
123.0ms	(* (/ 1.0 F) (tan (* PI l)))
63.0ms	(tan (* PI l))

simplify86.0ms

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

prune282.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
30.2b	(cos (* PI l))
30.6b	(sin (* PI l))

rewrite13.0ms

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:

4.0ms	(* PI l)
4.0ms	(* PI l)
2.0ms	(cos (* PI l))
2.0ms	(sin (* PI l))

series81.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
19.0ms	(* PI l)
17.0ms	(cos (* PI l))
26.0ms	(sin (* PI l))

simplify114.0ms

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

prune240.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.0b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt PI)
1.0b	(* (cbrt PI) (cbrt PI))
30.6b	(sin (* PI l))
30.7b	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`cbrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
7×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

1.0ms	(cbrt PI)
6.0ms	(* (cbrt PI) (cbrt PI))
2.0ms	(sin (* PI l))
4.0ms	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))

series48.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt PI)
0.0ms	(* (cbrt PI) (cbrt PI))
26.0ms	(sin (* PI l))
21.0ms	(cos (* (* (cbrt PI) (cbrt PI)) (* (cbrt PI) l)))

simplify125.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	187	382
1	694	343
2	3475	326
3	5002	318

prune243.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.0b

regimes443.0ms

Accuracy

86% (0.6b remaining)

Error of 8.4b against oracle of 7.8b and baseline of 12.4b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	42
1	54	42

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.5s	830×	body	2560	valid
909.0ms	1654×	body	1280	valid
243.0ms	969×	body	640	valid
210.0ms	4610×	body	80	valid
66.0ms	406×	body	320	valid
22.0ms	202×	body	160	valid
2.0ms	6×	body	10240	exit