Details

sample437.0ms

Algorithm

intervals

Results

92.0ms	28×	body	2560	valid
52.0ms	61×	body	1280	valid
15.0ms	137×	body	80	valid
14.0ms	33×	body	640	valid
3.0ms	11×	body	320	valid
2.0ms	7×	body	160	valid

simplify21.0ms

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: 17.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.6b	(/ 1.0 (* F F))
2.8b	(* (/ 1.0 (* F F)) (tan (* PI l)))
32.1b	(tan (* PI l))

rewrite28.0ms

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)
3.0ms	(/ 1.0 (* F F))
15.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
4.0ms	(tan (* PI l))

series251.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* PI l)
24.0ms	(/ 1.0 (* F F))
129.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
77.0ms	(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

prune260.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ (cbrt 1.0) F) (tan (* PI l)))
32.1b	(tan (* PI l))

rewrite25.0ms

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:

3.0ms	(* PI l)
3.0ms	(* PI l)
14.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
2.0ms	(tan (* PI l))

series264.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* PI l)
19.0ms	(* PI l)
161.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
64.0ms	(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

prune412.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 14.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) (* (sqrt PI) l))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
31.9b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`tan-quot` `associate-r` `*-commutative`

Counts

4 → 63

Calls

4 calls:

10.0ms	(* (sqrt PI) (* (sqrt PI) l))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
5.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series87.0ms

Counts

4 → 8

Calls

4 calls:

21.0ms	(* (sqrt PI) (* (sqrt PI) l))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
66.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify48.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	158	264
1	501	230
2	1518	229
3	5001	229

prune320.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 14.4b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
31.9b	(tan (* (sqrt (sqrt PI)) (* (sqrt (sqrt PI)) (* (sqrt PI) l))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`tan-quot`

Counts

4 → 55

Calls

4 calls:

1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
15.0ms	(tan (* (sqrt (sqrt PI)) (* (sqrt (sqrt PI)) (* (sqrt PI) l))))

series65.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
65.0ms	(tan (* (sqrt (sqrt PI)) (* (sqrt (sqrt PI)) (* (sqrt PI) l))))

simplify165.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	96	268
1	239	235
2	905	235
3	4924	235
4	5001	235

prune295.0ms

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 14.4b

regimes524.0ms

Accuracy

0% (0.3b remaining)

Error of 12.8b against oracle of 12.5b and baseline of 12.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	23
1	25	23

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.7s	841×	body	2560	valid
1.4s	1675×	body	1280	valid
514.0ms	4469×	body	80	valid
436.0ms	996×	body	640	valid
122.0ms	411×	body	320	valid
118.0ms	5×	body	10240	exit
46.0ms	213×	body	160	valid