Details

sample465.0ms

Algorithm

intervals

Results

141.0ms	60×	body	2560	valid
128.0ms	36×	body	5120	valid
117.0ms	146×	body	1280	valid
35.0ms	67×	body	640	valid
9.0ms	26×	body	320	valid
7.0ms	59×	body	80	valid
3.0ms	12×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	44	13
1	147	13
2	857	12
3	5002	11

prune18.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 41.1b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
20.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.0b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

337×	`add-exp-log`
220×	`prod-exp`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
24×	`associate-l`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
12×	`cbrt-undiv`
5×	`pow1` `associate-*r/`
4×	`associate-r` `add-log-exp` `sqr-pow`
3×	`tan-quot` `pow-unpow` `div-inv` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 179

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
5.0ms	(* (pow t 3.0) (tan k))
17.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
11.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ k t) 2.0)
52.0ms	(* (pow t 3.0) (tan k))
109.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
68.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify44.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1123	2068
1	5002	1738

prune305.0ms

Filtered

93 candidates to 191 candidates (-105.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	178	13	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	179	14	193

Merged error: 31.7b

Counts

193 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (pow t 3.0) (tan k))
16.6b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
19.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
20.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

1610×	`add-exp-log`
1168×	`prod-exp`
346×	`div-exp`
341×	`pow-exp`
205×	`pow-to-exp`
95×	`add-cbrt-cube`
55×	`cbrt-unprod`
41×	`associate-l`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`cbrt-undiv`
9×	`associate-*r/`
5×	`associate-r`
4×	`tan-quot` `pow1` `add-log-exp` `sqr-pow`
3×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 408

Calls

4 calls:

6.0ms	(* (pow t 3.0) (tan k))
20.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
11.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
29.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (pow t 3.0) (tan k))
67.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
67.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
116.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

simplify83.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1771	6487
1	5001	5612

prune382.0ms

Filtered

109 candidates to 420 candidates (-285.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	416	4	420
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	420	14	434

Merged error: 31.5b

Counts

434 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (* l l) (sin k))
16.6b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
19.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
19.6b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

1610×	`add-exp-log`
1029×	`prod-exp`
485×	`div-exp`
340×	`pow-exp`
204×	`pow-to-exp`
98×	`add-cbrt-cube`
48×	`cbrt-unprod`
42×	`associate-l`
30×	`add-sqr-sqrt`
28×	`times-frac`
26×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
24×	`cbrt-undiv`
9×	`associate-r/` `associate-r*`
6×	`pow1`
5×	`div-inv`
4×	`add-log-exp`
3×	`tan-quot` `associate-/r` `-commutative`
2×	`unswap-sqr` `sqr-pow`
1×	`frac-times` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r/` `associate-/l`

Counts

4 → 418

Calls

4 calls:

4.0ms	(/ (* l l) (sin k))
16.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
10.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
28.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (* l l) (sin k))
68.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
67.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
197.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))

simplify80.0ms

Algorithm

egg-herbie

Counts

430 → 430

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1730	6648
1	5001	5458

prune359.0ms

Filtered

106 candidates to 430 candidates (-305.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	423	7	430
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	428	16	444

Merged error: 26.0b

Counts

444 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (pow t 3.0) (tan k))
16.6b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
19.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
19.6b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ l (/ (sin k) l)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

1610×	`add-exp-log`
961×	`prod-exp`
553×	`div-exp`
341×	`pow-exp`
205×	`pow-to-exp`
95×	`add-cbrt-cube`
90×	`times-frac`
74×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
49×	`associate-r` `associate-l`
43×	`cbrt-unprod`
30×	`unpow-prod-down`
27×	`cbrt-undiv`
10×	`associate-*r/`
7×	`div-inv`
6×	`pow1` `unswap-sqr`
4×	`tan-quot` `*-commutative` `add-log-exp` `sqr-pow`
2×	`associate-/r/`
1×	`frac-times` `pow-prod-down` `associate-*l/`

Counts

4 → 461

Calls

4 calls:

5.0ms	(* (pow t 3.0) (tan k))
19.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
11.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
38.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ l (/ (sin k) l)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (pow t 3.0) (tan k))
68.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
66.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
193.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ l (/ (sin k) l)))

simplify98.0ms

Algorithm

egg-herbie

Counts

473 → 473

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	2087	7350
1	5002	6343

prune416.0ms

Filtered

156 candidates to 473 candidates (-203.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	465	8	473
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	469	20	489

Merged error: 24.2b

Counts

489 → 20

regimes1.1s

Accuracy

26.1% (9.6b remaining)

Error of 32.6b against oracle of 23.1b and baseline of 36.0b

bsearch448.0ms

Steps

Iters	Range	Point
9	2.3357597858079006e-109	8.637160713740627e-103	2.606794591212939e-108
11	-1.1291289217649937e-284	-3.3586306881229277e-306	-3.40834702810466e-306
6	-2.2117070478415092e-92	-5.358527878644732e-93	-5.419787240211035e-93

Iters

Range

Point

2.3357597858079006e-109

8.637160713740627e-103

2.606794591212939e-108

-1.1291289217649937e-284

-3.3586306881229277e-306

-3.40834702810466e-306

-2.2117070478415092e-92

-5.358527878644732e-93

-5.419787240211035e-93

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	110	82
1	110	82

end0.0ms

sample14.4s

Algorithm

intervals

Results

4.5s	2309×	body	2560	valid
4.1s	956×	body	5120	valid
3.3s	4088×	body	1280	valid
1.3s	2497×	body	640	valid
362.0ms	956×	body	320	valid
253.0ms	2053×	body	80	valid
128.0ms	471×	body	160	valid

Details

sample465.0ms

simplify28.0ms

prune18.0ms

localize19.0ms

rewrite48.0ms

series242.0ms

simplify44.0ms

prune305.0ms

localize20.0ms

rewrite106.0ms

series302.0ms

simplify83.0ms

prune382.0ms

localize20.0ms

rewrite100.0ms

series342.0ms

simplify80.0ms

prune359.0ms

localize21.0ms

rewrite124.0ms

series378.0ms

simplify98.0ms

prune416.0ms

regimes1.1s

bsearch448.0ms

simplify2.0ms

end0.0ms

sample14.4s

Profiling