Details

sample525.0ms

Algorithm

intervals

Results

166.0ms	30×	body	5120	valid
155.0ms	65×	body	2560	valid
102.0ms	132×	body	1280	valid
49.0ms	76×	body	640	valid
15.0ms	42×	body	320	valid
8.0ms	65×	body	80	valid
3.0ms	13×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (24.0ms)

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

prune19.0ms

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: 41.4b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
19.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.2b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite53.0ms

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))
18.0ms	(/ (* 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)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ k t) 2.0)
56.0ms	(* (pow t 3.0) (tan k))
114.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
69.0ms	(* (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

prune315.0ms

Filtered

191 candidates to 93 candidates (51.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	180	11	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	181	12	193

Merged error: 28.4b

Counts

193 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (pow t 3.0) (tan k))
13.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
19.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
20.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite109.0ms

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))
19.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (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)))
11.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (pow t 3.0) (tan k))
82.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
114.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
76.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify82.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1771	6487
1	5002	5612

prune425.0ms

Filtered

420 candidates to 110 candidates (73.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	414	6	420
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	417	15	432

Merged error: 28.4b

Counts

432 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

1.9b	(/ (* l l) (sin k))
13.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
18.7b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
20.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite107.0ms

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:

5.0ms	(/ (* l l) (sin k))
18.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
29.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
11.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* l l) (sin k))
71.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
204.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
77.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify84.0ms

Algorithm

egg-herbie

Counts

430 → 430

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1730	6648
1	5001	5458

prune399.0ms

Filtered

430 candidates to 107 candidates (75.1%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	420	10	430
Fresh	7	7	14
Picked	0	1	1
Done	0	0	0
Total	427	18	445

Merged error: 23.9b

Counts

445 → 18

localize23.0ms

Local error

Found 4 expressions with local error:

1.9b	(/ (* l l) (sin k))
14.5b	(* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
15.2b	(* (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
20.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

2259×	`add-exp-log`
1240×	`prod-exp`
875×	`div-exp`
338×	`pow-exp`
217×	`add-cbrt-cube`
207×	`pow-to-exp`
178×	`times-frac`
134×	`associate-l`
106×	`add-sqr-sqrt`
105×	`cbrt-unprod`
102×	`add-cube-cbrt` `*-un-lft-identity`
91×	`unpow-prod-down`
66×	`cbrt-undiv`
54×	`sqrt-prod`
11×	`pow1` `div-inv`
10×	`associate-*r/`
9×	`associate-r`
7×	`sqr-pow`
6×	`frac-times`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
3×	`associate-/r` `-commutative`
2×	`tan-quot` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 589

Calls

4 calls:

5.0ms	(/ (* l l) (sin k))
19.0ms	(* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
43.0ms	(* (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
11.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* l l) (sin k))
195.0ms	(* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
199.0ms	(* (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
74.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify132.0ms

Algorithm

egg-herbie

Counts

601 → 601

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	2394	11773
1	5001	10742

prune817.0ms

Filtered

601 candidates to 194 candidates (67.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	594	7	601
Fresh	4	12	16
Picked	1	0	1
Done	0	1	1
Total	599	20	619

Merged error: 22.0b

Counts

619 → 20

regimes1.3s

Accuracy

42.1% (5.9b remaining)

Error of 28.4b against oracle of 22.5b and baseline of 32.7b

bsearch506.0ms

Steps

Iters	Range	Point
10	2.146598932358039e-112	9.794742891101381e-98	1.60231479643995e-108
10	-1.2128248765666837e-307	1.3459246724270578e-298	-7.30602271957343e-309
10	-3.722248476023086e-102	-4.3018125905191136e-113	-2.7119492113822656e-108

Iters

Range

Point

2.146598932358039e-112

9.794742891101381e-98

1.60231479643995e-108

-1.2128248765666837e-307

1.3459246724270578e-298

-7.30602271957343e-309

-3.722248476023086e-102

-4.3018125905191136e-113

-2.7119492113822656e-108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	80
1	91	80
2	91	80

end0.0ms

sample15.1s

Algorithm

intervals

Results

4.6s	2254×	body	2560	valid
4.5s	990×	body	5120	valid
3.3s	4099×	body	1280	valid
1.3s	2480×	body	640	valid
384.0ms	994×	body	320	valid
266.0ms	2028×	body	80	valid
116.0ms	458×	body	160	valid

Details

sample525.0ms

simplify26.0ms

prune19.0ms

localize19.0ms

rewrite53.0ms

series252.0ms

simplify44.0ms

prune315.0ms

localize22.0ms

rewrite109.0ms

series325.0ms

simplify82.0ms

prune425.0ms

localize21.0ms

rewrite107.0ms

series361.0ms

simplify84.0ms

prune399.0ms

localize23.0ms

rewrite149.0ms

series479.0ms

simplify132.0ms

prune817.0ms

regimes1.3s

bsearch506.0ms

simplify2.0ms

end0.0ms

sample15.1s

Profiling