Details

sample434.0ms

Algorithm

intervals

Results

135.0ms	66×	body	2560	valid
114.0ms	142×	body	1280	valid
98.0ms	27×	body	5120	valid
35.0ms	68×	body	640	valid
17.0ms	45×	body	320	valid
10.0ms	79×	body	80	valid
3.0ms	14×	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

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 37.4b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.0b	(* (pow t 3.0) (tan k))
18.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.6b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite54.0ms

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)
6.0ms	(* (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)))

series899.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ k t) 2.0)
233.0ms	(* (pow t 3.0) (tan k))
364.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
239.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify140.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	974	1954
1	4995	1620
2	5001	1620

prune400.0ms

Filtered

191 candidates to 88 candidates (46.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	183	8	191
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	185	8	193

Merged error: 19.5b

Counts

193 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.7b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.0b	(* (pow k 2.0) (pow t 1.0))
14.3b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
509×	`pow-to-exp`
140×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
29×	`unpow-prod-down`
25×	`add-cbrt-cube`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 600

Calls

4 calls:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms	(* (pow k 2.0) (pow t 1.0))
25.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

385.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
84.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
328.0ms	(* (pow k 2.0) (pow t 1.0))
620.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify154.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	1316	7194
1	4162	7025
2	5002	7018

prune564.0ms

Filtered

612 candidates to 100 candidates (16.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	602	10	612
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	608	12	620

Merged error: 15.6b

Counts

620 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.5b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.7b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.3b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `-commutative` `inv-pow`

Counts

4 → 1460

Calls

4 calls:

2.0ms	(pow (sin k) 2)
12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
41.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin k) 2)
344.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
88.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
654.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify299.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	1742	23543
1	4574	19111
2	5002	17858

prune528.0ms

Filtered

1472 candidates to 87 candidates (5.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	1464	8	1472
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	1471	13	1484

Merged error: 12.0b

Counts

1484 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (sin k))
0.5b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.3b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
14.3b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

3841×	`add-exp-log`
2622×	`prod-exp`
1370×	`div-exp`
1330×	`pow-exp`
679×	`pow-to-exp`
248×	`rec-exp` `1-exp`
99×	`times-frac`
80×	`add-sqr-sqrt`
65×	`add-cbrt-cube`
59×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
24×	`associate-l`
22×	`cbrt-undiv` `cbrt-unprod`
8×	`div-inv`
7×	`pow1` `unpow-prod-down`
6×	`associate-/l*` `unswap-sqr`
5×	`associate-*r/`
4×	`associate-/r*` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `pow-prod-down` `associate-/r/` `inv-pow` `sqr-pow`

Counts

4 → 931

Calls

4 calls:

4.0ms	(/ (cos k) (sin k))
12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
26.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
32.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.1s

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (cos k) (sin k))
350.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
90.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
666.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify386.0ms

Algorithm

egg-herbie

Counts

943 → 943

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	2147	15097
1	5002	12259

prune622.0ms

Filtered

943 candidates to 134 candidates (14.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	937	6	943
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	944	12	956

Merged error: 8.0b

Counts

956 → 12

regimes331.0ms

Accuracy

50.1% (3.6b remaining)

Error of 12.2b against oracle of 8.6b and baseline of 15.8b

bsearch1.6s

Steps

Iters	Range		Point
8	4.220887567316556e+155	7.597600850764516e+158	4.265978622843499e+155
9	1.9964502276303598e-140	5.387884190878717e-133	3.6607201827589383e-140
10	-5.1141962640879435e-120	-4.146171549153613e-130	-4.2051688155039255e-130
10	-6.750681421237088e+158	-7.8545803948048655e+146	-1.3290890488547693e+154

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	60	88
1	63	88
2	69	34
3	72	34
4	78	34
5	89	34
6	96	34
7	97	34
8	97	34

end0.0ms

sample14.2s

Algorithm

intervals

Results

4.4s	2226×	body	2560	valid
3.9s	947×	body	5120	valid
3.3s	4115×	body	1280	valid
1.4s	2528×	body	640	valid
390.0ms	1026×	body	320	valid
262.0ms	2056×	body	80	valid
106.0ms	419×	body	160	valid

Details

sample434.0ms

simplify28.0ms

prune11.0ms

localize18.0ms

rewrite54.0ms

series899.0ms

simplify140.0ms

prune400.0ms

localize22.0ms

rewrite110.0ms

series1.4s

simplify154.0ms

prune564.0ms

localize25.0ms

rewrite281.0ms

series1.1s

simplify299.0ms

prune528.0ms

localize24.0ms

rewrite204.0ms

series1.1s

simplify386.0ms

prune622.0ms

regimes331.0ms

bsearch1.6s

simplify5.0ms

end0.0ms

sample14.2s

Profiling