Details

sample381.0ms

Algorithm

intervals

Results

129.0ms	71×	body	2560	valid
84.0ms	113×	body	1280	valid
80.0ms	29×	body	5120	valid
43.0ms	86×	body	640	valid
13.0ms	38×	body	320	valid
8.0ms	66×	body	80	valid
3.0ms	14×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (25.0ms)

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: 41.2b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.6b	(* (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)))
31.3b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite50.0ms

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)))

series933.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ k t) 2.0)
231.0ms	(* (pow t 3.0) (tan k))
383.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
252.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify141.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (22.0ms)

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

prune408.0ms

Filtered

191 candidates to 88 candidates (46.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	187	4	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	188	5	193

Merged error: 20.2b

Counts

193 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.8b	(* (pow k 2.0) (pow t 1.0))
15.6b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite104.0ms

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))
21.0ms	(* (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:

336.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
89.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
328.0ms	(* (pow k 2.0) (pow t 1.0))
646.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify160.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1316	7192
1	4162	7023
2	5002	7016

prune544.0ms

Filtered

612 candidates to 99 candidates (16.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	605	7	612
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	607	10	617

Merged error: 16.1b

Counts

617 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
1.4b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.6b	(* (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)))

rewrite283.0ms

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)
11.0ms	(/ 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))
38.0ms	(* (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:

19.0ms	(pow (sin k) 2)
344.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
90.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
658.0ms	(* (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)))

simplify305.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	1742	23541
1	4574	19109
2	5002	17856

prune522.0ms

Filtered

1472 candidates to 86 candidates (5.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	1465	7	1472
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	1470	12	1482

Merged error: 12.9b

Counts

1482 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
1.2b	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
1.4b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
15.6b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

29090×	`times-frac`
11907×	`add-sqr-sqrt`
11454×	`add-cube-cbrt` `*-un-lft-identity`
10485×	`add-exp-log`
7939×	`unpow-prod-down`
6490×	`div-exp`
5244×	`prod-exp`
4340×	`pow-exp`
3948×	`cbrt-prod`
3557×	`associate-r`
2573×	`pow-to-exp`
1377×	`sqr-pow`
668×	`unpow2`
620×	`rec-exp` `1-exp`
329×	`associate-/l*`
320×	`div-inv`
118×	`associate-/r*`
108×	`unswap-sqr`
56×	`add-cbrt-cube`
29×	`cbrt-undiv`
24×	`associate-/r/`
11×	`associate-l`
8×	`cbrt-unprod`
5×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-flip` `associate-r/` `-commutative` `associate-/l/` `inv-pow`

Counts

4 → 9995

Calls

4 calls:

24.0ms	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
346.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.0s	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
83.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
334.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
645.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

simplify2.7s

Algorithm

egg-herbie

Counts

10007 → 10007

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	10863	273541

prune53.8s

Filtered

10007 candidates to 6986 candidates (69.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	9991	16	10007
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	9998	21	10019

Merged error: 7.7b

Counts

10019 → 21

Details

sample381.0ms

simplify26.0ms

prune11.0ms

localize23.0ms

rewrite50.0ms

series933.0ms

simplify141.0ms

prune408.0ms

localize25.0ms

rewrite104.0ms

series1.4s

simplify160.0ms

prune544.0ms

localize24.0ms

rewrite283.0ms

series1.1s

simplify305.0ms

prune522.0ms

localize28.0ms

rewrite3.1s

series1.2s

simplify2.7s

prune53.8s

regimes580.0ms

bsearch6.0ms

Profiling