Details

sample368.0ms

Algorithm

intervals

Results

129.0ms	79×	body	2560	valid
93.0ms	133×	body	1280	valid
67.0ms	22×	body	5120	valid
40.0ms	81×	body	640	valid
10.0ms	30×	body	320	valid
7.0ms	55×	body	80	valid
2.0ms	10×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (27.0ms)

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: 38.7b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
1.1b	(* (pow t 3.0) (tan k))
21.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.4b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

392×	`add-exp-log`
265×	`prod-exp`
74×	`div-exp` `add-cbrt-cube`
61×	`pow-exp`
41×	`pow-to-exp`
40×	`cbrt-unprod`
25×	`associate-l`
21×	`add-sqr-sqrt`
17×	`unpow-prod-down`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-undiv`
10×	`times-frac`
7×	`associate-r/` `associate-r*`
6×	`pow1`
4×	`tan-quot` `add-log-exp`
3×	`*-commutative` `unswap-sqr` `sqr-pow`
2×	`associate-*l/` `div-inv`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `associate-/l`

Counts

4 → 185

Calls

4 calls:

13.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
6.0ms	(* (pow t 3.0) (tan k))
19.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
14.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.1s

Counts

4 → 12

Calls

4 calls:

276.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
237.0ms	(* (pow t 3.0) (tan k))
369.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
251.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify139.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	908	2174
1	4774	1790
2	5002	1790

prune373.0ms

Filtered

197 candidates to 80 candidates (40.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	189	8	197
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	190	9	199

Merged error: 22.4b

Counts

199 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.4b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.5b	(* (pow k 2.0) (pow t 1.0))
16.4b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite105.0ms

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))
22.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

357.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
92.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
352.0ms	(* (pow k 2.0) (pow t 1.0))
673.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify155.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (90.0ms)

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

prune576.0ms

Filtered

612 candidates to 99 candidates (16.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	602	10	612
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	609	12	621

Merged error: 19.2b

Counts

621 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.7b	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
7.5b	(* (pow k 2.0) (pow t 1.0))
16.4b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

3129×	`times-frac`
1393×	`add-sqr-sqrt`
1326×	`add-cube-cbrt` `*-un-lft-identity`
829×	`add-exp-log`
460×	`div-exp`
413×	`associate-r`
336×	`prod-exp`
269×	`pow-exp`
137×	`associate-/l*`
119×	`pow-to-exp`
95×	`div-inv`
60×	`rec-exp` `1-exp`
45×	`add-cbrt-cube`
24×	`unpow-prod-down` `unswap-sqr`
22×	`cbrt-undiv`
18×	`associate-l`
14×	`sqr-pow`
7×	`associate-/r/` `cbrt-unprod`
5×	`pow1`
4×	`associate-/r*` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `associate-/l/` `inv-pow`

Counts

4 → 1261

Calls

4 calls:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
37.0ms	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
10.0ms	(* (pow k 2.0) (pow t 1.0))
156.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

series1.5s

Counts

4 → 12

Calls

4 calls:

356.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
92.0ms	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
346.0ms	(* (pow k 2.0) (pow t 1.0))
704.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

simplify213.0ms

Algorithm

egg-herbie

Counts

1273 → 1273

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5001	21684

prune5.6s

Filtered

1273 candidates to 983 candidates (77.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	1261	12	1273
Fresh	9	2	11
Picked	0	1	1
Done	0	0	0
Total	1270	15	1285

Merged error: 12.9b

Counts

1285 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.3b	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l))) (/ (/ (cos k) (/ 1 l)) (sin k)))
6.3b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l)))
7.5b	(* (pow k 2.0) (pow t 1.0))

rewrite418.0ms

Algorithm

rewrite-expression-head

Rules

9054×	`add-exp-log`
5169×	`div-exp`
4368×	`prod-exp`
2425×	`pow-exp`
1194×	`rec-exp` `1-exp`
955×	`pow-to-exp`
420×	`times-frac`
247×	`add-sqr-sqrt`
204×	`*-un-lft-identity`
198×	`add-cube-cbrt`
187×	`associate-r`
100×	`add-cbrt-cube`
41×	`cbrt-undiv`
33×	`cbrt-unprod`
24×	`unpow-prod-down` `unswap-sqr`
19×	`associate-l` `div-inv`
14×	`sqr-pow`
7×	`pow1`
4×	`associate-*r/` `associate-/r/` `add-log-exp`
3×	`un-div-inv` `-commutative` `associate-/l`
2×	`frac-times` `associate-*l/`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `inv-pow`

Counts

4 → 1965

Calls

4 calls:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
75.0ms	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l))) (/ (/ (cos k) (/ 1 l)) (sin k)))
33.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l)))
8.0ms	(* (pow k 2.0) (pow t 1.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

355.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
679.0ms	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l))) (/ (/ (cos k) (/ 1 l)) (sin k)))
431.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l)))
350.0ms	(* (pow k 2.0) (pow t 1.0))

simplify332.0ms

Algorithm

egg-herbie

Counts

1977 → 1977

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5001	34219

prune1.6s

Filtered

1977 candidates to 293 candidates (14.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	1967	10	1977
Fresh	8	5	13
Picked	1	0	1
Done	0	1	1
Total	1976	16	1992

Merged error: 7.2b

Counts

1992 → 16

Details

sample368.0ms

simplify28.0ms

prune11.0ms

localize20.0ms

rewrite64.0ms

series1.1s

simplify139.0ms

prune373.0ms

localize27.0ms

rewrite105.0ms

series1.5s

simplify155.0ms

prune576.0ms

localize24.0ms

rewrite354.0ms

series1.5s

simplify213.0ms

prune5.6s

localize25.0ms

rewrite418.0ms

series1.8s

simplify332.0ms

prune1.6s

regimes299.0ms

bsearch5.0ms

Profiling