Details

analyze2.7s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.5%	0.5%	11
0%	99.1%	0.9%	12
0.4%	97.3%	2.3%	13
0.7%	95.8%	3.5%	14

sample844.0ms

Algorithm

intervals

Results

88.0ms	106×	body	1280	valid
51.0ms	36×	body	2560	valid
35.0ms	64×	body	640	valid
8.0ms	21×	body	320	valid
3.0ms	21×	body	80	valid
2.0ms	1×	body	5120	valid
2.0ms	7×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4842	21
1	4842	21

prune15.0ms

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: 37.9b

Counts

2 → 2

localize72.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
4.8b	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
9.4b	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
28.8b	(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

356×	`add-exp-log`
241×	`prod-exp`
74×	`add-cbrt-cube`
69×	`div-exp`
48×	`pow-exp`
40×	`cbrt-unprod`
36×	`pow-to-exp`
18×	`associate-l`
14×	`add-sqr-sqrt`
12×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
7×	`associate-*r/`
6×	`times-frac`
5×	`associate-r` `associate-*l/`
4×	`pow-prod-down` `add-log-exp`
3×	`tan-quot` `unpow-prod-down` `-commutative` `associate-/l`
2×	`associate-/r/` `div-inv`
1×	`frac-2neg` `clear-num` `associate-/r*` `unswap-sqr` `sqr-pow`

Counts

4 → 168

Calls

4 calls:

13.0ms	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
17.0ms	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
19.0ms	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
13.0ms	(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
125.0ms	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
163.0ms	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
77.0ms	(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4993	3531
1	4993	3531

prune276.0ms

Filtered

82 candidates to 180 candidates (-119.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	170	10	180
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	171	11	182

Merged error: 12.7b

Counts

182 → 11

localize81.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (/ (cos k) (pow (sin k) 2)) l)
4.8b	(* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0))
4.8b	(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))))
7.1b	(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))

rewrite436.0ms

Algorithm

rewrite-expression-head

Rules

6676×	`add-exp-log`
4537×	`prod-exp`
4223×	`pow-exp`
2300×	`div-exp`
1455×	`pow-to-exp`
572×	`unpow-prod-down`
412×	`add-sqr-sqrt`
392×	`times-frac`
183×	`associate-l`
152×	`sqr-pow`
137×	`add-cube-cbrt` `*-un-lft-identity`
119×	`unswap-sqr`
43×	`add-cbrt-cube`
30×	`associate-r`
23×	`cbrt-unprod`
11×	`pow1`
10×	`div-inv`
6×	`associate-*l/`
4×	`cbrt-undiv` `pow-prod-down` `*-commutative` `unpow2` `add-log-exp`
2×	`associate-*r/`

Counts

4 → 1673

Calls

4 calls:

9.0ms	(* (/ (cos k) (pow (sin k) 2)) l)
72.0ms	(* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0))
68.0ms	(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))))
28.0ms	(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))

series293.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (/ (cos k) (pow (sin k) 2)) l)
55.0ms	(* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0))
101.0ms	(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))))
116.0ms	(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))

simplify365.0ms

Algorithm

egg-herbie

Counts

1685 → 1685

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5155	53347

prune3.2s

Filtered

372 candidates to 1685 candidates (-353.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	1675	10	1685
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	1681	15	1696

Merged error: 8.2b

Counts

1696 → 15

localize87.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
1.2b	(* (/ (cos k) (pow (sin k) 2)) l)
4.8b	(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))))
7.1b	(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))

rewrite5.3s

Algorithm

rewrite-expression-head

Rules

101846×	`add-exp-log`
71721×	`prod-exp`
65298×	`pow-exp`
43941×	`div-exp`
21908×	`pow-to-exp`
6900×	`1-exp`
38×	`add-cbrt-cube`
36×	`add-sqr-sqrt`
32×	`associate-l`
28×	`times-frac`
24×	`add-cube-cbrt` `*-un-lft-identity`
21×	`cbrt-unprod`
14×	`unpow-prod-down`
12×	`pow1`
9×	`associate-r`
6×	`sqr-pow`
5×	`associate-*l/` `unpow2` `unswap-sqr`
4×	`pow-prod-down` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `*-commutative`
2×	`associate-*r/`
1×	`pow-pow` `div-inv`

Counts

4 → 15090

Calls

4 calls:

3.0ms	(pow (sin k) 2)
9.0ms	(* (/ (cos k) (pow (sin k) 2)) l)
682.0ms	(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))))
196.0ms	(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))

series238.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (sin k) 2)
20.0ms	(* (/ (cos k) (pow (sin k) 2)) l)
101.0ms	(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))))
112.0ms	(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))

simplify4.7s

Algorithm

egg-herbie

Counts

15102 → 15102

Iterations

Useful iterations: 0 (336.0ms)

Iter	Nodes	Cost
0	5031	831684

prune54.0s

Filtered

2789 candidates to 15102 candidates (-441.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	15094	8	15102
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	15100	17	15117

Merged error: 4.4b

Counts

15117 → 17

localize91.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
1.2b	(* (/ (cos k) (pow (sin k) 2)) l)
2.3b	(* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))
4.8b	(* l (* 2.0 (* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))))

rewrite5.3s

Algorithm

rewrite-expression-head

Rules

117988×	`add-exp-log`
89458×	`pow-exp`
84493×	`prod-exp`
48953×	`div-exp`
26234×	`pow-to-exp`
7020×	`1-exp`
50×	`add-cbrt-cube`
36×	`add-sqr-sqrt`
32×	`associate-l`
31×	`cbrt-unprod`
28×	`times-frac`
24×	`add-cube-cbrt` `*-un-lft-identity`
14×	`unpow-prod-down`
12×	`pow1`
9×	`associate-r`
7×	`associate-*l/`
6×	`sqr-pow`
5×	`unpow2` `unswap-sqr`
4×	`pow-prod-down` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `*-commutative`
2×	`associate-*r/`
1×	`pow-pow` `div-inv`

Counts

4 → 17896

Calls

4 calls:

3.0ms	(pow (sin k) 2)
10.0ms	(* (/ (cos k) (pow (sin k) 2)) l)
161.0ms	(* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))
699.0ms	(* l (* 2.0 (* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (sin k) 2)
21.0ms	(* (/ (cos k) (pow (sin k) 2)) l)
111.0ms	(* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))
103.0ms	(* l (* 2.0 (* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))))

simplify6.4s

Algorithm

egg-herbie

Counts

17908 → 17908

Iterations

Useful iterations: 0 (439.0ms)

Iter	Nodes	Cost
0	5117	1019930

prune1.1min

Filtered: 3227 candidates to 17908 candidates (-454.9%)

Details

analyze2.7s

sample844.0ms

simplify37.0ms

prune15.0ms

localize72.0ms

rewrite73.0ms

series471.0ms

simplify70.0ms

prune276.0ms

localize81.0ms

rewrite436.0ms

series293.0ms

simplify365.0ms

prune3.2s

localize87.0ms

rewrite5.3s

series238.0ms

simplify4.7s

prune54.0s

localize91.0ms

rewrite5.3s

series238.0ms

simplify6.4s

prune1.1min

Profiling