Details

sample63.0ms

Algorithm

intervals

Results

20.0ms	41×	body	1280	valid
16.0ms	40×	body	640	valid
10.0ms	142×	body	80	valid
5.0ms	21×	body	320	valid
2.0ms	12×	body	160	valid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	43	9
2	93	9
3	174	9
4	269	9
5	288	9
6	288	9

prune3.0ms

Filtered

1 candidates to 0 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: 13.2b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
13.1b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

193×	`associate-l`
181×	`add-sqr-sqrt`
167×	`times-frac`
106×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-*l/`
43×	`associate-/l*`
37×	`unswap-sqr`
33×	`associate-r`
31×	`add-exp-log` `add-cbrt-cube`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
11×	`*-commutative`
10×	`pow1`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `div-inv`
4×	`frac-2neg` `pow-prod-down` `clear-num`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`

Counts

3 → 266

Calls

3 calls:

20.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
11.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
31.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series204.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
99.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify63.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1002	3265
1	5001	2802

prune1.0s

Filtered

275 candidates to 219 candidates (79.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	264	11	275
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	265	11	276

Merged error: 0.0b

Counts

276 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (* x 0.5)) (sqrt (/ 8.0 3.0)))
0.1b	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
0.2b	(/ (sin x) (sin (* x 0.5)))
0.3b	(* (* (sin (* x 0.5)) (sqrt (/ 8.0 3.0))) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

1216×	`times-frac`
883×	`add-sqr-sqrt`
742×	`*-un-lft-identity`
741×	`add-cube-cbrt`
541×	`sqrt-prod`
486×	`sqrt-div`
428×	`associate-*r/`
369×	`frac-times`
348×	`associate-/l*`
314×	`associate-/r*`
253×	`associate-r`
99×	`associate-/l/`
85×	`div-inv`
69×	`clear-num`
68×	`frac-2neg`
55×	`unswap-sqr`
34×	`add-exp-log` `add-cbrt-cube`
33×	`associate-l`
18×	`associate-/r/`
11×	`pow1`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
9×	`associate-*l/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`un-div-inv`

Counts

4 → 1065

Calls

4 calls:

13.0ms	(* (sin (* x 0.5)) (sqrt (/ 8.0 3.0)))
22.0ms	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
6.0ms	(/ (sin x) (sin (* x 0.5)))
143.0ms	(* (* (sin (* x 0.5)) (sqrt (/ 8.0 3.0))) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin (* x 0.5)) (sqrt (/ 8.0 3.0)))
107.0ms	(/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5))))
48.0ms	(/ (sin x) (sin (* x 0.5)))
176.0ms	(* (* (sin (* x 0.5)) (sqrt (/ 8.0 3.0))) (/ (sqrt (/ 8.0 3.0)) (/ (sin x) (sin (* x 0.5)))))

simplify265.0ms

Algorithm

egg-herbie

Counts

1077 → 1077

Iterations

Useful iterations: 1 (104.0ms)

Iter	Nodes	Cost
0	4673	18209
1	5002	17754

prune3.5s

Filtered

1077 candidates to 763 candidates (70.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	1070	7	1077
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	1080	8	1088

Merged error: 0b

Counts

1088 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sin (* x 0.5)) (* (sqrt (/ 8.0 3.0)) (sqrt (/ (sqrt 8.0) (* (cbrt 3.0) (cbrt 3.0)))))) (/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0)))))
0.7b	(/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0))))
1.0b	(/ (sqrt 8.0) (cbrt 3.0))
1.0b	(/ (sqrt 8.0) (* (cbrt 3.0) (cbrt 3.0)))

rewrite59.6s

Algorithm

rewrite-expression-head

Rules

823265×	`times-frac`
593457×	`add-sqr-sqrt`
537380×	`sqrt-prod`
277187×	`add-cube-cbrt` `*-un-lft-identity`
263547×	`associate-r`
173678×	`cbrt-prod`
146555×	`unswap-sqr`
34842×	`swap-sqr`
31947×	`associate-l`
19462×	`div-inv`
11597×	`*-commutative`
5508×	`sqrt-div`
4883×	`associate-/r/`
3010×	`associate-/r*`
2460×	`associate-/l*`
405×	`associate-*r/`
387×	`associate-/l/`
375×	`frac-2neg` `clear-num`
324×	`frac-times`
58×	`add-cbrt-cube`
52×	`add-exp-log`
28×	`cbrt-undiv`
24×	`div-exp`
13×	`cbrt-unprod`
10×	`prod-exp`
9×	`associate-*l/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`

Counts

4 → 186678

Calls

4 calls:

4.7s	(/ (* (sin (* x 0.5)) (* (sqrt (/ 8.0 3.0)) (sqrt (/ (sqrt 8.0) (* (cbrt 3.0) (cbrt 3.0)))))) (/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0)))))
30.0ms	(/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0))))
5.0ms	(/ (sqrt 8.0) (cbrt 3.0))
15.0ms	(/ (sqrt 8.0) (* (cbrt 3.0) (cbrt 3.0)))

series592.0ms

Counts

4 → 8

Calls

4 calls:

397.0ms	(/ (* (sin (* x 0.5)) (* (sqrt (/ 8.0 3.0)) (sqrt (/ (sqrt 8.0) (* (cbrt 3.0) (cbrt 3.0)))))) (/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0)))))
193.0ms	(/ (/ (sin x) (sin (* x 0.5))) (sqrt (/ (sqrt 8.0) (cbrt 3.0))))
0.0ms	(/ (sqrt 8.0) (cbrt 3.0))
0.0ms	(/ (sqrt 8.0) (* (cbrt 3.0) (cbrt 3.0)))

simplify1.7m

Algorithm

egg-herbie

Counts

186686 → 186686

Iterations

Useful iterations: 0 (6.1s)

Iter	Nodes	Cost
0	113963	9334930

prune7.2m

Filtered: 186686 candidates to 87160 candidates (46.7%)