Details

sample849.0ms

Algorithm

intervals

Results

227.0ms	24×	body	320	valid
167.0ms	96×	body	1280	valid
155.0ms	40×	body	2560	valid
56.0ms	63×	body	640	valid
13.0ms	19×	body	160	valid
4.0ms	14×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	19
3	19
2	17
1	13
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.8b	(- x (tan x))
1.9b	(- x (sin x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `insert-posit16`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

18.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series206.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(/ (- x (sin x)) (- x (tan x)))
70.0ms	(- x (tan x))
46.0ms	(- x (sin x))

simplify1.0s

Counts

92 → 92

Iterations

Iter	Nodes
3	2994
2	1005
1	375
0	160

prune855.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
0.0b	(/ (- x (tan x)) (- x (sin x)))
1.8b	(- x (tan x))
1.9b	(- x (sin x))

rewrite545.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
200×	`add-sqr-sqrt` `*-un-lft-identity`
92×	`add-cube-cbrt`
54×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`flip3--` `div-exp` `flip--` `associate-/l*` `add-log-exp`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`rec-exp` `clear-num` `sub-neg` `frac-2neg` `diff-log` `1-exp` `associate-/l/`
1×	`div-sub` `pow-flip` `inv-pow`

Counts

4 → 232

Calls

4 calls:

501.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
27.0ms	(/ (- x (tan x)) (- x (sin x)))
4.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series373.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
115.0ms	(/ (- x (tan x)) (- x (sin x)))
88.0ms	(- x (tan x))
61.0ms	(- x (sin x))

simplify757.0ms

Counts

244 → 244

Iterations

Iter	Nodes
2	2469
1	827
0	324

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
0.1b	(log (exp (/ 1 (/ (- x (tan x)) (- x (sin x))))))
1.8b	(- x (tan x))
1.9b	(- x (sin x))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

361×	`times-frac`
290×	`add-sqr-sqrt` `*-un-lft-identity`
146×	`add-cube-cbrt`
99×	`log-pow`
98×	`exp-prod`
72×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-/r*`
16×	`associate-/r/`
15×	`add-exp-log`
9×	`flip3--` `add-cbrt-cube` `div-inv` `flip--`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
4×	`insert-posit16`
3×	`cbrt-undiv` `log-prod` `associate-/l*`
2×	`rec-exp` `sub-neg` `diff-log` `1-exp`
1×	`clear-num` `frac-2neg` `rem-log-exp` `pow-flip` `inv-pow`

Counts

4 → 290

Calls

4 calls:

32.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
41.0ms	(log (exp (/ 1 (/ (- x (tan x)) (- x (sin x))))))
4.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series342.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
88.0ms	(log (exp (/ 1 (/ (- x (tan x)) (- x (sin x))))))
92.0ms	(- x (tan x))
43.0ms	(- x (sin x))

simplify836.0ms

Counts

302 → 302

Iterations

Iter	Nodes
2	2266
1	888
0	450

prune3.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(/ (/ (sin x) x) (cos x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

300×	`times-frac`
172×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
52×	`associate-/l*`
24×	`add-cbrt-cube` `add-exp-log`
20×	`div-inv`
12×	`cbrt-undiv` `associate-/r*` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp` `associate-/l/`

Counts

4 → 284

Calls

4 calls:

20.0ms	(/ (/ (sin x) x) (cos x))
21.0ms	(/ (/ (sin x) x) (cos x))
14.0ms	(/ (/ (sin x) x) (cos x))
15.0ms	(/ (/ (sin x) x) (cos x))

series300.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (/ (sin x) x) (cos x))
69.0ms	(/ (/ (sin x) x) (cos x))
82.0ms	(/ (/ (sin x) x) (cos x))
80.0ms	(/ (/ (sin x) x) (cos x))

simplify1.1s

Counts

296 → 296

Iterations

Iter	Nodes
3	3342
2	917
1	357
0	161

prune3.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes57.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.7b

bsearch184.0ms

Steps

Iters	Range		Point
9	0.08974485042074802	9369.000823706243	2.4331115039478592
8	-15521.296822102611	-0.2777104116290821	-2.4489045375766514

simplify20.0ms

Iterations

Iter	Nodes
2	37
1	37
0	26

end0.0ms

sample16.3s

Algorithm

intervals

Results

6.8s	1630×	body	2560	valid
6.1s	2747×	body	1280	valid
2.1s	1896×	body	640	valid
734.0ms	931×	body	320	valid
216.0ms	424×	body	160	valid
94.0ms	372×	body	80	valid