Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	51×	body	2560	valid
9.0ms	42×	body	1280	valid
7.0ms	51×	body	640	valid
2.0ms	24×	body	320	valid
2.0ms	69×	body	80	valid
1.0ms	19×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize10.0ms

Local error

Found 2 expressions with local error:

1.4b	(- 1.0 (cos x))
14.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
19.0ms	(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.4s

Counts

48 → 48

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	88	507
1	212	489
2	548	441
3	1500	441
done	5000	441

prune108.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
12.8b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

12.0ms	(* 1/720 (pow x 4))
12.0ms	(* 1/24 (pow x 2))
55.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series107.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 1/720 (pow x 4))
25.0ms	(* 1/24 (pow x 2))
46.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify1.7s

Counts

75 → 75

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	121	780
1	272	701
2	685	643
3	2993	629
done	5002	626

prune157.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
1.4b	(- 1.0 (cos x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

16.0ms	(/ (- 1.0 (cos x)) x)
40.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms	(- 1.0 (cos x))

series111.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (- 1.0 (cos x)) x)
43.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
23.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

123 → 123

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	189	1536
1	496	1379
2	1535	1227
done	5000	1226

prune222.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 x) (* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x)))
0.2b	(* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x))
1.4b	(- 1.0 (cos x))
1.4b	(- 1.0 (cos x))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
48×	`add-exp-log`
40×	`*-un-lft-identity`
37×	`times-frac`
30×	`add-cbrt-cube`
29×	`associate-r`
28×	`add-cube-cbrt`
25×	`sqrt-prod`
22×	`prod-exp`
21×	`associate-l`
12×	`sqrt-div` `cbrt-unprod`
11×	`pow1` `frac-times` `div-exp`
8×	`flip3--` `associate-*r/` `flip--` `add-log-exp`
7×	`associate-*l/`
6×	`cbrt-undiv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
4×	`pow-prod-down`
3×	`rec-exp` `1-exp`
2×	`sub-neg` `diff-log` `*-commutative` `div-inv`

Counts

4 → 141

Calls

4 calls:

67.0ms	(* (/ 1 x) (* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x)))
48.0ms	(* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x))
9.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series130.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (/ 1 x) (* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x)))
43.0ms	(* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x))
19.0ms	(- 1.0 (cos x))
20.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

153 → 153

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	229	2703
1	555	1942
2	1866	1658
done	5000	1626

prune285.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.2b

regimes126.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.0b

bsearch68.0ms

Steps

Iters	Range		Point
10	0.0001820196720056695	1126179.5725289274	0.034744172255630555
9	-76786.820650899	-0.0002772006047103471	-0.02623489072028306

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	50
1	39	50
done	39	50

end0.0ms

sample1.6s

Algorithm

intervals

Results

767.0ms	1714×	body	2560	valid
296.0ms	1271×	body	1280	valid
206.0ms	1449×	body	640	valid
90.0ms	911×	body	320	valid
73.0ms	2190×	body	80	valid
38.0ms	465×	body	160	valid