Details

sample100.0ms

Algorithm

intervals

Results

41.0ms	53×	body	2560	valid
18.0ms	42×	body	1280	valid
17.0ms	54×	body	640	valid
5.0ms	27×	body	320	valid
4.0ms	60×	body	80	valid
3.0ms	20×	body	160	valid

simplify19.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize15.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
15.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite67.0ms

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:

8.0ms	(- 1.0 (cos x))
57.0ms	(/ (- 1.0 (cos x)) (* x x))

series146.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(- 1.0 (cos x))
99.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.1s

Counts

48 → 48

Iterations

Useful iterations: 2 (108.0ms)

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

prune154.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.4b	(* 1/24 (pow x 2))
10.2b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite154.0ms

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:

22.0ms	(* 1/720 (pow x 4))
22.0ms	(* 1/24 (pow x 2))
106.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* 1/720 (pow x 4))
41.0ms	(* 1/24 (pow x 2))
56.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify2.7s

Counts

75 → 75

Iterations

Useful iterations: done (2.7s)

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

prune205.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-sqr-sqrt`
156×	`times-frac`
143×	`*-un-lft-identity`
104×	`sqrt-prod`
89×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 206

Calls

4 calls:

17.0ms	(/ (sqrt (- 1.0 (cos x))) x)
72.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
13.0ms	(- 1.0 (cos x))
20.0ms	(- 1.0 (cos x))

series219.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (sqrt (- 1.0 (cos x))) x)
62.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
25.0ms	(- 1.0 (cos x))
20.0ms	(- 1.0 (cos x))

simplify1.9s

Counts

218 → 218

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	231	4237
1	631	3612
2	2234	3070
done	5000	2909

prune579.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ 1 x) x)
1.9b	(- 1.0 (cos x))
16.2b	(* (- 1.0 (cos x)) (/ (/ 1 x) x))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

146×	`times-frac`
98×	`add-sqr-sqrt`
86×	`*-un-lft-identity`
81×	`add-cube-cbrt`
43×	`associate-r`
27×	`add-exp-log`
17×	`add-cbrt-cube`
13×	`associate-/l*`
12×	`div-exp`
10×	`div-inv`
8×	`pow1`
6×	`cbrt-undiv`
5×	`associate-l` `prod-exp` `add-log-exp` `unswap-sqr`
3×	`flip3--` `associate-/r*` `flip--` `cbrt-unprod`
2×	`frac-times` `rec-exp` `1-exp` `associate-*l/` `distribute-lft-out--` `difference-of-squares` `pow-div`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `inv-pow`

Counts

3 → 163

Calls

3 calls:

17.0ms	(/ (/ 1 x) x)
10.0ms	(- 1.0 (cos x))
76.0ms	(* (- 1.0 (cos x)) (/ (/ 1 x) x))

series97.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ (/ 1 x) x)
21.0ms	(- 1.0 (cos x))
57.0ms	(* (- 1.0 (cos x)) (/ (/ 1 x) x))

simplify1.5s

Counts

172 → 172

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	255	2186
1	584	1834
2	1430	1613
done	5001	1579

prune384.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.0b

regimes123.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.4b

bsearch107.0ms

Steps

Iters	Range		Point
9	0.0030847216915828425	5729.342694487068	0.03427235887658297
11	-30636816361710.875	-9.292394687435822e-10	-0.03169561986009639

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	25	41
1	34	32
done	34	32

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	1577×	body	2560	valid
512.0ms	1251×	body	1280	valid
347.0ms	1504×	body	640	valid
201.0ms	940×	body	320	valid
120.0ms	483×	body	160	valid
119.0ms	2245×	body	80	valid