Details

sample107.0ms

Algorithm

intervals

Results

40.0ms	45×	body	2560	valid
20.0ms	42×	body	1280	valid
15.0ms	47×	body	640	valid
8.0ms	34×	body	320	valid
6.0ms	68×	body	80	valid
3.0ms	20×	body	160	valid

simplify17.0ms

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: 31.2b

localize30.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1.0 (cos x))
13.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite34.0ms

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:

9.0ms	(- 1.0 (cos x))
23.0ms	(/ (- 1.0 (cos x)) (* x x))

series130.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- 1.0 (cos x))
106.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.2s

Counts

48 → 48

Iterations

Useful iterations: 2 (156.0ms)

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

prune196.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(/ (/ (- 1.0 (cos x)) x) x)
2.4b	(- 1.0 (cos x))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

38.0ms	(/ (- 1.0 (cos x)) x)
35.0ms	(/ (/ (- 1.0 (cos x)) x) x)
8.0ms	(- 1.0 (cos x))

series190.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- 1.0 (cos x)) x)
84.0ms	(/ (/ (- 1.0 (cos x)) x) x)
31.0ms	(- 1.0 (cos x))

simplify2.6s

Counts

156 → 156

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	229	2262
1	522	2156
2	1254	2046
3	3200	2024
done	5000	2009

prune440.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b	(/ (cos x) x)
2.5b	(- (/ 1.0 x) (/ (cos x) x))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
95×	`times-frac`
78×	`*-un-lft-identity`
38×	`add-cube-cbrt`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/l*`
12×	`div-inv`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`distribute-rgt-out--` `add-log-exp`
4×	`associate-/l/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub`

Counts

3 → 118

Calls

3 calls:

103.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
18.0ms	(/ (cos x) x)
61.0ms	(- (/ 1.0 x) (/ (cos x) x))

series311.0ms

Counts

3 → 9

Calls

3 calls:

160.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
57.0ms	(/ (cos x) x)
94.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify2.5s

Counts

127 → 127

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	203	1857
1	461	1635
2	1036	1570
3	2708	1565
done	5000	1545

prune316.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (/ 1.0 x) (* (cos x) (/ 1 x))) x)
0.2b	(* (cos x) (/ 1 x))
2.5b	(- (/ 1.0 x) (* (cos x) (/ 1 x)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
23×	`times-frac`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
7×	`div-inv`
6×	`associate-/l/`
5×	`pow1` `distribute-rgt-out--` `associate-*r/` `un-div-inv` `add-log-exp`
4×	`prod-exp` `frac-sub` `associate-/l*` `sub-div`
3×	`div-exp` `associate-l` `associate-/r*` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `flip--` `cbrt-unprod`
1×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `div-sub` `pow-prod-down` `clear-num` `*-commutative`

Counts

3 → 91

Calls

3 calls:

68.0ms	(/ (- (/ 1.0 x) (* (cos x) (/ 1 x))) x)
17.0ms	(* (cos x) (/ 1 x))
21.0ms	(- (/ 1.0 x) (* (cos x) (/ 1 x)))

series249.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(/ (- (/ 1.0 x) (* (cos x) (/ 1 x))) x)
50.0ms	(* (cos x) (/ 1 x))
78.0ms	(- (/ 1.0 x) (* (cos x) (/ 1 x)))

simplify2.6s

Counts

100 → 100

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	171	1331
1	417	967
2	1149	887
3	3381	872
done	5000	872

prune177.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes94.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch114.0ms

Steps

Iters	Range		Point
10	1.5244367550608482e-07	9556.682540875734	0.03328058389703145
9	-1501.2167507114543	-0.006495210018506858	-0.03086110959069604

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	45
1	36	45
done	36	45

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	1538×	body	2560	valid
558.0ms	1280×	body	1280	valid
427.0ms	1481×	body	640	valid
208.0ms	957×	body	320	valid
122.0ms	2287×	body	80	valid
53.0ms	457×	body	160	valid