Details

sample123.0ms

Algorithm

intervals

Results

40.0ms	38×	body	2560	valid
20.0ms	80×	body	80	valid
20.0ms	56×	body	640	valid
19.0ms	38×	body	1280	valid
6.0ms	25×	body	320	valid
3.0ms	19×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize9.0ms

Local error

Found 2 expressions with local error:

1.6b	(- 1.0 (cos x))
12.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
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×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

5.0ms	(- 1.0 (cos x))
16.0ms	(/ (- 1.0 (cos x)) (* x x))

series90.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- 1.0 (cos x))
69.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify723.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
2	1129
1	232
0	88

prune166.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ 1 x) x)
1.6b	(- 1.0 (cos x))
13.4b	(* (- 1.0 (cos x)) (/ (/ 1 x) x))

rewrite103.0ms

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×	`associate-/r*` `flip3--` `cbrt-unprod` `flip--`
2×	`frac-times` `rec-exp` `1-exp` `associate-*l/` `distribute-lft-out--` `difference-of-squares` `pow-div`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `associate-r/` `-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

3 → 163

Calls

3 calls:

12.0ms	(/ (/ 1 x) x)
10.0ms	(- 1.0 (cos x))
70.0ms	(* (- 1.0 (cos x)) (/ (/ 1 x) x))

series97.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ (/ 1 x) x)
27.0ms	(- 1.0 (cos x))
52.0ms	(* (- 1.0 (cos x)) (/ (/ 1 x) x))

simplify929.0ms

Counts

172 → 172

Iterations

Iter	Nodes
done	5001
1	674
0	255

prune673.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.6b	(- 1.0 (cos x))

rewrite48.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

23.0ms	(/ (/ (- 1.0 (cos x)) x) x)
14.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(- 1.0 (cos x))

series119.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (/ (- 1.0 (cos x)) x) x)
48.0ms	(/ (- 1.0 (cos x)) x)
21.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	2463
1	549
0	229

prune705.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b	(/ (cos x) x)
1.7b	(- (/ 1.0 x) (/ (cos x) x))

rewrite148.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
5×	`distribute-rgt-out--` `add-log-exp`
4×	`associate-/l/`
3×	`pow1`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub`

Counts

3 → 118

Calls

3 calls:

95.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
10.0ms	(/ (cos x) x)
36.0ms	(- (/ 1.0 x) (/ (cos x) x))

series308.0ms

Counts

3 → 9

Calls

3 calls:

177.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
57.0ms	(/ (cos x) x)
73.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify1.1s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	1844
1	478
0	203

prune674.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes86.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch102.0ms

Steps

Iters	Range		Point
8	0.00104763160503943	5.1212688054922095	0.035978223766907506
9	-205.8624528279525	-0.0007095347148853646	-0.0346527842528457

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	31

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	1504×	body	2560	valid
943.0ms	1529×	body	640	valid
631.0ms	1298×	body	1280	valid
258.0ms	980×	body	320	valid
179.0ms	2199×	body	80	valid
64.0ms	490×	body	160	valid