Details

sample77.0ms

Algorithm

intervals

Results

30.0ms	51×	body	2560	valid
13.0ms	57×	body	640	valid
13.0ms	40×	body	1280	valid
5.0ms	27×	body	320	valid
4.0ms	63×	body	80	valid
2.0ms	18×	body	160	valid

simplify3.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize7.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
15.7b	(/ (- 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))
20.0ms	(/ (- 1.0 (cos x)) (* x x))

series88.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
68.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify61.0ms

Counts: 48 → 48

prune116.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite55.0ms

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:

21.0ms	(/ (/ (- 1.0 (cos x)) x) x)
20.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series117.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify47.0ms

Counts: 156 → 156

prune284.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite69.0ms

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-l`
17×	`add-cbrt-cube`
13×	`associate-r`
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` `un-div-inv` `*-commutative`

Counts

3 → 115

Calls

3 calls:

37.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
21.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series122.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
48.0ms	(/ (- 1.0 (cos x)) x)
24.0ms	(- 1.0 (cos x))

simplify56.0ms

Counts: 124 → 124

prune237.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite115.0ms

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:

72.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
9.0ms	(/ (cos x) x)
26.0ms	(- (/ 1.0 x) (/ (cos x) x))

series198.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
35.0ms	(/ (cos x) x)
60.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify40.0ms

Counts: 127 → 127

prune264.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes65.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.4b

bsearch84.0ms

Steps

Iters	Range		Point
9	5.155942382976535e-09	0.21963308938311268	0.029805544534800093
11	-2445851338.3862987	-4.2674702477225e-16	-0.03339438899281232

simplify1.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

955.0ms	1593×	body	2560	valid
696.0ms	1236×	body	1280	valid
299.0ms	1486×	body	640	valid
204.0ms	946×	body	320	valid
167.0ms	2264×	body	80	valid
79.0ms	475×	body	160	valid