Details

sample89.0ms

Algorithm

intervals

Results

36.0ms	51×	body	2560	valid
13.0ms	52×	body	640	valid
12.0ms	29×	body	1280	valid
6.0ms	79×	body	80	valid
6.0ms	31×	body	320	valid
2.0ms	14×	body	160	valid

simplify42.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize49.0ms

Local error

Found 2 expressions with local error:

1.3b	(- 1.0 (cos x))
15.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite59.0ms

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:

13.0ms	(- 1.0 (cos x))
43.0ms	(/ (- 1.0 (cos x)) (* x x))

series116.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(- 1.0 (cos x))
83.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify926.0ms

Counts: 48 → 48

prune139.0ms

Pruning

8 alts after pruning (8 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)
0.3b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
1.3b	(- 1.0 (cos x))

rewrite72.0ms

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:

17.0ms	(/ (- 1.0 (cos x)) x)
43.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
7.0ms	(- 1.0 (cos x))

series183.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- 1.0 (cos x)) x)
82.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
21.0ms	(- 1.0 (cos x))

simplify1.1s

Counts: 123 → 123

prune371.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (cos x) x)
0.3b	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
1.7b	(- (/ 1.0 x) (/ (cos x) x))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 106

Calls

3 calls:

19.0ms	(/ (cos x) x)
178.0ms	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
51.0ms	(- (/ 1.0 x) (/ (cos x) x))

series286.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (cos x) x)
142.0ms	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
107.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify905.0ms

Counts: 115 → 115

prune355.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

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)
1.3b	(- 1.0 (cos x))

rewrite71.0ms

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:

29.0ms	(/ (/ (- 1.0 (cos x)) x) x)
24.0ms	(/ (- 1.0 (cos x)) x)
11.0ms	(- 1.0 (cos x))

series145.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (/ (- 1.0 (cos x)) x) x)
65.0ms	(/ (- 1.0 (cos x)) x)
32.0ms	(- 1.0 (cos x))

simplify730.0ms

Counts: 156 → 156

prune393.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes83.0ms

Accuracy

99.5% (0.1b remaining)

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

bsearch92.0ms

Steps

Iters	Range		Point
9	0.0024368900564104884	555.6593536559827	0.031138807283541618
10	-248837311.7084542	-0.0006576197608759923	-0.033797397342550294

simplify550.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.7s	1639×	body	2560	valid
589.0ms	955×	body	320	valid
447.0ms	1250×	body	1280	valid
387.0ms	1415×	body	640	valid
177.0ms	2280×	body	80	valid
103.0ms	461×	body	160	valid