Details

sample89.0ms

Algorithm

intervals

Results

34.0ms	48×	body	2560	valid
16.0ms	42×	body	1280	valid
16.0ms	52×	body	640	valid
5.0ms	27×	body	320	valid
4.0ms	68×	body	80	valid
2.0ms	19×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize9.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
15.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite32.0ms

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:

7.0ms	(- 1.0 (cos x))
24.0ms	(/ (- 1.0 (cos x)) (* x x))

series94.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
74.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify599.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
2	1129
1	232
0	88

prune205.0ms

Pruning

11 alts after pruning (11 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) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.1b	(- 1.0 (cos x))

rewrite47.0ms

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:

19.0ms	(/ (/ (- 1.0 (cos x)) x) x)
13.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(- 1.0 (cos x))

series178.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (/ (- 1.0 (cos x)) x) x)
72.0ms	(/ (- 1.0 (cos x)) x)
33.0ms	(- 1.0 (cos x))

simplify975.0ms

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	2463
1	549
0	229

prune647.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
0.5b	(+ 1.0 (cos x))
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-cbrt-cube` `add-exp-log`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3-+` `flip3--` `div-exp` `associate-*l/` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `+-commutative` `clear-num` `associate-/r*` `sum-log` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

3.0ms	(pow (cos x) 3)
80.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
5.0ms	(+ 1.0 (cos x))
32.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series366.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(pow (cos x) 3)
263.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
11.0ms	(+ 1.0 (cos x))
55.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.9s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
2	3398
1	634
0	219

prune826.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b	(/ (cos x) x)
2.2b	(- (/ 1.0 x) (/ (cos x) x))

rewrite112.0ms

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:

66.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
7.0ms	(/ (cos x) x)
29.0ms	(- (/ 1.0 x) (/ (cos x) x))

series297.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
49.0ms	(/ (cos x) x)
96.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify1.1s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	1844
1	478
0	203

prune638.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes122.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch85.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	160.65039477392645	0.033302914266201536
8	-0.9341403346610884	-0.003292329160956242	-0.034055167795293766

simplify5.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.4s	1623×	body	2560	valid
1.1s	1237×	body	1280	valid
1.0s	1505×	body	640	valid
298.0ms	2205×	body	80	valid
292.0ms	923×	body	320	valid
81.0ms	507×	body	160	valid