Details

sample58.0ms

Algorithm

intervals

Results

29.0ms	60×	body	2560	valid
9.0ms	41×	body	1280	valid
5.0ms	36×	body	640	valid
3.0ms	26×	body	320	valid
3.0ms	84×	body	80	valid
1.0ms	9×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize6.0ms

Local error

Found 2 expressions with local error:

1.0b	(- 1.0 (cos x))
17.5b	(/ (- 1.0 (cos x)) (* x x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

7.0ms	(- 1.0 (cos x))
20.0ms	(/ (- 1.0 (cos x)) (* x x))

series64.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
46.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify31.0ms

Counts

64 → 64

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317
done	5001	317

prune125.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(/ (sqrt (- 1.0 (cos x))) x)
1.0b	(- 1.0 (cos x))
1.0b	(- 1.0 (cos x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
48×	`times-frac`
40×	`sqrt-prod`
18×	`prod-diff`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`fma-neg` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 158

Calls

4 calls:

15.0ms	(/ (sqrt (- 1.0 (cos x))) x)
15.0ms	(/ (sqrt (- 1.0 (cos x))) x)
7.0ms	(- 1.0 (cos x))
9.0ms	(- 1.0 (cos x))

series213.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (sqrt (- 1.0 (cos x))) x)
87.0ms	(/ (sqrt (- 1.0 (cos x))) x)
18.0ms	(- 1.0 (cos x))
22.0ms	(- 1.0 (cos x))

simplify171.0ms

Counts

170 → 170

Iterations

Useful iterations: 3 (159.0ms)

Iter	Nodes	Cost
0	301	1368
1	936	1148
2	4953	1118
3	5001	1112
done	5001	1112

prune360.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.9b	(- (pow 1.0 3) (pow (cos x) 3))
1.0b	(- 1.0 (cos x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

153×	`prod-diff`
115×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
90×	`unpow-prod-down` `cube-prod`
89×	`add-cube-cbrt`
34×	`sqr-pow`
26×	`cube-mult` `unpow3`
17×	`difference-of-squares`
15×	`fma-neg`
10×	`add-log-exp`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`difference-cubes` `+-commutative` `pow-to-exp` `sqr-cos` `associate-+l+` `distribute-rgt-out` `pow-pow` `fma-def` `flip3-+` `pow-exp` `sum-log` `flip-+` `rem-cube-cbrt`

Counts

4 → 261

Calls

4 calls:

3.0ms	(pow (cos x) 3)
13.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
33.0ms	(- (pow 1.0 3) (pow (cos x) 3))
7.0ms	(- 1.0 (cos x))

series136.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (cos x) 3)
45.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
45.0ms	(- (pow 1.0 3) (pow (cos x) 3))
19.0ms	(- 1.0 (cos x))

simplify138.0ms

Counts

273 → 273

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	673	2891
1	2715	1964
2	5001	1932
done	5001	1932

prune436.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.9b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
0.9b	(log (exp (pow (cos x) 3)))
1.0b	(- 1.0 (cos x))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

201×	`prod-diff`
170×	`log-pow`
156×	`exp-prod`
124×	`add-sqr-sqrt`
120×	`*-un-lft-identity`
115×	`add-cube-cbrt`
91×	`unpow-prod-down` `cube-prod`
31×	`sqr-pow`
30×	`cube-mult` `unpow3`
18×	`pow1`
15×	`fma-neg`
9×	`add-log-exp`
6×	`log-prod`
5×	`difference-of-squares`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`associate--r+` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`+-commutative` `sqr-cos` `associate-+l+` `distribute-rgt-out` `fma-def` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 297

Calls

4 calls:

13.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
51.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
7.0ms	(log (exp (pow (cos x) 3)))
7.0ms	(- 1.0 (cos x))

series144.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
48.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
27.0ms	(log (exp (pow (cos x) 3)))
24.0ms	(- 1.0 (cos x))

simplify146.0ms

Counts

309 → 309

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	763	4420
1	2733	2292
2	5001	2283
done	5001	2283

prune461.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes77.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.6b

bsearch73.0ms

Steps

Iters	Range		Point
8	0.02319676823116778	7.055123656280252	0.031819146549010704
7	-0.15939393977811658	-0.001391736753177052	-0.02708053868306139

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	30
1	49	30
done	49	30

end0.0ms

sample1.6s

Algorithm

intervals

Results

716.0ms	1569×	body	2560	valid
291.0ms	1230×	body	1280	valid
233.0ms	1551×	body	640	valid
98.0ms	907×	body	320	valid
72.0ms	2307×	body	80	valid
36.0ms	436×	body	160	valid