Details

sample51.0ms

Algorithm

intervals

Results

19.0ms	44×	body	2560	valid
7.0ms	32×	body	1280	valid
7.0ms	52×	body	640	valid
4.0ms	38×	body	320	valid
3.0ms	76×	body	80	valid
1.0ms	14×	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: 29.1b

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
14.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite25.0ms

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))
19.0ms	(/ (- 1.0 (cos x)) (* x x))

series67.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- 1.0 (cos x))
48.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239
done	5002	239

prune115.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
1.5b	(- 1.0 (cos x))
1.5b	(- 1.0 (cos x))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-sqr-sqrt`
156×	`times-frac`
143×	`*-un-lft-identity`
104×	`sqrt-prod`
89×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 206

Calls

4 calls:

17.0ms	(/ (sqrt (- 1.0 (cos x))) x)
62.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series175.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (sqrt (- 1.0 (cos x))) x)
47.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
19.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify87.0ms

Counts

218 → 218

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	667	2403
1	3340	2087
2	5001	1922
done	5001	1922

prune393.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 (cos x)))
1.5b	(- 1.0 (cos x))
1.5b	(- 1.0 (cos x))
1.5b	(- 1.0 (cos x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

4.0ms	(cbrt (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series180.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (- 1.0 (cos x)))
22.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
20.0ms	(- 1.0 (cos x))

simplify51.0ms

Counts

69 → 69

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	150	361
1	391	327
2	1222	320
3	5001	309
done	5001	309

prune231.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

1.5b	(- 1.0 (cos x))
1.5b	(- 1.0 (cos x))
1.5b	(- 1.0 (cos x))
1.7b	(log (exp (- 1.0 (cos x))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
6×	`add-cube-cbrt` `log-pow`
5×	`pow1` `log-prod` `exp-prod`
4×	`add-exp-log` `sub-neg` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `diff-log` `flip--`
2×	`exp-sum`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 62

Calls

4 calls:

8.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))
14.0ms	(log (exp (- 1.0 (cos x))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))
20.0ms	(log (exp (- 1.0 (cos x))))

simplify123.0ms

Counts

74 → 74

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	127	319
1	313	294
2	787	294
3	3371	294
4	5002	294
done	5002	294

prune224.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes133.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.1b

bsearch85.0ms

Steps

Iters	Range		Point
8	0.016621422887445694	5.276955647516397	0.0357523883624483
9	-0.05800990145057735	-1.1864783425707322e-08	-0.034229541342750226

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	32
1	52	32
done	52	32

end0.0ms

sample1.6s

Algorithm

intervals

Results

720.0ms	1606×	body	2560	valid
281.0ms	1284×	body	1280	valid
212.0ms	1504×	body	640	valid
97.0ms	940×	body	320	valid
75.0ms	2201×	body	80	valid
31.0ms	465×	body	160	valid