Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	49×	body	2560	valid
10.0ms	46×	body	1280	valid
5.0ms	41×	body	640	valid
3.0ms	32×	body	320	valid
2.0ms	71×	body	80	valid
1.0ms	17×	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: 31.6b

localize6.0ms

Local error

Found 2 expressions with local error:

2.5b	(- 1.0 (cos x))
15.5b	(/ (- 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))
18.0ms	(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify59.0ms

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

prune105.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.5b	(- 1.0 (cos x))

rewrite49.0ms

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:

22.0ms	(/ (/ (- 1.0 (cos x)) x) x)
15.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series106.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (/ (- 1.0 (cos x)) x) x)
45.0ms	(/ (- 1.0 (cos x)) x)
19.0ms	(- 1.0 (cos x))

simplify47.0ms

Counts

156 → 156

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	531	1270
1	1899	1197
2	5001	1186
done	5001	1186

prune258.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.4b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
2.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

72.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
3.0ms	(pow (cos x) 3)
6.0ms	(+ (cos x) 1.0)
24.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series215.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
27.0ms	(pow (cos x) 3)
10.0ms	(+ (cos x) 1.0)
51.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify90.0ms

Counts

201 → 201

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	617	2953
1	2699	2889
2	5001	2810
done	5001	2810

prune382.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
2.3b	(- (pow 1.0 3) (pow (cos x) 3))
2.4b	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
32×	`difference-of-squares`
31×	`*-un-lft-identity`
27×	`unpow-prod-down` `cube-prod`
26×	`log-pow`
25×	`exp-prod`
17×	`sqr-pow`
10×	`distribute-lft-out--`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log` `log-prod` `add-cbrt-cube`
3×	`pow-unpow`
2×	`difference-cubes` `sub-neg` `exp-sum`
1×	`+-commutative` `cube-mult` `pow-to-exp` `log-div` `flip3--` `pow-pow` `flip3-+` `exp-diff` `diff-log` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 109

Calls

4 calls:

3.0ms	(pow (cos x) 3)
6.0ms	(+ (cos x) 1.0)
21.0ms	(- (pow 1.0 3) (pow (cos x) 3))
64.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (cos x) 3)
15.0ms	(+ (cos x) 1.0)
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))
49.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify45.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	348	673
1	1242	636
2	5001	608
done	5001	608

prune268.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.2b

bsearch72.0ms

Steps

Iters	Range		Point
9	0.00021078761332869983	22.544919195950573	0.03037211695605043
8	-1.6220908197114983	-0.002799490342594777	-0.02739833596085252

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	36
1	45	36
done	45	36

end0.0ms

sample1.6s

Algorithm

intervals

Results

706.0ms	1573×	body	2560	valid
295.0ms	1254×	body	1280	valid
204.0ms	1484×	body	640	valid
99.0ms	944×	body	320	valid
68.0ms	2284×	body	80	valid
32.0ms	461×	body	160	valid