Details

sample55.0ms

Algorithm

intervals

Results

27.0ms	50×	body	2560	valid
8.0ms	36×	body	1280	valid
6.0ms	46×	body	640	valid
3.0ms	27×	body	320	valid
3.0ms	76×	body	80	valid
1.0ms	21×	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: 29.7b

localize6.0ms

Local error

Found 2 expressions with local error:

2.3b	(- 1.0 (cos x))
13.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite27.0ms

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))
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))

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

prune107.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
2.3b	(- 1.0 (cos x))

rewrite66.0ms

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:

39.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
16.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series106.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
45.0ms	(/ (- 1.0 (cos x)) x)
19.0ms	(- 1.0 (cos x))

simplify58.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	521	814
1	2334	726
2	5001	690
done	5001	690

prune226.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
2.1b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite123.0ms

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:

77.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
7.0ms	(+ (cos x) 1.0)
3.0ms	(pow (cos x) 3)
26.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series214.0ms

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)))
10.0ms	(+ (cos x) 1.0)
27.0ms	(pow (cos x) 3)
50.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify91.0ms

Counts

201 → 201

Iterations

Useful iterations: 2 (69.0ms)

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

prune438.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
1.2b	(log (exp (pow (cos x) 3)))
2.1b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`log-pow`
12×	`add-cube-cbrt` `exp-prod`
7×	`pow1` `unpow-prod-down` `cube-prod` `add-log-exp`
6×	`log-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`difference-of-squares`
3×	`pow-unpow` `associate--r+` `sqr-pow`
2×	`cube-mult` `unpow3` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `diff-log` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 80

Calls

4 calls:

7.0ms	(+ (cos x) 1.0)
3.0ms	(pow (cos x) 3)
8.0ms	(log (exp (pow (cos x) 3)))
39.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (cos x) 1.0)
27.0ms	(pow (cos x) 3)
27.0ms	(log (exp (pow (cos x) 3)))
49.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify40.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	296	446
1	1109	381
2	5001	373
done	5001	373

prune244.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes74.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.9b

bsearch74.0ms

Steps

Iters	Range		Point
9	9.85435867085541e-08	110.15968793260775	0.031416007424221945
8	-0.1517943218839364	-1.6640733670284383e-05	-0.03396454979348009

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	43
1	59	43
done	59	43

end0.0ms

sample1.6s

Algorithm

intervals

Results

706.0ms	1592×	body	2560	valid
296.0ms	1298×	body	1280	valid
204.0ms	1478×	body	640	valid
105.0ms	894×	body	320	valid
66.0ms	2272×	body	80	valid
32.0ms	466×	body	160	valid