Details

sample215.0ms

Algorithm

intervals

Results

85.0ms	83×	body	1280	valid
77.0ms	42×	body	2560	valid
27.0ms	66×	body	640	valid
11.0ms	37×	body	320	valid
3.0ms	17×	body	160	valid
1.0ms	11×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 1.0 (cos x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

25.0ms	(/ (- 1.0 (cos x)) (sin x))
13.0ms	(- 1.0 (cos x))

series528.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(/ (- 1.0 (cos x)) (sin x))
458.0ms	(- 1.0 (cos x))

simplify2.8s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	106	665
1	235	645
2	531	609
3	1194	609
4	3136	608
done	5000	608

prune284.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.9b	(- 1.0 (cos x))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

27.0ms	(/ (- 1.0 (cos x)) (sin x))
27.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
44.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

series199.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (- 1.0 (cos x)) (sin x))
81.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
46.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
28.0ms	(- 1.0 (cos x))

simplify2.9s

Counts

124 → 124

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	163	1406
1	304	1293
2	639	1220
3	1394	1218
4	3567	1217
done	5000	1217

prune538.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.4b	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
1.9b	(- 1.0 (cos x))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`exp-prod`
31×	`log-pow`
28×	`log-prod`
24×	`times-frac`
23×	`add-cube-cbrt`
20×	`exp-sum`
7×	`pow1`
6×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
5×	`add-exp-log`
4×	`log-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`exp-diff` `rem-log-exp`
1×	`sub-neg` `diff-log` `div-inv` `rem-exp-log`

Counts

4 → 89

Calls

4 calls:

13.0ms	(exp (log (- 1.0 (cos x))))
9.0ms	(log (- 1.0 (cos x)))
32.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
12.0ms	(- 1.0 (cos x))

series237.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(exp (log (- 1.0 (cos x))))
127.0ms	(log (- 1.0 (cos x)))
39.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
40.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

101 → 101

Iterations

Useful iterations: 4 (940.0ms)

Iter	Nodes	Cost
0	194	1170
1	297	919
2	548	849
3	1090	849
4	2650	831
done	5000	831

prune390.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ 1.0 (cos x)))
0.3b	(+ 1.0 (cos x))
0.4b	(pow (cos x) 3)
1.7b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

35.0ms	(* (cos x) (+ 1.0 (cos x)))
12.0ms	(+ 1.0 (cos x))
4.0ms	(pow (cos x) 3)
25.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series145.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (cos x) (+ 1.0 (cos x)))
11.0ms	(+ 1.0 (cos x))
40.0ms	(pow (cos x) 3)
64.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.1s

Counts

104 → 104

Iterations

Useful iterations: 2 (318.0ms)

Iter	Nodes	Cost
0	145	1155
1	350	1045
2	1384	988
done	5001	988

prune375.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.1b

regimes303.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.5b

bsearch114.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	0.020771119462007017
9	-7465.585501010854	-0.008005822963963436	-0.023647737046597096

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	64
1	49	64
done	49	64

end0.0ms

sample8.7s

Algorithm

intervals

Results

4.1s	1652×	body	2560	valid
2.4s	2679×	body	1280	valid
982.0ms	1931×	body	640	valid
800.0ms	933×	body	320	valid
95.0ms	433×	body	160	valid
41.0ms	368×	body	80	valid
16.0ms	4×	body	5120	valid