Details

sample132.0ms

Algorithm

intervals

Results

63.0ms	52×	body	2560	valid
41.0ms	92×	body	1280	valid
12.0ms	57×	body	640	valid
5.0ms	33×	body	320	valid
2.0ms	16×	body	160	valid
0.0ms	6×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4
done	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.2b	(- 1.0 (cos x))

rewrite25.0ms

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:

17.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify78.0ms

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373
done	5001	373

prune160.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ (cos x) 1.0))
0.4b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite60.0ms

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:

24.0ms	(* (cos x) (+ (cos x) 1.0))
6.0ms	(+ (cos x) 1.0)
3.0ms	(pow (cos x) 3)
23.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series120.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (cos x) (+ (cos x) 1.0))
16.0ms	(+ (cos x) 1.0)
28.0ms	(pow (cos x) 3)
48.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify67.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	353	593
1	1734	555
2	5001	535
done	5001	535

prune289.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (pow (cos x) 3) 3)
0.4b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
1.9b	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
56×	`unpow-prod-down` `cube-prod`
44×	`difference-of-squares`
40×	`cbrt-prod`
27×	`sqr-pow`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube`
5×	`pow1` `pow-exp`
4×	`cube-mult` `unpow3`
3×	`pow-to-exp`
2×	`pow-pow` `rem-cube-cbrt`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 135

Calls

4 calls:

6.0ms	(pow (pow (cos x) 3) 3)
6.0ms	(+ (cos x) 1.0)
3.0ms	(pow (cos x) 3)
46.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (pow (cos x) 3) 3)
10.0ms	(+ (cos x) 1.0)
28.0ms	(pow (cos x) 3)
48.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify60.0ms

Counts

147 → 147

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	421	1014
1	1553	953
2	5002	916
done	5002	916

prune325.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))
2.1b	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite107.0ms

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:

6.0ms	(+ (cos x) 1.0)
3.0ms	(pow (cos x) 3)
24.0ms	(- (pow 1.0 3) (pow (cos x) 3))
69.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series140.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (cos x) 1.0)
28.0ms	(pow (cos x) 3)
53.0ms	(- (pow 1.0 3) (pow (cos x) 3))
48.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify46.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (38.0ms)

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

prune324.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

regimes167.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.8b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	55
1	60	55
done	60	55

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	1626×	body	2560	valid
1.2s	2815×	body	1280	valid
398.0ms	1799×	body	640	valid
335.0ms	915×	body	320	valid
52.0ms	494×	body	160	valid
22.0ms	348×	body	80	valid
13.0ms	3×	body	5120	valid