Details

sample221.0ms

Algorithm

intervals

Results

98.0ms	58×	body	2560	valid
73.0ms	75×	body	1280	valid
26.0ms	65×	body	640	valid
8.0ms	33×	body	320	valid
3.0ms	13×	body	160	valid
1.0ms	12×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.0b	(- 1.0 (cos x))

rewrite32.0ms

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:

19.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(- 1.0 (cos x))

series89.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- 1.0 (cos x)) (sin x))
40.0ms	(- 1.0 (cos x))

simplify3.0s

Counts

58 → 58

Iterations

Useful iterations: 3 (870.0ms)

Iter	Nodes	Cost
0	106	665
1	240	645
2	805	611
3	4711	609
done	5002	609

prune229.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/240 (pow x 5)) (* 1/2 x))
0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.1b	(* 1/24 (pow x 3))
0.3b	(* 1/240 (pow x 5))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

20.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
40.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
19.0ms	(* 1/24 (pow x 3))
25.0ms	(* 1/240 (pow x 5))

series441.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
84.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
70.0ms	(* 1/24 (pow x 3))
77.0ms	(* 1/240 (pow x 5))

simplify998.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (312.0ms)

Iter	Nodes	Cost
0	138	1055
1	390	917
2	1671	873
done	5000	873

prune387.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.2b	(/ (- 1.0 (cos x)) (sin x))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.0b	(- 1.0 (cos x))

rewrite103.0ms

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:

25.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
30.0ms	(/ (- 1.0 (cos x)) (sin x))
33.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
7.0ms	(- 1.0 (cos x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
39.0ms	(/ (- 1.0 (cos x)) (sin x))
67.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
37.0ms	(- 1.0 (cos x))

simplify680.0ms

Counts

124 → 124

Iterations

Useful iterations: done (675.0ms)

Iter	Nodes	Cost
0	163	1406
1	318	1293
2	951	1222
done	5000	1218

prune555.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ 1.0 (cos x))
0.2b	(* (cos x) (+ 1.0 (cos x)))
0.3b	(pow (cos x) 3)
2.0b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite99.0ms

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:

7.0ms	(+ 1.0 (cos x))
38.0ms	(* (cos x) (+ 1.0 (cos x)))
8.0ms	(pow (cos x) 3)
44.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series147.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ 1.0 (cos x))
35.0ms	(* (cos x) (+ 1.0 (cos x)))
31.0ms	(pow (cos x) 3)
63.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.9s

Counts

104 → 104

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	145	1155
1	412	1045
2	2431	990
done	5000	988

prune387.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.2b

regimes243.0ms

Accuracy

98.9% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 32.2b

bsearch98.0ms

Steps

Iters	Range		Point
8	0.0004268116563047139	15.006088268796836	0.02174222265971262
8	-0.031678663534995	-9.641814872486784e-07	-0.021849564525527353

simplify18.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	80
1	50	80
2	51	80
done	51	80

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.1s	1541×	body	2560	valid
2.5s	2807×	body	1280	valid
912.0ms	1887×	body	640	valid
258.0ms	933×	body	320	valid
97.0ms	455×	body	160	valid
41.0ms	373×	body	80	valid
18.0ms	4×	body	5120	valid