Details

sample252.0ms

Algorithm

intervals

Results

100.0ms	51×	body	2560	valid
66.0ms	92×	body	1280	valid
52.0ms	45×	body	640	valid
11.0ms	39×	body	320	valid
5.0ms	1×	body	5120	valid
4.0ms	20×	body	160	valid
1.0ms	8×	body	80	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	15	7
2	16	7
done	16	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite49.0ms

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:

33.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(- 1.0 (cos x))

series101.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(/ (- 1.0 (cos x)) (sin x))
37.0ms	(- 1.0 (cos x))

simplify5.2s

Counts

58 → 58

Iterations

Useful iterations: done (5.2s)

Iter	Nodes	Cost
0	106	665
1	476	645
done	5000	609

prune262.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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))

rewrite104.0ms

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:

23.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
42.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
23.0ms	(* 1/24 (pow x 3))
12.0ms	(* 1/240 (pow x 5))

series458.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
84.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
75.0ms	(* 1/24 (pow x 3))
70.0ms	(* 1/240 (pow x 5))

simplify1.5s

Counts

92 → 92

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	138	1055
1	1043	931
done	5000	885

prune324.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ 1.0 (cos x)))
0.3b	(+ 1.0 (cos x))
0.3b	(pow (cos x) 3)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite97.0ms

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:

28.0ms	(* (cos x) (+ 1.0 (cos x)))
14.0ms	(+ 1.0 (cos x))
7.0ms	(pow (cos x) 3)
44.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series134.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (cos x) (+ 1.0 (cos x)))
12.0ms	(+ 1.0 (cos x))
36.0ms	(pow (cos x) 3)
55.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify3.2s

Counts

104 → 104

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	145	1155
1	1352	1054
done	5000	996

prune439.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 159

Calls

3 calls:

40.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
28.0ms	(/ (sin x) (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series135.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
57.0ms	(/ (sin x) (- 1.0 (cos x)))
24.0ms	(- 1.0 (cos x))

simplify3.6s

Counts

168 → 168

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	239	2702
1	1683	2304
done	5002	2210

prune384.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes108.0ms

Accuracy

99% (0.3b remaining)

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

bsearch532.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	0.020706483323998073
8	-11.923248480236845	-0.0008047768791668974	-0.024087893247376972

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	58
1	48	58
done	48	58

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.9s	1581×	body	2560	valid
2.9s	2788×	body	1280	valid
1.1s	1866×	body	640	valid
389.0ms	960×	body	320	valid
94.0ms	464×	body	160	valid
58.0ms	7×	body	5120	valid
39.0ms	334×	body	80	valid