Details

sample239.0ms

Algorithm

intervals

Results

124.0ms	59×	body	2560	valid
65.0ms	91×	body	1280	valid
26.0ms	58×	body	640	valid
7.0ms	22×	body	320	valid
2.0ms	11×	body	160	valid
2.0ms	15×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	202
1	11	202
2	14	202
3	16	202
done	16	202

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize69.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

26.0ms	(/ (- 1.0 (cos x)) (sin x))
10.0ms	(- 1.0 (cos x))

series108.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (- 1.0 (cos x)) (sin x))
34.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

58 → 58

Iterations

Useful iterations: 3 (611.0ms)

Iter	Nodes	Cost
0	106	19054
1	240	17685
2	596	17605
3	1941	17525
done	5002	17525

prune326.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (cos x))
0.2b	(* (cos x) (cos x))
0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.8b	(- (* 1.0 (* 1.0 1.0)) (* (cos x) (* (cos x) (cos x))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`sqr-cos`
2×	`pow2` `pow-plus` `cube-unmult` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`distribute-rgt-in` `difference-cubes` `+-commutative` `associate-+l+` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `distribute-rgt-out` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 82

Calls

4 calls:

16.0ms	(* (cos x) (cos x))
16.0ms	(* (cos x) (cos x))
20.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
45.0ms	(- (* 1.0 (* 1.0 1.0)) (* (cos x) (* (cos x) (cos x))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (cos x) (cos x))
32.0ms	(* (cos x) (cos x))
61.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
70.0ms	(- (* 1.0 (* 1.0 1.0)) (* (cos x) (* (cos x) (cos x))))

simplify4.6s

Counts

94 → 94

Iterations

Useful iterations: 3 (2.1s)

Iter	Nodes	Cost
0	121	22747
1	330	17544
2	1233	17373
3	3927	17213
done	5001	17213

prune613.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (- (* 1.0 (* 1.0 1.0)) (* (cos x) 1/2)) (* (cos x) (* 1/2 (cos (* 2 x))))) (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x))))) (sin x))
0.2b	(* (cos x) (cos x))
0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.8b	(- (- (* 1.0 (* 1.0 1.0)) (* (cos x) 1/2)) (* (cos x) (* 1/2 (cos (* 2 x)))))

rewrite488.0ms

Algorithm

rewrite-expression-head

Rules

81×	`times-frac`
54×	`add-sqr-sqrt`
52×	`*-un-lft-identity` `add-cube-cbrt`
15×	`associate-/l*`
11×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
8×	`associate-/r/`
5×	`flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `associate-/r` `diff-log` `swap-sqr` `div-exp` `associate-r` `associate-l*`
2×	`sqr-cos` `sub-neg` `div-sub` `associate--l+`
1×	`associate--l-` `pow2` `+-commutative` `associate-+l+` `clear-num` `sum-log` `frac-2neg` `pow-plus` `distribute-rgt-out` `flip3--` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`

Counts

4 → 135

Calls

4 calls:

288.0ms	(/ (/ (- (- (* 1.0 (* 1.0 1.0)) (* (cos x) 1/2)) (* (cos x) (* 1/2 (cos (* 2 x))))) (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x))))) (sin x))
8.0ms	(* (cos x) (cos x))
17.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
167.0ms	(- (- (* 1.0 (* 1.0 1.0)) (* (cos x) 1/2)) (* (cos x) (* 1/2 (cos (* 2 x)))))

series562.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(/ (/ (- (- (* 1.0 (* 1.0 1.0)) (* (cos x) 1/2)) (* (cos x) (* 1/2 (cos (* 2 x))))) (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x))))) (sin x))
31.0ms	(* (cos x) (cos x))
62.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
148.0ms	(- (- (* 1.0 (* 1.0 1.0)) (* (cos x) 1/2)) (* (cos x) (* 1/2 (cos (* 2 x)))))

simplify3.6s

Counts

147 → 147

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	312	116577
1	858	101033
2	3221	100270
done	5005	100230

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize121.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (cos x))
0.3b	(* (* (cos x) (cos x)) (* (cos x) (cos x)))
1.8b	(- (- (* 1.0 (* 1.0 1.0)) (* (cos x) 1/2)) (* (cos x) (* 1/2 (cos (* 2 x)))))
2.0b	(- (* 1.0 (cos x)) (* (cos x) (cos x)))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

122×	`pow1`
37×	`pow-prod-up`
24×	`pow-prod-down`
23×	`pow-sqr`
19×	`pow-plus`
18×	`add-cbrt-cube` `add-exp-log`
14×	`pow2`
11×	`add-log-exp`
10×	`add-sqr-sqrt`
9×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`cos-mult`
4×	`sqr-cos` `diff-log` `swap-sqr` `associate-r` `associate-l`
3×	`sub-neg`
2×	`flip3--` `associate--l+` `*-commutative` `flip--` `unswap-sqr`
1×	`associate--l-` `distribute-rgt-in` `frac-times` `distribute-lft-in` `distribute-rgt-out--` `associate-l/` `associate-r/` `associate--r+`

Counts

4 → 125

Calls

4 calls:

15.0ms	(* (cos x) (cos x))
56.0ms	(* (* (cos x) (cos x)) (* (cos x) (cos x)))
165.0ms	(- (- (* 1.0 (* 1.0 1.0)) (* (cos x) 1/2)) (* (cos x) (* 1/2 (cos (* 2 x)))))
15.0ms	(- (* 1.0 (cos x)) (* (cos x) (cos x)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (cos x) (cos x))
42.0ms	(* (* (cos x) (cos x)) (* (cos x) (cos x)))
135.0ms	(- (- (* 1.0 (* 1.0 1.0)) (* (cos x) 1/2)) (* (cos x) (* 1/2 (cos (* 2 x)))))
111.0ms	(- (* 1.0 (cos x)) (* (cos x) (cos x)))

simplify3.1s

Counts

137 → 137

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	170	32076
1	518	24564
2	2137	23402
done	5002	23241

prune707.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes159.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.0b

bsearch156.0ms

Steps

Iters	Range		Point
9	5.312512837176874e-08	0.1909160003853501	0.018647140340288516
7	-0.18371106458419734	-0.0075399940621682995	-0.019689929419869922

simplify18.0ms

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	54	2140
1	78	2140
done	78	2140

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.2s	1554×	body	2560	valid
2.8s	2855×	body	1280	valid
1.4s	1841×	body	640	valid
470.0ms	464×	body	160	valid
320.0ms	930×	body	320	valid
40.0ms	350×	body	80	valid
27.0ms	6×	body	5120	valid