Details

sample88.0ms

Algorithm

intervals

Results

38.0ms	115×	body	1280	valid
20.0ms	24×	body	2560	valid
15.0ms	78×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	14×	body	160	valid
0.0ms	1×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize8.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (cos (+ x eps)) (cos x))
3.9b	(cos (+ x eps))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

15.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

series69.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify112.0ms

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164
done	5002	164

prune87.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
3.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

10.0ms	(* (cos x) (cos eps))
18.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
12.0ms	(* (sin x) (sin eps))
58.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series302.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos x) (cos eps))
81.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
49.0ms	(* (sin x) (sin eps))
129.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify111.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4487	583
3	5002	583
done	5002	583

prune233.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.1b	(* (cos eps) (cos x))
0.2b	(* (sin x) (sin eps))
3.3b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `sin-mult` `associate--r+`

Counts

4 → 65

Calls

4 calls:

12.0ms	(+ (* (sin x) (sin eps)) (cos x))
10.0ms	(* (cos eps) (cos x))
13.0ms	(* (sin x) (sin eps))
27.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* (sin x) (sin eps)) (cos x))
41.0ms	(* (cos eps) (cos x))
46.0ms	(* (sin x) (sin eps))
141.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify41.0ms

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	329	606
1	1247	575
2	5002	567
done	5002	567

prune263.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps)))))
0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.5b	(pow (* (cos x) (cos eps)) 3)
8.5b	(- (/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x))

rewrite819.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
41×	`cos-mult`
40×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`times-frac`
27×	`frac-add`
23×	`associate-/r/`
21×	`add-exp-log` `add-cbrt-cube`
20×	`sin-mult`
19×	`add-cube-cbrt`
18×	`pow-prod-down` `difference-of-squares`
17×	`frac-times` `associate-*r/` `sqr-pow`
11×	`associate-*l/`
9×	`prod-exp` `cbrt-unprod` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
5×	`cube-div` `distribute-lft-out--`
4×	`difference-cubes` `pow-sqr` `pow-prod-up` `associate-/l/`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `pow-pow` `pow-plus` `div-sub` `pow-exp` `flip--` `rem-cube-cbrt`
1×	`cbrt-undiv` `associate--l-` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `frac-2neg` `diff-log` `unpow3` `cube-prod` `swap-sqr` `div-exp` `associate-r` `associate-l` `clear-num` `*-commutative` `frac-sub` `div-inv` `sub-div`

Counts

4 → 155

Calls

4 calls:

113.0ms	(/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps)))))
40.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
8.0ms	(pow (* (cos x) (cos eps)) 3)
650.0ms	(- (/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x))

series1.2s

Counts

4 → 12

Calls

4 calls:

386.0ms	(/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps)))))
55.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
65.0ms	(pow (* (cos x) (cos eps)) 3)
702.0ms	(- (/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x))

simplify57.0ms

Counts

167 → 167

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1072	4866
1	5001	4706
done	5001	4706

prune600.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.0b

regimes246.0ms

Accuracy

86.6% (1.3b remaining)

Error of 15.8b against oracle of 14.5b and baseline of 24.2b

bsearch127.0ms

Steps

Iters	Range		Point
9	0.00021078761332869983	101.51334682654779	0.000213035825894572
9	-2.5466144345707062e-05	-2.1789434937933663e-14	-9.206885999863947e-07

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	55
1	60	55
2	60	55
done	60	55

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4457×	body	1280	valid
563.0ms	646×	body	2560	valid
394.0ms	1868×	body	640	valid
92.0ms	682×	body	320	valid
24.0ms	256×	body	160	valid
4.0ms	91×	body	80	valid