Details

sample76.0ms

Algorithm

intervals

Results

26.0ms	42×	body	2560	valid
14.0ms	40×	body	1280	valid
13.0ms	54×	body	640	valid
6.0ms	34×	body	320	valid
4.0ms	67×	body	80	valid
2.0ms	19×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
4	28
3	26
2	21
1	13
0	6

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize11.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1.0 (cos x))
12.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
24.0ms	(/ (- 1.0 (cos x)) (* x x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- 1.0 (cos x))
81.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.8s

Counts

48 → 48

Iterations

Iter	Nodes
done	5074
3	2415
2	651
1	217
0	88

prune234.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-sqr-sqrt`
156×	`times-frac`
143×	`*-un-lft-identity`
104×	`sqrt-prod`
89×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-/r*` `flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 206

Calls

4 calls:

12.0ms	(/ (sqrt (- 1.0 (cos x))) x)
75.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
10.0ms	(- 1.0 (cos x))
10.0ms	(- 1.0 (cos x))

series301.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (sqrt (- 1.0 (cos x))) x)
91.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
38.0ms	(- 1.0 (cos x))
36.0ms	(- 1.0 (cos x))

simplify2.4s

Counts

218 → 218

Iterations

Iter	Nodes
done	5000
2	2361
1	724
0	231

prune993.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.2b	(/ (- 1.0 (cos x)) x)
1.2b	(- 1.0 (cos x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

21.0ms	(/ (/ (- 1.0 (cos x)) x) x)
18.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(- 1.0 (cos x))

series155.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (/ (- 1.0 (cos x)) x) x)
56.0ms	(/ (- 1.0 (cos x)) x)
25.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	1389
1	530
0	229

prune618.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

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-cbrt-cube` `add-exp-log`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `difference-cubes` `+-commutative` `sum-log` `sub-neg` `pow-pow` `distribute-lft-in` `flip3--` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

31.0ms	(* (cos x) (+ 1.0 (cos x)))
15.0ms	(+ 1.0 (cos x))
5.0ms	(pow (cos x) 3)
39.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series147.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (cos x) (+ 1.0 (cos x)))
11.0ms	(+ 1.0 (cos x))
35.0ms	(pow (cos x) 3)
66.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	5003
2	1427
1	412
0	146

prune389.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes114.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch108.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	0.033817197098290584
10	-17239113253358.373	-4.96108325192681e-05	-0.031198749760063066

simplify6.0ms

Iterations

Iter	Nodes
done	31
1	31
0	22

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	1664×	body	2560	valid
571.0ms	1176×	body	1280	valid
485.0ms	1501×	body	640	valid
210.0ms	2244×	body	80	valid
168.0ms	941×	body	320	valid
60.0ms	474×	body	160	valid