Details

sample136.0ms

Algorithm

intervals

Results

56.0ms	57×	body	2560	valid
23.0ms	44×	body	1280	valid
19.0ms	56×	body	640	valid
7.0ms	28×	body	320	valid
6.0ms	57×	body	80	valid
3.0ms	14×	body	160	valid

simplify87.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize63.0ms

Local error

Found 2 expressions with local error:

2.6b	(- 1.0 (cos x))
17.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite57.0ms

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` `insert-posit16` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 44

Calls

2 calls:

9.0ms	(- 1.0 (cos x))
45.0ms	(/ (- 1.0 (cos x)) (* x x))

series439.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(- 1.0 (cos x))
408.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify3.7s

Counts

50 → 50

Iterations

Iter	Nodes
done	5000
3	2322
2	625
1	219
0	90

prune549.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (* x x) 1/720) 1/24)
0.1b	(* (* x x) (- (* (* x x) 1/720) 1/24))
0.2b	(* (* x x) 1/720)

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`sub-neg` `insert-posit16`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-l` `associate-r/` `-commutative` `flip--` `unswap-sqr`
1×	`diff-log`

Counts

3 → 59

Calls

3 calls:

51.0ms	(- (* (* x x) 1/720) 1/24)
217.0ms	(* (* x x) (- (* (* x x) 1/720) 1/24))
35.0ms	(* (* x x) 1/720)

series340.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(- (* (* x x) 1/720) 1/24)
186.0ms	(* (* x x) (- (* (* x x) 1/720) 1/24))
47.0ms	(* (* x x) 1/720)

simplify6.8s

Counts

68 → 68

Iterations

Iter	Nodes
done	5015
3	3296
2	816
1	254
0	90

prune609.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.6b	(- 1.0 (cos x))

rewrite123.0ms

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` `insert-posit16` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 150

Calls

3 calls:

34.0ms	(/ (/ (- 1.0 (cos x)) x) x)
50.0ms	(/ (- 1.0 (cos x)) x)
17.0ms	(- 1.0 (cos x))

series192.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ (/ (- 1.0 (cos x)) x) x)
78.0ms	(/ (- 1.0 (cos x)) x)
42.0ms	(- 1.0 (cos x))

simplify2.9s

Counts

159 → 159

Iterations

Iter	Nodes
done	5001
2	1357
1	527
0	232

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (- 1.0 (cos x))) (/ (/ (sqrt (- 1.0 (cos x))) x) x))
0.1b	(/ (sqrt (- 1.0 (cos x))) x)
2.6b	(- 1.0 (cos x))
2.6b	(- 1.0 (cos x))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

190×	`times-frac`
155×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
97×	`add-cube-cbrt`
88×	`associate-r`
76×	`sqrt-prod`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-cbrt-cube` `add-exp-log`
8×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
6×	`pow1` `sqrt-div`
5×	`flip3--` `div-inv` `flip--`
4×	`cbrt-undiv` `div-exp` `insert-posit16`
3×	`associate-/r*` `prod-exp` `cbrt-unprod`
2×	`frac-times` `sub-neg` `diff-log` `associate-*l/` `associate-/l/`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 205

Calls

4 calls:

149.0ms	(* (sqrt (- 1.0 (cos x))) (/ (/ (sqrt (- 1.0 (cos x))) x) x))
37.0ms	(/ (sqrt (- 1.0 (cos x))) x)
18.0ms	(- 1.0 (cos x))
17.0ms	(- 1.0 (cos x))

series331.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (sqrt (- 1.0 (cos x))) (/ (/ (sqrt (- 1.0 (cos x))) x) x))
156.0ms	(/ (sqrt (- 1.0 (cos x))) x)
48.0ms	(- 1.0 (cos x))
44.0ms	(- 1.0 (cos x))

simplify4.5s

Counts

217 → 217

Iterations

Iter	Nodes
done	5067
2	2451
1	824
0	310

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes342.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.9b

bsearch176.0ms

Steps

Iters	Range		Point
10	1.508099977930646e-06	2590629949647.022	0.031106757764091195
10	-26711381.42537418	-6.803810524357175e-07	-0.027405319297458403

simplify34.0ms

Iterations

Iter	Nodes
done	33
1	33
0	28

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.8s	1604×	body	2560	valid
656.0ms	1239×	body	1280	valid
466.0ms	1505×	body	640	valid
230.0ms	931×	body	320	valid
127.0ms	2254×	body	80	valid
59.0ms	467×	body	160	valid