Details

sample110.0ms

Algorithm

intervals

Results

45.0ms	52×	body	2560	valid
23.0ms	46×	body	1280	valid
11.0ms	37×	body	640	valid
9.0ms	39×	body	320	valid
4.0ms	64×	body	80	valid
3.0ms	18×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	17	8
2	28	8
done	28	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize14.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
15.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
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×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

35.0ms	(- 1.0 (cos x))
38.0ms	(/ (- 1.0 (cos x)) (* x x))

series111.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(- 1.0 (cos x))
78.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify5.5s

Counts

48 → 48

Iterations

Useful iterations: done (5.5s)

Iter	Nodes	Cost
0	88	507
1	490	493
done	5001	441

prune205.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
11.2b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

23.0ms	(* 1/720 (pow x 4))
23.0ms	(* 1/24 (pow x 2))
84.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series221.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(* 1/720 (pow x 4))
50.0ms	(* 1/24 (pow x 2))
93.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify2.2s

Counts

75 → 75

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	121	780
1	1334	689
done	5000	642

prune239.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.0b	(- 1.0 (cos x))

rewrite66.0ms

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

Counts

3 → 147

Calls

3 calls:

32.0ms	(/ (/ (- 1.0 (cos x)) x) x)
16.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series148.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ (/ (- 1.0 (cos x)) x) x)
70.0ms	(/ (- 1.0 (cos x)) x)
21.0ms	(- 1.0 (cos x))

simplify4.1s

Counts

156 → 156

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	229	2262
1	1267	2160
done	5001	2046

prune518.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (sqrt (- 1.0 (cos x))))
0.2b	(/ (sqrt (- 1.0 (cos x))) (/ x (sqrt (- 1.0 (cos x)))))
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
346×	`add-sqr-sqrt` `*-un-lft-identity`
310×	`sqrt-prod`
218×	`add-cube-cbrt`
64×	`distribute-lft-out--` `difference-of-squares`
38×	`associate-/r*`
22×	`sqrt-div`
21×	`associate-/r/`
13×	`flip3--` `flip--`
11×	`add-exp-log` `add-cbrt-cube` `div-inv` `associate-/l*`
8×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `div-exp`
2×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 372

Calls

4 calls:

19.0ms	(/ x (sqrt (- 1.0 (cos x))))
57.0ms	(/ (sqrt (- 1.0 (cos x))) (/ x (sqrt (- 1.0 (cos x)))))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series338.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ x (sqrt (- 1.0 (cos x))))
50.0ms	(/ (sqrt (- 1.0 (cos x))) (/ x (sqrt (- 1.0 (cos x)))))
38.0ms	(- 1.0 (cos x))
44.0ms	(- 1.0 (cos x))

simplify6.2s

Counts

384 → 384

Iterations

Useful iterations: done (6.2s)

Iter	Nodes	Cost
0	432	9569
1	2552	8327
done	5000	8104

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 32.0b

bsearch108.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	0.03981852127604897
8	-11.923248480236845	-0.0008047768791668974	-0.030846791202208904

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	48
1	36	46
done	36	46

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.9s	1589×	body	2560	valid
602.0ms	1496×	body	640	valid
599.0ms	1241×	body	1280	valid
299.0ms	953×	body	320	valid
144.0ms	2253×	body	80	valid
76.0ms	468×	body	160	valid