Details

sample52.0ms

Algorithm

intervals

Results

24.0ms	54×	body	2560	valid
8.0ms	37×	body	1280	valid
8.0ms	52×	body	640	valid
3.0ms	29×	body	320	valid
2.0ms	71×	body	80	valid
1.0ms	13×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	29	8
done	29	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize7.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1.0 (cos x))
16.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

7.0ms	(- 1.0 (cos x))
10.0ms	(/ (- 1.0 (cos x)) (* x x))

series60.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
43.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.8s

Counts

64 → 64

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	116	808
1	272	678
2	845	566
3	3719	526
done	5000	525

prune142.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
48×	`times-frac`
40×	`sqrt-prod`
18×	`prod-diff`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`fma-neg` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 158

Calls

4 calls:

8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (sqrt (- 1.0 (cos x))) x)
90.0ms	(/ (sqrt (- 1.0 (cos x))) x)
21.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

170 → 170

Iterations

Useful iterations: 3 (630.0ms)

Iter	Nodes	Cost
0	160	2330
1	298	1990
2	728	1792
3	2795	1714
done	5000	1714

prune353.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 (cos x)))
1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
5×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

2.0ms	(cbrt (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series177.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (- 1.0 (cos x)))
22.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify928.0ms

Counts

113 → 113

Iterations

Useful iterations: 3 (295.0ms)

Iter	Nodes	Cost
0	104	1488
1	207	1135
2	522	888
3	1845	754
done	5001	754

prune254.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))
1.3b	(log (exp (- 1.0 (cos x))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
33×	`add-cube-cbrt`
14×	`log-prod`
11×	`exp-sum`
10×	`add-log-exp`
9×	`fma-neg`
6×	`log-pow`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 115

Calls

4 calls:

3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
9.0ms	(log (exp (- 1.0 (cos x))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
22.0ms	(log (exp (- 1.0 (cos x))))

simplify1.1s

Counts

127 → 127

Iterations

Useful iterations: 3 (271.0ms)

Iter	Nodes	Cost
0	124	1778
1	206	1240
2	442	947
3	1407	791
done	5001	791

prune304.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0.1b

regimes64.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.6b

bsearch69.0ms

Steps

Iters	Range		Point
10	3.2824798326487284e-15	0.08347146558812443	0.03157722500580303
9	-5.7596417613087905	-6.7357437175194845e-09	-0.03315307006442389

simplify1.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	44
done	26	44

end0.0ms

sample1.6s

Algorithm

intervals

Results

714.0ms	1570×	body	2560	valid
305.0ms	1251×	body	1280	valid
212.0ms	1507×	body	640	valid
94.0ms	935×	body	320	valid
75.0ms	2289×	body	80	valid
32.0ms	448×	body	160	valid