Details

sample47.0ms

Algorithm

intervals

Results

19.0ms	44×	body	2560	valid
8.0ms	37×	body	1280	valid
5.0ms	38×	body	640	valid
3.0ms	32×	body	320	valid
2.0ms	80×	body	80	valid
2.0ms	25×	body	160	valid

simplify13.0ms

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: 28.5b

localize6.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
14.8b	(/ (- 1.0 (cos x)) (* x x))

rewrite16.0ms

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:

3.0ms	(- 1.0 (cos x))
11.0ms	(/ (- 1.0 (cos x)) (* x x))

series64.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
46.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.2s

Counts

64 → 64

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	116	808
1	276	686
2	835	566
3	3656	526
done	5000	525

prune141.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite16.0ms

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))

series176.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))
21.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify1.0s

Counts

113 → 113

Iterations

Useful iterations: 3 (305.0ms)

Iter	Nodes	Cost
0	104	1488
1	211	1135
2	520	888
3	1707	754
done	5001	754

prune256.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

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

series77.0ms

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	(- 1.0 (cos x))

simplify2.0s

Counts

124 → 124

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	71	1684
1	148	1228
2	358	940
3	1201	784
done	5000	748

prune321.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

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

series74.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

124 → 124

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	71	1684
1	148	1228
2	358	940
3	1201	784
done	5000	748

prune328.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes64.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 30.9b

bsearch75.0ms

Steps

Iters	Range		Point
9	3.182061564411226e-09	0.0591185632533196	0.03476390489487963
8	-0.04390830018224924	-1.7961213486546931e-06	-0.03415862644372414

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	88
1	47	88
done	47	88

end0.0ms

sample1.6s

Algorithm

intervals

Results

743.0ms	1610×	body	2560	valid
284.0ms	1251×	body	1280	valid
212.0ms	1470×	body	640	valid
96.0ms	947×	body	320	valid
75.0ms	2245×	body	80	valid
39.0ms	477×	body	160	valid