Details

sample62.0ms

Algorithm

intervals

Results

21.0ms	41×	body	2560	valid
12.0ms	41×	body	1280	valid
7.0ms	45×	body	640	valid
4.0ms	36×	body	320	valid
2.0ms	70×	body	80	valid
2.0ms	23×	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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
13.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

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:

4.0ms	(- 1.0 (cos x))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
6.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.8s

Counts

48 → 48

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	88	507
1	218	489
2	636	441
3	2192	441
done	5000	440

prune107.0ms

Filtered

34 candidates to 48 candidates (-41.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	37	11	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	11	49

Merged error: 0.2b

Counts

49 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
28×	`cbrt-prod`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1`
10×	`swap-sqr` `add-log-exp`
9×	`flip3--` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log` `pow1/3`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 98

Calls

4 calls:

14.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series36.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

simplify1.0s

Counts

110 → 110

Iterations

Useful iterations: 3 (305.0ms)

Iter	Nodes	Cost
0	119	1410
1	224	1280
2	553	1212
3	1590	1117
done	5001	1117

prune219.0ms

Filtered

70 candidates to 110 candidates (-57.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Merged error: 0.1b

Counts

121 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.3b	(log (exp (- 1.0 (cos x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
6×	`add-cube-cbrt` `log-pow`
5×	`pow1` `log-prod` `exp-prod`
4×	`add-exp-log` `sub-neg` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `diff-log` `flip--`
2×	`exp-sum`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 62

Calls

4 calls:

7.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
6.0ms	(log (exp (- 1.0 (cos x))))

series13.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.8s

Counts

74 → 74

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	72	615
1	128	556
2	245	519
3	518	519
4	1770	519
done	5001	519

prune180.0ms

Filtered

52 candidates to 74 candidates (-42.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	74	11	85

Merged error: 0.1b

Counts

85 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.3b	(log (exp (- 1.0 (cos x))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
6×	`add-cube-cbrt` `log-pow`
5×	`pow1` `log-prod` `exp-prod`
4×	`add-exp-log` `sub-neg` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `diff-log` `flip--`
2×	`exp-sum`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 62

Calls

4 calls:

4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
6.0ms	(log (exp (- 1.0 (cos x))))

series16.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
6.0ms	(log (exp (- 1.0 (cos x))))

simplify1.7s

Counts

74 → 74

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	72	615
1	128	556
2	245	519
3	518	519
4	1770	519
done	5001	519

prune166.0ms

Filtered

52 candidates to 74 candidates (-42.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	74	11	85

Merged error: 0.1b

Counts

85 → 11

regimes146.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 31.4b

bsearch28.0ms

Steps

Iters	Range		Point
9	0.009971872296741319	901.3230478674768	0.0342323272118313
7	-0.0552767792151412	-0.0004813576712207844	-0.03453332244767238

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	58
1	41	58
done	41	58

end0.0ms

sample1.9s

Algorithm

intervals

Results

888.0ms	1637×	body	2560	valid
356.0ms	1266×	body	1280	valid
253.0ms	1449×	body	640	valid
112.0ms	912×	body	320	valid
84.0ms	2278×	body	80	valid
39.0ms	458×	body	160	valid

Details

sample62.0ms

simplify12.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series9.0ms

simplify1.8s

prune107.0ms

localize10.0ms

rewrite30.0ms

series36.0ms

simplify1.0s

prune219.0ms

localize14.0ms

rewrite22.0ms

series13.0ms

simplify1.8s

prune180.0ms

localize19.0ms

rewrite20.0ms

series16.0ms

simplify1.7s

prune166.0ms

regimes146.0ms

bsearch28.0ms

simplify3.0ms

end0.0ms

sample1.9s

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