Details

sample64.0ms

Algorithm

intervals

Results

22.0ms	41×	body	2560	valid
12.0ms	41×	body	1280	valid
7.0ms	45×	body	640	valid
5.0ms	36×	body	320	valid
3.0ms	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))

rewrite13.0ms

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))

series10.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify740.0ms

Counts

48 → 48

Iterations

Useful iterations: done (739.0ms)

Iter	Nodes	Cost
0	88	507
1	220	499
2	676	445
3	1934	441
done	5000	440

prune113.0ms

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:

11.0ms	(* (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))

series39.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

110 → 110

Iterations

Useful iterations: 4 (592.0ms)

Iter	Nodes	Cost
0	119	1410
1	226	1296
2	662	1212
3	1701	1129
4	4760	1097
done	5000	1097

prune220.0ms

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

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (- 1.0 (cos x)) 2))
1.7b	(log (exp (cbrt (pow (- 1.0 (cos x)) 2))))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod`
18×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`log-pow`
13×	`exp-prod`
10×	`add-cube-cbrt` `unpow-prod-down`
8×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`log-prod`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `unpow2` `sqr-pow`
1×	`pow1/3` `rem-log-exp`

Counts

4 → 71

Calls

4 calls:

5.0ms	(cbrt (pow (- 1.0 (cos x)) 2))
7.0ms	(log (exp (cbrt (pow (- 1.0 (cos x)) 2))))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series65.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt (pow (- 1.0 (cos x)) 2))
31.0ms	(log (exp (cbrt (pow (- 1.0 (cos x)) 2))))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

83 → 83

Iterations

Useful iterations: 4 (570.0ms)

Iter	Nodes	Cost
0	129	932
1	231	843
2	519	724
3	1411	690
4	4400	686
done	5000	686

prune204.0ms

Filtered

57 candidates to 83 candidates (-45.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	82	12	94

Merged error: 0.1b

Counts

94 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

1.7b	(log (exp (cbrt (pow (- 1.0 (cos x)) 2))))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.3b	(log (exp (- 1.0 (cos x))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

20×	`log-pow`
18×	`add-sqr-sqrt` `exp-prod` `*-un-lft-identity`
10×	`cbrt-prod` `add-cube-cbrt`
8×	`log-prod` `add-log-exp`
6×	`pow1`
5×	`unpow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg`
2×	`flip3--` `diff-log` `rem-log-exp` `exp-sum` `flip--`
1×	`log-div` `exp-diff` `unpow2` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

7.0ms	(log (exp (cbrt (pow (- 1.0 (cos x)) 2))))
4.0ms	(- 1.0 (cos x))
5.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(log (exp (cbrt (pow (- 1.0 (cos x)) 2))))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
3.0ms	(log (exp (- 1.0 (cos x))))

simplify1.7s

Counts

85 → 85

Iterations

Useful iterations: 4 (630.0ms)

Iter	Nodes	Cost
0	147	838
1	257	715
2	566	645
3	1486	630
4	4393	622
done	5000	622

prune194.0ms

Filtered

60 candidates to 85 candidates (-41.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	86	11	97

Merged error: 0.1b

Counts

97 → 11

regimes86.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.3b

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	35	53
1	40	53
done	40	53

end0.0ms

sample1.9s

Algorithm

intervals

Results

880.0ms	1637×	body	2560	valid
352.0ms	1266×	body	1280	valid
272.0ms	1449×	body	640	valid
114.0ms	912×	body	320	valid
93.0ms	2278×	body	80	valid
40.0ms	458×	body	160	valid

Details

sample64.0ms

simplify12.0ms

prune2.0ms

localize6.0ms

rewrite13.0ms

series10.0ms

simplify740.0ms

prune113.0ms

localize10.0ms

rewrite30.0ms

series39.0ms

simplify1.6s

prune220.0ms

localize15.0ms

rewrite23.0ms

series65.0ms

simplify1.5s

prune204.0ms

localize18.0ms

rewrite23.0ms

series37.0ms

simplify1.7s

prune194.0ms

regimes86.0ms

bsearch28.0ms

simplify3.0ms

end0.0ms

sample1.9s

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