Details

sample130.0ms

Algorithm

intervals

Results

55.0ms	41×	body	2560	valid
42.0ms	91×	body	1280	valid
13.0ms	55×	body	640	valid
6.0ms	37×	body	320	valid
3.0ms	22×	body	160	valid
1.0ms	10×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune9.0ms

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: 29.5b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series12.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

simplify949.0ms

Counts

58 → 58

Iterations

Useful iterations: 4 (411.0ms)

Iter	Nodes	Cost
0	106	665
1	235	645
2	560	611
3	1377	609
4	3599	608
done	5001	608

prune137.0ms

Filtered

42 candidates to 58 candidates (-38.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	43	15	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	15	59

Merged error: 0.2b

Counts

59 → 15

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.1b	(- 1.0 (cos x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

8.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
5.0ms	(exp (log (- 1.0 (cos x))))
4.0ms	(log (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series29.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms	(exp (log (- 1.0 (cos x))))
14.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

110 → 110

Iterations

Useful iterations: 4 (512.0ms)

Iter	Nodes	Cost
0	168	1421
1	295	1184
2	728	1117
3	1703	1115
4	4404	1104
done	5000	1104

prune181.0ms

Filtered

67 candidates to 110 candidates (-64.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	108	17	125

Merged error: 0.2b

Counts

125 → 17

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.1b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series32.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

124 → 124

Iterations

Useful iterations: 4 (495.0ms)

Iter	Nodes	Cost
0	163	1406
1	305	1295
2	672	1222
3	1642	1218
4	4439	1217
done	5000	1217

prune225.0ms

Filtered

90 candidates to 124 candidates (-37.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	116	8	124
Fresh	8	8	16
Picked	1	0	1
Done	0	0	0
Total	125	16	141

Merged error: 0.2b

Counts

141 → 16

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(log (- 1.0 (cos x)))
0.4b	(pow E (log (- 1.0 (cos x))))
2.1b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`times-frac`
33×	`add-cube-cbrt`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `pow-sub`
3×	`associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 124

Calls

4 calls:

12.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
3.0ms	(log (- 1.0 (cos x)))
5.0ms	(pow E (log (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))

series84.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
14.0ms	(log (- 1.0 (cos x)))
31.0ms	(pow E (log (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

simplify912.0ms

Counts

136 → 136

Iterations

Useful iterations: 3 (318.0ms)

Iter	Nodes	Cost
0	214	2049
1	413	1947
2	1126	1818
3	3790	1625
done	5000	1625

prune192.0ms

Filtered

96 candidates to 136 candidates (-41.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	130	6	136
Fresh	4	11	15
Picked	0	1	1
Done	0	0	0
Total	134	18	152

Merged error: 0.2b

Counts

152 → 18

regimes277.0ms

Accuracy

98.5% (0.5b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.7b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	55
1	38	46
2	40	46
done	40	46

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.2s	1629×	body	2560	valid
1.3s	2779×	body	1280	valid
486.0ms	1838×	body	640	valid
162.0ms	914×	body	320	valid
57.0ms	456×	body	160	valid
34.0ms	377×	body	80	valid
13.0ms	7×	body	5120	valid

Details

sample130.0ms

simplify6.0ms

prune9.0ms

localize7.0ms

rewrite12.0ms

series12.0ms

simplify949.0ms

prune137.0ms

localize10.0ms

rewrite25.0ms

series29.0ms

simplify1.1s

prune181.0ms

localize10.0ms

rewrite30.0ms

series32.0ms

simplify1.1s

prune225.0ms

localize11.0ms

rewrite30.0ms

series84.0ms

simplify912.0ms

prune192.0ms

regimes277.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample4.5s

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