Details

sample97.0ms

Algorithm

intervals

Results

25.0ms	100×	body	2560	nan
18.0ms	500×	body	80	nan
15.0ms	83×	body	1280	nan
11.0ms	256×	body	80	valid
4.0ms	30×	body	640	nan
2.0ms	20×	body	320	nan
0.0ms	5×	body	160	nan

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	11	9
done	11	9

prune3.0ms

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: 32.9b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(log (+ x (sqrt (- (* x x) 1.0))))
30.5b	(sqrt (- (* x x) 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-cube-cbrt` `log-prod` `sqrt-prod`
3×	`add-exp-log`
2×	`log-div` `sqrt-div` `add-cbrt-cube` `add-log-exp`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `log-pow` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

2 → 31

Calls

2 calls:

7.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms	(sqrt (- (* x x) 1.0))

series14.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(sqrt (- (* x x) 1.0))

simplify603.0ms

Counts

37 → 37

Iterations

Useful iterations: 3 (214.0ms)

Iter	Nodes	Cost
0	125	556
1	270	507
2	762	456
3	2577	448
done	5000	448

prune76.0ms

Filtered

31 candidates to 37 candidates (-19.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	3	38

Merged error: 0.0b

Counts

38 → 3

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
11×	`*-un-lft-identity`
9×	`associate-r`
7×	`pow1` `add-cube-cbrt` `associate-l`
5×	`add-exp-log`
4×	`frac-times` `flip3-+` `add-cbrt-cube` `flip-+` `unswap-sqr`
3×	`log-prod` `flip3--` `pow-prod-down` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `add-log-exp` `difference-of-squares`
1×	`sqrt-unprod` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 56

Calls

2 calls:

3.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
14.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series28.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify948.0ms

Counts

62 → 62

Iterations

Useful iterations: 3 (375.0ms)

Iter	Nodes	Cost
0	178	1279
1	391	1098
2	1296	1042
3	4413	1026
done	5000	1026

prune152.0ms

Filtered

48 candidates to 62 candidates (-29.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	62	3	65

Merged error: 0.0b

Counts

65 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2)))
0.1b	(/ 0.09375 (pow x 4))
0.2b	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))
0.5b	(/ 0.25 (pow x 2))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
47×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
24×	`unpow-prod-down`
18×	`distribute-lft-out--`
15×	`associate-/r*`
14×	`add-exp-log`
13×	`pow1`
10×	`add-log-exp`
9×	`log-pow`
8×	`add-cbrt-cube` `sqr-pow`
6×	`div-exp` `distribute-lft-out` `associate-/l*`
5×	`diff-log`
4×	`associate--l+` `unpow2`
3×	`log-prod` `associate--r+`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `frac-2neg` `pow-exp` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `flip3--` `flip3-+` `frac-add` `flip--` `flip-+` `associate--r-` `difference-of-squares`

Counts

4 → 140

Calls

4 calls:

39.0ms	(+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2)))
5.0ms	(/ 0.09375 (pow x 4))
45.0ms	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))
5.0ms	(/ 0.25 (pow x 2))

series28.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2)))
4.0ms	(/ 0.09375 (pow x 4))
11.0ms	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))
3.0ms	(/ 0.25 (pow x 2))

simplify407.0ms

Counts

152 → 152

Iterations

Useful iterations: 2 (140.0ms)

Iter	Nodes	Cost
0	246	2115
1	514	1971
2	1613	1793
done	5000	1793

prune262.0ms

Filtered

93 candidates to 152 candidates (-63.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	152	3	155

Merged error: 0b

Counts

155 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))
0.5b	(/ 0.25 (pow x 2))
0.5b	(/ 0.25 (pow x 2))
0.5b	(* (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))) (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

642×	`*-un-lft-identity`
450×	`distribute-lft-out--`
282×	`sqrt-prod`
244×	`pow1`
225×	`log-pow`
129×	`swap-sqr`
100×	`distribute-lft-out`
69×	`add-sqr-sqrt`
48×	`times-frac`
47×	`add-cube-cbrt`
24×	`unpow-prod-down`
17×	`associate-r` `associate-l`
16×	`add-exp-log` `associate-/r*`
12×	`sqrt-div`
10×	`add-cbrt-cube`
8×	`sqrt-pow1` `pow1/2` `unpow2` `add-log-exp` `sqr-pow`
7×	`flip3--` `flip--`
6×	`div-exp` `associate-/l*`
5×	`diff-log` `pow-prod-up` `difference-of-squares`
4×	`frac-times` `associate--l+` `unswap-sqr`
3×	`log-prod` `pow-prod-down` `pow-sqr` `associate--r+`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `frac-2neg` `associate-r/` `associate-l/` `pow-exp` `clear-num` `div-inv`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `associate--r-`

Counts

4 → 330

Calls

4 calls:

47.0ms	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))
5.0ms	(/ 0.25 (pow x 2))
6.0ms	(/ 0.25 (pow x 2))
105.0ms	(* (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))) (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))))

series31.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))
3.0ms	(/ 0.25 (pow x 2))
3.0ms	(/ 0.25 (pow x 2))
13.0ms	(* (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))) (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))))

simplify389.0ms

Counts

342 → 342

Iterations

Useful iterations: 2 (129.0ms)

Iter	Nodes	Cost
0	221	10526
1	420	6259
2	1337	5840
done	5000	5840

prune772.0ms

Filtered

117 candidates to 342 candidates (-192.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	342	0	342
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	342	3	345

Merged error: 0b

Counts

345 → 3

regimes105.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
done	13	14

end0.0ms

sample2.8s

Algorithm

intervals

Results

641.0ms	3003×	body	2560	nan
594.0ms	15817×	body	80	nan
436.0ms	2477×	body	1280	nan
343.0ms	8000×	body	80	valid
176.0ms	1227×	body	640	nan
62.0ms	596×	body	320	nan
22.0ms	304×	body	160	nan

Details

sample97.0ms

simplify5.0ms

prune3.0ms

localize9.0ms

rewrite13.0ms

series14.0ms

simplify603.0ms

prune76.0ms

localize11.0ms

rewrite19.0ms

series28.0ms

simplify948.0ms

prune152.0ms

localize14.0ms

rewrite101.0ms

series28.0ms

simplify407.0ms

prune262.0ms

localize18.0ms

rewrite195.0ms

series31.0ms

simplify389.0ms

prune772.0ms

regimes105.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling