Details

sample95.0ms

Algorithm

intervals

Results

25.0ms	100×	body	2560	nan
18.0ms	500×	body	80	nan
14.0ms	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

simplify4.0ms

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

localize7.0ms

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))

simplify645.0ms

Counts

37 → 37

Iterations

Useful iterations: 3 (210.0ms)

Iter	Nodes	Cost
0	125	556
1	270	511
2	788	456
3	2759	448
done	5001	448

prune74.0ms

Filtered

30 candidates to 37 candidates (-23.3%)

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

localize10.0ms

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))))

simplify1.1s

Counts

62 → 62

Iterations

Useful iterations: 3 (386.0ms)

Iter	Nodes	Cost
0	178	1279
1	391	1107
2	1295	1043
3	4654	1032
done	5000	1032

prune150.0ms

Filtered

47 candidates to 62 candidates (-31.9%)

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))

rewrite99.0ms

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:

38.0ms	(+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2)))
5.0ms	(/ 0.09375 (pow x 4))
44.0ms	(- (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))

simplify481.0ms

Counts

152 → 152

Iterations

Useful iterations: done (477.0ms)

Iter	Nodes	Cost
0	246	2115
1	514	1989
2	1641	1815
done	5000	1799

prune274.0ms

Filtered

98 candidates to 152 candidates (-55.1%)

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

localize17.0ms

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)))))

rewrite191.0ms

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:

45.0ms	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (pow x 2))) (log x)))
5.0ms	(/ 0.25 (pow x 2))
5.0ms	(/ 0.25 (pow x 2))
103.0ms	(* (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)))))

series36.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (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)))))

simplify434.0ms

Counts

342 → 342

Iterations

Useful iterations: done (413.0ms)

Iter	Nodes	Cost
0	221	10526
1	420	6280
2	1367	5850
done	5000	5846

prune586.0ms

Filtered

120 candidates to 342 candidates (-185.0%)

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

regimes104.0ms

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

619.0ms	3003×	body	2560	nan
581.0ms	15817×	body	80	nan
430.0ms	2477×	body	1280	nan
346.0ms	8000×	body	80	valid
168.0ms	1227×	body	640	nan
61.0ms	596×	body	320	nan
22.0ms	304×	body	160	nan

Details

sample95.0ms

simplify4.0ms

prune3.0ms

localize7.0ms

rewrite13.0ms

series14.0ms

simplify645.0ms

prune74.0ms

localize10.0ms

rewrite19.0ms

series28.0ms

simplify1.1s

prune150.0ms

localize14.0ms

rewrite99.0ms

series28.0ms

simplify481.0ms

prune274.0ms

localize17.0ms

rewrite191.0ms

series36.0ms

simplify434.0ms

prune586.0ms

regimes104.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling