Details

sample984.0ms

Algorithm

intervals

Results

464.0ms	140×	body	80	valid
119.0ms	103×	body	1280	valid
70.0ms	39×	body	10240	exit
58.0ms	28×	body	1280	nan
42.0ms	59×	body	640	valid
18.0ms	189×	body	80	nan
16.0ms	25×	body	640	nan
13.0ms	18×	body	320	valid
3.0ms	13×	body	160	valid
3.0ms	7×	body	320	nan
2.0ms	8×	body	160	nan

simplify14.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	2880
5	687
4	225
3	81
2	34
1	17
0	8

prune61.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize64.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.1b	(pow (+ x 1.0) (/ 1.0 n))

rewrite591.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

56.0ms	(pow x (/ 1.0 n))
471.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
58.0ms	(pow (+ x 1.0) (/ 1.0 n))

series2.1s

Counts

3 → 9

Calls

3 calls:

181.0ms	(pow x (/ 1.0 n))
1.5s	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
407.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify15.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	4863
2	1448
1	532
0	190

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1.0 n))
0.8b	(pow x (/ 1.0 n))
1.4b	(pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
1.5b	(- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite712.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
24×	`unpow-prod-down` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`times-frac`
15×	`difference-of-squares`
14×	`pow-unpow`
13×	`cbrt-prod` `sqr-pow`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `cbrt-div` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 93

Calls

4 calls:

14.0ms	(cbrt (/ 1.0 n))
10.0ms	(pow x (/ 1.0 n))
24.0ms	(pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
641.0ms	(- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))

series5.7s

Counts

4 → 12

Calls

4 calls:

929.0ms	(cbrt (/ 1.0 n))
136.0ms	(pow x (/ 1.0 n))
1.6s	(pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
3.0s	(- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify7.3s

Counts

105 → 105

Iterations

Iter	Nodes
done	5005
2	2329
1	771
0	304

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.5b

localize75.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
0.8b	(pow x (/ 1.0 n))
1.1b	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
2.2b	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
30×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
14×	`pow1`
12×	`pow-pow`
11×	`unpow-prod-down`
9×	`add-exp-log`
7×	`pow1/3`
6×	`add-log-exp`
4×	`cbrt-prod` `pow-exp` `add-cbrt-cube`
3×	`pow-to-exp` `div-inv` `sqr-pow`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `flip--` `distribute-lft-out`

Counts

4 → 105

Calls

4 calls:

59.0ms	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
13.0ms	(pow x (/ 1.0 n))
26.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
174.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

series8.4s

Counts

4 → 12

Calls

4 calls:

1.3s	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
365.0ms	(pow x (/ 1.0 n))
2.1s	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
4.6s	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify9.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	5032
2	2528
1	835
0	273

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.4b

localize85.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.2b	(log (exp (- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))))
1.4b	(pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
1.5b	(- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
41×	`unpow-prod-down`
30×	`difference-of-squares`
24×	`sqr-pow`
21×	`*-un-lft-identity`
20×	`log-pow`
19×	`exp-prod`
15×	`add-cube-cbrt`
14×	`pow-unpow`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

4 → 105

Calls

4 calls:

28.0ms	(pow x (/ 1.0 n))
1.9s	(log (exp (- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))))
21.0ms	(pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
487.0ms	(- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))

series8.8s

Counts

4 → 12

Calls

4 calls:

604.0ms	(pow x (/ 1.0 n))
4.2s	(log (exp (- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))))
1.4s	(pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
2.6s	(- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify9.6s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	2524
1	826
0	320

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.3b

regimes1.1s

Accuracy

81.6% (1.6b remaining)

Error of 22.1b against oracle of 20.5b and baseline of 29.4b

bsearch825.0ms

Steps

Iters	Range		Point
9	4.314336213415071e-06	0.6307682633451466	0.6224037324982906
10	-88176342586.65536	-1.963203309137196e-05	-24784678.57450563

simplify66.0ms

Iterations

Iter	Nodes
done	63
5	63
4	61
3	58
2	54
1	52
0	44

end11.0ms

sample40.1s

Algorithm

intervals

Results

11.2s	1586×	body	640	valid
9.2s	3166×	body	1280	valid
8.0s	1154×	body	10240	exit
2.7s	625×	body	1280	nan
2.1s	871×	body	320	valid
1.9s	634×	body	640	nan
1.5s	5030×	body	80	nan
1.3s	4669×	body	80	valid
603.0ms	462×	body	160	valid
271.0ms	317×	body	320	nan
81.0ms	202×	body	160	nan