Details

sample193.0ms

Algorithm

intervals

Results

61.0ms	98×	body	1280	valid
23.0ms	53×	body	640	valid
23.0ms	33×	body	10240	exit
13.0ms	173×	body	80	valid
11.0ms	178×	body	80	nan
11.0ms	23×	body	640	nan
9.0ms	12×	body	1280	nan
6.0ms	19×	body	320	valid
4.0ms	17×	body	320	nan
1.0ms	9×	body	160	nan
1.0ms	8×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1231
4	238
3	81
2	34
1	17
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.5b	(pow (+ 1.0 x) (/ 1.0 n))
1.1b	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite85.0ms

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:

3.0ms	(pow x (/ 1.0 n))
9.0ms	(pow (+ 1.0 x) (/ 1.0 n))
69.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))

series650.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(pow x (/ 1.0 n))
225.0ms	(pow (+ 1.0 x) (/ 1.0 n))
327.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify986.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2071
1	544
0	189

prune526.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.1b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 109

Calls

4 calls:

3.0ms	(pow x (/ 1.0 n))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))
95.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
219.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

95.0ms	(pow x (/ 1.0 n))
252.0ms	(pow (+ x 1.0) (/ 1.0 n))
461.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
430.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify1.0s

Counts

121 → 121

Iterations

Iter	Nodes
done	5001
2	2309
1	629
0	234

prune821.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.1b

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.1b	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.2b	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite510.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
40×	`unpow-prod-down`
38×	`*-un-lft-identity`
36×	`log-pow` `difference-of-squares`
32×	`sqrt-pow1`
30×	`exp-prod`
24×	`sqr-pow`
16×	`log-prod`
12×	`distribute-lft-out--`
10×	`add-cube-cbrt` `sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`sub-neg` `add-cbrt-cube` `exp-sum` `distribute-lft-out`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 118

Calls

4 calls:

90.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))
74.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))
170.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n))))))
171.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

436.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))
470.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))
683.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n))))))
682.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify472.0ms

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1035
1	356
0	168

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.1b

localize47.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.4b	(log (sqrt (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
1.4b	(log (sqrt (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

rewrite723.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-pow1`
63×	`add-sqr-sqrt`
58×	`log-pow`
45×	`exp-prod`
43×	`*-un-lft-identity`
40×	`unpow-prod-down`
36×	`difference-of-squares`
31×	`sqrt-prod`
30×	`log-prod`
24×	`sqr-pow`
15×	`add-cube-cbrt`
12×	`pow1` `distribute-lft-out--`
7×	`add-exp-log`
6×	`exp-sum` `add-log-exp`
5×	`pow1/2` `sqrt-div`
4×	`sub-neg` `add-cbrt-cube` `distribute-lft-out`
3×	`log-div` `exp-diff` `rem-log-exp`
1×	`flip3--` `diff-log` `flip--`

Counts

4 → 139

Calls

4 calls:

83.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))
209.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n))))))
213.0ms	(log (sqrt (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
211.0ms	(log (sqrt (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

391.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))
749.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n))))))
680.0ms	(log (sqrt (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
740.0ms	(log (sqrt (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

simplify640.0ms

Counts

151 → 151

Iterations

Iter	Nodes
done	5001
2	1270
1	431
0	210

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 20.1b

regimes665.0ms

Accuracy

80.9% (1.7b remaining)

Error of 22.2b against oracle of 20.5b and baseline of 29.3b

bsearch2.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	47
2	47
1	45
0	37

end0.0ms

sample8.5s

Algorithm

intervals

Results

2.8s	3148×	body	1280	valid
1.4s	1102×	body	10240	exit
1.0s	1592×	body	640	valid
594.0ms	672×	body	1280	nan
594.0ms	4688×	body	80	valid
383.0ms	656×	body	640	nan
354.0ms	5119×	body	80	nan
300.0ms	864×	body	320	valid
154.0ms	360×	body	320	nan
91.0ms	428×	body	160	valid
35.0ms	191×	body	160	nan