Details

sample131.0ms

Algorithm

intervals

Results

46.0ms	95×	body	1280	valid
15.0ms	42×	body	640	valid
14.0ms	33×	body	10240	exit
10.0ms	20×	body	1280	nan
7.0ms	143×	body	80	valid
7.0ms	19×	body	640	nan
6.0ms	170×	body	80	nan
6.0ms	25×	body	320	valid
3.0ms	13×	body	320	nan
2.0ms	18×	body	160	valid
1.0ms	5×	body	160	nan

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	34	13
3	81	13
4	212	13
5	710	13
6	3120	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite50.0ms

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:

2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series478.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
141.0ms	(pow (+ x 1.0) (/ 1.0 n))
277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.5s

Counts

88 → 88

Iterations

Useful iterations: 3 (689.0ms)

Iter	Nodes	Cost
0	190	1337
1	478	1246
2	1265	1206
3	3956	1183
done	5001	1183

prune235.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.7b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
3.1b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite149.0ms

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:

2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
96.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series968.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(pow x (/ 1.0 n))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
283.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
283.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.6s

Counts

121 → 121

Iterations

Useful iterations: 3 (740.0ms)

Iter	Nodes	Cost
0	235	1971
1	543	1802
2	1366	1714
3	4113	1683
done	5000	1683

prune348.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.7b

localize15.0ms

Local error

Found 4 expressions with local error:

3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
3.1b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`unpow-prod-down`
18×	`difference-of-squares`
16×	`log-prod`
12×	`sqr-pow`
10×	`cbrt-prod`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`sub-neg` `exp-sum` `log-pow` `add-cbrt-cube`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
38.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
38.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
290.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
464.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
453.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: 3 (296.0ms)

Iter	Nodes	Cost
0	141	2446
1	301	2376
2	751	2198
3	2317	2150
done	5000	2150

prune473.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.6b

localize17.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (+ x 1.0) (/ 1.0 n))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
39.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

154.0ms	(pow (+ x 1.0) (/ 1.0 n))
289.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
291.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
459.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify1.4s

Counts

107 → 107

Iterations

Useful iterations: 3 (612.0ms)

Iter	Nodes	Cost
0	195	2249
1	439	2153
2	1098	2026
3	3193	1993
done	5001	1993

prune438.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.6b

regimes247.0ms

Accuracy

79.8% (1.7b remaining)

Error of 23.0b against oracle of 21.3b and baseline of 29.7b

bsearch214.0ms

Steps

Iters	Range		Point
11	1.316736141892985e-13	3568380.5266111037	142153.58580214932
7	-6.957256490440221e+20	-4.3263376605350497e+18	-4.3921114290106465e+18

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	37	90
1	50	68
done	50	68

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	3173×	body	1280	valid
542.0ms	1552×	body	640	valid
488.0ms	1149×	body	10240	exit
292.0ms	620×	body	1280	nan
265.0ms	4667×	body	80	valid
216.0ms	653×	body	640	nan
186.0ms	828×	body	320	valid
185.0ms	5001×	body	80	nan
73.0ms	374×	body	320	nan
67.0ms	461×	body	160	valid
20.0ms	173×	body	160	nan