Details

sample246.0ms

Algorithm

intervals

Results

76.0ms	95×	body	1280	valid
33.0ms	50×	body	10240	exit
26.0ms	44×	body	640	valid
17.0ms	174×	body	80	valid
15.0ms	23×	body	1280	nan
14.0ms	193×	body	80	nan
11.0ms	30×	body	320	valid
9.0ms	20×	body	640	nan
4.0ms	11×	body	320	nan
4.0ms	14×	body	160	valid
2.0ms	9×	body	160	nan

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	34	13
3	81	13
4	238	13
5	1224	13
done	5000	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite156.0ms

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:

9.0ms	(pow x (/ 1.0 n))
22.0ms	(pow (+ x 1.0) (/ 1.0 n))
120.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

3 → 9

Calls

3 calls:

512.0ms	(pow x (/ 1.0 n))
204.0ms	(pow (+ x 1.0) (/ 1.0 n))
408.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.3s

Counts

88 → 88

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	190	1337
1	546	1246
2	2100	1206
done	5000	1204

prune314.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite405.0ms

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:

8.0ms	(pow x (/ 1.0 n))
18.0ms	(pow (+ x 1.0) (/ 1.0 n))
109.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
261.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

107.0ms	(pow x (/ 1.0 n))
244.0ms	(pow (+ x 1.0) (/ 1.0 n))
389.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
392.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify1.4s

Counts

121 → 121

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	235	1971
1	631	1802
2	2341	1714
done	5000	1712

prune523.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.3b

localize32.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite473.0ms

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:

130.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
120.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
107.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
111.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series2.1s

Counts

4 → 12

Calls

4 calls:

469.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
426.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
693.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
556.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify607.0ms

Counts

98 → 98

Iterations

Useful iterations: done (601.0ms)

Iter	Nodes	Cost
0	141	2446
1	305	2374
2	950	2196
done	5001	2156

prune712.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.2b

localize45.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down`
9×	`difference-of-squares`
7×	`pow1` `add-exp-log`
6×	`exp-sum` `log-pow` `add-log-exp` `sqr-pow`
4×	`sub-neg` `add-cbrt-cube`
3×	`log-div` `cbrt-div` `exp-diff` `pow1/3` `rem-log-exp` `distribute-lft-out--`
1×	`flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

122.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
87.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
93.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
109.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

424.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
693.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
695.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
729.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify650.0ms

Counts

93 → 93

Iterations

Useful iterations: done (645.0ms)

Iter	Nodes	Cost
0	141	2325
1	305	2269
2	950	2070
done	5001	2018

prune708.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.2b

regimes278.0ms

Accuracy

81.2% (1.5b remaining)

Error of 22.3b against oracle of 20.8b and baseline of 28.8b

bsearch266.0ms

Steps

Iters	Range		Point
8	2.774806821063677e+19	8.926171046859927e+23	2.8287508845642576e+19
10	-2793354732730.816	-0.0035923013514488687	-73053226.23717305

simplify31.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	73
1	41	49
2	45	49
3	48	49
done	48	49

end0.0ms

sample8.5s

Algorithm

intervals

Results

2.4s	3070×	body	1280	valid
1.5s	1179×	body	10240	exit
1.2s	1546×	body	640	valid
625.0ms	654×	body	1280	nan
473.0ms	4787×	body	80	valid
454.0ms	5076×	body	80	nan
394.0ms	679×	body	640	nan
330.0ms	915×	body	320	valid
110.0ms	338×	body	320	nan
95.0ms	435×	body	160	valid
32.0ms	163×	body	160	nan