Details

sample243.0ms

Algorithm

intervals

Results

93.0ms	110×	body	1280	valid
32.0ms	56×	body	640	valid
21.0ms	37×	body	10240	exit
21.0ms	20×	body	1280	nan
12.0ms	21×	body	640	nan
11.0ms	131×	body	80	valid
8.0ms	22×	body	320	valid
8.0ms	110×	body	80	nan
5.0ms	13×	body	320	nan
3.0ms	11×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	245	13
5	730	13
6	3688	13
done	5000	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

4.0ms	(pow x (/ 1.0 n))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))
166.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series718.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(pow x (/ 1.0 n))
219.0ms	(pow (+ x 1.0) (/ 1.0 n))
410.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.6s

Counts

158 → 158

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	271	4785
1	647	3566
2	1620	3020
done	5000	2646

prune468.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ (/ 1.0 n) 2))
0.8b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.8b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.2b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
171×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
129×	`pow-unpow`
77×	`unpow-prod-down`
56×	`prod-diff`
25×	`sqr-pow`
12×	`div-inv`
11×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 269

Calls

4 calls:

12.0ms	(pow x (/ (/ 1.0 n) 2))
15.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
19.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
127.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

412.0ms	(pow x (/ (/ 1.0 n) 2))
184.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
202.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
485.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify1.8s

Counts

281 → 281

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	378	7611
1	958	5824
2	2415	5145
done	5000	4547

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite504.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 300

Calls

4 calls:

11.0ms	(pow (+ x 1.0) (/ 1.0 n))
126.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
148.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
201.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.5s

Counts

4 → 12

Calls

4 calls:

253.0ms	(pow (+ x 1.0) (/ 1.0 n))
429.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
400.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
370.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify3.6s

Counts

312 → 312

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	234	12646
1	537	9161
2	1315	7533
3	4460	6435
done	5000	6435

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.5b

localize94.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(fma (pow (cbrt x) (/ 1.0 n)) (- (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))) (pow (cbrt (pow (+ x 1.0) (/ 1.0 n))) 3))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

136×	`unpow-prod-down`
124×	`*-un-lft-identity`
112×	`prod-diff`
100×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
45×	`sqr-pow`
19×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
13×	`pow-unpow`
9×	`times-frac`
8×	`add-log-exp`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `div-inv`

Counts

4 → 220

Calls

4 calls:

13.0ms	(pow (+ x 1.0) (/ 1.0 n))
143.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
163.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.0ms	(fma (pow (cbrt x) (/ 1.0 n)) (- (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))) (pow (cbrt (pow (+ x 1.0) (/ 1.0 n))) 3))

series2.0s

Counts

4 → 12

Calls

4 calls:

233.0ms	(pow (+ x 1.0) (/ 1.0 n))
440.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
388.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
917.0ms	(fma (pow (cbrt x) (/ 1.0 n)) (- (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))) (pow (cbrt (pow (+ x 1.0) (/ 1.0 n))) 3))

simplify1.8s

Counts

232 → 232

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	335	9194
1	841	6404
2	2414	5295
done	5000	4807

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.5b

regimes449.0ms

Accuracy

84.7% (1.3b remaining)

Error of 21.8b against oracle of 20.5b and baseline of 29.3b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	87
1	48	87
done	48	87

end0.0ms

sample8.7s

Algorithm

intervals

Results

2.5s	3165×	body	1280	valid
982.0ms	4619×	body	80	valid
966.0ms	1156×	body	10240	exit
941.0ms	620×	body	640	nan
888.0ms	1531×	body	640	valid
560.0ms	691×	body	1280	nan
456.0ms	860×	body	320	valid
363.0ms	5017×	body	80	nan
146.0ms	337×	body	320	nan
97.0ms	424×	body	160	valid
33.0ms	179×	body	160	nan