Details

sample208.0ms

Algorithm

intervals

Results

62.0ms	111×	body	1280	valid
35.0ms	141×	body	80	valid
27.0ms	67×	body	640	valid
15.0ms	42×	body	10240	exit
11.0ms	179×	body	80	nan
9.0ms	20×	body	1280	nan
7.0ms	17×	body	640	nan
6.0ms	23×	body	320	valid
4.0ms	27×	body	160	valid
3.0ms	13×	body	320	nan
0.0ms	3×	body	160	nan

simplify3.4s

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: 34.6b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite186.0ms

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))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
164.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series750.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(pow x (/ 1.0 n))
215.0ms	(pow (+ x 1.0) (/ 1.0 n))
465.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.3s

Counts

158 → 158

Iterations

Useful iterations: done (1.3s)

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

prune429.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite441.0ms

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:

22.0ms	(pow (+ x 1.0) (/ 1.0 n))
150.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
122.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
112.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.5s

Counts

4 → 12

Calls

4 calls:

217.0ms	(pow (+ x 1.0) (/ 1.0 n))
426.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
441.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
446.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify3.4s

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

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.8b

localize43.0ms

Local error

Found 4 expressions with local error:

3.2b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite781.0ms

Algorithm

rewrite-expression-head

Rules

260×	`unpow-prod-down`
224×	`prod-diff`
222×	`*-un-lft-identity`
180×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
87×	`sqr-pow`
61×	`log-prod`
58×	`exp-sum`
36×	`difference-of-squares`
35×	`distribute-lft-out`
24×	`fma-neg`
16×	`log-pow`
15×	`exp-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 358

Calls

4 calls:

279.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
168.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
130.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
180.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.8s

Counts

4 → 12

Calls

4 calls:

405.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
451.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
459.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
459.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify3.2s

Counts

370 → 370

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	344	16510
1	588	11634
2	1247	9453
3	4232	7993
done	5000	7993

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.8b

localize60.0ms

Local error

Found 4 expressions with local error:

3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite530.0ms

Algorithm

rewrite-expression-head

Rules

264×	`unpow-prod-down`
224×	`*-un-lft-identity` `prod-diff`
180×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
88×	`sqr-pow`
36×	`distribute-lft-out` `difference-of-squares`
32×	`fma-neg`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 360

Calls

4 calls:

118.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
113.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
112.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
147.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.7s

Counts

4 → 12

Calls

4 calls:

423.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
412.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
435.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
403.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.5s

Counts

372 → 372

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	185	16368
1	410	11772
2	988	9604
3	3766	8144
done	5000	8140

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.8b

regimes216.0ms

Accuracy

85.6% (1.3b remaining)

Error of 22.1b against oracle of 20.7b and baseline of 29.9b

bsearch283.0ms

Steps

Iters	Range		Point
8	117903708159.89047	4303156525810183.0	119943181516.0245
10	-30636816361710.875	-0.0033222573907591745	-116897986.76797193

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	38	162
1	51	140
done	51	140

end0.0ms

sample8.9s

Algorithm

intervals

Results

2.5s	3179×	body	1280	valid
1.1s	1200×	body	10240	exit
1.1s	667×	body	1280	nan
1000.0ms	1691×	body	640	valid
758.0ms	842×	body	320	valid
573.0ms	4649×	body	80	valid
372.0ms	5048×	body	80	nan
338.0ms	602×	body	640	nan
154.0ms	362×	body	320	nan
121.0ms	196×	body	160	nan
99.0ms	455×	body	160	valid