Details

sample138.0ms

Algorithm

intervals

Results

48.0ms	95×	body	1280	valid
21.0ms	57×	body	640	valid
9.0ms	18×	body	1280	nan
9.0ms	29×	body	10240	exit
9.0ms	150×	body	80	valid
7.0ms	15×	body	640	nan
6.0ms	158×	body	80	nan
5.0ms	22×	body	320	valid
3.0ms	17×	body	320	nan
3.0ms	19×	body	160	valid
1.0ms	7×	body	160	nan

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	229	13
5	753	13
6	3894	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite76.0ms

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:

3.0ms	(pow x (/ 1.0 n))
7.0ms	(pow (+ x 1.0) (/ 1.0 n))
59.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series564.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(pow x (/ 1.0 n))
153.0ms	(pow (+ x 1.0) (/ 1.0 n))
352.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.3s

Counts

158 → 158

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	271	4785
1	661	3566
2	2163	3020
done	5000	3012

prune400.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite214.0ms

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:

7.0ms	(pow (+ x 1.0) (/ 1.0 n))
64.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
68.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
57.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

159.0ms	(pow (+ x 1.0) (/ 1.0 n))
298.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
334.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
332.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify927.0ms

Counts

312 → 312

Iterations

Useful iterations: done (900.0ms)

Iter	Nodes	Cost
0	234	12646
1	545	9161
2	1691	7533
done	5000	7509

prune869.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 24.9b

localize21.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite366.0ms

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:

68.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
77.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
76.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
124.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

358.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
306.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
408.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
313.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify766.0ms

Counts

370 → 370

Iterations

Useful iterations: done (737.0ms)

Iter	Nodes	Cost
0	344	16510
1	594	11634
2	1441	9453
done	5002	9401

prune975.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (pow x (/ 1.0 n)) 3))
0.3b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

244×	`unpow-prod-down`
204×	`cbrt-prod`
184×	`prod-diff`
173×	`*-un-lft-identity`
157×	`add-sqr-sqrt`
121×	`add-cube-cbrt`
72×	`cube-prod`
71×	`sqr-pow`
27×	`difference-of-squares`
26×	`pow-unpow`
25×	`distribute-lft-out`
18×	`times-frac`
9×	`cube-mult` `unpow3`
8×	`fma-neg`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `rem-cbrt-cube` `distribute-lft-out--`

Counts

4 → 324

Calls

4 calls:

3.0ms	(cbrt (pow (pow x (/ 1.0 n)) 3))
2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
69.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt (pow (pow x (/ 1.0 n)) 3))
63.0ms	(pow x (/ 1.0 n))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

simplify1.7s

Counts

336 → 336

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	422	17070
1	969	9750
2	2867	7991
done	5001	7975

prune494.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 24.9b

regimes262.0ms

Accuracy

80.5% (1.6b remaining)

Error of 22.7b against oracle of 21.0b and baseline of 29.4b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	96
1	42	96
done	42	96

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	3161×	body	1280	valid
557.0ms	1557×	body	640	valid
469.0ms	1094×	body	10240	exit
328.0ms	654×	body	1280	nan
252.0ms	4668×	body	80	valid
210.0ms	615×	body	640	nan
189.0ms	807×	body	320	valid
184.0ms	4983×	body	80	nan
65.0ms	331×	body	320	nan
65.0ms	454×	body	160	valid
21.0ms	183×	body	160	nan