Details

sample187.0ms

Algorithm

intervals

Results

61.0ms	91×	body	1280	valid
27.0ms	60×	body	640	valid
21.0ms	28×	body	10240	exit
13.0ms	22×	body	1280	nan
11.0ms	37×	body	320	valid
11.0ms	139×	body	80	valid
8.0ms	154×	body	80	nan
8.0ms	19×	body	640	nan
3.0ms	16×	body	160	valid
3.0ms	11×	body	320	nan
1.0ms	7×	body	160	nan

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3086
5	673
4	238
3	86
2	35
1	17
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.2b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite137.0ms

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:

8.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
107.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series777.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(pow x (/ 1.0 n))
242.0ms	(pow (+ x 1.0) (/ 1.0 n))
459.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.8s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	1895
1	711
0	270

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 22.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
3.2b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

3.0ms	(pow x (/ 1.0 n))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))
227.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
138.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

97.0ms	(pow x (/ 1.0 n))
209.0ms	(pow (+ x 1.0) (/ 1.0 n))
440.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
394.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.0s

Counts

249 → 249

Iterations

Iter	Nodes
done	5001
2	2218
1	900
0	429

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.7b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite780.0ms

Algorithm

rewrite-expression-head

Rules

256×	`unpow-prod-down`
224×	`prod-diff`
222×	`*-un-lft-identity`
182×	`add-sqr-sqrt`
134×	`add-cube-cbrt`
128×	`log-prod`
122×	`sqrt-prod`
116×	`exp-sum`
86×	`sqr-pow`
36×	`log-pow` `difference-of-squares`
34×	`distribute-lft-out`
32×	`sqrt-pow1`
30×	`exp-prod`
16×	`fma-neg`
12×	`distribute-lft-out--`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 366

Calls

4 calls:

115.0ms	(- (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)))
260.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
229.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

372.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
404.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
727.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
750.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify3.2s

Counts

378 → 378

Iterations

Iter	Nodes
done	5000
3	4653
2	1565
1	720
0	427

prune3.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.7b

localize109.0ms

Local error

Found 4 expressions with local error:

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

rewrite685.0ms

Algorithm

rewrite-expression-head

Rules

180×	`unpow-prod-down`
168×	`prod-diff`
161×	`*-un-lft-identity`
135×	`log-prod`
127×	`add-sqr-sqrt`
126×	`sqrt-prod`
116×	`exp-sum`
103×	`add-cube-cbrt`
61×	`cbrt-prod`
58×	`sqr-pow`
33×	`log-pow`
27×	`sqrt-pow1`
24×	`distribute-lft-out`
18×	`difference-of-squares`
17×	`pow1`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1/3` `add-exp-log`
6×	`exp-diff` `distribute-lft-out--` `add-log-exp`
5×	`log-div` `cbrt-div` `sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `pow1/2` `rem-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `flip3--` `diff-log` `associate-l/` `associate-r/` `flip--`

Counts

4 → 293

Calls

4 calls:

93.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
200.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
276.0ms	(log (sqrt (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))))
95.0ms	(log (sqrt (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

414.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
624.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
650.0ms	(log (sqrt (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))))
627.0ms	(log (sqrt (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

simplify2.6s

Counts

305 → 305

Iterations

Iter	Nodes
done	5000
2	2253
1	1064
0	691

prune3.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.7b

regimes548.0ms

Accuracy

83.8% (1.4b remaining)

Error of 22.6b against oracle of 21.2b and baseline of 29.8b

bsearch1.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	46
1	46
0	36

end0.0ms

sample7.9s

Algorithm

intervals

Results

2.4s	3203×	body	1280	valid
921.0ms	1181×	body	10240	exit
851.0ms	4719×	body	80	valid
810.0ms	1578×	body	640	valid
620.0ms	686×	body	1280	nan
584.0ms	331×	body	320	nan
425.0ms	5102×	body	80	nan
322.0ms	606×	body	640	nan
288.0ms	861×	body	320	valid
98.0ms	446×	body	160	valid
33.0ms	187×	body	160	nan