Details

sample147.0ms

Algorithm

intervals

Results

48.0ms	101×	body	1280	valid
19.0ms	36×	body	10240	exit
17.0ms	40×	body	640	valid
15.0ms	28×	body	1280	nan
8.0ms	24×	body	640	nan
8.0ms	146×	body	80	valid
7.0ms	32×	body	320	valid
5.0ms	136×	body	80	nan
2.0ms	12×	body	320	nan
2.0ms	15×	body	160	valid
0.0ms	5×	body	160	nan

simplify1.7s

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	224	13
5	687	13
6	3245	13
done	5001	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite68.0ms

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:

2.0ms	(pow x (/ 1.0 n))
53.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series484.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(pow x (/ 1.0 n))
277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
151.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify646.0ms

Counts

158 → 158

Iterations

Useful iterations: done (636.0ms)

Iter	Nodes	Cost
0	271	4785
1	626	3566
2	1690	3020
done	5000	2998

prune337.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
1.0b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

108×	`unpow-prod-down`
94×	`*-un-lft-identity`
91×	`add-sqr-sqrt`
56×	`prod-diff`
55×	`add-cube-cbrt`
37×	`sqr-pow`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
18×	`times-frac`
15×	`cube-prod`
12×	`distribute-lft-out`
9×	`distribute-lft-out--`
8×	`fma-neg`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 198

Calls

4 calls:

45.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
2.0ms	(pow x (/ 1.0 n))
51.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))

series957.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
61.0ms	(pow x (/ 1.0 n))
465.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify802.0ms

Counts

210 → 210

Iterations

Useful iterations: done (793.0ms)

Iter	Nodes	Cost
0	344	6422
1	837	4859
2	2364	4454
done	5000	4406

prune515.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
1.0b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

108×	`unpow-prod-down`
94×	`*-un-lft-identity`
91×	`add-sqr-sqrt`
56×	`prod-diff`
55×	`add-cube-cbrt`
37×	`sqr-pow`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
18×	`times-frac`
15×	`cube-prod`
12×	`distribute-lft-out`
9×	`distribute-lft-out--`
8×	`fma-neg`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 198

Calls

4 calls:

42.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
3.0ms	(pow x (/ 1.0 n))
54.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series773.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
58.0ms	(pow x (/ 1.0 n))
285.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
146.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify802.0ms

Counts

210 → 210

Iterations

Useful iterations: done (794.0ms)

Iter	Nodes	Cost
0	344	6422
1	837	4859
2	2364	4454
done	5000	4406

prune599.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
1.0b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

108×	`unpow-prod-down`
94×	`*-un-lft-identity`
91×	`add-sqr-sqrt`
56×	`prod-diff`
55×	`add-cube-cbrt`
37×	`sqr-pow`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
18×	`times-frac`
15×	`cube-prod`
12×	`distribute-lft-out`
9×	`distribute-lft-out--`
8×	`fma-neg`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 198

Calls

4 calls:

42.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
4.0ms	(pow x (/ 1.0 n))
50.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series764.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
62.0ms	(pow x (/ 1.0 n))
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify798.0ms

Counts

210 → 210

Iterations

Useful iterations: done (790.0ms)

Iter	Nodes	Cost
0	344	6422
1	837	4859
2	2364	4454
done	5000	4406

prune662.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.2b

regimes226.0ms

Accuracy

83.9% (1.4b remaining)

Error of 21.9b against oracle of 20.4b and baseline of 29.4b

bsearch1.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	36	86
1	44	62
done	44	62

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	3138×	body	1280	valid
547.0ms	1574×	body	640	valid
446.0ms	1147×	body	10240	exit
288.0ms	618×	body	1280	nan
251.0ms	4726×	body	80	valid
220.0ms	669×	body	640	nan
206.0ms	885×	body	320	valid
193.0ms	5002×	body	80	nan
70.0ms	449×	body	160	valid
62.0ms	327×	body	320	nan
19.0ms	170×	body	160	nan