Details

sample58.0ms

Algorithm

intervals

Results

22.0ms	416×	body	80	valid
9.0ms	156×	body	80	nan

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	12	15
1	24	15
2	53	13
3	107	12
4	254	12
5	735	12
6	2729	12
done	5001	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (fma k (+ 10.0 k) 1.0) (pow k m))
2.1b	(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
100×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`unpow-prod-down`
32×	`associate-/r*`
17×	`add-exp-log`
16×	`sqr-pow`
10×	`div-exp`
9×	`add-cbrt-cube`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv`
2×	`pow1` `expm1-log1p-u` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/`

Counts

2 → 169

Calls

2 calls:

10.0ms	(/ (fma k (+ 10.0 k) 1.0) (pow k m))
14.0ms	(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

series274.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(/ (fma k (+ 10.0 k) 1.0) (pow k m))
175.0ms	(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

simplify2.0s

Counts

175 → 175

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	331	4107
1	713	3899
2	2357	3762
done	5000	3717

prune758.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k (/ m 2)))
0.0b	(/ (/ a (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k (/ m 2)))) (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k (/ m 2))))
16.4b	(sqrt (fma k (+ 10.0 k) 1.0))
16.4b	(sqrt (fma k (+ 10.0 k) 1.0))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

25076×	`times-frac`
9942×	`add-sqr-sqrt`
9940×	`add-cube-cbrt` `*-un-lft-identity`
6015×	`sqrt-prod`
5151×	`unpow-prod-down`
1717×	`sqr-pow`
334×	`div-inv`
149×	`associate-/l*`
83×	`add-exp-log`
66×	`div-exp`
53×	`associate-/r*`
48×	`associate-/r/`
27×	`add-cbrt-cube`
16×	`cbrt-undiv`
10×	`pow-to-exp` `pow-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 6908

Calls

4 calls:

19.0ms	(/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k (/ m 2)))
286.0ms	(/ (/ a (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k (/ m 2)))) (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k (/ m 2))))
3.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
3.0ms	(sqrt (fma k (+ 10.0 k) 1.0))

series521.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k (/ m 2)))
189.0ms	(/ (/ a (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k (/ m 2)))) (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k (/ m 2))))
66.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
104.0ms	(sqrt (fma k (+ 10.0 k) 1.0))

simplify4.7s

Counts

6920 → 6920

Iterations

Useful iterations: 0 (1.3s)

Iter	Nodes	Cost
0	7559	461738
done	7559	461738

prune41.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt k)
16.4b	(sqrt (fma k (+ 10.0 k) 1.0))
16.4b	(sqrt (fma k (+ 10.0 k) 1.0))
16.4b	(sqrt (fma k (+ 10.0 k) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow1/3`

Counts

4 → 58

Calls

4 calls:

1.0ms	(cbrt k)
2.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
12.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
2.0ms	(sqrt (fma k (+ 10.0 k) 1.0))

series458.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(cbrt k)
73.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
76.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
71.0ms	(sqrt (fma k (+ 10.0 k) 1.0))

simplify1.7s

Counts

70 → 70

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	68	656
1	132	589
2	306	553
3	736	532
4	1995	529
done	5001	520

prune356.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

16.4b	(sqrt (fma k (+ 10.0 k) 1.0))
16.4b	(sqrt (fma k (+ 10.0 k) 1.0))
16.4b	(sqrt (fma k (+ 10.0 k) 1.0))
16.4b	(sqrt (fma k (+ 10.0 k) 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

1.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
1.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
1.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
2.0ms	(sqrt (fma k (+ 10.0 k) 1.0))

series223.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
50.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
56.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
61.0ms	(sqrt (fma k (+ 10.0 k) 1.0))

simplify1.8s

Counts

72 → 72

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	45	780
1	94	696
2	228	656
3	581	632
4	1601	628
done	5000	616

prune312.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes87.0ms

Accuracy

98.3% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.0b

bsearch51.0ms

Steps

Iters	Range		Point
7	3.169316652691789e+110	2.502942302693858e+112	3.7123001813996137e+111

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	52
1	33	48
done	33	48

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	11904×	body	80	valid
204.0ms	4108×	body	80	nan