Details

sample38.0ms

Algorithm

intervals

Results

17.0ms	367×	body	80	valid
5.0ms	141×	body	80	nan

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	12	15
1	24	15
2	47	13
3	91	13
4	220	13
5	650	13
6	2323	13
done	5000	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* k (+ 10.0 k))
0.2b	(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k m))
3.3b	(/ a (+ (* k (+ 10.0 k)) 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`times-frac`
20×	`add-exp-log`
18×	`associate-l`
12×	`add-cbrt-cube`
11×	`associate-r`
7×	`prod-exp` `unswap-sqr`
5×	`pow1` `unpow-prod-down`
4×	`div-exp` `associate-/r/`
3×	`flip3-+` `associate-/r` `cbrt-unprod` `flip-+` `associate-/l` `add-log-exp` `sqr-pow`
2×	`cbrt-undiv` `pow-to-exp` `associate-r/` `pow-exp` `-commutative` `div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-*l/` `clear-num` `distribute-lft-out`

Counts

3 → 97

Calls

3 calls:

10.0ms	(* k (+ 10.0 k))
27.0ms	(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k m))
9.0ms	(/ a (+ (* k (+ 10.0 k)) 1.0))

series232.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* k (+ 10.0 k))
125.0ms	(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k m))
65.0ms	(/ a (+ (* k (+ 10.0 k)) 1.0))

simplify674.0ms

Counts

106 → 106

Iterations

Useful iterations: done (671.0ms)

Iter	Nodes	Cost
0	210	1673
1	550	1610
2	1726	1490
done	5001	1487

prune281.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2)))
0.0b	(* (* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2))) (pow k (/ m 2)))
0.0b	(* k (+ 10.0 k))
3.3b	(/ a (+ (* k (+ 10.0 k)) 1.0))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
46×	`prod-exp`
40×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
22×	`add-cbrt-cube`
21×	`times-frac`
19×	`associate-l`
18×	`associate-r`
15×	`pow-to-exp` `pow-exp`
13×	`div-exp`
8×	`unpow-prod-down` `cbrt-unprod`
7×	`unswap-sqr`
6×	`pow1`
4×	`associate-/r/` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `flip3-+` `associate-l/` `associate-/r` `-commutative` `flip-+` `associate-/l`
2×	`associate-*r/` `div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `distribute-lft-out`

Counts

4 → 138

Calls

4 calls:

30.0ms	(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2)))
35.0ms	(* (* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2))) (pow k (/ m 2)))
9.0ms	(* k (+ 10.0 k))
9.0ms	(/ a (+ (* k (+ 10.0 k)) 1.0))

series389.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2)))
149.0ms	(* (* (/ a (+ (* k (+ 10.0 k)) 1.0)) (pow k (/ m 2))) (pow k (/ m 2)))
42.0ms	(* k (+ 10.0 k))
70.0ms	(/ a (+ (* k (+ 10.0 k)) 1.0))

simplify880.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (373.0ms)

Iter	Nodes	Cost
0	265	3042
1	731	2747
2	2509	2471
done	5000	2471

prune362.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
0.2b	(* (/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (pow k m))
14.4b	(sqrt (+ (* k (+ 10.0 k)) 1.0))
14.4b	(sqrt (+ (* k (+ 10.0 k)) 1.0))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

552×	`times-frac`
343×	`add-sqr-sqrt`
285×	`sqrt-prod`
276×	`add-cube-cbrt` `*-un-lft-identity`
150×	`associate-l`
34×	`sqrt-div`
33×	`add-exp-log`
30×	`associate-/r/`
24×	`associate-/l*`
21×	`unswap-sqr`
18×	`add-cbrt-cube`
17×	`flip3-+` `flip-+`
15×	`div-inv`
12×	`div-exp`
10×	`unpow-prod-down`
9×	`prod-exp`
8×	`sqr-pow`
7×	`associate-r`
6×	`pow1` `cbrt-undiv` `associate-/r*`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-l/` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 420

Calls

4 calls:

30.0ms	(/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
99.0ms	(* (/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (pow k m))
8.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))
8.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))

series294.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
118.0ms	(* (/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (pow k m))
52.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))
54.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))

simplify1.3s

Counts

432 → 432

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	477	13990
1	1219	12359
2	3308	11311
done	5001	11309

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0)))) (pow k m))
14.4b	(sqrt (+ (* k (+ 10.0 k)) 1.0))
14.4b	(sqrt (+ (* k (+ 10.0 k)) 1.0))
14.4b	(sqrt (+ (* k (+ 10.0 k)) 1.0))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

423×	`times-frac`
342×	`sqrt-prod`
297×	`add-sqr-sqrt`
222×	`associate-l`
199×	`add-cube-cbrt` `*-un-lft-identity`
30×	`unswap-sqr`
28×	`add-exp-log` `sqrt-div`
20×	`associate-/r/`
13×	`unpow-prod-down` `flip3-+` `add-cbrt-cube` `flip-+`
11×	`sqr-pow`
10×	`div-inv`
9×	`div-exp` `prod-exp`
7×	`pow1` `associate-r`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `cbrt-unprod`
1×	`associate-l/` `-commutative`

Counts

4 → 325

Calls

4 calls:

122.0ms	(* (/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0)))) (pow k m))
7.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))
7.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))
11.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))

series416.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(* (/ (/ a (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (sqrt (+ (* k (+ 10.0 k)) 1.0)))) (pow k m))
55.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))
48.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))
56.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))

simplify1.2s

Counts

337 → 337

Iterations

Useful iterations: 2 (604.0ms)

Iter	Nodes	Cost
0	382	9300
1	977	8936
2	2977	8304
done	5000	8304

prune1.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 1.2b

regimes83.0ms

Accuracy

0% (0.1b remaining)

Error of 2.0b against oracle of 1.9b and baseline of 2.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	19	21
done	19	21

end0.0ms

sample958.0ms

Algorithm

intervals

Results

475.0ms	11825×	body	80	valid
141.0ms	4243×	body	80	nan