Details

sample55.0ms

Algorithm

intervals

Results

25.0ms	382×	body	80	valid
6.0ms	133×	body	80	nan

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	15
1	24	15
2	47	13
3	91	13
4	220	13
5	649	13
6	2339	13
done	5001	13

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 2.7b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ a (+ 1.0 (* k (+ 10.0 k)))) (pow k m))
0.0b	(* k (+ 10.0 k))
5.2b	(/ a (+ 1.0 (* k (+ 10.0 k))))

rewrite26.0ms

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	(* (/ a (+ 1.0 (* k (+ 10.0 k)))) (pow k m))
9.0ms	(* k (+ 10.0 k))
5.0ms	(/ a (+ 1.0 (* k (+ 10.0 k))))

series57.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* (/ a (+ 1.0 (* k (+ 10.0 k)))) (pow k m))
5.0ms	(* k (+ 10.0 k))
15.0ms	(/ a (+ 1.0 (* k (+ 10.0 k))))

simplify1.0s

Counts

106 → 106

Iterations

Useful iterations: 2 (444.0ms)

Iter	Nodes	Cost
0	215	1685
1	560	1617
2	1777	1480
done	5000	1480

prune165.0ms

Filtered

79 candidates to 106 candidates (-34.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	5	107

Merged error: 2.7b

Counts

107 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ a (sqrt (+ 1.0 (* k (+ 10.0 k)))))
0.1b	(/ (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
15.9b	(sqrt (+ 1.0 (* k (+ 10.0 k))))
15.9b	(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 262

Calls

4 calls:

9.0ms	(/ a (sqrt (+ 1.0 (* k (+ 10.0 k)))))
14.0ms	(/ (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ a (sqrt (+ 1.0 (* k (+ 10.0 k)))))
15.0ms	(/ (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
4.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
4.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify973.0ms

Counts

274 → 274

Iterations

Useful iterations: done (961.0ms)

Iter	Nodes	Cost
0	344	8946
1	805	7846
2	1926	7327
done	5000	7292

prune455.0ms

Filtered

149 candidates to 274 candidates (-83.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	274	5	279

Merged error: 2.7b

Counts

279 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (/ 1 (* (cbrt (+ 1.0 (* k (+ 10.0 k)))) (cbrt (+ 1.0 (* k (+ 10.0 k)))))) (/ a (cbrt (+ 1.0 (* k (+ 10.0 k))))))
16.4b	(cbrt (+ 1.0 (* k (+ 10.0 k))))
16.4b	(cbrt (+ 1.0 (* k (+ 10.0 k))))
16.4b	(cbrt (+ 1.0 (* k (+ 10.0 k))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
43×	`add-sqr-sqrt`
33×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-r`
22×	`add-cube-cbrt`
21×	`cbrt-prod`
20×	`cbrt-div` `prod-exp`
18×	`add-cbrt-cube`
15×	`div-exp` `associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1`
5×	`frac-times`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 119

Calls

4 calls:

25.0ms	(* (/ 1 (* (cbrt (+ 1.0 (* k (+ 10.0 k)))) (cbrt (+ 1.0 (* k (+ 10.0 k)))))) (/ a (cbrt (+ 1.0 (* k (+ 10.0 k))))))
3.0ms	(cbrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms	(cbrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms	(cbrt (+ 1.0 (* k (+ 10.0 k))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (/ 1 (* (cbrt (+ 1.0 (* k (+ 10.0 k)))) (cbrt (+ 1.0 (* k (+ 10.0 k)))))) (/ a (cbrt (+ 1.0 (* k (+ 10.0 k))))))
11.0ms	(cbrt (+ 1.0 (* k (+ 10.0 k))))
8.0ms	(cbrt (+ 1.0 (* k (+ 10.0 k))))
8.0ms	(cbrt (+ 1.0 (* k (+ 10.0 k))))

simplify806.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (283.0ms)

Iter	Nodes	Cost
0	239	4082
1	701	3755
2	2177	2963
done	5000	2963

prune364.0ms

Filtered

102 candidates to 131 candidates (-28.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	131	5	136

Merged error: 2.7b

Counts

136 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt a)
0.5b	(cbrt a)
2.1b	(/ (cbrt a) (+ 1.0 (* k (+ 10.0 k))))
3.3b	(* (* (cbrt a) (cbrt a)) (/ (cbrt a) (+ 1.0 (* k (+ 10.0 k)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
28×	`cbrt-prod`
24×	`associate-r`
18×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod` `associate-/l*`
4×	`associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r*` `unswap-sqr`
2×	`flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 110

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
6.0ms	(/ (cbrt a) (+ 1.0 (* k (+ 10.0 k))))
17.0ms	(* (* (cbrt a) (cbrt a)) (/ (cbrt a) (+ 1.0 (* k (+ 10.0 k)))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt a)
23.0ms	(cbrt a)
26.0ms	(/ (cbrt a) (+ 1.0 (* k (+ 10.0 k))))
17.0ms	(* (* (cbrt a) (cbrt a)) (/ (cbrt a) (+ 1.0 (* k (+ 10.0 k)))))

simplify952.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (354.0ms)

Iter	Nodes	Cost
0	189	2112
1	520	2035
2	1833	1832
done	5001	1832

prune165.0ms

Filtered

98 candidates to 122 candidates (-24.5%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	121	6	127

Merged error: 2.4b

Counts

127 → 6

regimes182.0ms

Accuracy

0% (0.4b remaining)

Error of 1.9b against oracle of 1.5b and baseline of 1.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	15	13
done	15	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

815.0ms	11935×	body	80	valid
197.0ms	4097×	body	80	nan

Details

sample55.0ms

simplify2.9s

prune12.0ms

localize9.0ms

rewrite26.0ms

series57.0ms

simplify1.0s

prune165.0ms

localize12.0ms

rewrite43.0ms

series42.0ms

simplify973.0ms

prune455.0ms

localize15.0ms

rewrite38.0ms

series37.0ms

simplify806.0ms

prune364.0ms

localize13.0ms

rewrite29.0ms

series94.0ms

simplify952.0ms

prune165.0ms

regimes182.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.7s

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