Details

sample62.0ms

Algorithm

intervals

Results

30.0ms	382×	body	80	valid
6.0ms	133×	body	80	nan

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	15
1	24	15
2	47	13
3	93	13
4	233	13
5	716	13
6	2609	13
done	5000	13

prune8.0ms

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

localize10.0ms

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))))

rewrite30.0ms

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:

15.0ms	(* (/ a (+ 1.0 (* k (+ 10.0 k)))) (pow k m))
6.0ms	(* k (+ 10.0 k))
5.0ms	(/ a (+ 1.0 (* k (+ 10.0 k))))

series56.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (/ 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))))

simplify552.0ms

Counts

106 → 106

Iterations

Useful iterations: done (549.0ms)

Iter	Nodes	Cost
0	215	1685
1	574	1638
2	1907	1499
done	5000	1492

prune178.0ms

Filtered

86 candidates to 106 candidates (-23.3%)

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))))

rewrite41.0ms

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:

6.0ms	(/ 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))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify573.0ms

Counts

274 → 274

Iterations

Useful iterations: done (559.0ms)

Iter	Nodes	Cost
0	344	8946
1	811	7974
2	2343	7352
done	5000	7330

prune474.0ms

Filtered

151 candidates to 274 candidates (-81.5%)

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))))

rewrite39.0ms

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))))

series38.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (/ 1 (* (cbrt (+ 1.0 (* k (+ 10.0 k)))) (cbrt (+ 1.0 (* k (+ 10.0 k)))))) (/ a (cbrt (+ 1.0 (* k (+ 10.0 k))))))
12.0ms	(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))))

simplify628.0ms

Counts

131 → 131

Iterations

Useful iterations: done (623.0ms)

Iter	Nodes	Cost
0	239	4082
1	709	3781
2	2630	3139
done	5000	2963

prune376.0ms

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)))))

rewrite28.0ms

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))))
15.0ms	(* (* (cbrt a) (cbrt a)) (/ (cbrt a) (+ 1.0 (* k (+ 10.0 k)))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt a)
24.0ms	(cbrt a)
30.0ms	(/ (cbrt a) (+ 1.0 (* k (+ 10.0 k))))
17.0ms	(* (* (cbrt a) (cbrt a)) (/ (cbrt a) (+ 1.0 (* k (+ 10.0 k)))))

simplify523.0ms

Counts

122 → 122

Iterations

Useful iterations: done (519.0ms)

Iter	Nodes	Cost
0	189	2112
1	526	2048
2	2036	1778
done	5000	1763

prune182.0ms

Filtered

99 candidates to 122 candidates (-23.2%)

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: 2.0b

Counts

127 → 6

regimes198.0ms

Accuracy

0% (0.3b remaining)

Error of 1.9b against oracle of 1.6b 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

847.0ms	11935×	body	80	valid
208.0ms	4097×	body	80	nan

Details

sample62.0ms

simplify1.0s

prune8.0ms

localize10.0ms

rewrite30.0ms

series56.0ms

simplify552.0ms

prune178.0ms

localize12.0ms

rewrite41.0ms

series47.0ms

simplify573.0ms

prune474.0ms

localize15.0ms

rewrite39.0ms

series38.0ms

simplify628.0ms

prune376.0ms

localize13.0ms

rewrite28.0ms

series98.0ms

simplify523.0ms

prune182.0ms

regimes198.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.7s

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