Details

sample52.0ms

Algorithm

intervals

Results

28.0ms	396×	body	80	valid
7.0ms	156×	body	80	nan

simplify124.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	24	7
1	48	7
2	96	6
3	256	6
4	891	6
5	3963	6
6	5002	6

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 1.7b

Counts

2 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(* a (pow k m))
1.7b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
13×	`add-sqr-sqrt`
10×	`add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
6×	`prod-exp`
5×	`add-log-exp`
4×	`unpow-prod-down` `div-exp`
3×	`pow1` `times-frac` `associate-l` `associate-/r*` `unswap-sqr`
2×	`cbrt-undiv` `pow-to-exp` `flip3-+` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`+-commutative` `frac-2neg` `clear-num` `sum-log` `-commutative` `div-inv` `associate-/l`

Counts

3 → 61

Calls

3 calls:

2.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(* a (pow k m))
8.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series205.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ 1.0 (* 10.0 k))
60.0ms	(* a (pow k m))
114.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify56.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	422	500
1	2032	446
2	5003	443

prune155.0ms

Filtered

70 candidates to 52 candidates (74.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	66	6	72

Merged error: 1.7b

Counts

72 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
0.0b	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
17.3b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
17.3b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
72×	`sqrt-prod`
59×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
30×	`add-exp-log`
22×	`sqrt-div`
18×	`associate-/r/` `add-cbrt-cube`
13×	`div-exp` `associate-/l*`
12×	`associate-/r*`
11×	`flip3-+` `flip-+`
9×	`div-inv`
7×	`cbrt-undiv`
6×	`pow1` `prod-exp`
4×	`add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `cbrt-unprod`
1×	`associate-/l/`

Counts

4 → 172

Calls

4 calls:

9.0ms	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
15.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
111.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
51.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
50.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify89.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	756	3435
1	3282	3085
2	5001	3085

prune379.0ms

Filtered

184 candidates to 114 candidates (62.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	184	6	190

Merged error: 1.7b

Counts

190 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m))
1.7b	(/ a (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
101×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`unpow-prod-down`
32×	`associate-/r*`
18×	`add-exp-log`
16×	`sqr-pow`
10×	`div-exp` `add-cbrt-cube`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv`
3×	`pow1`
2×	`pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `associate-/r/`

Counts

3 → 178

Calls

3 calls:

3.0ms	(+ 1.0 (* 10.0 k))
13.0ms	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m))
10.0ms	(/ a (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m)))

series214.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ 1.0 (* 10.0 k))
67.0ms	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m))
115.0ms	(/ a (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) (pow k m)))

simplify110.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	850	2535
1	4046	2446
2	5002	2446

prune450.0ms

Filtered

187 candidates to 148 candidates (79.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	186	7	193

Merged error: 1.7b

Counts

193 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
0.1b	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
17.3b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
17.3b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

146×	`add-sqr-sqrt`
134×	`times-frac`
76×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
48×	`associate-r`
45×	`unpow-prod-down`
33×	`add-exp-log`
24×	`associate-l`
21×	`unswap-sqr`
19×	`sqr-pow`
18×	`add-cbrt-cube`
13×	`div-exp`
10×	`sqrt-div`
8×	`pow1` `prod-exp`
7×	`associate-/l*`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 218

Calls

4 calls:

8.0ms	(/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
38.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
122.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
46.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
55.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify108.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	899	3695
1	3999	3453
2	5002	3348

prune495.0ms

Filtered

230 candidates to 148 candidates (64.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	230	7	237

Merged error: 1.7b

Counts

237 → 7

regimes87.0ms

Accuracy

0% (0.1b remaining)

Error of 2.1b against oracle of 2.0b and baseline of 2.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	14
1	18	14

end0.0ms

sample1.4s

Algorithm

intervals

Results

840.0ms	11864×	body	80	valid
203.0ms	4344×	body	80	nan

Details

sample52.0ms

simplify124.0ms

prune7.0ms

localize13.0ms

rewrite17.0ms

series205.0ms

simplify56.0ms

prune155.0ms

localize12.0ms

rewrite39.0ms

series369.0ms

simplify89.0ms

prune379.0ms

localize10.0ms

rewrite34.0ms

series214.0ms

simplify110.0ms

prune450.0ms

localize13.0ms

rewrite65.0ms

series333.0ms

simplify108.0ms

prune495.0ms

regimes87.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.4s

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