Details

sample44.0ms

Algorithm

intervals

Results

24.0ms	370×	body	80	valid
5.0ms	110×	body	80	nan

simplify106.0ms

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

prune6.0ms

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: 2.2b

Counts

2 → 2

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.2b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

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

series170.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ 1.0 (* 10.0 k))
19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
113.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify48.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	404	484
1	1787	427
2	5001	418

prune124.0ms

Filtered

58 candidates to 41 candidates (70.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	56	4	60

Merged error: 2.1b

Counts

60 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.1b	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
2.2b	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

2.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
7.0ms	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.0ms	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ 1.0 (* 10.0 k))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
67.0ms	(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
113.0ms	(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

simplify72.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	613	1313
1	2800	1220
2	5001	1214

prune266.0ms

Filtered

133 candidates to 102 candidates (76.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	133	4	137

Merged error: 2.1b

Counts

137 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 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))))
12.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
66×	`sqrt-prod`
55×	`add-sqr-sqrt`
53×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `sqrt-div`
16×	`associate-/r/`
13×	`add-cbrt-cube`
12×	`associate-/l*`
11×	`flip3-+` `flip-+`
9×	`div-exp` `add-log-exp`
8×	`div-inv`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv`
3×	`prod-exp` `sum-log`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `associate-/l/`

Counts

4 → 154

Calls

4 calls:

5.0ms	(+ (+ 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)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
115.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (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)))

simplify88.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	728	3104
1	3221	2772
2	5001	2769

prune345.0ms

Filtered

166 candidates to 102 candidates (61.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	166	4	170

Merged error: 2.1b

Counts

170 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 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)))))
12.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
92×	`times-frac`
52×	`sqrt-prod`
48×	`associate-r`
46×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log`
24×	`unpow-prod-down` `associate-l`
21×	`unswap-sqr`
16×	`add-cbrt-cube`
12×	`sqr-pow`
10×	`div-exp`
9×	`add-log-exp`
8×	`pow1` `sqrt-div` `prod-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
3×	`sum-log`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `div-inv`
1×	`+-commutative` `frac-times` `associate-+l+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 160

Calls

4 calls:

5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
37.0ms	(* (/ 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)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
119.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
47.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
54.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify93.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	859	2730
1	3871	2549
2	5001	2435

prune355.0ms

Filtered

172 candidates to 112 candidates (65.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	172	4	176

Merged error: 2.1b

Counts

176 → 4

regimes81.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

sample1.4s

Algorithm

intervals

Results

803.0ms	11973×	body	80	valid
182.0ms	4260×	body	80	nan

Details

sample44.0ms

simplify106.0ms

prune6.0ms

localize14.0ms

rewrite16.0ms

series170.0ms

simplify48.0ms

prune124.0ms

localize10.0ms

rewrite30.0ms

series234.0ms

simplify72.0ms

prune266.0ms

localize17.0ms

rewrite34.0ms

series239.0ms

simplify88.0ms

prune345.0ms

localize13.0ms

rewrite57.0ms

series237.0ms

simplify93.0ms

prune355.0ms

regimes81.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.4s

Profiling