Details

sample52.0ms

Algorithm

intervals

Results

25.0ms	383×	body	80	valid
6.0ms	134×	body	80	nan

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (3.0ms)

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

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 2.1b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.1b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

2.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(* a (pow k m))
7.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
8.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ 1.0 (* 10.0 k))
15.0ms	(* a (pow k m))
3.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
31.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify59.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	471	611
1	2227	545
2	5002	538

prune111.0ms

Filtered

86 candidates to 63 candidates (26.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	83	5	88

Merged error: 2.1b

Counts

88 → 5

localize14.0ms

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))))
17.7b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
17.7b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite35.0ms

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)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
35.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
3.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify87.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	738	3111
1	3265	2780
2	5002	2777

prune271.0ms

Filtered

166 candidates to 103 candidates (38.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	166	5	171

Merged error: 2.1b

Counts

171 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* k (+ 10.0 k))
0.4b	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
1.6b	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 120

Calls

3 calls:

5.0ms	(* k (+ 10.0 k))
9.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
14.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

series51.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* k (+ 10.0 k))
15.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
31.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

simplify70.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	627	1119
1	2587	1052
2	5001	1052

prune160.0ms

Filtered

129 candidates to 98 candidates (24.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	129	5	134

Merged error: 2.1b

Counts

134 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)
1.4b	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) (* (cbrt a) (cbrt a)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
27×	`add-sqr-sqrt` `associate-l`
24×	`times-frac`
21×	`add-cube-cbrt` `*-un-lft-identity`
12×	`prod-exp` `add-cbrt-cube`
10×	`unpow-prod-down`
9×	`pow1` `cbrt-prod`
6×	`div-exp` `cbrt-unprod`
4×	`add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow1/3` `pow-prod-down`
2×	`cbrt-undiv` `pow-to-exp` `pow-exp` `associate-/r/`
1×	`flip3-+` `associate-r` `associate-l/` `-commutative` `flip-+` `div-inv`

Counts

4 → 88

Calls

4 calls:

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

series120.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt a)
22.0ms	(cbrt a)
21.0ms	(cbrt a)
56.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) (* (cbrt a) (cbrt a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	564	953
1	1945	862
2	5002	795

prune122.0ms

Filtered

100 candidates to 76 candidates (24.0%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	99	6	105

Merged error: 1.3b

Counts

105 → 6

regimes242.0ms

Accuracy

0% (0.7b remaining)

Error of 2.3b against oracle of 1.5b and baseline of 2.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	14
1	18	14

end0.0ms

sample1.5s

Algorithm

intervals

Results

801.0ms	12035×	body	80	valid
189.0ms	4401×	body	80	nan

Details

sample52.0ms

simplify105.0ms

prune10.0ms

localize10.0ms

rewrite24.0ms

series52.0ms

simplify59.0ms

prune111.0ms

localize14.0ms

rewrite35.0ms

series44.0ms

simplify87.0ms

prune271.0ms

localize9.0ms

rewrite32.0ms

series51.0ms

simplify70.0ms

prune160.0ms

localize13.0ms

rewrite22.0ms

series120.0ms

simplify50.0ms

prune122.0ms

regimes242.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.5s

Profiling