Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

sample39.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
7.0ms	89×	body	80	invalid
2.0ms	55×	body	80	nan

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4961	13
1	4961	13

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: 1.2b

Counts

2 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* k (+ k 10.0))
0.2b	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
1.0b	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 120

Calls

3 calls:

6.0ms	(* k (+ k 10.0))
6.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
12.0ms	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

series53.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* k (+ k 10.0))
16.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
33.0ms	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5031	1960

prune169.0ms

Filtered

94 candidates to 129 candidates (-37.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	125	4	129
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	127	4	131

Merged error: 1.2b

Counts

131 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(* k (+ k 10.0))
1.2b	(/ (* a (pow k m)) (+ 1.0 (* k (+ k 10.0))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

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

series54.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(* a (pow k m))
4.0ms	(* k (+ k 10.0))
35.0ms	(/ (* a (pow k m)) (+ 1.0 (* k (+ k 10.0))))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4950	824
1	4950	824

prune88.0ms

Filtered

55 candidates to 82 candidates (-49.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	82	4	86

Merged error: 1.2b

Counts

86 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* k (+ k 10.0))
0.1b	(/ (* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (pow k m)) (sqrt (+ 1.0 (* k (+ k 10.0)))))
12.4b	(sqrt (+ 1.0 (* k (+ k 10.0))))
12.4b	(sqrt (+ 1.0 (* k (+ k 10.0))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
16×	`add-sqr-sqrt`
15×	`add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt` `sqrt-prod`
10×	`div-exp`
8×	`pow1`
7×	`prod-exp`
6×	`times-frac` `sqrt-div` `associate-/r*`
4×	`cbrt-undiv` `flip3-+` `associate-r` `flip-+` `add-log-exp`
3×	`associate-l` `cbrt-unprod`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `pow-exp` `associate-/r/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l*` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

5.0ms	(* k (+ k 10.0))
11.0ms	(/ (* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (pow k m)) (sqrt (+ 1.0 (* k (+ k 10.0)))))
2.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* k (+ k 10.0))
32.0ms	(/ (* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (pow k m)) (sqrt (+ 1.0 (* k (+ k 10.0)))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))
4.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4997	1368
1	4997	1368

prune146.0ms

Filtered

69 candidates to 101 candidates (-46.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	101	4	105

Merged error: 1.2b

Counts

105 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
0.2b	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
4.9b	(sqrt (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))
4.9b	(sqrt (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
76×	`add-sqr-sqrt`
64×	`add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
44×	`unpow-prod-down`
16×	`sqr-pow`
14×	`add-exp-log` `associate-/l*`
8×	`rem-sqrt-square` `associate-/r/` `add-cbrt-cube`
6×	`pow1` `div-exp` `associate-/r*`
4×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `clear-num`

Counts

4 → 176

Calls

4 calls:

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

series78.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
18.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
22.0ms	(sqrt (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))
23.0ms	(sqrt (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4906	3604
1	4906	3604

prune363.0ms

Filtered

152 candidates to 188 candidates (-23.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	188	4	192

Merged error: 1.2b

Counts

192 → 4

regimes145.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	13
1	15	13

end0.0ms

sample1.2s

Algorithm

intervals

Results

505.0ms	8000×	body	80	valid
267.0ms	3327×	body	80	invalid
93.0ms	1973×	body	80	nan

Details

analyze1.1s

sample39.0ms

simplify86.0ms

prune10.0ms

localize13.0ms

rewrite29.0ms

series53.0ms

simplify40.0ms

prune169.0ms

localize9.0ms

rewrite19.0ms

series54.0ms

simplify41.0ms

prune88.0ms

localize11.0ms

rewrite24.0ms

series43.0ms

simplify47.0ms

prune146.0ms

localize13.0ms

rewrite29.0ms

series78.0ms

simplify65.0ms

prune363.0ms

regimes145.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling