Details

analyze3.0s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 24.485115%

Guaranteed chance to sample good point: 56.882289%

sample44.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
10.0ms	122×	body	80	invalid
1.0ms	24×	body	80	nan

simplify109.0ms

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

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: 1.6b

Counts

2 → 2

localize11.0ms

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

rewrite27.0ms

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:

4.0ms	(+ 1.0 (* 10.0 k))
7.0ms	(* a (pow k m))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
8.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series71.0ms

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))
50.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify58.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (50.0ms)

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

prune107.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Merged error: 1.6b

Counts

88 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

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

series54.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(* a (pow k m))
4.0ms	(* k (+ 10.0 k))
35.0ms	(/ (* a (pow k m)) (+ 1.0 (* k (+ 10.0 k))))

simplify62.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	460	505
1	2306	453
2	5001	448

prune97.0ms

Filtered

57 candidates to 82 candidates (-43.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	81	4	85

Merged error: 1.6b

Counts

85 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
0.0b	(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
15.1b	(sqrt (+ 1.0 (* k (+ 10.0 k))))
15.1b	(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite33.0ms

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:

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

series77.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
33.0ms	(/ (/ (* a (pow k m)) (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))))

simplify91.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	772	3001
1	3302	2697
2	5001	2697

prune307.0ms

Filtered

113 candidates to 184 candidates (-62.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	184	4	188

Merged error: 1.6b

Counts

188 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
0.0b	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
15.1b	(sqrt (+ 1.0 (* k (+ 10.0 k))))
15.1b	(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite53.0ms

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:

6.0ms	(/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
32.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
2.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
2.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
33.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k m) (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))))

simplify104.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	915	3267
1	4004	3058
2	5001	2977

prune393.0ms

Filtered

147 candidates to 230 candidates (-56.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	230	4	234

Merged error: 1.6b

Counts

234 → 4

regimes139.0ms

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	15	6
1	15	6

end0.0ms

analyze3.0s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 24.485115%

Guaranteed chance to sample good point: 56.882289%

sample1.1s

Algorithm

intervals

Results

513.0ms	8000×	body	80	valid
245.0ms	3078×	body	80	invalid
49.0ms	1125×	body	80	nan

Details

analyze3.0s

sample44.0ms

simplify109.0ms

prune10.0ms

localize11.0ms

rewrite27.0ms

series71.0ms

simplify58.0ms

prune107.0ms

localize9.0ms

rewrite18.0ms

series54.0ms

simplify62.0ms

prune97.0ms

localize12.0ms

rewrite33.0ms

series77.0ms

simplify91.0ms

prune307.0ms

localize12.0ms

rewrite53.0ms

series62.0ms

simplify104.0ms

prune393.0ms

regimes139.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze3.0s

sample1.1s

Profiling