Details

analyze986.0ms

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

sample43.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
8.0ms	101×	body	80	invalid
2.0ms	52×	body	80	nan

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4961	13
1	4961	13

prune11.0ms

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: 2.9b

Counts

2 → 2

localize9.0ms

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))))
2.7b	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

rewrite27.0ms

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))))
11.0ms	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

series56.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* k (+ k 10.0))
15.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
36.0ms	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

simplify37.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5031	1960

prune182.0ms

Filtered

94 candidates to 129 candidates (-37.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	126	5	131

Merged error: 2.8b

Counts

131 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt k)
0.5b	(cbrt k)
0.5b	(* (cbrt k) (cbrt k))
2.7b	(* a (* (pow (* (cbrt k) (cbrt k)) m) (/ (pow (cbrt k) m) (+ 1.0 (* k (+ k 10.0))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
38×	`prod-exp`
23×	`add-sqr-sqrt`
22×	`cbrt-prod`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-cbrt-cube`
12×	`div-exp` `pow-exp`
9×	`associate-l`
8×	`pow-to-exp` `pow1/3`
7×	`associate-r`
6×	`swap-sqr` `cbrt-unprod`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down`
2×	`associate-r/` `pow-sqr` `-commutative` `pow-prod-up`
1×	`cbrt-undiv` `pow2` `pow-plus`

Counts

4 → 96

Calls

4 calls:

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

series177.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt k)
22.0ms	(cbrt k)
26.0ms	(* (cbrt k) (cbrt k))
108.0ms	(* a (* (pow (* (cbrt k) (cbrt k)) m) (/ (pow (cbrt k) m) (+ 1.0 (* k (+ k 10.0))))))

simplify30.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5156	1240

prune124.0ms

Filtered

64 candidates to 108 candidates (-68.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	108	5	113

Merged error: 2.8b

Counts

113 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0)))))
0.1b	(* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))))
15.2b	(sqrt (+ 1.0 (* k (+ k 10.0))))
15.2b	(sqrt (+ 1.0 (* k (+ k 10.0))))

rewrite59.0ms

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:

7.0ms	(/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0)))))
33.0ms	(* (/ 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))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (pow k m) (sqrt (+ 1.0 (* 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))))

simplify92.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4967	5224
1	4967	5224

prune394.0ms

Filtered

147 candidates to 230 candidates (-56.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	228	2	230
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	230	5	235

Merged error: 0.0b

Counts

235 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* a (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0)))))) (sqrt (+ 1.0 (* k (+ k 10.0)))))
0.1b	(* a (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))))
15.2b	(sqrt (+ 1.0 (* k (+ k 10.0))))
15.2b	(sqrt (+ 1.0 (* k (+ k 10.0))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
54×	`times-frac`
48×	`associate-r`
38×	`add-cube-cbrt` `*-un-lft-identity`
36×	`sqrt-prod`
30×	`add-exp-log`
20×	`unpow-prod-down`
18×	`add-cbrt-cube`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `sqr-pow`
7×	`unswap-sqr`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`flip3-+` `associate-/r/` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`associate-l`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `pow-exp` `div-inv`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 138

Calls

4 calls:

13.0ms	(/ (* a (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0)))))) (sqrt (+ 1.0 (* k (+ k 10.0)))))
16.0ms	(* a (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* a (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0)))))) (sqrt (+ 1.0 (* k (+ k 10.0)))))
40.0ms	(* a (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))))
4.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))
4.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))

simplify38.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5015	2431

prune421.0ms

Filtered

99 candidates to 150 candidates (-51.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	150	5	155

Merged error: 0.0b

Counts

155 → 5

regimes179.0ms

Accuracy

98.1% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch26.0ms

Steps

Iters	Range		Point
8	9.501940478643842e+22	2.93675584348729e+27	5.2465810226145275e+23

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	95	59
1	95	59

end0.0ms

sample1.2s

Algorithm

intervals

Results

516.0ms	8000×	body	80	valid
272.0ms	3372×	body	80	invalid
88.0ms	1975×	body	80	nan

Details

analyze986.0ms

sample43.0ms

simplify83.0ms

prune11.0ms

localize9.0ms

rewrite27.0ms

series56.0ms

simplify37.0ms

prune182.0ms

localize15.0ms

rewrite23.0ms

series177.0ms

simplify30.0ms

prune124.0ms

localize12.0ms

rewrite59.0ms

series58.0ms

simplify92.0ms

prune394.0ms

localize14.0ms

rewrite41.0ms

series80.0ms

simplify38.0ms

prune421.0ms

regimes179.0ms

bsearch26.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling