Details

sample5.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 52.539063%

Guaranteed chance to sample good point: 29.62963%

Results

54.0ms	351×	body	80	nan
45.0ms	256×	body	80	valid
25.0ms	140×	body	80	invalid

simplify198.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	17
1	174	17
2	710	17
3	4940	17
4	5002	17

prune6.0ms

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: 28.4b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

6.9b	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.8b	(pow (/ d l) (/ 1.0 2.0))
11.2b	(pow (/ d h) (/ 1.0 2.0))
12.9b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
107×	`prod-exp`
55×	`div-exp`
45×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
30×	`add-cbrt-cube`
26×	`unpow-prod-down` `pow-unpow`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`distribute-rgt-in` `sub-neg` `pow-pow` `distribute-lft-in` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 176

Calls

4 calls:

13.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
6.0ms	(pow (/ d l) (/ 1.0 2.0))
5.0ms	(pow (/ d h) (/ 1.0 2.0))
16.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series520.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.0ms	(pow (/ d l) (/ 1.0 2.0))
13.0ms	(pow (/ d h) (/ 1.0 2.0))
226.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify52.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1519	2226
1	5002	2033

prune597.0ms

Filtered

109 candidates to 188 candidates (-72.5%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	162	26	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	26	189

Merged error: 13.7b

Counts

189 → 26

localize44.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ (* M D) (* 2.0 d))
6.9b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.8b	(pow (/ d l) (/ 1.0 2.0))
12.9b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

738×	`add-exp-log`
487×	`prod-exp`
216×	`pow-exp`
171×	`div-exp`
78×	`pow-to-exp`
46×	`add-cbrt-cube`
28×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`cbrt-unprod`
16×	`associate-r`
13×	`unpow-prod-down` `pow-unpow`
9×	`pow1` `cbrt-undiv`
4×	`div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `pow-prod-down` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 260

Calls

4 calls:

5.0ms	(/ (* M D) (* 2.0 d))
29.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.0ms	(pow (/ d l) (/ 1.0 2.0))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series541.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
268.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.0ms	(pow (/ d l) (/ 1.0 2.0))
255.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify75.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1934	5729
1	5001	5431

prune569.0ms

Filtered

95 candidates to 272 candidates (-186.3%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	263	9	272
Fresh	1	24	25
Picked	1	0	1
Done	0	0	0
Total	265	33	298

Merged error: 12.9b

Counts

298 → 33

localize44.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.7b	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
6.9b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
10.8b	(pow (/ d l) (/ 1.0 2.0))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

700×	`add-exp-log`
475×	`prod-exp`
211×	`pow-exp`
152×	`div-exp`
77×	`pow-to-exp`
39×	`add-cbrt-cube`
22×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`times-frac`
18×	`cbrt-unprod`
13×	`unpow-prod-down` `pow-unpow`
9×	`pow1`
8×	`associate-r`
6×	`cbrt-undiv`
4×	`add-log-exp`
3×	`div-inv`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r/` `associate-l` `pow-prod-down` `-commutative`
1×	`flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 239

Calls

4 calls:

7.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
14.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
30.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
6.0ms	(pow (/ d l) (/ 1.0 2.0))

series733.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
230.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
283.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
12.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1807	5702
1	5001	5404

prune599.0ms

Filtered

85 candidates to 251 candidates (-195.3%)

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	242	9	251
Fresh	5	27	32
Picked	1	0	1
Done	0	0	0
Total	248	36	284

Merged error: 12.0b

Counts

284 → 36

localize57.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ (* M D) (* 2.0 d))
5.0b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.7b	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
6.9b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

5908×	`add-exp-log`
4305×	`prod-exp`
1987×	`pow-exp`
1368×	`div-exp`
641×	`pow-to-exp`
60×	`add-cbrt-cube`
29×	`cbrt-unprod`
11×	`pow1`
10×	`cbrt-undiv`
8×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*`
6×	`add-cube-cbrt`
4×	`pow-prod-down` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `times-frac` `associate-r/` `associate-l` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 950

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
10.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
74.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

series708.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
207.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
225.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
271.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

simplify326.0ms

Algorithm

egg-herbie

Counts

962 → 962

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	4189	38107
1	5001	37902

prune371.0ms

Filtered

71 candidates to 962 candidates (-1254.9%)

Pruning

39 alts after pruning (38 fresh and 1 done)

	Pruned	Kept	Total
New	959	3	962
Fresh	0	35	35
Picked	0	1	1
Done	0	0	0
Total	959	39	998

Merged error: 11.7b

Counts

998 → 39

regimes2.0s

Accuracy

8.1% (4.2b remaining)

Error of 15.7b against oracle of 11.5b and baseline of 16.1b

bsearch403.0ms

Steps

Iters	Range		Point
8	4.096073418760359e-188	4.41391696384508e-184	3.748248705033733e-186
10	-1.425159513329315e-294	4.680088884579237e-304	1.6875689345001513e-308

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	93
1	78	93

end0.0ms

sample10.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 52.539063%

Guaranteed chance to sample good point: 29.62963%

Results

1.6s	11486×	body	80	nan
1.4s	8000×	body	80	valid
1.1s	4785×	body	80	invalid

Details

sample5.3s

simplify198.0ms

prune6.0ms

localize28.0ms

rewrite49.0ms

series520.0ms

simplify52.0ms

prune597.0ms

localize44.0ms

rewrite76.0ms

series541.0ms

simplify75.0ms

prune569.0ms

localize44.0ms

rewrite75.0ms

series733.0ms

simplify76.0ms

prune599.0ms

localize57.0ms

rewrite254.0ms

series708.0ms

simplify326.0ms

prune371.0ms

regimes2.0s

bsearch403.0ms

simplify2.0ms

end0.0ms

sample10.5s

Profiling