Details

analyze1.9s

Algorithm: search

sample144.0ms

Algorithm

intervals

Results

47.0ms	256×	body	80	valid
38.0ms	274×	body	80	nan
28.0ms	159×	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

prune5.0ms

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: 26.1b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

6.1b	(* (* (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))))
11.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.3b	(pow (/ d h) (/ 1.0 2.0))
13.1b	(pow (/ d l) (/ 1.0 2.0))

rewrite48.0ms

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

series535.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(* (* (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))))
234.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0ms	(pow (/ d h) (/ 1.0 2.0))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1519	2226
1	5002	2033

prune572.0ms

Filtered

109 candidates to 188 candidates (-72.5%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	163	25	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	25	189

Merged error: 10.7b

Counts

189 → 25

localize41.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (* M D) (* 2.0 d))
6.1b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
11.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.1b	(pow (/ d l) (/ 1.0 2.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

674×	`add-exp-log`
455×	`prod-exp`
216×	`pow-exp`
171×	`div-exp`
78×	`pow-to-exp`
46×	`add-cbrt-cube`
32×	`1-exp`
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:

6.0ms	(/ (* M D) (* 2.0 d))
24.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
7.0ms	(pow (/ d l) (/ 1.0 2.0))

series581.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
328.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
229.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
18.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1940	5142
1	5001	4754

prune576.0ms

Filtered

95 candidates to 272 candidates (-186.3%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	263	9	272
Fresh	3	21	24
Picked	1	0	1
Done	0	0	0
Total	267	30	297

Merged error: 9.9b

Counts

297 → 30

localize54.0ms

Local error

Found 4 expressions with local error:

2.9b	(pow (/ (cbrt d) h) (/ 1.0 2.0))
3.6b	(/ (* M D) (* 2.0 d))
6.1b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite484.0ms

Algorithm

rewrite-expression-head

Rules

6373×	`add-exp-log`
4949×	`prod-exp`
2614×	`pow-exp`
1626×	`div-exp`
789×	`pow-to-exp`
528×	`1-exp`
232×	`rec-exp`
55×	`add-cbrt-cube`
37×	`times-frac`
32×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`cbrt-unprod`
22×	`unpow-prod-down`
16×	`associate-r`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-undiv` `cbrt-prod`
4×	`pow-prod-down` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 1229

Calls

4 calls:

7.0ms	(pow (/ (cbrt d) h) (/ 1.0 2.0))
5.0ms	(/ (* M D) (* 2.0 d))
76.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series564.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(pow (/ (cbrt d) h) (/ 1.0 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
284.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
235.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify340.0ms

Algorithm

egg-herbie

Counts

1241 → 1241

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5001	39626

prune944.0ms

Filtered

131 candidates to 1241 candidates (-847.3%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	1233	8	1241
Fresh	6	23	29
Picked	1	0	1
Done	0	0	0
Total	1240	31	1271

Merged error: 8.9b

Counts

1271 → 31

localize55.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (* M D) (* 2.0 d))
5.2b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.1b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
6.2b	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

6344×	`add-exp-log`
4941×	`prod-exp`
2607×	`pow-exp`
1610×	`div-exp`
787×	`pow-to-exp`
528×	`1-exp`
232×	`rec-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 → 1182

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
75.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
10.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

series735.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
212.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
283.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) h) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
234.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

simplify331.0ms

Algorithm

egg-herbie

Counts

1194 → 1194

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5001	37858

prune434.0ms

Filtered

78 candidates to 1194 candidates (-1430.8%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	1189	5	1194
Fresh	0	30	30
Picked	1	0	1
Done	0	0	0
Total	1190	35	1225

Merged error: 8.7b

Counts

1225 → 35

regimes2.4s

Accuracy

35.5% (4.3b remaining)

Error of 14.7b against oracle of 10.4b and baseline of 17.1b

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	127
1	78	127

end0.0ms

analyze1.9s

Algorithm: search

sample4.3s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8428×	body	80	nan
869.0ms	4739×	body	80	invalid

Details

analyze1.9s

sample144.0ms

simplify198.0ms

prune5.0ms

localize29.0ms

rewrite48.0ms

series535.0ms

simplify51.0ms

prune572.0ms

localize41.0ms

rewrite67.0ms

series581.0ms

simplify79.0ms

prune576.0ms

localize54.0ms

rewrite484.0ms

series564.0ms

simplify340.0ms

prune944.0ms

localize55.0ms

rewrite285.0ms

series735.0ms

simplify331.0ms

prune434.0ms

regimes2.4s

bsearch4.0ms

simplify2.0ms

end0.0ms

analyze1.9s

sample4.3s

Profiling