Details

analyze2.3s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

sample195.0ms

Algorithm

intervals

Results

59.0ms	320×	body	80	nan
54.0ms	256×	body	80	valid
36.0ms	180×	body	80	invalid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5402	52

prune21.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 24.7b

Counts

2 → 1

localize42.0ms

Local error

Found 4 expressions with local error:

7.3b	(* (* (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))))
9.8b	(pow (/ d h) (/ 1.0 2.0))
11.4b	(pow (/ d l) (/ 1.0 2.0))
13.7b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite103.0ms

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×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `frac-times` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 174

Calls

4 calls:

38.0ms	(* (* (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))))
11.0ms	(pow (/ d h) (/ 1.0 2.0))
12.0ms	(pow (/ d l) (/ 1.0 2.0))
25.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series888.0ms

Counts

4 → 12

Calls

4 calls:

502.0ms	(* (* (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))))
24.0ms	(pow (/ d h) (/ 1.0 2.0))
14.0ms	(pow (/ d l) (/ 1.0 2.0))
349.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify141.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5553	5559

prune851.0ms

Filtered

109 candidates to 186 candidates (-70.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	169	17	186
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	170	17	187

Merged error: 11.4b

Counts

187 → 17

localize70.0ms

Local error

Found 4 expressions with local error:

4.3b	(/ (* M D) (* 2.0 d))
7.3b	(* (* (pow (/ 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))))
9.8b	(pow (/ d h) (/ 1.0 2.0))
13.7b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

818×	`add-exp-log`
567×	`prod-exp`
280×	`pow-exp`
187×	`div-exp`
94×	`pow-to-exp`
46×	`add-cbrt-cube`
32×	`rec-exp` `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×	`sub-neg` `associate-l` `pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 290

Calls

4 calls:

11.0ms	(/ (* M D) (* 2.0 d))
42.0ms	(* (* (pow (/ 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))))
10.0ms	(pow (/ d h) (/ 1.0 2.0))
19.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series977.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (* M D) (* 2.0 d))
544.0ms	(* (* (pow (/ 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))))
25.0ms	(pow (/ d h) (/ 1.0 2.0))
396.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify258.0ms

Algorithm

egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5065	14330

prune857.0ms

Filtered

90 candidates to 302 candidates (-235.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	296	6	302
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	300	19	319

Merged error: 11.3b

Counts

319 → 19

localize86.0ms

Local error

Found 4 expressions with local error:

3.4b	(pow (/ (cbrt d) h) (/ 1.0 2.0))
4.3b	(/ (* M D) (* 2.0 d))
7.3b	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 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))))
13.7b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

3529×	`add-exp-log`
2893×	`prod-exp`
1396×	`pow-exp`
623×	`div-exp`
522×	`pow-to-exp`
136×	`rec-exp` `1-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×	`sub-neg` `associate-l` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 783

Calls

4 calls:

14.0ms	(pow (/ (cbrt d) h) (/ 1.0 2.0))
11.0ms	(/ (* M D) (* 2.0 d))
117.0ms	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 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))))
28.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series945.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(pow (/ (cbrt d) h) (/ 1.0 2.0))
11.0ms	(/ (* M D) (* 2.0 d))
434.0ms	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 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))))
429.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify570.0ms

Algorithm

egg-herbie

Counts

795 → 795

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5066	53718

prune845.0ms

Filtered

99 candidates to 795 candidates (-703.0%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	792	3	795
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	795	19	814

Merged error: 10.7b

Counts

814 → 19

localize91.0ms

Local error

Found 4 expressions with local error:

3.1b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.3b	(/ (* M D) (* 2.0 d))
7.3b	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (* (pow (cbrt (* (cbrt d) (cbrt d))) (/ 1.0 2.0)) (pow (/ (cbrt (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))))
13.7b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite829.0ms

Algorithm

rewrite-expression-head

Rules

11913×	`add-exp-log`
10726×	`prod-exp`
4902×	`pow-exp`
2211×	`pow-to-exp`
1819×	`div-exp`
424×	`rec-exp` `1-exp`
66×	`add-cbrt-cube`
37×	`times-frac`
36×	`cbrt-unprod`
32×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
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×	`sub-neg` `associate-l` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 2117

Calls

4 calls:

14.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
27.0ms	(/ (* M D) (* 2.0 d))
151.0ms	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (* (pow (cbrt (* (cbrt d) (cbrt d))) (/ 1.0 2.0)) (pow (/ (cbrt (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))))
25.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.2s

Counts

4 → 12

Calls

4 calls:

75.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
12.0ms	(/ (* M D) (* 2.0 d))
511.0ms	(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (* (pow (cbrt (* (cbrt d) (cbrt d))) (/ 1.0 2.0)) (pow (/ (cbrt (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))))
606.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.1s

Algorithm

egg-herbie

Counts

2129 → 2129

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	5047	198994

prune970.0ms

Filtered

109 candidates to 2129 candidates (-1853.2%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	2123	6	2129
Fresh	0	18	18
Picked	1	0	1
Done	0	0	0
Total	2124	24	2148

Merged error: 10.4b

Counts

2148 → 24

regimes2.4s

Accuracy

-4.7% (6.0b remaining)

Error of 17.5b against oracle of 11.4b and baseline of 17.2b

bsearch721.0ms

Steps

Iters	Range		Point
11	3.8974993543624163e-193	1.5115890368843031e-170	8.16851537488987e-179
10	9.357663946993284e-300	1.3314382295180214e-285	1.0097243451344419e-288

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	132	174
1	132	174

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.1s	8000×	body	80	valid
2.0s	8598×	body	80	nan
1.2s	4821×	body	80	invalid

Details

analyze2.3s

sample195.0ms

simplify47.0ms

prune21.0ms

localize42.0ms

rewrite103.0ms

series888.0ms

simplify141.0ms

prune851.0ms

localize70.0ms

rewrite114.0ms

series977.0ms

simplify258.0ms

prune857.0ms

localize86.0ms

rewrite362.0ms

series945.0ms

simplify570.0ms

prune845.0ms

localize91.0ms

rewrite829.0ms

series1.2s

simplify2.1s

prune970.0ms

regimes2.4s

bsearch721.0ms

simplify5.0ms

end0.0ms

sample6.5s

Profiling