Details

sample288.0ms

Algorithm

intervals

Results

148.0ms	1310×	body	80	nan
63.0ms	425×	body	80	valid

simplify214.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

Filtered

1 candidates to 0 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: 24.5b

Counts

2 → 1

localize37.0ms

Local error

Found 4 expressions with local error:

6.4b	(* (* (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))))
10.1b	(pow (/ d h) (/ 1.0 2.0))
12.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.4b	(pow (/ d l) (/ 1.0 2.0))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

680×	`add-sqr-sqrt`
344×	`associate-l`
337×	`times-frac`
291×	`associate-r`
282×	`unpow-prod-down`
243×	`unswap-sqr`
205×	`add-exp-log`
186×	`*-un-lft-identity`
179×	`add-cube-cbrt`
107×	`prod-exp`
99×	`associate-*l/`
81×	`frac-times`
61×	`associate-/l*`
60×	`associate-/r*`
55×	`div-exp`
40×	`pow-exp`
31×	`difference-of-squares` `sqr-pow`
30×	`add-cbrt-cube`
28×	`*-commutative`
26×	`pow-unpow`
21×	`clear-num`
20×	`frac-2neg`
16×	`pow1`
14×	`pow-to-exp`
13×	`cbrt-unprod`
11×	`associate-*r/`
9×	`div-inv`
6×	`pow-prod-down`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`distribute-lft-out--`
2×	`distribute-rgt-in` `sub-neg` `pow-pow` `distribute-lft-in` `un-div-inv`
1×	`flip3--` `flip--`

Counts

4 → 594

Calls

4 calls:

229.0ms	(* (* (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))))
5.0ms	(pow (/ d h) (/ 1.0 2.0))
131.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

706.0ms	(* (* (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))))
64.0ms	(pow (/ d h) (/ 1.0 2.0))
849.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
86.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify162.0ms

Algorithm

egg-herbie

Counts

606 → 606

Iterations

Useful iterations: 1 (75.0ms)

Iter	Nodes	Cost
0	3591	7501
1	5001	7398

prune2.4s

Filtered

606 candidates to 461 candidates (76.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	585	21	606
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	586	21	607

Merged error: 7.8b

Counts

607 → 21

localize44.0ms

Local error

Found 4 expressions with local error:

4.0b	(* (* (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))))
5.2b	(/ (* M D) (* 2.0 d))
12.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.4b	(pow (/ d l) (/ 1.0 2.0))

rewrite473.0ms

Algorithm

rewrite-expression-head

Rules

898×	`add-sqr-sqrt`
520×	`times-frac`
488×	`associate-l`
369×	`associate-r`
332×	`unpow-prod-down`
305×	`unswap-sqr`
268×	`*-un-lft-identity`
261×	`add-cube-cbrt`
214×	`add-exp-log`
111×	`prod-exp`
99×	`associate-*l/`
81×	`frac-times`
73×	`associate-/l*`
72×	`associate-/r*`
68×	`cbrt-prod`
58×	`div-exp`
54×	`*-commutative`
42×	`add-cbrt-cube`
38×	`pow-exp`
36×	`sqr-pow`
31×	`difference-of-squares`
22×	`clear-num`
21×	`frac-2neg`
17×	`cbrt-unprod`
15×	`pow1`
13×	`pow-to-exp` `pow-unpow`
11×	`associate-*r/`
9×	`cbrt-undiv`
8×	`div-inv`
6×	`pow-prod-down`
4×	`add-log-exp`
3×	`distribute-lft-out--`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `un-div-inv`
1×	`flip3--` `pow-pow` `flip--`

Counts

4 → 793

Calls

4 calls:

256.0ms	(* (* (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	(/ (* M D) (* 2.0 d))
128.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms	(pow (/ d l) (/ 1.0 2.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

991.0ms	(* (* (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))))
29.0ms	(/ (* M D) (* 2.0 d))
844.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
87.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify185.0ms

Algorithm

egg-herbie

Counts

805 → 805

Iterations

Useful iterations: 1 (77.0ms)

Iter	Nodes	Cost
0	4196	10248
1	5001	10167

prune4.0s

Filtered

805 candidates to 616 candidates (76.5%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	795	10	805
Fresh	6	14	20
Picked	1	0	1
Done	0	0	0
Total	802	24	826

Merged error: 7.1b

Counts

826 → 24

localize55.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (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 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))))
3.5b	(* (* (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 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))))
5.2b	(/ (* M D) (* 2.0 d))
12.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite4.1m

Algorithm

rewrite-expression-head

Rules

3748056×	`add-sqr-sqrt`
2249474×	`unswap-sqr`
1467844×	`cbrt-prod`
1328183×	`unpow-prod-down`
1210234×	`times-frac`
344520×	`swap-sqr`
171995×	`*-commutative`
118181×	`sqr-pow`
9205×	`associate-r`
7700×	`add-exp-log`
5532×	`prod-exp`
4986×	`associate-l`
2574×	`pow-exp`
1799×	`*-un-lft-identity`
1786×	`add-cube-cbrt`
1785×	`div-exp`
822×	`pow-to-exp`
99×	`associate-*l/`
81×	`frac-times`
73×	`associate-/l*`
72×	`associate-/r*`
67×	`add-cbrt-cube`
62×	`difference-of-squares`
39×	`pow1`
35×	`cbrt-unprod`
32×	`distribute-rgt-in` `distribute-lft-in`
24×	`pow-prod-down`
22×	`clear-num`
21×	`frac-2neg`
19×	`associate-*r/`
12×	`sub-neg`
11×	`div-inv`
9×	`cbrt-undiv`
6×	`distribute-lft-out--`
4×	`add-log-exp`
2×	`flip3--` `un-div-inv` `flip--`

Counts

4 → 410781

Calls

4 calls:

54.9s	(* (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 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))))
2.2s	(* (* (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 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))))
13.0ms	(/ (* M D) (* 2.0 d))
124.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.1s

Counts

4 → 12

Calls

4 calls:

641.0ms	(* (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 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))))
710.0ms	(* (* (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 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))))
29.0ms	(/ (* M D) (* 2.0 d))
762.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify5.7m

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (23.3s)

Iter	Nodes	Cost
0	95975	39442811