Details

sample263.0ms

Algorithm

intervals

Results

138.0ms	1244×	body	80	nan
62.0ms	410×	body	80	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	54	17
1	174	17
2	720	17
3	5001	17

prune4.0ms

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: 27.1b

Counts

2 → 1

localize29.0ms

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))))
10.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.5b	(pow (/ d h) (/ 1.0 2.0))
10.9b	(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`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
40×	`pow-exp`
30×	`add-cbrt-cube`
26×	`unpow-prod-down` `pow-unpow`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
6×	`prod-diff`
5×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 190

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))))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
8.0ms	(pow (/ d h) (/ 1.0 2.0))
5.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

640.0ms	(* (* (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))))
738.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
60.0ms	(pow (/ d h) (/ 1.0 2.0))
65.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1287	2382
1	5001	2125

prune763.0ms

Filtered

202 candidates to 119 candidates (58.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	182	20	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	183	20	203

Merged error: 11.6b

Counts

203 → 20

localize43.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (* 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))))
10.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.9b	(pow (/ d l) (/ 1.0 2.0))

rewrite77.0ms

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×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
20×	`cbrt-unprod`
16×	`associate-r`
13×	`unpow-prod-down` `pow-unpow`
9×	`pow1` `cbrt-undiv`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `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 → 274

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
32.0ms	(* (* (* (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))))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (* M D) (* 2.0 d))
671.0ms	(* (* (* (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))))
751.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
72.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify86.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1710	6060
1	5001	5717

prune874.0ms

Filtered

286 candidates to 104 candidates (36.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	276	10	286
Fresh	7	12	19
Picked	1	0	1
Done	0	0	0
Total	284	22	306

Merged error: 11.1b

Counts

306 → 22

localize62.0ms

Local error

Found 4 expressions with local error:

3.2b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.5b	(/ (* 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 (/ 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))))
10.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

6965×	`add-exp-log`
5245×	`prod-exp`
2614×	`pow-exp`
1626×	`div-exp`
789×	`pow-to-exp`
232×	`rec-exp` `1-exp`
55×	`add-cbrt-cube`
37×	`times-frac`
34×	`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`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `associate-l` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 1243

Calls

4 calls:

7.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
79.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.0s

Counts

4 → 12

Calls

4 calls:

186.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
34.0ms	(/ (* M D) (* 2.0 d))
982.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))
755.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify383.0ms

Algorithm

egg-herbie

Counts

1255 → 1255

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5001	45180

prune1.5s

Filtered

1255 candidates to 145 candidates (11.6%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	1246	9	1255
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	1250	27	1277

Merged error: 9.8b

Counts

1277 → 27

localize61.0ms

Local error

Found 4 expressions with local error:

4.1b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
4.5b	(/ (* M D) (* 2.0 d))
5.0b	(/ (* (* 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 (/ 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))))

rewrite519.0ms

Algorithm

rewrite-expression-head

Rules

6936×	`add-exp-log`
5237×	`prod-exp`
2607×	`pow-exp`
1610×	`div-exp`
787×	`pow-to-exp`
232×	`rec-exp` `1-exp`
60×	`add-cbrt-cube`
30×	`prod-diff`
29×	`cbrt-unprod`
24×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1`
10×	`cbrt-undiv`
8×	`times-frac` `associate-r` `div-inv`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `associate-r/` `associate-l` `clear-num` `associate-/r` `-commutative` `associate-/l`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 1220

Calls

4 calls:

7.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
83.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))

series2.5s

Counts

4 → 12

Calls

4 calls:

783.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
28.0ms	(/ (* M D) (* 2.0 d))
747.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
978.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))

simplify394.0ms

Algorithm

egg-herbie

Counts

1232 → 1232

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5001	46241

prune840.0ms

Filtered

1232 candidates to 94 candidates (7.6%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	1227	5	1232
Fresh	7	19	26
Picked	1	0	1
Done	0	0	0
Total	1235	24	1259

Merged error: 9.8b

Counts

1259 → 24

regimes1.3s

Accuracy

21.6% (4.7b remaining)

Error of 14.5b against oracle of 9.7b and baseline of 15.8b

bsearch5.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	153
1	92	153

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.3s	38284×	body	80	nan
1.9s	12748×	body	80	valid