Details

sample294.0ms

Algorithm

intervals

Results

154.0ms	1258×	body	80	nan
73.0ms	418×	body	80	valid

simplify195.0ms

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

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: 29.0b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

9.7b	(* (* (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))))
12.7b	(pow (/ d l) (/ 1.0 2.0))
14.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
15.6b	(pow (/ d h) (/ 1.0 2.0))

rewrite52.0ms

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:

16.0ms	(* (* (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))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms	(pow (/ d h) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

651.0ms	(* (* (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))))
67.0ms	(pow (/ d l) (/ 1.0 2.0))
747.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
62.0ms	(pow (/ d h) (/ 1.0 2.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1228	2042
1	5001	1847

prune700.0ms

Filtered

188 candidates to 109 candidates (58.0%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	168	20	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	169	20	189

Merged error: 14.5b

Counts

189 → 20

localize50.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
9.7b	(* (* (* (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))))
12.7b	(pow (/ d l) (/ 1.0 2.0))
14.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite80.0ms

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:

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

series1.5s

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* M D) (* 2.0 d))
650.0ms	(* (* (* (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))))
61.0ms	(pow (/ d l) (/ 1.0 2.0))
754.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify83.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1642	5552
1	5002	5211

prune697.0ms

Filtered

272 candidates to 88 candidates (32.4%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	266	6	272
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	269	23	292

Merged error: 14.0b

Counts

292 → 23

localize61.0ms

Local error

Found 4 expressions with local error:

2.7b	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
4.6b	(/ (* M D) (* 2.0 d))
9.7b	(* (* (* (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))))
14.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

5947×	`add-exp-log`
4317×	`prod-exp`
1997×	`pow-exp`
1387×	`div-exp`
643×	`pow-to-exp`
55×	`add-cbrt-cube`
27×	`cbrt-unprod`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
16×	`associate-r`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-undiv`
5×	`unpow-prod-down`
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 → 983

Calls

4 calls:

11.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
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 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

120.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
34.0ms	(/ (* M D) (* 2.0 d))
646.0ms	(* (* (* (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))))
754.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify335.0ms

Algorithm

egg-herbie

Counts

995 → 995

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	4083	38233
1	5001	38031

prune835.0ms

Filtered

995 candidates to 89 candidates (8.9%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	992	3	995
Fresh	2	20	22
Picked	1	0	1
Done	0	0	0
Total	995	23	1018

Merged error: 12.3b

Counts

1018 → 23

localize60.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
6.0b	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
7.2b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
9.7b	(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

rewrite267.0ms

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))
10.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
8.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
75.0ms	(* (* (* (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))))

series2.3s

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (* M D) (* 2.0 d))
706.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
947.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
648.0ms	(* (* (* (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))))

simplify311.0ms

Algorithm

egg-herbie

Counts

962 → 962

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	3876	37890
1	5001	37685

prune539.0ms

Filtered

962 candidates to 70 candidates (7.3%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	960	2	962
Fresh	0	22	22
Picked	1	0	1
Done	0	0	0
Total	961	24	985

Merged error: 12.0b

Counts

985 → 24

regimes1.3s

Accuracy

28.6% (3.6b remaining)

Error of 14.3b against oracle of 10.6b and baseline of 15.7b

bsearch463.0ms

Steps

Iters	Range		Point
7	3.432581516423483e-49	2.646456886040572e-47	1.5422825791862263e-47
6	-1.5343906860921258e-63	-3.076153805814668e-64	-6.164335148124461e-64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	82
1	66	82

end0.0ms

sample8.6s

Algorithm

intervals

Results

4.7s	38276×	body	80	nan
2.1s	12871×	body	80	valid