Details

sample286.0ms

Algorithm

intervals

Results

159.0ms	1275×	body	80	nan
61.0ms	393×	body	80	valid

simplify183.0ms

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

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: 28.0b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

8.9b	(* (* (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))))
11.6b	(pow (/ d h) (/ 1.0 2.0))
12.2b	(pow (/ d l) (/ 1.0 2.0))
12.5b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite50.0ms

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:

17.0ms	(* (* (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 h) (/ 1.0 2.0))
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))

series1.7s

Counts

4 → 12

Calls

4 calls:

625.0ms	(* (* (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))
60.0ms	(pow (/ d l) (/ 1.0 2.0))
911.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify49.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1228	2042
1	5001	1847

prune675.0ms

Filtered

188 candidates to 109 candidates (58.0%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	170	18	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	18	189

Merged error: 12.9b

Counts

189 → 18

localize40.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* M D) (* 2.0 d))
8.9b	(* (* (* (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))))
12.2b	(pow (/ d l) (/ 1.0 2.0))
12.5b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite75.0ms

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))
30.0ms	(* (* (* (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))))
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))

series1.8s

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* M D) (* 2.0 d))
961.0ms	(* (* (* (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))))
67.0ms	(pow (/ d l) (/ 1.0 2.0))
729.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify77.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1667	4960
1	5001	4530

prune619.0ms

Filtered

272 candidates to 88 candidates (32.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	266	6	272
Fresh	1	16	17
Picked	1	0	1
Done	0	0	0
Total	268	22	290

Merged error: 12.6b

Counts

290 → 22

localize55.0ms

Local error

Found 4 expressions with local error:

2.9b	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
3.2b	(/ (* M D) (* 2.0 d))
8.9b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))
12.5b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

5483×	`add-exp-log`
4085×	`prod-exp`
1997×	`pow-exp`
1387×	`div-exp`
643×	`pow-to-exp`
232×	`1-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 l) (cbrt l))) (/ 1.0 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
71.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.8s

Counts

4 → 12

Calls

4 calls:

115.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
33.0ms	(/ (* M D) (* 2.0 d))
972.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))
717.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify334.0ms

Algorithm

egg-herbie

Counts

995 → 995

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	4111	33873
1	5003	33679

prune758.0ms

Filtered

995 candidates to 89 candidates (8.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	988	7	995
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	992	25	1017

Merged error: 11.2b

Counts

1017 → 25

localize58.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* M D) (* 2.0 d))
5.2b	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
5.4b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
8.9b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

5444×	`add-exp-log`
4073×	`prod-exp`
1987×	`pow-exp`
1368×	`div-exp`
641×	`pow-to-exp`
232×	`1-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))
11.0ms	(/ (* (* 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)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))

series2.5s

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* M D) (* 2.0 d))
756.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
763.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
958.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))

simplify305.0ms

Algorithm

egg-herbie

Counts

962 → 962

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	3908	33522
1	5001	33325

prune533.0ms

Filtered

962 candidates to 68 candidates (7.1%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	958	4	962
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	961	26	987

Merged error: 11.2b

Counts

987 → 26

regimes1.5s

Accuracy

6.6% (5.8b remaining)

Error of 16.1b against oracle of 10.3b and baseline of 16.5b

bsearch601.0ms

Steps

Iters	Range		Point
9	1.5053062010065768e-82	3.6177285477854536e-75	6.952712762929639e-82
9	-1.0444048500662454e-19	-8.012786377735694e-26	-2.95032860738234e-24

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	74
1	67	74

end0.0ms

sample8.7s

Algorithm

intervals

Results

4.8s	39268×	body	80	nan
2.1s	12807×	body	80	valid