Details

sample237.0ms

Algorithm

intervals

Results

121.0ms	1070×	body	80	nan
55.0ms	374×	body	80	valid

simplify32.0ms

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

prune7.0ms

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: 25.2b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (* (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))))
11.1b	(pow (/ d h) (/ 1.0 2.0))
13.1b	(pow (/ d l) (/ 1.0 2.0))
13.9b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

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:

14.0ms	(* (* (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))
13.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

630.0ms	(* (* (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))))
66.0ms	(pow (/ d h) (/ 1.0 2.0))
67.0ms	(pow (/ d l) (/ 1.0 2.0))
736.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify53.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1287	2382
1	5002	2125

prune770.0ms

Filtered

202 candidates to 119 candidates (58.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	181	21	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	21	203

Merged error: 10.0b

Counts

203 → 21

localize49.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (* M D) (* 2.0 d))
4.7b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
13.1b	(pow (/ d l) (/ 1.0 2.0))
13.9b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite81.0ms

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×	`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 → 306

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
28.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))

series1.7s

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (* M D) (* 2.0 d))
866.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))
748.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify84.0ms

Algorithm

egg-herbie

Counts

318 → 318

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1876	6250
1	5002	5934

prune798.0ms

Filtered

318 candidates to 105 candidates (33.0%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	305	13	318
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	311	28	339

Merged error: 8.5b

Counts

339 → 28

localize61.0ms

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))
4.7b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
13.9b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

8121×	`add-exp-log`
6369×	`prod-exp`
3426×	`pow-exp`
1900×	`div-exp`
967×	`pow-to-exp`
592×	`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 → 1539

Calls

4 calls:

7.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
90.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))

series1.8s

Counts

4 → 12

Calls

4 calls:

175.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
27.0ms	(/ (* M D) (* 2.0 d))
867.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
731.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify442.0ms

Algorithm

egg-herbie

Counts

1551 → 1551

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5001	50947

prune1.5s

Filtered

1551 candidates to 145 candidates (9.3%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	1545	6	1551
Fresh	5	22	27
Picked	1	0	1
Done	0	0	0
Total	1551	28	1579

Merged error: 6.6b

Counts

1579 → 28

localize55.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (* M D) (* 2.0 d))
4.7b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
7.8b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
8.5b	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

8092×	`add-exp-log`
6361×	`prod-exp`
3419×	`pow-exp`
1884×	`div-exp`
965×	`pow-to-exp`
592×	`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 → 1516

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
90.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
8.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
15.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

series2.3s

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* M D) (* 2.0 d))
845.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
723.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
701.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

simplify455.0ms

Algorithm

egg-herbie

Counts

1528 → 1528

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5001	52866

prune1.0s

Filtered

1528 candidates to 128 candidates (8.4%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	1524	4	1528
Fresh	1	26	27
Picked	1	0	1
Done	0	0	0
Total	1526	30	1556

Merged error: 5.4b

Counts

1556 → 30

regimes1.7s

Accuracy

35.9% (5.6b remaining)

Error of 14.6b against oracle of 9.0b and baseline of 17.8b

bsearch5.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	173
1	84	173

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.3s	38791×	body	80	nan
1.9s	12843×	body	80	valid