Details

sample491.0ms

Algorithm

intervals

Results

260.0ms	1231×	body	80	nan
127.0ms	420×	body	80	valid

simplify6.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	1117
1	54	1117
2	170	1117
3	645	1117
4	3841	1117
done	5000	1117

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize77.0ms

Local error

Found 4 expressions with local error:

7.9b	(* (* (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))))
10.3b	(pow (/ d h) (/ 1.0 2.0))
11.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.4b	(pow (/ d l) (/ 1.0 2.0))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
107×	`prod-exp`
55×	`div-exp`
45×	`times-frac`
40×	`add-sqr-sqrt` `*-un-lft-identity` `pow-exp` `add-cube-cbrt`
30×	`add-cbrt-cube`
26×	`pow-unpow` `unpow-prod-down`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`add-log-exp`
3×	`associate-l/` `associate-r/`
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:

96.0ms	(* (* (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	(pow (/ d h) (/ 1.0 2.0))
59.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

series2.3s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (* (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))))
82.0ms	(pow (/ d h) (/ 1.0 2.0))
1.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
94.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify4.7s

Counts

188 → 188

Iterations

Useful iterations: done (4.6s)

Iter	Nodes	Cost
0	437	131818
1	1322	119464
2	4318	117202
done	5001	115032

prune1.6s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.4b

localize137.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ (* M D) (* 2.0 d))
7.9b	(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
10.3b	(pow (/ d h) (/ 1.0 2.0))
11.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite364.0ms

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` `*-un-lft-identity` `add-cube-cbrt`
20×	`cbrt-unprod`
16×	`associate-r`
13×	`pow-unpow` `unpow-prod-down`
9×	`pow1` `cbrt-undiv`
4×	`div-inv` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `pow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `associate-/r` `pow-pow` `frac-2neg` `flip3--` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 260

Calls

4 calls:

10.0ms	(/ (* M D) (* 2.0 d))
246.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
11.0ms	(pow (/ d h) (/ 1.0 2.0))
62.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.1s

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (* M D) (* 2.0 d))
917.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
96.0ms	(pow (/ d h) (/ 1.0 2.0))
1.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify5.0s

Counts

272 → 272

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	546	290294
1	1548	255912
done	5000	239126

prune1.7s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 8.2b

localize239.0ms

Local error

Found 4 expressions with local error:

2.2b	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
3.4b	(/ (* M D) (* 2.0 d))
7.9b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
11.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite956.0ms

Algorithm

rewrite-expression-head

Rules

6975×	`add-exp-log`
5249×	`prod-exp`
2617×	`pow-exp`
1629×	`div-exp`
789×	`pow-to-exp`
232×	`rec-exp` `1-exp`
55×	`add-cbrt-cube`
27×	`cbrt-unprod`
19×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
16×	`associate-r`
13×	`pow-unpow`
9×	`cbrt-undiv`
6×	`pow-pow`
5×	`pow-prod-down`
4×	`add-log-exp`
3×	`associate-l/` `associate-r/` `div-inv`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`
1×	`pow2` `frac-times` `clear-num` `associate-/r` `unpow-prod-down` `frac-2neg` `pow-plus` `flip3--` `pow-sqr` `pow-prod-up` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 1216

Calls

4 calls:

16.0ms	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
10.0ms	(/ (* M D) (* 2.0 d))
613.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
59.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.5s

Counts

4 → 12

Calls

4 calls:

200.0ms	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
36.0ms	(/ (* M D) (* 2.0 d))
1.3s	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (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))))
991.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify48.9s

Counts

1228 → 1228

Iterations

Useful iterations: done (48.6s)

Iter	Nodes	Cost
0	1423	2138399
1	3906	1841219
done	5000	1839857

prune1.5s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 5.9b

localize164.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))
3.4b	(/ (* M D) (* 2.0 d))
4.3b	(* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ 1.0 2.0)))
7.9b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))))

rewrite889.0ms

Algorithm

rewrite-expression-head

Rules

8382×	`add-exp-log`
6058×	`prod-exp`
2742×	`pow-exp`
2061×	`div-exp`
814×	`pow-to-exp`
232×	`rec-exp` `1-exp`
187×	`add-cbrt-cube`
160×	`cbrt-unprod`
71×	`cbrt-undiv`
44×	`associate-r`
37×	`times-frac`
36×	`cbrt-prod`
30×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
24×	`associate-*r/`
23×	`pow1`
22×	`frac-times` `associate-*l/`
12×	`pow-prod-down`
4×	`add-log-exp`
3×	`associate-l` `*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-inv`
1×	`clear-num` `associate-/r` `frac-2neg` `flip3--` `flip--` `associate-/l`

Counts

4 → 1480

Calls

4 calls:

257.0ms	(* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))
9.0ms	(/ (* M D) (* 2.0 d))
69.0ms	(* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ 1.0 2.0)))
356.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

441.0ms	(* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))
31.0ms	(/ (* M D) (* 2.0 d))
563.0ms	(* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ 1.0 2.0)))
867.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))))

simplify2.0m

Counts

1492 → 1492

Iterations

Useful iterations: done (2.0m)

Iter	Nodes	Cost
0	1706	2516108
1	4078	2132386
done	5002	2130380

prune1.5s

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.9b

regimes2.3s

Accuracy

-3% (7.0b remaining)

Error of 15.9b against oracle of 9.0b and baseline of 15.7b

bsearch612.0ms

Steps

Iters	Range		Point
9	1.9106710751339173e+77	1.0224583151050328e+85	1.1785184720998613e+79
10	8.785394195191027e-90	1.124156856980492e-75	1.1021362549393407e-75

simplify34.0ms

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	68	4303
1	89	4303
done	89	4303

end0.0ms

sample10.8s

Algorithm

intervals

Results

6.5s	38949×	body	80	nan
2.5s	12877×	body	80	valid