Details

sample664.0ms

Algorithm

intervals

Results

434.0ms	1088×	body	80	nan
155.0ms	411×	body	80	valid

simplify5.0s

Counts

1 → 1

Iterations

Iter	Nodes
4	9507
3	1091
2	188
1	55
0	22

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.6b

localize101.0ms

Local error

Found 4 expressions with local error:

6.4b	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
9.0b	(pow (/ d l) (/ 1 2))
11.2b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.5b	(pow (/ d h) (/ 1 2))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

331×	`add-exp-log`
179×	`prod-exp`
99×	`div-exp`
60×	`pow-exp`
45×	`times-frac`
42×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
30×	`add-cbrt-cube`
26×	`pow-unpow` `unpow-prod-down`
18×	`pow-to-exp`
16×	`associate-r`
14×	`rec-exp` `1-exp`
13×	`cbrt-unprod`
10×	`pow1`
6×	`prod-diff`
5×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 222

Calls

4 calls:

49.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
7.0ms	(pow (/ d l) (/ 1 2))
57.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
5.0ms	(pow (/ d h) (/ 1 2))

series710.0ms

Counts

4 → 12

Calls

4 calls:

437.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
71.0ms	(pow (/ d l) (/ 1 2))
117.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
85.0ms	(pow (/ d h) (/ 1 2))

simplify7.4s

Counts

234 → 234

Iterations

Iter	Nodes
2	4109
1	1309
0	461

prune4.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.0b

localize103.0ms

Local error

Found 4 expressions with local error:

5.0b	(/ (* M D) (* 2 d))
6.4b	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
9.0b	(pow (/ d l) (/ 1 2))
11.2b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite962.0ms

Algorithm

rewrite-expression-head

Rules

320×	`add-exp-log`
171×	`prod-exp`
96×	`div-exp`
46×	`add-cbrt-cube` `associate-*l/` `pow-exp`
30×	`frac-times` `sqrt-div`
28×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
20×	`cbrt-unprod`
16×	`associate-r`
14×	`rec-exp` `1-exp`
13×	`pow-unpow` `unpow-prod-down`
12×	`associate-*r/`
11×	`pow-to-exp`
9×	`pow1` `cbrt-undiv`
8×	`flip3--` `flip--`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`sub-neg` `associate-l` `pow-prod-down` `*-commutative`
1×	`clear-num` `associate-/r` `pow-pow` `frac-2neg` `associate-/l` `sqr-pow`

Counts

4 → 219

Calls

4 calls:

26.0ms	(/ (* M D) (* 2 d))
836.0ms	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
7.0ms	(pow (/ d l) (/ 1 2))
83.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series662.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (* M D) (* 2 d))
418.0ms	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
86.0ms	(pow (/ d l) (/ 1 2))
116.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify6.2s

Counts

231 → 231

Iterations

Iter	Nodes
2	5362
1	1456
0	491

prune5.3s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.3b

localize132.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (/ d (cbrt l)))
5.0b	(/ (* M D) (* 2 d))
6.4b	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
11.2b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

305×	`add-exp-log`
217×	`sqrt-div`
210×	`frac-times`
163×	`prod-exp`
139×	`associate-*l/`
93×	`div-exp`
72×	`associate-*r/`
55×	`add-cbrt-cube`
40×	`pow-exp`
32×	`add-sqr-sqrt` `flip3--` `flip--`
30×	`times-frac`
27×	`*-un-lft-identity` `add-cube-cbrt` `cbrt-unprod`
25×	`pow1`
22×	`sqrt-prod`
16×	`associate-r`
14×	`rec-exp` `1-exp` `pow-prod-down`
10×	`cbrt-prod`
9×	`cbrt-undiv`
8×	`pow-to-exp`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `div-inv`
2×	`sub-neg` `associate-l` `*-commutative`
1×	`clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l`

Counts

4 → 290

Calls

4 calls:

6.0ms	(sqrt (/ d (cbrt l)))
24.0ms	(/ (* M D) (* 2 d))
1.0s	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
63.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series1.8s

Counts

4 → 12

Calls

4 calls:

227.0ms	(sqrt (/ d (cbrt l)))
30.0ms	(/ (* M D) (* 2 d))
1.4s	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
136.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.7s

Counts

302 → 302

Iterations

Iter	Nodes
1	2125
0	697

prune8.1s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 8.4b

localize138.0ms

Local error

Found 4 expressions with local error:

5.0b	(/ (* M D) (* d 2))
5.0b	(/ (* M D) (* d 2))
6.0b	(/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))
6.4b	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

443×	`add-cbrt-cube` `add-exp-log`
230×	`prod-exp` `cbrt-unprod`
216×	`sqrt-div`
210×	`frac-times`
142×	`cbrt-undiv` `div-exp`
137×	`associate-*l/`
75×	`associate-*r/`
32×	`flip3--` `flip--`
30×	`prod-diff`
24×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`pow1`
21×	`add-cube-cbrt`
17×	`distribute-rgt-in` `distribute-lft-in`
13×	`pow-prod-down`
9×	`times-frac` `div-inv`
6×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `associate-/r` `frac-2neg` `associate-/l` `associate-/l/`
2×	`sub-neg` `difference-of-squares`
1×	`associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 337

Calls

4 calls:

13.0ms	(/ (* M D) (* d 2))
22.0ms	(/ (* M D) (* d 2))
169.0ms	(/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))
1.1s	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))))

series1.6s

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* M D) (* d 2))
49.0ms	(/ (* M D) (* d 2))
128.0ms	(/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))
1.4s	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))))

simplify1.8s

Counts

349 → 349

Iterations

Iter	Nodes
1	2516
0	723

prune10.1s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 7.2b

regimes3.1s

Accuracy

15.4% (5.9b remaining)

Error of 13.4b against oracle of 7.6b and baseline of 14.5b

bsearch5.0ms

simplify31.0ms

Iterations

Iter	Nodes
2	83
1	83
0	65

end0.0ms

sample24.1s

Algorithm

intervals

Results

15.3s	37686×	body	80	nan
5.9s	12698×	body	80	valid