Details

sample1.1s

Algorithm

intervals

Results

818.0ms	1299×	body	80	nan
156.0ms	423×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
4	2006
3	1271
2	198
1	58
0	22

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.5b

localize59.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
10.3b	(pow (/ d h) (/ 1 2))
11.2b	(pow (/ d l) (/ 1 2))
12.8b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite129.0ms

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:

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

series684.0ms

Counts

4 → 12

Calls

4 calls:

388.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
89.0ms	(pow (/ d h) (/ 1 2))
90.0ms	(pow (/ d l) (/ 1 2))
117.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.5s

Counts

234 → 234

Iterations

Iter	Nodes
done	2002
2	2002
1	1360
0	461

prune4.4s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.5b

localize81.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ (* M D) (* 2 d))
6.5b	(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
10.3b	(pow (/ d h) (/ 1 2))
12.8b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

320×	`add-exp-log`
171×	`prod-exp`
96×	`div-exp`
46×	`add-cbrt-cube` `pow-exp`
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`
11×	`pow-to-exp`
9×	`pow1` `cbrt-undiv` `associate-*r/`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-times` `sqrt-div`
2×	`sub-neg` `flip3--` `associate-l` `pow-prod-down` `*-commutative` `flip--`
1×	`clear-num` `associate-/r` `pow-pow` `frac-2neg` `associate-/l` `sqr-pow`

Counts

4 → 201

Calls

4 calls:

11.0ms	(/ (* M D) (* 2 d))
287.0ms	(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
13.0ms	(pow (/ d h) (/ 1 2))
56.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series1.7s

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (* M D) (* 2 d))
1.5s	(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
89.0ms	(pow (/ d h) (/ 1 2))
96.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.5s

Counts

213 → 213

Iterations

Iter	Nodes
done	2000
2	2000
1	1425
0	476

prune4.8s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 9.6b

localize87.0ms

Local error

Found 4 expressions with local error:

3.0b	(sqrt (/ (cbrt d) l))
4.1b	(/ (* M D) (* 2 d))
6.5b	(* (* (* (sqrt (/ (/ 1 (cbrt h)) (cbrt h))) (sqrt (/ d (cbrt h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
12.8b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite555.0ms

Algorithm

rewrite-expression-head

Rules

305×	`add-exp-log`
163×	`prod-exp`
93×	`div-exp`
55×	`add-cbrt-cube`
40×	`pow-exp`
37×	`sqrt-div`
32×	`add-sqr-sqrt`
30×	`frac-times` `times-frac`
27×	`*-un-lft-identity` `add-cube-cbrt` `cbrt-unprod`
25×	`pow1` `associate-*l/`
24×	`associate-*r/`
22×	`sqrt-prod`
16×	`associate-r`
14×	`rec-exp` `1-exp` `pow-prod-down`
10×	`cbrt-prod`
9×	`cbrt-undiv`
8×	`pow-to-exp` `flip3--` `flip--`
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 → 218

Calls

4 calls:

6.0ms	(sqrt (/ (cbrt d) l))
15.0ms	(/ (* M D) (* 2 d))
478.0ms	(* (* (* (sqrt (/ (/ 1 (cbrt h)) (cbrt h))) (sqrt (/ d (cbrt h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
47.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series2.3s

Counts

4 → 12

Calls

4 calls:

217.0ms	(sqrt (/ (cbrt d) l))
46.0ms	(/ (* M D) (* 2 d))
2.0s	(* (* (* (sqrt (/ (/ 1 (cbrt h)) (cbrt h))) (sqrt (/ d (cbrt h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
92.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify2.2s

Counts

230 → 230

Iterations

Iter	Nodes
done	2011
2	2011
1	1603
0	565

prune6.8s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 7.5b

localize95.0ms

Local error

Found 4 expressions with local error:

3.0b	(sqrt (/ (cbrt d) l))
4.9b	(* (/ M 2) (/ D d))
4.9b	(* (/ M 2) (/ D d))
12.8b	(* (/ h l) (* 1/2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))))

rewrite625.0ms

Algorithm

rewrite-expression-head

Rules

425×	`add-cbrt-cube` `add-exp-log`
244×	`prod-exp` `cbrt-unprod`
115×	`cbrt-undiv` `div-exp`
81×	`add-sqr-sqrt`
73×	`times-frac`
69×	`associate-*r/`
52×	`*-un-lft-identity` `add-cube-cbrt`
51×	`frac-times`
39×	`associate-l`
34×	`pow1`
27×	`associate-r`
25×	`associate-*l/`
22×	`sqrt-prod`
21×	`pow-prod-down`
10×	`cbrt-prod`
8×	`unswap-sqr`
6×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `*-commutative`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 314

Calls

4 calls:

3.0ms	(sqrt (/ (cbrt d) l))
16.0ms	(* (/ M 2) (/ D d))
27.0ms	(* (/ M 2) (/ D d))
570.0ms	(* (/ h l) (* 1/2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))))

series483.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(sqrt (/ (cbrt d) l))
41.0ms	(* (/ M 2) (/ D d))
48.0ms	(* (/ M 2) (/ D d))
208.0ms	(* (/ h l) (* 1/2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))))

simplify1.5s

Counts

326 → 326

Iterations

Iter	Nodes
done	2008
2	2008
1	1702
0	601

prune7.7s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 7.5b

regimes2.9s

Accuracy

1.2% (6.7b remaining)

Error of 15.2b against oracle of 8.4b and baseline of 15.2b

bsearch4.0ms

simplify19.0ms

Iterations

Iter	Nodes
done	68
1	68
0	49

end0.0ms

sample21.8s

Algorithm

intervals

Results

13.7s	37962×	body	80	nan
5.8s	12796×	body	80	valid