Details

sample638.0ms

Algorithm

intervals

Results

423.0ms	1199×	body	80	nan
142.0ms	405×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
4	2006
3	1261
2	198
1	58
0	22

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.2b

localize71.0ms

Local error

Found 4 expressions with local error:

6.8b	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
10.9b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.0b	(pow (/ d l) (/ 1 2))
13.0b	(pow (/ d h) (/ 1 2))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

331×	`add-exp-log`
179×	`prod-exp`
99×	`div-exp`
60×	`pow-exp`
45×	`times-frac`
40×	`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`
5×	`cbrt-undiv` `div-inv`
4×	`insert-posit16` `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 → 208

Calls

4 calls:

39.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
45.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
5.0ms	(pow (/ d l) (/ 1 2))
7.0ms	(pow (/ d h) (/ 1 2))

series617.0ms

Counts

4 → 12

Calls

4 calls:

358.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
107.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
83.0ms	(pow (/ d l) (/ 1 2))
69.0ms	(pow (/ d h) (/ 1 2))

simplify1.3s

Counts

220 → 220

Iterations

Iter	Nodes
done	2002
2	2002
1	1290
0	438

prune1.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 10.7b

localize75.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ (* M D) (* 2 d))
6.8b	(* (* (* (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))))
10.9b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.0b	(pow (/ d l) (/ 1 2))

rewrite984.0ms

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×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `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--`
4×	`insert-posit16` `div-inv` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `pow-prod-down` `*-commutative`
1×	`clear-num` `associate-/r` `pow-pow` `frac-2neg` `associate-/l` `sqr-pow`

Counts

4 → 205

Calls

4 calls:

17.0ms	(/ (* M D) (* 2 d))
894.0ms	(* (* (* (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))))
57.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
6.0ms	(pow (/ d l) (/ 1 2))

series744.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (* M D) (* 2 d))
451.0ms	(* (* (* (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))))
128.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
115.0ms	(pow (/ d l) (/ 1 2))

simplify1.8s

Counts

217 → 217

Iterations

Iter	Nodes
done	2002
2	2002
1	1381
0	468

prune2.0s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 9.3b

localize93.0ms

Local error

Found 4 expressions with local error:

3.1b	(sqrt (/ (cbrt d) l))
4.9b	(/ (* M D) (* 2 d))
6.8b	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
10.9b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 228

Calls

4 calls:

5.0ms	(sqrt (/ (cbrt d) l))
22.0ms	(/ (* M D) (* 2 d))
942.0ms	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
79.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series2.1s

Counts

4 → 12

Calls

4 calls:

222.0ms	(sqrt (/ (cbrt d) l))
51.0ms	(/ (* M D) (* 2 d))
1.7s	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
154.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify2.3s

Counts

240 → 240

Iterations

Iter	Nodes
done	2025
2	2025
1	1678
0	569

prune2.9s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 8.2b

localize138.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (/ M d) (/ D 2))
4.7b	(* (/ M d) (/ D 2))
6.7b	(* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)
6.8b	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (- 1 (/ (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) l) 2)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

203×	`add-cbrt-cube` `add-exp-log`
112×	`prod-exp` `cbrt-unprod`
100×	`frac-times`
94×	`associate-*l/`
84×	`sqrt-div`
67×	`add-sqr-sqrt`
60×	`associate-*r/`
48×	`cbrt-undiv` `div-exp`
46×	`times-frac`
44×	`pow1`
38×	`*-un-lft-identity`
37×	`associate-r`
34×	`add-cube-cbrt`
28×	`associate-l` `pow-prod-down`
16×	`flip3--` `flip--`
9×	`unswap-sqr`
4×	`*-commutative` `insert-posit16` `div-inv` `add-log-exp` `difference-of-squares`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`distribute-lft-out--`

Counts

4 → 272

Calls

4 calls:

26.0ms	(* (/ M d) (/ D 2))
25.0ms	(* (/ M d) (/ D 2))
245.0ms	(* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)
887.0ms	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (- 1 (/ (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) l) 2)))

series2.0s

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (/ M d) (/ D 2))
31.0ms	(* (/ M d) (/ D 2))
103.0ms	(* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)
1.8s	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (- 1 (/ (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) l) 2)))

simplify2.4s

Counts

284 → 284

Iterations

Iter	Nodes
done	2012
2	2012
1	1732
0	524

prune3.2s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 7.4b

regimes3.8s

Accuracy

26.6% (4.9b remaining)

Error of 12.5b against oracle of 7.6b and baseline of 14.3b

bsearch11.0ms

simplify28.0ms

Iterations

Iter	Nodes
done	94
1	94
0	70

end0.0ms

sample26.2s

Algorithm

intervals

Results

17.6s	38360×	body	80	nan
6.0s	12737×	body	80	valid