Details

sample793.0ms

Algorithm

intervals

Results

503.0ms	1199×	body	80	nan
179.0ms	405×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.9b

localize109.0ms

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))

rewrite169.0ms

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:

79.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
62.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.0ms	(pow (/ d l) (/ 1 2))
10.0ms	(pow (/ d h) (/ 1 2))

series714.0ms

Counts

4 → 12

Calls

4 calls:

394.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
138.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
80.0ms	(pow (/ d l) (/ 1 2))
101.0ms	(pow (/ d h) (/ 1 2))

simplify1.5s

Counts

234 → 234

Iterations

Iter	Nodes
done	2001
2	2001
1	1335
0	461

prune1.9s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 11.5b

localize128.0ms

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))

rewrite916.0ms

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:

23.0ms	(/ (* M D) (* 2 d))
820.0ms	(* (* (* (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))))
56.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
9.0ms	(pow (/ d l) (/ 1 2))

series634.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (* M D) (* 2 d))
372.0ms	(* (* (* (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))))
115.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
110.0ms	(pow (/ d l) (/ 1 2))

simplify1.4s

Counts

231 → 231

Iterations

Iter	Nodes
done	2007
2	2007
1	1439
0	491

prune2.1s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.3b

localize124.0ms

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))

rewrite953.0ms

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`
32×	`add-sqr-sqrt`
30×	`times-frac`
27×	`*-un-lft-identity` `add-cube-cbrt` `cbrt-unprod`
25×	`pow1`
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`
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 → 242

Calls

4 calls:

6.0ms	(sqrt (/ (cbrt d) l))
17.0ms	(/ (* M D) (* 2 d))
870.0ms	(* (* (* (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))))
50.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series2.1s

Counts

4 → 12

Calls

4 calls:

202.0ms	(sqrt (/ (cbrt d) l))
47.0ms	(/ (* 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))))
127.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify2.1s

Counts

254 → 254

Iterations

Iter	Nodes
done	2001
2	2001
1	1761
0	593

prune3.2s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 9.0b

localize104.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ (/ (* M D) 2) d)
4.9b	(/ (/ (* M D) 2) d)
6.7b	(* h (* (/ (/ (* M D) 2) d) (/ (/ (* 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 (/ (* h (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d))) (* 2 l))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

138×	`add-cbrt-cube` `add-exp-log`
84×	`sqrt-div`
82×	`frac-times`
72×	`times-frac`
67×	`associate-*l/`
58×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
56×	`prod-exp` `cbrt-unprod`
54×	`add-cube-cbrt`
51×	`associate-*r/`
50×	`cbrt-undiv` `div-exp`
30×	`prod-diff`
27×	`pow1`
17×	`distribute-rgt-in` `distribute-lft-in`
16×	`flip3--` `pow-prod-down` `div-inv` `flip--`
14×	`associate-/l*`
7×	`associate-r`
6×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `sub-neg` `frac-2neg` `*-commutative` `difference-of-squares` `associate-/l/`
1×	`distribute-lft-out--` `unswap-sqr`

Counts

4 → 271

Calls

4 calls:

11.0ms	(/ (/ (* M D) 2) d)
11.0ms	(/ (/ (* M D) 2) d)
90.0ms	(* h (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)))
1.1s	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (- 1 (/ (* h (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d))) (* 2 l))))

series1.9s

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (/ (* M D) 2) d)
47.0ms	(/ (/ (* M D) 2) d)
129.0ms	(* h (* (/ (/ (* M D) 2) d) (/ (/ (* 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 (/ (* h (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d))) (* 2 l))))

simplify2.5s

Counts

283 → 283

Iterations

Iter	Nodes
done	2006
2	2006
1	1734
0	547

prune3.4s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 8.3b

regimes2.9s

Accuracy

0% (5.4b remaining)

Error of 13.7b against oracle of 8.3b and baseline of 13.7b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	38
1	38
0	28

end0.0ms

sample25.8s

Algorithm

intervals

Results

17.2s	38360×	body	80	nan
6.0s	12737×	body	80	valid