Details

sample669.0ms

Algorithm

intervals

Results

403.0ms	1088×	body	80	nan
185.0ms	411×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.6b

localize108.0ms

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))

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:

71.0ms	(* (* (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 l) (/ 1 2))
75.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.0ms	(pow (/ d h) (/ 1 2))

series707.0ms

Counts

4 → 12

Calls

4 calls:

430.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
80.0ms	(pow (/ d l) (/ 1 2))
112.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
85.0ms	(pow (/ d h) (/ 1 2))

simplify1.2s

Counts

234 → 234

Iterations

Iter	Nodes
done	2004
2	2004
1	1325
0	461

prune4.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.8b

localize128.0ms

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))

rewrite842.0ms

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:

11.0ms	(/ (* M D) (* 2 d))
763.0ms	(* (* (* (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))))
5.0ms	(pow (/ d l) (/ 1 2))
59.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series619.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (* M D) (* 2 d))
389.0ms	(* (* (* (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))))
92.0ms	(pow (/ d l) (/ 1 2))
99.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.5s

Counts

231 → 231

Iterations

Iter	Nodes
done	2009
2	2009
1	1474
0	491

prune5.4s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.3b

localize90.0ms

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))

rewrite1.2s

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)))
17.0ms	(/ (* M D) (* 2 d))
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 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
63.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series2.0s

Counts

4 → 12

Calls

4 calls:

223.0ms	(sqrt (/ d (cbrt l)))
34.0ms	(/ (* M D) (* 2 d))
1.6s	(* (* (* (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))))
151.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify2.6s

Counts

302 → 302

Iterations

Iter	Nodes
done	2000
1	2000
0	711

prune8.5s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 8.3b

localize134.0ms

Local error

Found 4 expressions with local error:

5.0b	(/ (* M D) (* d 2))
5.0b	(/ (* M D) (* d 2))
6.0b	(/ (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) h) 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 (/ (/ (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) h) l) 2)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

231×	`add-cbrt-cube` `add-exp-log`
216×	`sqrt-div`
210×	`frac-times`
187×	`times-frac`
150×	`prod-diff`
149×	`add-sqr-sqrt`
145×	`*-un-lft-identity`
141×	`add-cube-cbrt`
140×	`associate-*l/`
112×	`prod-exp` `cbrt-unprod`
77×	`distribute-rgt-in` `distribute-lft-in`
75×	`cbrt-undiv` `div-exp`
72×	`associate-*r/`
32×	`flip3--` `flip--`
27×	`div-inv`
22×	`pow1`
13×	`pow-prod-down`
8×	`associate-r`
5×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`
2×	`sub-neg`
1×	`associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 409

Calls

4 calls:

11.0ms	(/ (* M D) (* d 2))
11.0ms	(/ (* M D) (* d 2))
184.0ms	(/ (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) h) l)
1.2s	(* (* (* (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 (/ (/ (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) h) l) 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (* M D) (* d 2))
43.0ms	(/ (* M D) (* d 2))
108.0ms	(/ (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) h) l)
1.5s	(* (* (* (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 (/ (/ (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) h) l) 2)))

simplify2.8s

Counts

421 → 421

Iterations

Iter	Nodes
done	2001
1	2001
0	1035

prune12.1s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 7.3b

regimes3.0s

Accuracy

18.2% (5.7b remaining)

Error of 13.5b against oracle of 7.7b and baseline of 14.8b

bsearch5.0ms

simplify35.0ms

Iterations

Iter	Nodes
done	84
1	84
0	64

end0.0ms

sample23.7s

Algorithm

intervals

Results

14.7s	37686×	body	80	nan
6.0s	12698×	body	80	valid