Details

sample664.0ms

Algorithm

intervals

Results

411.0ms	1299×	body	80	nan
138.0ms	423×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.4b

localize74.0ms

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))

rewrite143.0ms

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:

74.0ms	(* (* (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))
55.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series756.0ms

Counts

4 → 12

Calls

4 calls:

433.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
110.0ms	(pow (/ d h) (/ 1 2))
79.0ms	(pow (/ d l) (/ 1 2))
133.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.4s

Counts

220 → 220

Iterations

Iter	Nodes
done	2002
2	2002
1	1295
0	438

prune4.2s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 11.1b

localize64.0ms

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))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 187

Calls

4 calls:

11.0ms	(/ (* M D) (* 2 d))
235.0ms	(* (* (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))))
9.0ms	(pow (/ d h) (/ 1 2))
41.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series1.8s

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (* 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))))
115.0ms	(pow (/ d h) (/ 1 2))
108.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify2.0s

Counts

199 → 199

Iterations

Iter	Nodes
done	2019
2	2019
1	1348
0	453

prune4.4s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 9.3b

localize91.0ms

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))

rewrite868.0ms

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`
30×	`add-sqr-sqrt` `frac-times` `times-frac`
27×	`cbrt-unprod`
25×	`pow1` `-un-lft-identity` `associate-l/` `add-cube-cbrt`
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--`
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 → 204

Calls

4 calls:

5.0ms	(sqrt (/ (cbrt d) l))
22.0ms	(/ (* M D) (* 2 d))
766.0ms	(* (* (* (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))))
67.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series2.5s

Counts

4 → 12

Calls

4 calls:

186.0ms	(sqrt (/ (cbrt d) l))
48.0ms	(/ (* M D) (* 2 d))
2.1s	(* (* (* (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))))
123.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify2.3s

Counts

216 → 216

Iterations

Iter	Nodes
done	2008
2	2008
1	1562
0	545

prune5.7s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 7.7b

localize155.0ms

Local error

Found 4 expressions with local error:

4.9b	(* (/ M 2) (/ D d))
4.9b	(* (/ M 2) (/ D 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 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
7.0b	(* (* (* 1/2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))

rewrite3.5s

Algorithm

rewrite-expression-head

Rules

3478×	`add-exp-log`
2215×	`prod-exp`
1376×	`add-cbrt-cube`
974×	`div-exp`
947×	`cbrt-unprod`
438×	`cbrt-undiv`
161×	`frac-times`
132×	`associate-*r/`
130×	`associate-*l/`
108×	`rec-exp` `1-exp`
70×	`add-sqr-sqrt`
62×	`times-frac`
59×	`pow1`
51×	`associate-r`
46×	`*-un-lft-identity` `add-cube-cbrt`
41×	`pow-prod-down`
36×	`sqrt-div`
28×	`associate-l`
9×	`cbrt-prod`
8×	`flip3--` `flip--` `unswap-sqr`
5×	`div-inv`
4×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `un-div-inv`

Counts

4 → 805

Calls

4 calls:

18.0ms	(* (/ M 2) (/ D d))
26.0ms	(* (/ M 2) (/ D d))
791.0ms	(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (* 1/2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
2.6s	(* (* (* 1/2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))

series2.4s

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (/ M 2) (/ D d))
39.0ms	(* (/ M 2) (/ D d))
2.2s	(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (* 1/2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
178.0ms	(* (* (* 1/2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))

simplify12.2s

Counts

817 → 817

Iterations

Iter	Nodes
done	2000
1	2000
0	1515

prune23.7s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 7.0b

regimes2.9s

Accuracy

4.4% (8.4b remaining)

Error of 16.1b against oracle of 7.7b and baseline of 16.4b

bsearch3.0ms

simplify42.0ms

Iterations

Iter	Nodes
done	106
1	106
0	79

end0.0ms

sample23.0s

Algorithm

intervals

Results

13.9s	37962×	body	80	nan
6.3s	12796×	body	80	valid