Details

sample468.0ms

Algorithm

intervals

Results

270.0ms	1293×	body	80	nan
114.0ms	418×	body	80	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1261
2	198
1	58
0	22

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.1b

localize113.0ms

Local error

Found 4 expressions with local error:

6.9b	(/ (* M D) (* 2 d))
11.0b	(pow (/ d l) (/ 1 2))
12.2b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.6b	(pow (/ d h) (/ 1 2))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

293×	`add-exp-log`
150×	`prod-exp`
95×	`div-exp`
46×	`times-frac`
44×	`pow-exp`
39×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
37×	`add-cbrt-cube`
26×	`pow-unpow` `unpow-prod-down`
14×	`rec-exp` `1-exp` `cbrt-unprod`
13×	`associate-r`
10×	`pow-to-exp`
9×	`cbrt-undiv`
8×	`pow1`
6×	`div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`associate-*l/`
2×	`pow-pow` `sqr-pow`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `associate-l` `pow-prod-down` `associate-r/` `-commutative` `associate-/l`

Counts

4 → 191

Calls

4 calls:

13.0ms	(/ (* M D) (* 2 d))
15.0ms	(pow (/ d l) (/ 1 2))
84.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
15.0ms	(pow (/ d h) (/ 1 2))

series314.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (* M D) (* 2 d))
93.0ms	(pow (/ d l) (/ 1 2))
109.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
72.0ms	(pow (/ d h) (/ 1 2))

simplify2.4s

Counts

203 → 203

Iterations

Iter	Nodes
done	5003
2	3984
1	1191
0	408

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.4b

localize107.0ms

Local error

Found 4 expressions with local error:

4.6b	(* (* (* (fabs (/ (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))))
6.9b	(/ (* M D) (* 2 d))
11.0b	(pow (/ d l) (/ 1 2))
12.2b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite365.0ms

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`
7×	`associate-*l/`
6×	`associate-*r/`
4×	`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:

225.0ms	(* (* (* (fabs (/ (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))))
23.0ms	(/ (* M D) (* 2 d))
9.0ms	(pow (/ d l) (/ 1 2))
99.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.4s	(* (* (* (fabs (/ (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))))
43.0ms	(/ (* M D) (* 2 d))
84.0ms	(pow (/ d l) (/ 1 2))
142.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify2.5s

Counts

199 → 199

Iterations

Iter	Nodes
done	5001
1	1398
0	475

prune1.4s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 9.0b

localize94.0ms

Local error

Found 4 expressions with local error:

4.6b	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* 1/2 (* (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))) (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
6.9b	(/ (/ M (/ 2 D)) d)
6.9b	(/ (/ M (/ 2 D)) d)
11.0b	(pow (/ d l) (/ 1 2))

rewrite456.0ms

Algorithm

rewrite-expression-head

Rules

810×	`times-frac`
389×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
88×	`associate-/l*`
55×	`add-exp-log`
36×	`div-inv`
31×	`add-cbrt-cube`
21×	`prod-exp`
15×	`div-exp`
13×	`pow-unpow` `unpow-prod-down`
12×	`cbrt-undiv`
8×	`associate-/r/`
7×	`pow1`
6×	`associate-/r*` `pow-exp` `cbrt-unprod`
5×	`associate-*r/`
4×	`associate-*l/` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `sqrt-div` `associate-r`
2×	`distribute-rgt-in` `frac-times` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3--` `flip--` `associate-/l/`
1×	`pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`

Counts

4 → 468

Calls

4 calls:

363.0ms	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* 1/2 (* (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))) (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
22.0ms	(/ (/ M (/ 2 D)) d)
34.0ms	(/ (/ M (/ 2 D)) d)
8.0ms	(pow (/ d l) (/ 1 2))

series1.7s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* 1/2 (* (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))) (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
56.0ms	(/ (/ M (/ 2 D)) d)
50.0ms	(/ (/ M (/ 2 D)) d)
119.0ms	(pow (/ d l) (/ 1 2))

simplify3.0s

Counts

480 → 480

Iterations

Iter	Nodes
done	5001
1	2039
0	707

prune6.4s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 5.9b

localize151.0ms

Local error

Found 4 expressions with local error:

2.2b	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
4.6b	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* 1/2 (* (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))) (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
6.9b	(/ (/ M (/ 2 D)) d)
6.9b	(/ (/ M (/ 2 D)) d)

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

792×	`times-frac`
375×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
88×	`associate-/l*`
87×	`sqrt-div`
82×	`frac-times`
66×	`associate-*r/`
49×	`associate-*l/`
40×	`add-cbrt-cube` `add-exp-log`
34×	`div-inv`
30×	`pow1`
16×	`flip3--` `flip--`
14×	`pow-prod-down`
13×	`prod-exp` `cbrt-unprod`
12×	`cbrt-undiv` `div-exp`
8×	`associate-/r/`
6×	`associate-/r*` `sqrt-pow1`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `associate-/l/`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `associate-l` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-prod`

Counts

4 → 493

Calls

4 calls:

27.0ms	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
1.5s	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* 1/2 (* (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))) (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
25.0ms	(/ (/ M (/ 2 D)) d)
28.0ms	(/ (/ M (/ 2 D)) d)

series1.7s

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
1.5s	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* 1/2 (* (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))) (* (/ (/ M (/ 2 D)) d) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
37.0ms	(/ (/ M (/ 2 D)) d)
41.0ms	(/ (/ M (/ 2 D)) d)

simplify3.6s

Counts

505 → 505

Iterations

Iter	Nodes
done	5000
1	2173
0	742

prune7.0s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 5.4b

regimes2.4s

Accuracy

0% (2.5b remaining)

Error of 9.7b against oracle of 7.2b and baseline of 9.7b

bsearch0.0ms

simplify16.0ms

Iterations

Iter	Nodes
done	40
1	40
0	30

end0.0ms

sample15.1s

Algorithm

intervals

Results

9.8s	38749×	body	80	nan
3.3s	12797×	body	80	valid