Details

sample734.0ms

Algorithm

intervals

Results

498.0ms	1258×	body	80	nan
149.0ms	404×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.9b

localize63.0ms

Local error

Found 4 expressions with local error:

6.9b	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
9.9b	(pow (/ d l) (/ 1 2))
10.5b	(pow (/ d h) (/ 1 2))
12.4b	(* (* (/ 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:

80.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
9.0ms	(pow (/ d l) (/ 1 2))
5.0ms	(pow (/ d h) (/ 1 2))
40.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series671.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
86.0ms	(pow (/ d l) (/ 1 2))
112.0ms	(pow (/ d h) (/ 1 2))
134.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify2.9s

Counts

220 → 220

Iterations

Iter	Nodes
done	5030
2	3979
1	1295
0	438

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.2b

localize74.0ms

Local error

Found 4 expressions with local error:

6.1b	(/ (* M D) (* 2 d))
6.9b	(* (* (* (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))))
9.9b	(pow (/ d l) (/ 1 2))
12.4b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite270.0ms

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:

23.0ms	(/ (* M D) (* 2 d))
146.0ms	(* (* (* (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))))
10.0ms	(pow (/ d l) (/ 1 2))
83.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series1.9s

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (* M D) (* 2 d))
1.6s	(* (* (* (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))))
94.0ms	(pow (/ d l) (/ 1 2))
112.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify2.3s

Counts

199 → 199

Iterations

Iter	Nodes
done	5000
1	1404
0	475

prune1.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 10.9b

localize66.0ms

Local error

Found 4 expressions with local error:

5.2b	(* (/ M (/ 2 (/ D d))) h)
6.2b	(/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))
6.9b	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))))
9.9b	(pow (/ d l) (/ 1 2))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

355×	`times-frac`
336×	`add-exp-log`
312×	`add-cbrt-cube`
187×	`add-sqr-sqrt`
173×	`*-un-lft-identity`
170×	`add-cube-cbrt`
159×	`div-exp`
156×	`cbrt-undiv`
138×	`associate-l`
118×	`prod-exp`
103×	`cbrt-unprod`
16×	`div-inv`
13×	`pow-unpow` `unpow-prod-down`
9×	`pow1` `associate-r`
8×	`associate-*l/`
6×	`pow-exp` `associate-*r/`
4×	`associate-/r/` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`frac-times` `pow-to-exp` `sqrt-div` `associate-/l/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `pow-prod-down` `*-commutative` `flip--` `difference-of-squares`
1×	`clear-num` `associate-/r` `pow-pow` `frac-2neg` `associate-/l` `distribute-lft-out--` `sqr-pow`

Counts

4 → 341

Calls

4 calls:

18.0ms	(* (/ M (/ 2 (/ D d))) h)
62.0ms	(/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))
174.0ms	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))))
5.0ms	(pow (/ d l) (/ 1 2))

series1.6s

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (/ M (/ 2 (/ D d))) h)
127.0ms	(/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))
1.4s	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))))
75.0ms	(pow (/ d l) (/ 1 2))

simplify3.6s

Counts

353 → 353

Iterations

Iter	Nodes
done	5002
1	2316
0	797

prune3.5s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 8.3b

localize89.0ms

Local error

Found 4 expressions with local error:

4.2b	(/ M (/ 2 (/ D d)))
5.2b	(* (/ M (/ 2 (/ D d))) h)
6.2b	(/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))
6.9b	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))))

rewrite630.0ms

Algorithm

rewrite-expression-head

Rules

733×	`times-frac`
358×	`add-sqr-sqrt`
344×	`*-un-lft-identity`
341×	`add-cube-cbrt`
330×	`add-cbrt-cube` `add-exp-log`
162×	`cbrt-undiv` `div-exp`
138×	`associate-l`
110×	`prod-exp` `cbrt-unprod`
45×	`associate-/r*`
36×	`sqrt-div`
31×	`div-inv`
30×	`frac-times` `associate-*r/`
24×	`pow1`
20×	`associate-*l/`
14×	`pow-prod-down`
9×	`associate-r` `associate-/r/`
8×	`flip3--` `flip--`
4×	`insert-posit16` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`associate-/l/`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `*-commutative` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 519

Calls

4 calls:

7.0ms	(/ M (/ 2 (/ D d)))
21.0ms	(* (/ M (/ 2 (/ D d))) h)
65.0ms	(/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))
514.0ms	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))))

series2.4s

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ M (/ 2 (/ D d)))
71.0ms	(* (/ M (/ 2 (/ D d))) h)
119.0ms	(/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))
2.1s	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h)) (* 2 l))))

simplify4.5s

Counts

531 → 531

Iterations

Iter	Nodes
done	5010
1	3260
0	1013

prune6.4s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 7.3b

regimes3.4s

Accuracy

5.3% (5.2b remaining)

Error of 12.5b against oracle of 7.3b and baseline of 12.8b

bsearch1.1s

Steps

Iters	Range		Point
6	5.139658762215447e+191	3.770144916277579e+192	6.989147569313924e+191
9	2.2464363086714817e-87	3.807220384445716e-78	9.167067702253803e-79

simplify64.0ms

Iterations

Iter	Nodes
done	90
1	90
0	68

end0.0ms

sample23.5s

Algorithm

intervals

Results

15.2s	38867×	body	80	nan
5.8s	12785×	body	80	valid