Details

sample377.0ms

Algorithm

intervals

Results

181.0ms	1255×	body	80	nan
123.0ms	432×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.1b

localize77.0ms

Local error

Found 4 expressions with local error:

7.7b	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
11.5b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
13.7b	(pow (/ d h) (/ 1 2))
15.2b	(pow (/ d l) (/ 1 2))

rewrite100.0ms

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:

36.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
49.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
5.0ms	(pow (/ d h) (/ 1 2))
5.0ms	(pow (/ d l) (/ 1 2))

series629.0ms

Counts

4 → 12

Calls

4 calls:

338.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
113.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
110.0ms	(pow (/ d h) (/ 1 2))
67.0ms	(pow (/ d l) (/ 1 2))

simplify2.5s

Counts

220 → 220

Iterations

Iter	Nodes
done	5006
2	4073
1	1290
0	438

prune1.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.8b

localize99.0ms

Local error

Found 4 expressions with local error:

5.1b	(/ (* M D) (* 2 d))
7.7b	(* (* (* (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))))
11.5b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
15.2b	(pow (/ d l) (/ 1 2))

rewrite276.0ms

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:

22.0ms	(/ (* M D) (* 2 d))
171.0ms	(* (* (* (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))))
72.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
5.0ms	(pow (/ d l) (/ 1 2))

series1.6s

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (* M D) (* 2 d))
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))))
126.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
92.0ms	(pow (/ d l) (/ 1 2))

simplify2.7s

Counts

199 → 199

Iterations

Iter	Nodes
done	5003
1	1385
0	475

prune1.5s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 9.9b

localize134.0ms

Local error

Found 4 expressions with local error:

4.6b	(sqrt (/ d (cbrt l)))
5.1b	(/ (* M D) (* 2 d))
7.7b	(* (* (* (fabs (/ (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))))
11.5b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite486.0ms

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` `associate-*r/`
27×	`cbrt-unprod`
25×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
22×	`sqrt-prod`
19×	`associate-*l/`
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 (/ d (cbrt l)))
22.0ms	(/ (* M D) (* 2 d))
367.0ms	(* (* (* (fabs (/ (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))))
82.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series2.4s

Counts

4 → 12

Calls

4 calls:

234.0ms	(sqrt (/ d (cbrt l)))
37.0ms	(/ (* M D) (* 2 d))
2.0s	(* (* (* (fabs (/ (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))))
110.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify3.9s

Counts

216 → 216

Iterations

Iter	Nodes
done	5000
1	1667
0	583

prune2.1s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 8.4b

localize137.0ms

Local error

Found 4 expressions with local error:

5.4b	(/ M (/ (* d 2) D))
5.7b	(/ (/ (* (/ M (/ (* d 2) D)) (/ M (/ (* d 2) D))) 2) (* (cbrt l) (cbrt l)))
7.7b	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (/ (/ (* (/ M (/ (* d 2) D)) (/ M (/ (* d 2) D))) 2) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
7.7b	(* (/ (/ (* (/ M (/ (* d 2) D)) (/ M (/ (* d 2) D))) 2) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

rewrite628.0ms

Algorithm

rewrite-expression-head

Rules

900×	`add-exp-log`
755×	`add-cbrt-cube`
492×	`cbrt-undiv` `div-exp`
286×	`prod-exp` `cbrt-unprod`
89×	`times-frac`
65×	`add-sqr-sqrt`
41×	`*-un-lft-identity` `add-cube-cbrt`
36×	`sqrt-div`
30×	`frac-times` `associate-*r/`
25×	`associate-r`
24×	`pow1`
17×	`associate-*l/`
14×	`pow-prod-down`
12×	`cbrt-prod` `associate-l`
11×	`div-inv`
10×	`associate-/l*`
9×	`unswap-sqr`
8×	`associate-/r*` `flip3--` `flip--`
4×	`insert-posit16` `add-log-exp`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`associate-/r/` `associate-/l/`

Counts

4 → 406

Calls

4 calls:

14.0ms	(/ M (/ (* d 2) D))
62.0ms	(/ (/ (* (/ M (/ (* d 2) D)) (/ M (/ (* d 2) D))) 2) (* (cbrt l) (cbrt l)))
326.0ms	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (/ (/ (* (/ M (/ (* d 2) D)) (/ M (/ (* d 2) D))) 2) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
198.0ms	(* (/ (/ (* (/ M (/ (* d 2) D)) (/ M (/ (* d 2) D))) 2) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

series2.7s

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ M (/ (* d 2) D))
330.0ms	(/ (/ (* (/ M (/ (* d 2) D)) (/ M (/ (* d 2) D))) 2) (* (cbrt l) (cbrt l)))
2.2s	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (/ (/ (* (/ M (/ (* d 2) D)) (/ M (/ (* d 2) D))) 2) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
157.0ms	(* (/ (/ (* (/ M (/ (* d 2) D)) (/ M (/ (* d 2) D))) 2) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

simplify3.5s

Counts

418 → 418

Iterations

Iter	Nodes
done	5001
1	2626
0	801

prune3.7s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 7.5b

regimes3.2s

Accuracy

22.4% (4.2b remaining)

Error of 11.5b against oracle of 7.3b and baseline of 12.7b

bsearch9.0ms

simplify36.0ms

Iterations

Iter	Nodes
done	98
1	98
0	73

end0.0ms

sample15.9s

Algorithm

intervals

Results

9.8s	37893×	body	80	nan
4.0s	12792×	body	80	valid