Details

sample527.0ms

Algorithm

intervals

Results

290.0ms	1301×	body	80	nan
95.0ms	427×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	710
2	174
1	54
0	22

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize67.0ms

Local error

Found 4 expressions with local error:

5.6b	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
9.4b	(pow (/ d h) (/ 1.0 2.0))
14.8b	(pow (/ d l) (/ 1.0 2.0))
14.9b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
107×	`prod-exp`
55×	`div-exp`
45×	`times-frac`
40×	`add-sqr-sqrt` `*-un-lft-identity` `pow-exp` `add-cube-cbrt`
30×	`add-cbrt-cube`
26×	`pow-unpow` `unpow-prod-down`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`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 → 176

Calls

4 calls:

73.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
9.0ms	(pow (/ d h) (/ 1.0 2.0))
12.0ms	(pow (/ d l) (/ 1.0 2.0))
65.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.3s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
82.0ms	(pow (/ d h) (/ 1.0 2.0))
81.0ms	(pow (/ d l) (/ 1.0 2.0))
1.0s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.3s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
1	1404
0	437

prune1.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.1b

localize133.0ms

Local error

Found 4 expressions with local error:

5.1b	(/ (* M D) (* 2.0 d))
5.6b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.8b	(pow (/ d l) (/ 1.0 2.0))
14.9b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite482.0ms

Algorithm

rewrite-expression-head

Rules

818×	`add-exp-log`
567×	`prod-exp`
280×	`pow-exp`
187×	`div-exp`
94×	`pow-to-exp`
46×	`add-cbrt-cube`
32×	`rec-exp` `1-exp`
28×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
20×	`cbrt-unprod`
16×	`associate-r`
13×	`pow-unpow` `unpow-prod-down`
9×	`pow1` `cbrt-undiv`
4×	`div-inv` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `pow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `associate-/r` `pow-pow` `frac-2neg` `flip3--` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 292

Calls

4 calls:

15.0ms	(/ (* M D) (* 2.0 d))
361.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.0ms	(pow (/ d l) (/ 1.0 2.0))
62.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.4s

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (* M D) (* 2.0 d))
1.2s	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
88.0ms	(pow (/ d l) (/ 1.0 2.0))
1.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.3s

Counts

304 → 304

Iterations

Iter	Nodes
done	5001
1	1953
0	606

prune1.6s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 9.5b

localize239.0ms

Local error

Found 4 expressions with local error:

3.4b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
5.1b	(/ (* M D) (* 2.0 d))
5.6b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.9b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite931.0ms

Algorithm

rewrite-expression-head

Rules

8121×	`add-exp-log`
6369×	`prod-exp`
3426×	`pow-exp`
1900×	`div-exp`
967×	`pow-to-exp`
592×	`rec-exp` `1-exp`
55×	`add-cbrt-cube`
37×	`times-frac`
32×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`cbrt-unprod`
22×	`unpow-prod-down`
16×	`associate-r`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-prod` `cbrt-undiv`
4×	`pow-prod-down` `div-inv` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`
1×	`frac-times` `clear-num` `associate-/r` `pow-pow` `frac-2neg` `flip3--` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 1525

Calls

4 calls:

14.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
10.0ms	(/ (* M D) (* 2.0 d))
484.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
80.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.9s

Counts

4 → 12

Calls

4 calls:

617.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
32.0ms	(/ (* M D) (* 2.0 d))
1.3s	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
1.0s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify4.0s

Counts

1537 → 1537

Iterations

Iter	Nodes
done	5001
0	1798

prune2.8s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 7.3b

localize235.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h)))
5.1b	(* (/ M 2.0) (/ D d))
5.6b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
8.3b	(* (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

8503×	`add-exp-log`
6624×	`prod-exp`
3464×	`pow-exp`
1975×	`div-exp`
974×	`pow-to-exp`
592×	`rec-exp` `1-exp`
95×	`add-cbrt-cube`
70×	`cbrt-unprod`
44×	`add-sqr-sqrt`
40×	`times-frac`
39×	`associate-r`
32×	`*-un-lft-identity` `add-cube-cbrt`
25×	`pow1`
17×	`cbrt-undiv`
16×	`associate-l`
13×	`pow-prod-down`
9×	`cbrt-prod`
8×	`associate-*l/`
4×	`associate-r/` `-commutative` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`distribute-rgt-in` `frac-times` `sub-neg` `distribute-lft-in`
1×	`flip3--` `flip--`

Counts

4 → 1607

Calls

4 calls:

91.0ms	(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h)))
24.0ms	(* (/ M 2.0) (/ D d))
637.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
165.0ms	(* (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

series3.3s

Counts

4 → 12

Calls

4 calls:

742.0ms	(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h)))
44.0ms	(* (/ M 2.0) (/ D d))
1.4s	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
1.1s	(* (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

simplify3.8s

Counts

1619 → 1619

Iterations

Iter	Nodes
done	5001
0	1839

prune2.6s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 6.8b

regimes3.5s

Accuracy

8.8% (7.1b remaining)

Error of 15.2b against oracle of 8.1b and baseline of 15.9b

bsearch11.0ms

simplify31.0ms

Iterations

Iter	Nodes
done	96
1	96
0	73

end0.0ms

sample18.1s

Algorithm

intervals

Results

9.7s	38741×	body	80	nan
4.4s	12885×	body	80	valid