Details

sample551.0ms

Algorithm

intervals

Results

295.0ms	1362×	body	80	nan
149.0ms	430×	body	80	valid

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3968
3	655
2	170
1	54
0	22

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize67.0ms

Local error

Found 4 expressions with local error:

9.2b	(* (* (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))))
9.5b	(pow (/ d h) (/ 1.0 2.0))
10.9b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.0b	(pow (/ d l) (/ 1.0 2.0))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
107×	`prod-exp`
55×	`div-exp`
45×	`times-frac`
42×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
40×	`pow-exp`
30×	`add-cbrt-cube`
26×	`pow-unpow` `unpow-prod-down`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
6×	`prod-diff`
5×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 190

Calls

4 calls:

83.0ms	(* (* (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))))
7.0ms	(pow (/ d h) (/ 1.0 2.0))
77.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (* (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))))
81.0ms	(pow (/ d h) (/ 1.0 2.0))
1.0s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
88.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify3.4s

Counts

202 → 202

Iterations

Iter	Nodes
done	5000
2	4603
1	1382
0	460

prune1.6s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.8b

localize106.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ (* M D) (* 2.0 d))
9.2b	(* (* (pow (/ d 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))))
9.5b	(pow (/ d h) (/ 1.0 2.0))
10.9b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite422.0ms

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×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
20×	`cbrt-unprod`
16×	`associate-r`
13×	`pow-unpow` `unpow-prod-down`
9×	`pow1` `cbrt-undiv`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`sub-neg` `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 → 306

Calls

4 calls:

19.0ms	(/ (* M D) (* 2.0 d))
286.0ms	(* (* (pow (/ d 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))))
7.0ms	(pow (/ d h) (/ 1.0 2.0))
66.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.5s

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* M D) (* 2.0 d))
1.4s	(* (* (pow (/ d 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))))
78.0ms	(pow (/ d h) (/ 1.0 2.0))
1.0s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.3s

Counts

318 → 318

Iterations

Iter	Nodes
done	5001
1	1753
0	631

prune1.6s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 12.0b

localize173.0ms

Local error

Found 4 expressions with local error:

2.9b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.8b	(/ (* M D) (* 2.0 d))
9.2b	(* (* (* (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))))
10.9b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.2s

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`
34×	`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`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`sub-neg` `associate-l` `*-commutative`
1×	`frac-times` `clear-num` `associate-/r` `pow-pow` `frac-2neg` `flip3--` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 1539

Calls

4 calls:

9.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
15.0ms	(/ (* M D) (* 2.0 d))
549.0ms	(* (* (* (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))))
73.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.4s

Counts

4 → 12

Calls

4 calls:

242.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
38.0ms	(/ (* 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 (/ 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))))
892.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify15.0s

Counts

1551 → 1551

Iterations

Iter	Nodes
done	5000
1	4763
0	1821

prune2.5s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 10.8b

localize228.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ (* M D) (* 2.0 d))
6.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.9b	(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
9.2b	(* (* (* (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) (/ 1 l))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

8382×	`add-exp-log`
6544×	`prod-exp`
3454×	`pow-exp`
1961×	`div-exp`
972×	`pow-to-exp`
608×	`rec-exp` `1-exp`
75×	`add-cbrt-cube`
40×	`cbrt-unprod`
19×	`associate-r`
16×	`pow1`
15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`cbrt-undiv`
10×	`times-frac`
7×	`pow-prod-down` `associate-*l/`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-r/` `-commutative`
2×	`sub-neg` `div-inv`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `flip3--` `un-div-inv` `flip--` `associate-/l`

Counts

4 → 1562

Calls

4 calls:

20.0ms	(/ (* M D) (* 2.0 d))
57.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
200.0ms	(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
651.0ms	(* (* (* (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) (/ 1 l))))

series3.6s

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (* M D) (* 2.0 d))
1.2s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
1.1s	(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
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) (/ 1 l))))

simplify5.4s

Counts

1574 → 1574

Iterations

Iter	Nodes
done	5001
1	3685
0	1775

prune2.2s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 10.4b

regimes3.4s

Accuracy

12.8% (7.5b remaining)

Error of 16.4b against oracle of 8.9b and baseline of 17.5b

bsearch652.0ms

Steps

Iters	Range		Point
4	31569366244039.77	52646127474730.805	31955175104594.195
7	-3032771.8047137302	-130570.50659473319	-132349.35391058022

simplify31.0ms

Iterations

Iter	Nodes
done	65
1	65
0	48

end0.0ms

sample17.1s

Algorithm

intervals

Results

9.5s	38075×	body	80	nan
5.0s	12747×	body	80	valid