Details

sample404.0ms

Algorithm

intervals

Results

175.0ms	1101×	body	80	nan
110.0ms	402×	body	80	valid

simplify8.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3841
3	645
2	170
1	54
0	22

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize130.0ms

Local error

Found 4 expressions with local error:

7.5b	(* (* (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))))
12.2b	(pow (/ d h) (/ 1.0 2.0))
14.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
15.5b	(pow (/ d l) (/ 1.0 2.0))

rewrite270.0ms

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×	`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 → 180

Calls

4 calls:

117.0ms	(* (* (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))))
19.0ms	(pow (/ d h) (/ 1.0 2.0))
100.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.0ms	(pow (/ d l) (/ 1.0 2.0))

series4.6s

Counts

4 → 12

Calls

4 calls:

2.2s	(* (* (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))))
146.0ms	(pow (/ d h) (/ 1.0 2.0))
2.0s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
163.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify7.2s

Counts

192 → 192

Iterations

Iter	Nodes
done	5001
2	4320
1	1311
0	441

prune3.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.7b

localize242.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* M D) (* 2.0 d))
7.5b	(* (* (* (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))))
14.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
15.5b	(pow (/ d l) (/ 1.0 2.0))

rewrite775.0ms

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×	`insert-posit16` `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 → 296

Calls

4 calls:

16.0ms	(/ (* M D) (* 2.0 d))
587.0ms	(* (* (* (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))))
99.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.0ms	(pow (/ d l) (/ 1.0 2.0))

series5.1s

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (* M D) (* 2.0 d))
2.8s	(* (* (* (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))))
2.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
148.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify5.1s

Counts

308 → 308

Iterations

Iter	Nodes
done	5002
1	1748
0	610

prune3.3s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.7b

localize357.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* M D) (* 2.0 d))
4.0b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
7.5b	(* (* (* (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))))
14.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite2.0s

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` `insert-posit16` `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 → 1529

Calls

4 calls:

16.0ms	(/ (* M D) (* 2.0 d))
14.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
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))))
110.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series5.2s

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (* M D) (* 2.0 d))
353.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
2.8s	(* (* (* (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))))
2.0s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify54.9s

Counts

1541 → 1541

Iterations

Iter	Nodes
done	5000
0	1802

prune5.0s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 8.2b

localize468.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* M D) (* 2.0 d))
4.0b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
7.5b	(* (* (* (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
7.8b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

8421×	`add-exp-log`
6540×	`prod-exp`
3456×	`pow-exp`
1990×	`div-exp`
973×	`pow-to-exp`
592×	`rec-exp` `1-exp`
79×	`add-cbrt-cube`
54×	`cbrt-unprod`
29×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
22×	`unpow-prod-down`
21×	`cbrt-undiv`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-prod`
8×	`associate-r`
4×	`pow-prod-down` `insert-posit16` `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 → 1575

Calls

4 calls:

16.0ms	(/ (* M D) (* 2.0 d))
15.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
1.1s	(* (* (* (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
129.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series5.0s

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (* M D) (* 2.0 d))
381.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
2.6s	(* (* (* (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
2.0s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify32.3s

Counts

1587 → 1587

Iterations

Iter	Nodes
done	5001
1	4903
0	1865

prune3.3s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 6.6b

regimes6.7s

Accuracy

-1.3% (6.7b remaining)

Error of 15.0b against oracle of 8.4b and baseline of 14.9b

bsearch858.0ms

Steps

Iters	Range		Point
8	1.7282526621614818e+100	3.2725200431160383e+104	4.043801827212356e+102
10	5.505307671539634e-31	1.0831529566227919e-13	5.76307619801312e-17

simplify64.0ms

Iterations

Iter	Nodes
done	92
1	92
0	72

end0.0ms

sample12.5s

Algorithm

intervals

Results

7.3s	38005×	body	80	nan
2.8s	12701×	body	80	valid