Details

sample430.0ms

Algorithm

intervals

Results

242.0ms	1103×	body	80	nan
93.0ms	408×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize62.0ms

Local error

Found 4 expressions with local error:

5.5b	(/ (* M D) (* 2.0 d))
9.5b	(pow (/ d h) (/ 1.0 2.0))
12.5b	(pow (/ d l) (/ 1.0 2.0))
14.5b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-exp-log`
78×	`prod-exp`
51×	`div-exp`
46×	`times-frac`
39×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
37×	`add-cbrt-cube`
26×	`pow-unpow` `unpow-prod-down`
24×	`pow-exp`
14×	`cbrt-unprod`
13×	`associate-r`
9×	`cbrt-undiv`
8×	`pow1`
6×	`pow-to-exp` `div-inv`
4×	`add-log-exp`
3×	`associate-*l/`
2×	`pow-pow` `sqr-pow`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `associate-l` `pow-prod-down` `associate-r/` `-commutative` `associate-/l`

Counts

4 → 159

Calls

4 calls:

14.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(pow (/ d h) (/ 1.0 2.0))
9.0ms	(pow (/ d l) (/ 1.0 2.0))
51.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.3s

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (* M D) (* 2.0 d))
88.0ms	(pow (/ d h) (/ 1.0 2.0))
97.0ms	(pow (/ d l) (/ 1.0 2.0))
1.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.2s

Counts

171 → 171

Iterations

Iter	Nodes
done	5001
1	1245
0	384

prune1.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 13.0b

localize107.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (* (* (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))))
5.5b	(/ (* M D) (* 2.0 d))
12.5b	(pow (/ d l) (/ 1.0 2.0))
14.5b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite371.0ms

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:

283.0ms	(* (* (* (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))))
9.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(pow (/ d l) (/ 1.0 2.0))
48.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.3s

Counts

4 → 12

Calls

4 calls:

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))))
42.0ms	(/ (* M D) (* 2.0 d))
93.0ms	(pow (/ d l) (/ 1.0 2.0))
963.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.9s

Counts

304 → 304

Iterations

Iter	Nodes
done	5001
1	1941
0	606

prune1.4s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 8.8b

localize111.0ms

Local error

Found 4 expressions with local error:

5.5b	(/ (* M D) (* 2.0 d))
6.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.7b	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
12.5b	(pow (/ d l) (/ 1.0 2.0))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-exp-log`
78×	`prod-exp`
51×	`div-exp`
39×	`add-cbrt-cube`
22×	`times-frac` `pow-exp`
21×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
14×	`cbrt-unprod`
13×	`pow-unpow` `unpow-prod-down`
10×	`cbrt-undiv`
7×	`pow1`
5×	`pow-to-exp`
4×	`associate-/r` `associate-l/` `div-inv` `add-log-exp`
3×	`associate-r`
2×	`clear-num` `frac-2neg` `associate-/l*`
1×	`pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow` `associate-/l/`

Counts

4 → 129

Calls

4 calls:

12.0ms	(/ (* M D) (* 2.0 d))
36.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
42.0ms	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
6.0ms	(pow (/ d l) (/ 1.0 2.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (* M D) (* 2.0 d))
920.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
1.0s	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
94.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify1.3s

Counts

141 → 141

Iterations

Iter	Nodes
done	5001
1	996
0	329

prune1.3s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 7.3b

localize195.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
5.5b	(/ (* M D) (* 2.0 d))
6.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.7b	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

rewrite742.0ms

Algorithm

rewrite-expression-head

Rules

3528×	`add-exp-log`
2893×	`prod-exp`
1394×	`pow-exp`
623×	`div-exp`
521×	`pow-to-exp`
136×	`rec-exp` `1-exp`
57×	`add-cbrt-cube`
27×	`cbrt-unprod`
11×	`pow1`
10×	`add-sqr-sqrt` `cbrt-undiv` `*-un-lft-identity`
8×	`associate-r` `add-cube-cbrt`
4×	`associate-/r` `times-frac` `pow-prod-down` `associate-l/` `add-log-exp`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `associate-l` `associate-r/` `-commutative` `div-inv` `associate-/l*`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares` `associate-/l/`

Counts

4 → 748

Calls

4 calls:

482.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
13.0ms	(/ (* M D) (* 2.0 d))
45.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
55.0ms	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

series2.9s

Counts

4 → 12

Calls

4 calls:

905.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
31.0ms	(/ (* M D) (* 2.0 d))
980.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
983.0ms	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

simplify2.8s

Counts

760 → 760

Iterations

Iter	Nodes
done	5000
1	3361
0	891

prune1.4s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 6.3b

regimes2.6s

Accuracy

-0.4% (8.4b remaining)

Error of 16.1b against oracle of 7.7b and baseline of 16.1b

bsearch665.0ms

Steps

Iters	Range		Point
4	1.0545286570800463e+145	1.7458295492381215e+145	1.0683641516926155e+145
9	1.9386984315328244e-42	3.079903166760186e-34	1.803215210159374e-41

simplify46.0ms

Iterations

Iter	Nodes
done	81
2	81
1	79
0	61

end0.0ms

sample16.7s

Algorithm

intervals

Results

10.4s	38309×	body	80	nan
3.7s	12742×	body	80	valid