Details

sample787.0ms

Algorithm

intervals

Results

492.0ms	1242×	body	80	nan
199.0ms	406×	body	80	valid

simplify5.2s

Counts

1 → 1

Iterations

Iter	Nodes
4	9030
3	1081
2	188
1	55
0	22

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.1b

localize61.0ms

Local error

Found 4 expressions with local error:

6.0b	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
10.3b	(pow (/ d h) (/ 1 2))
12.1b	(pow (/ d l) (/ 1 2))
13.7b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite105.0ms

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:

46.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.0ms	(pow (/ d h) (/ 1 2))
4.0ms	(pow (/ d l) (/ 1 2))
42.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series593.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
91.0ms	(pow (/ d h) (/ 1 2))
82.0ms	(pow (/ d l) (/ 1 2))
95.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify7.7s

Counts

220 → 220

Iterations

Iter	Nodes
2	4118
1	1283
0	438

prune4.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.8b

localize104.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ (* M D) (* 2 d))
6.0b	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (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))))
12.1b	(pow (/ d l) (/ 1 2))
13.7b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite952.0ms

Algorithm

rewrite-expression-head

Rules

320×	`add-exp-log`
171×	`prod-exp`
96×	`div-exp`
46×	`add-cbrt-cube` `associate-*l/` `pow-exp`
30×	`frac-times` `sqrt-div`
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`
12×	`associate-*r/`
11×	`pow-to-exp`
9×	`pow1` `cbrt-undiv`
8×	`flip3--` `flip--`
4×	`insert-posit16` `div-inv` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `pow-prod-down` `*-commutative`
1×	`clear-num` `associate-/r` `pow-pow` `frac-2neg` `associate-/l` `sqr-pow`

Counts

4 → 205

Calls

4 calls:

16.0ms	(/ (* M D) (* 2 d))
847.0ms	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (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))))
4.0ms	(pow (/ d l) (/ 1 2))
78.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series646.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (* M D) (* 2 d))
370.0ms	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (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))))
93.0ms	(pow (/ d l) (/ 1 2))
127.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify5.0s

Counts

217 → 217

Iterations

Iter	Nodes
2	5164
1	1395
0	468

prune5.0s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 11.0b

localize142.0ms

Local error

Found 4 expressions with local error:

2.3b	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
4.9b	(/ (* M D) (* 2 d))
6.0b	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
13.7b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

515×	`frac-times`
483×	`sqrt-div`
328×	`associate-*l/`
305×	`add-exp-log`
169×	`associate-*r/`
163×	`prod-exp`
93×	`div-exp`
64×	`flip3--` `flip--`
55×	`add-cbrt-cube`
40×	`pow-exp`
32×	`pow1`
27×	`cbrt-unprod`
16×	`associate-r`
15×	`pow-prod-down`
14×	`rec-exp` `1-exp`
12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`times-frac`
9×	`cbrt-undiv`
8×	`pow-to-exp`
6×	`sqrt-pow1`
4×	`insert-posit16` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative` `div-inv`
1×	`pow2` `rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up` `sqrt-prod` `associate-/l`

Counts

4 → 356

Calls

4 calls:

13.0ms	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
21.0ms	(/ (* M D) (* 2 d))
1.7s	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
50.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series739.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
53.0ms	(/ (* M D) (* 2 d))
455.0ms	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
134.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.5s

Counts

368 → 368

Iterations

Iter	Nodes
1	2385
0	705

prune10.5s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 6.8b

localize130.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ (* M D) (* d 2))
5.4b	(* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))))
6.0b	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))))
7.5b	(/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

588×	`add-cbrt-cube` `add-exp-log`
515×	`frac-times`
480×	`sqrt-div`
326×	`associate-*l/`
317×	`prod-exp` `cbrt-unprod`
178×	`cbrt-undiv` `div-exp`
175×	`associate-*r/`
64×	`flip3--` `flip--`
27×	`pow1`
16×	`pow-prod-down`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`associate-r`
6×	`add-cube-cbrt`
4×	`associate-l` `insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`distribute-rgt-in` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `distribute-lft-in` `times-frac` `-commutative` `div-inv` `associate-/l*` `difference-of-squares`
1×	`distribute-lft-out--` `unswap-sqr`

Counts

4 → 444

Calls

4 calls:

13.0ms	(/ (* M D) (* d 2))
127.0ms	(* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))))
1.5s	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))))
123.0ms	(/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))

series819.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (* M D) (* d 2))
174.0ms	(* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))))
429.0ms	(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))))
167.0ms	(/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))

simplify1.5s

Counts

456 → 456

Iterations

Iter	Nodes
1	2904
0	788

prune12.9s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 5.8b

regimes4.3s

Accuracy

13.8% (3.8b remaining)

Error of 11.1b against oracle of 7.3b and baseline of 11.7b

bsearch6.0ms

simplify18.0ms

Iterations

Iter	Nodes
2	82
1	82
0	63

end0.0ms

sample26.2s

Algorithm

intervals

Results

17.8s	38207×	body	80	nan
5.6s	12656×	body	80	valid