Details

sample523.0ms

Algorithm

intervals

Results

332.0ms	1107×	body	80	nan
119.0ms	398×	body	80	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
4	9507
3	1091
2	188
1	55
0	22

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.1b

localize62.0ms

Local error

Found 4 expressions with local error:

9.2b	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
11.0b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
13.5b	(pow (/ d l) (/ 1 2))
13.7b	(pow (/ d h) (/ 1 2))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

331×	`add-exp-log`
179×	`prod-exp`
99×	`div-exp`
60×	`pow-exp`
45×	`times-frac`
42×	`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`
6×	`prod-diff`
5×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `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 → 222

Calls

4 calls:

42.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
75.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
6.0ms	(pow (/ d l) (/ 1 2))
8.0ms	(pow (/ d h) (/ 1 2))

series569.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
108.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
77.0ms	(pow (/ d l) (/ 1 2))
68.0ms	(pow (/ d h) (/ 1 2))

simplify6.7s

Counts

234 → 234

Iterations

Iter	Nodes
2	4112
1	1320
0	461

prune4.8s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.1b

localize81.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* M D) (* 2 d))
9.2b	(* (* (* (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))))
11.0b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
13.5b	(pow (/ d l) (/ 1 2))

rewrite939.0ms

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×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `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--`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`sub-neg` `associate-l` `pow-prod-down` `*-commutative`
1×	`clear-num` `associate-/r` `pow-pow` `frac-2neg` `associate-/l` `sqr-pow`

Counts

4 → 219

Calls

4 calls:

12.0ms	(/ (* M D) (* 2 d))
842.0ms	(* (* (* (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))))
71.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
9.0ms	(pow (/ d l) (/ 1 2))

series580.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (* M D) (* 2 d))
377.0ms	(* (* (* (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))))
87.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
67.0ms	(pow (/ d l) (/ 1 2))

simplify4.7s

Counts

231 → 231

Iterations

Iter	Nodes
2	5197
1	1422
0	491

prune5.6s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 10.8b

localize139.0ms

Local error

Found 4 expressions with local error:

3.1b	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
3.8b	(/ (* M D) (* 2 d))
9.2b	(* (* (* (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))))
11.0b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite1.4s

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×	`add-sqr-sqrt` `rec-exp` `*-un-lft-identity` `1-exp` `add-cube-cbrt`
10×	`times-frac`
9×	`cbrt-undiv`
8×	`pow-to-exp`
6×	`sqrt-pow1` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `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 → 370

Calls

4 calls:

16.0ms	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
23.0ms	(/ (* M D) (* 2 d))
1.3s	(* (* (* (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))))
65.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series674.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
47.0ms	(/ (* M D) (* 2 d))
393.0ms	(* (* (* (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))))
120.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.8s

Counts

382 → 382

Iterations

Iter	Nodes
1	2470
0	731

prune10.8s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 7.6b

localize176.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (/ (* M D) 2) d)
5.8b	(* (* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2)) (/ 1 l))
6.3b	(* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2))
9.2b	(* (* (* (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) 2) d) (/ (/ (* M D) 2) d)) 2)) (/ 1 l))))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

715×	`add-exp-log`
514×	`frac-times`
480×	`sqrt-div`
441×	`add-cbrt-cube`
328×	`div-exp`
325×	`associate-*l/`
300×	`prod-exp`
195×	`cbrt-undiv`
178×	`cbrt-unprod`
171×	`associate-*r/`
64×	`flip3--` `flip--`
46×	`times-frac`
37×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
29×	`pow1`
23×	`associate-r`
19×	`rec-exp` `1-exp`
17×	`pow-prod-down`
7×	`div-inv` `associate-/l*`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative`
2×	`sub-neg` `unswap-sqr`
1×	`clear-num` `frac-2neg` `un-div-inv` `associate-/l/`

Counts

4 → 488

Calls

4 calls:

11.0ms	(/ (/ (* M D) 2) d)
321.0ms	(* (* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2)) (/ 1 l))
99.0ms	(* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2))
1.8s	(* (* (* (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) 2) d) (/ (/ (* M D) 2) d)) 2)) (/ 1 l))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (/ (* M D) 2) d)
113.0ms	(* (* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2)) (/ 1 l))
111.0ms	(* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2))
430.0ms	(* (* (* (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) 2) d) (/ (/ (* M D) 2) d)) 2)) (/ 1 l))))

simplify2.5s

Counts

500 → 500

Iterations

Iter	Nodes
1	3162
0	908

prune13.1s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 6.8b

regimes4.0s

Accuracy

-25.2% (5.5b remaining)

Error of 12.1b against oracle of 6.5b and baseline of 10.9b

bsearch6.0ms

simplify94.0ms

Iterations

Iter	Nodes
9	153
8	153
7	151
6	145
5	143
4	135
3	117
2	106
1	102
0	75

end0.0ms

sample24.0s

Algorithm

intervals

Results

14.8s	38268×	body	80	nan
5.7s	12725×	body	80	valid