Details

sample777.0ms

Algorithm

intervals

Results

500.0ms	1242×	body	80	nan
196.0ms	406×	body	80	valid

simplify5.2s

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.1b

localize73.0ms

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))

rewrite144.0ms

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:

67.0ms	(* (* (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))
7.0ms	(pow (/ d l) (/ 1 2))
60.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series674.0ms

Counts

4 → 12

Calls

4 calls:

393.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
88.0ms	(pow (/ d h) (/ 1 2))
82.0ms	(pow (/ d l) (/ 1 2))
111.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify11.5s

Counts

234 → 234

Iterations

Iter	Nodes
2	4293
1	1343
0	461

prune4.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.1b

localize98.0ms

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))

rewrite760.0ms

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:

21.0ms	(/ (* M D) (* 2 d))
686.0ms	(* (* (* (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))))
5.0ms	(pow (/ d l) (/ 1 2))
44.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series574.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (* M D) (* 2 d))
348.0ms	(* (* (* (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))))
76.0ms	(pow (/ d l) (/ 1 2))
104.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify6.4s

Counts

231 → 231

Iterations

Iter	Nodes
2	5362
1	1456
0	491

prune5.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 11.8b

localize143.0ms

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))

rewrite1.3s

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:

8.0ms	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
20.0ms	(/ (* M D) (* 2 d))
1.2s	(* (* (* (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))))
60.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series580.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
36.0ms	(/ (* M D) (* 2 d))
347.0ms	(* (* (* (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))))
109.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.5s

Counts

382 → 382

Iterations

Iter	Nodes
1	2470
0	731

prune10.2s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 7.9b

localize89.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ (/ (* M D) 2) d)
5.4b	(* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) 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) 2) d) (/ (/ (* M D) 2) d)) 2)) l)))
7.5b	(/ (* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2)) l)

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

513×	`frac-times`
480×	`sqrt-div`
324×	`associate-*l/`
285×	`add-cbrt-cube` `add-exp-log`
169×	`associate-*r/`
138×	`cbrt-undiv` `div-exp`
98×	`prod-exp` `cbrt-unprod`
64×	`flip3--` `flip--`
59×	`add-sqr-sqrt`
58×	`times-frac`
55×	`*-un-lft-identity`
52×	`add-cube-cbrt`
42×	`prod-diff`
24×	`pow1`
23×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow-prod-down`
13×	`associate-r` `div-inv`
8×	`associate-/l*`
6×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `sub-neg` `frac-2neg` `*-commutative` `difference-of-squares` `unswap-sqr` `associate-/l/`
1×	`distribute-lft-out--`

Counts

4 → 441

Calls

4 calls:

21.0ms	(/ (/ (* M D) 2) d)
84.0ms	(* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2))
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 (/ (* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2)) l)))
91.0ms	(/ (* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2)) l)

series682.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (/ (* M D) 2) d)
132.0ms	(* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2))
370.0ms	(* (* (* (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)) l)))
131.0ms	(/ (* h (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) 2)) l)

simplify2.0s

Counts

453 → 453

Iterations

Iter	Nodes
1	3154
0	903

prune12.5s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 6.9b

regimes3.2s

Accuracy

2% (5.2b remaining)

Error of 13.3b against oracle of 8.2b and baseline of 13.4b

bsearch854.0ms

Steps

Iters	Range		Point
7	5.31952523173493e-130	7.272451862634168e-128	5.603024486665334e-129
8	-5.780247606153402e-278	-1.3248945513789935e-281	-4.2998422524441214e-279

simplify21.0ms

Iterations

Iter	Nodes
2	72
1	72
0	56

end0.0ms

sample24.0s

Algorithm

intervals

Results

15.8s	38207×	body	80	nan
5.7s	12656×	body	80	valid