Details

sample698.0ms

Algorithm

intervals

Results

444.0ms	1220×	body	80	nan
152.0ms	405×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
4	2006
3	1271
2	198
1	58
0	22

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.9b

localize75.0ms

Local error

Found 4 expressions with local error:

7.5b	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
11.6b	(pow (/ d h) (/ 1 2))
13.2b	(pow (/ d l) (/ 1 2))
13.5b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite187.0ms

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:

74.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
10.0ms	(pow (/ d h) (/ 1 2))
10.0ms	(pow (/ d l) (/ 1 2))
88.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series619.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
89.0ms	(pow (/ d h) (/ 1 2))
78.0ms	(pow (/ d l) (/ 1 2))
113.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.4s

Counts

234 → 234

Iterations

Iter	Nodes
done	2002
2	2002
1	1360
0	461

prune1.4s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.6b

localize99.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ (* M D) (* 2 d))
7.5b	(* (* (* (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))))
13.2b	(pow (/ d l) (/ 1 2))
13.5b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite941.0ms

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))
856.0ms	(* (* (* (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))))
6.0ms	(pow (/ d l) (/ 1 2))
62.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series650.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* M D) (* 2 d))
385.0ms	(* (* (* (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))))
98.0ms	(pow (/ d l) (/ 1 2))
113.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.3s

Counts

231 → 231

Iterations

Iter	Nodes
done	2009
2	2009
1	1474
0	491

prune1.9s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 10.7b

localize101.0ms

Local error

Found 4 expressions with local error:

2.4b	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
3.5b	(/ (* M D) (* 2 d))
7.5b	(* (* (* (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))))
13.5b	(* (* (/ 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))))
22.0ms	(/ (* 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))))
54.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series642.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
39.0ms	(/ (* M D) (* 2 d))
396.0ms	(* (* (* (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))))
128.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.7s

Counts

382 → 382

Iterations

Iter	Nodes
done	2001
1	2001
0	731

prune4.7s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 8.5b

localize147.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ (/ (* M D) 2) d)
5.4b	(* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ 1 (* (cbrt l) (cbrt l))))
7.5b	(* (* (* (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) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ 1 (* (cbrt l) (cbrt l))))) (/ h (cbrt l)))))
8.5b	(* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ 1 (* (cbrt l) (cbrt l))))) (/ h (cbrt l)))

rewrite3.3s

Algorithm

rewrite-expression-head

Rules

9623×	`add-exp-log`
4978×	`prod-exp`
4098×	`div-exp`
2114×	`add-cbrt-cube`
1132×	`cbrt-unprod`
984×	`cbrt-undiv`
571×	`frac-times`
546×	`rec-exp` `1-exp`
480×	`sqrt-div`
368×	`associate-*l/`
199×	`associate-*r/`
64×	`flip3--` `flip--`
56×	`times-frac`
41×	`pow1`
40×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
38×	`add-cube-cbrt`
32×	`associate-r`
26×	`pow-prod-down`
9×	`cbrt-prod`
7×	`div-inv` `associate-/l*`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `un-div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `-commutative` `unswap-sqr`
2×	`sub-neg`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

4 → 1729

Calls

4 calls:

25.0ms	(/ (/ (* M D) 2) d)
174.0ms	(* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ 1 (* (cbrt l) (cbrt l))))
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) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ 1 (* (cbrt l) (cbrt l))))) (/ h (cbrt l)))))
1.6s	(* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ 1 (* (cbrt l) (cbrt l))))) (/ h (cbrt l)))

series1.1s

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (/ (* M D) 2) d)
371.0ms	(* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ 1 (* (cbrt l) (cbrt l))))
450.0ms	(* (* (* (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) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ 1 (* (cbrt l) (cbrt l))))) (/ h (cbrt l)))))
204.0ms	(* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ 1 (* (cbrt l) (cbrt l))))) (/ h (cbrt l)))

simplify3.9s

Counts

1741 → 1741

Iterations

Iter	Nodes
done	2779
0	2779

prune29.8s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 8.5b

regimes3.0s

Accuracy

30.4% (4.1b remaining)

Error of 12.1b against oracle of 8.0b and baseline of 13.9b

bsearch6.0ms

simplify46.0ms

Iterations

Iter	Nodes
done	108
1	108
0	79

end0.0ms

sample22.5s

Algorithm

intervals

Results

14.0s	39069×	body	80	nan
5.3s	12798×	body	80	valid