Details

sample582.0ms

Algorithm

intervals

Results

359.0ms	1135×	body	80	nan
128.0ms	394×	body	80	valid

simplify4.9s

Counts: 1 → 1

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.9b

localize69.0ms

Local error

Found 4 expressions with local error:

12.9b	(pow (/ d l) (/ 1 2))
11.0b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
9.4b	(pow (/ d h) (/ 1 2))
6.0b	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

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:

Slowest

79.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
39.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
5.0ms	(pow (/ d l) (/ 1 2))
4.0ms	(pow (/ d h) (/ 1 2))

series748.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

413.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
126.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
116.0ms	(pow (/ d l) (/ 1 2))
93.0ms	(pow (/ d h) (/ 1 2))

simplify4.5s

Counts: 234 → 234

prune4.1s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.8b

localize95.0ms

Local error

Found 4 expressions with local error:

11.0b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
9.4b	(pow (/ d h) (/ 1 2))
6.0b	(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.3b	(/ (* M D) (* 2 d))

rewrite494.0ms

Algorithm

rewrite-expression-head

Rules

320×	`add-exp-log`
171×	`prod-exp`
96×	`div-exp`
46×	`add-cbrt-cube` `pow-exp`
28×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
20×	`cbrt-unprod`
16×	`associate-r`
15×	`associate-*r/`
14×	`rec-exp` `1-exp`
13×	`pow-unpow` `unpow-prod-down`
12×	`sqrt-div`
11×	`pow-to-exp`
10×	`frac-times`
9×	`pow1` `cbrt-undiv` `associate-*l/`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `div-inv` `flip--` `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 → 207

Calls

4 calls:

Slowest

430.0ms	(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
44.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.0ms	(/ (* M D) (* 2 d))
4.0ms	(pow (/ d h) (/ 1 2))

series1.6s

Counts

4 → 12

Calls

4 calls:

Slowest

1.4s	(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
90.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
83.0ms	(pow (/ d h) (/ 1 2))
41.0ms	(/ (* M D) (* 2 d))

simplify1.5s

Counts: 219 → 219

prune4.9s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.9b

localize126.0ms

Local error

Found 4 expressions with local error:

11.0b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
6.0b	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) 1/2) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.3b	(/ (* M D) (* 2 d))
2.8b	(sqrt (/ d (cbrt l)))

rewrite772.0ms

Algorithm

rewrite-expression-head

Rules

604×	`add-exp-log`
384×	`prod-exp`
139×	`div-exp`
108×	`pow-exp`
55×	`add-cbrt-cube`
32×	`add-sqr-sqrt`
30×	`pow-to-exp` `times-frac`
27×	`*-un-lft-identity` `add-cube-cbrt` `cbrt-unprod`
22×	`sqrt-prod`
16×	`pow1` `associate-r`
15×	`associate-*r/`
14×	`rec-exp` `1-exp`
13×	`sqrt-div`
10×	`cbrt-prod` `frac-times`
9×	`cbrt-undiv` `associate-*l/`
7×	`pow-prod-down`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`rem-sqrt-square` `div-inv`
2×	`sub-neg` `associate-l` `*-commutative`
1×	`clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l`

Counts

4 → 258

Calls

4 calls:

Slowest

695.0ms	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) 1/2) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
48.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
18.0ms	(/ (* M D) (* 2 d))
3.0ms	(sqrt (/ d (cbrt l)))

series2.2s

Counts

4 → 12

Calls

4 calls:

Slowest

1.8s	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) 1/2) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
165.0ms	(sqrt (/ d (cbrt l)))
108.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
36.0ms	(/ (* M D) (* 2 d))

simplify1.7s

Counts: 270 → 270

prune7.7s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 8.2b

localize160.0ms

Local error

Found 4 expressions with local error:

6.0b	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) 1/2) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))))
6.0b	(/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))
5.3b	(/ (* M D) (* d 2))
5.3b	(/ (* M D) (* d 2))

rewrite751.0ms

Algorithm

rewrite-expression-head

Rules

742×	`add-exp-log`
451×	`prod-exp`
443×	`add-cbrt-cube`
230×	`cbrt-unprod`
188×	`div-exp`
142×	`cbrt-undiv`
68×	`pow-exp`
30×	`prod-diff`
24×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`pow-to-exp`
21×	`add-cube-cbrt`
18×	`associate-*r/`
17×	`distribute-rgt-in` `distribute-lft-in`
13×	`pow1`
12×	`sqrt-div`
10×	`frac-times`
9×	`times-frac` `div-inv`
7×	`associate-*l/`
6×	`associate-r` `pow-prod-down`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`clear-num` `associate-/r` `frac-2neg` `associate-/l` `associate-/l/`
2×	`sub-neg` `difference-of-squares`
1×	`associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 305

Calls

4 calls:

Slowest

555.0ms	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) 1/2) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))))
135.0ms	(/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))
23.0ms	(/ (* M D) (* d 2))
19.0ms	(/ (* M D) (* d 2))

series1.7s

Counts

4 → 12

Calls

4 calls:

Slowest

1.5s	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) 1/2) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))))
120.0ms	(/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))
57.0ms	(/ (* M D) (* d 2))
33.0ms	(/ (* M D) (* d 2))

simplify2.0s

Counts: 317 → 317

prune9.5s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 7.9b

regimes2.6s

Accuracy

17.1% (4.9b remaining)

Error of 13.9b against oracle of 9.0b and baseline of 14.9b

bsearch32.0ms

end0.0ms

sample23.7s

Algorithm

intervals

Results

14.7s	37634×	body	80	nan
5.7s	12646×	body	80	valid