Details

Time bar (total: 2.4m)

sample753.0ms

Algorithm
intervals
Results
499.0ms1271×body80nan
163.0ms438×body80valid

simplify4.5s

Counts
1 → 1

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.3b

localize97.0ms

Local error

Found 4 expressions with local error:

12.5b
(pow (/ d l) (/ 1 2))
10.1b
(pow (/ d h) (/ 1 2))
9.9b
(/ (/ (* l 2) h) (* M (/ (/ D d) 2)))
6.3b
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ (* l 2) h) (* M (/ (/ D d) 2))))) (* (pow (/ d l) (/ 1 2)) (pow (/ d h) (/ 1 2))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
114×add-exp-log
63×add-cbrt-cube
49×times-frac
46×prod-exp
40×add-sqr-sqrt *-un-lft-identity
39×div-exp
37×add-cube-cbrt
29×cbrt-undiv
26×pow-unpow unpow-prod-down
20×pow-exp
16×cbrt-unprod
10×pow-to-exp
8×pow1
7×div-inv associate-/l*
6×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow-pow associate-*l/ difference-of-squares sqr-pow
1×clear-num associate-/r* frac-2neg flip3-- associate-*r* pow-prod-down associate-*r/ associate-/r/ *-commutative flip-- distribute-lft-out-- associate-/l/
Counts
4 → 176
Calls
4 calls:
Slowest
141.0ms
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ (* l 2) h) (* M (/ (/ D d) 2))))) (* (pow (/ d l) (/ 1 2)) (pow (/ d h) (/ 1 2))))
22.0ms
(/ (/ (* l 2) h) (* M (/ (/ D d) 2)))
10.0ms
(pow (/ d h) (/ 1 2))
6.0ms
(pow (/ d l) (/ 1 2))

series588.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
341.0ms
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ (* l 2) h) (* M (/ (/ D d) 2))))) (* (pow (/ d l) (/ 1 2)) (pow (/ d h) (/ 1 2))))
92.0ms
(pow (/ d h) (/ 1 2))
79.0ms
(pow (/ d l) (/ 1 2))
76.0ms
(/ (/ (* l 2) h) (* M (/ (/ D d) 2)))

simplify1.9s

Counts
188 → 188

prune4.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 10.3b

localize105.0ms

Local error

Found 4 expressions with local error:

12.5b
(pow (/ d l) (/ 1 2))
9.9b
(/ (/ (* l 2) h) (* M (/ (/ D d) 2)))
6.3b
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ (* l 2) h) (* M (/ (/ D d) 2))))) (* (pow (/ d l) (/ 1 2)) (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))))
6.3b
(* M (/ (/ D d) 2))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
644×add-exp-log
425×prod-exp
196×pow-exp
154×div-exp
100×times-frac
76×add-cbrt-cube
74×pow-to-exp
71×add-sqr-sqrt
62×*-un-lft-identity
59×add-cube-cbrt
44×associate-*r*
32×cbrt-undiv
22×cbrt-unprod
13×pow-unpow unpow-prod-down
9×pow1 associate-*l* div-inv
7×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ *-commutative difference-of-squares
1×clear-num associate-/r* pow-pow frac-2neg flip3-- associate-/r/ flip-- distribute-lft-out-- sqr-pow associate-/l/
Counts
4 → 304
Calls
4 calls:
Slowest
181.0ms
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ (* l 2) h) (* M (/ (/ D d) 2))))) (* (pow (/ d l) (/ 1 2)) (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))))
18.0ms
(* M (/ (/ D d) 2))
17.0ms
(/ (/ (* l 2) h) (* M (/ (/ D d) 2)))
5.0ms
(pow (/ d l) (/ 1 2))

series514.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
288.0ms
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ (* l 2) h) (* M (/ (/ D d) 2))))) (* (pow (/ d l) (/ 1 2)) (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))))
107.0ms
(pow (/ d l) (/ 1 2))
89.0ms
(/ (/ (* l 2) h) (* M (/ (/ D d) 2)))
31.0ms
(* M (/ (/ D d) 2))

simplify727.0ms

Counts
316 → 316

prune8.4s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.0b

localize218.0ms

Local error

Found 4 expressions with local error:

9.9b
(/ (/ (* l 2) h) (* M (/ (/ D d) 2)))
6.3b
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ (* l 2) h) (* M (/ (/ D d) 2))))) (* (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1 2)) (pow (/ d (cbrt l)) (/ 1 2))) (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))))
6.3b
(* M (/ (/ D d) 2))
6.3b
(* M (/ (/ D d) 2))

rewrite607.0ms

Algorithm
rewrite-expression-head
Rules
6877×add-exp-log
5186×prod-exp
2592×pow-exp
1611×div-exp
784×pow-to-exp
232×rec-exp 1-exp
151×times-frac
102×add-sqr-sqrt
94×add-cbrt-cube
87×associate-*r*
84×*-un-lft-identity
81×add-cube-cbrt
35×cbrt-undiv
32×cbrt-unprod
13×pow1
12×associate-*l*
11×div-inv
7×associate-/l*
6×unswap-sqr
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r/ *-commutative
2×associate-*l/ difference-of-squares
1×clear-num associate-/r* frac-2neg flip3-- associate-/r/ flip-- distribute-lft-out-- associate-/l/
Counts
4 → 1291
Calls
4 calls:
Slowest
413.0ms
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ (* l 2) h) (* M (/ (/ D d) 2))))) (* (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1 2)) (pow (/ d (cbrt l)) (/ 1 2))) (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))))
33.0ms
(/ (/ (* l 2) h) (* M (/ (/ D d) 2)))
24.0ms
(* M (/ (/ D d) 2))
23.0ms
(* M (/ (/ D d) 2))

series613.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
432.0ms
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ (* l 2) h) (* M (/ (/ D d) 2))))) (* (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1 2)) (pow (/ d (cbrt l)) (/ 1 2))) (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))))
106.0ms
(/ (/ (* l 2) h) (* M (/ (/ D d) 2)))
40.0ms
(* M (/ (/ D d) 2))
34.0ms
(* M (/ (/ D d) 2))

simplify13.5s

Counts
1303 → 1303

prune40.1s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 7.5b

localize202.0ms

Local error

Found 4 expressions with local error:

6.3b
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ l 1) (/ (* M (/ (/ D d) 2)) (/ 2 h))))) (* (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1 2)) (pow (/ d (cbrt l)) (/ 1 2))) (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))))
6.3b
(* M (/ (/ D d) 2))
6.3b
(* M (/ (/ D d) 2))
5.4b
(/ (/ l 1) (/ (* M (/ (/ D d) 2)) (/ 2 h)))

rewrite620.0ms

Algorithm
rewrite-expression-head
Rules
6958×add-exp-log
5191×prod-exp
2592×pow-exp
1681×div-exp
851×times-frac
784×pow-to-exp
343×add-sqr-sqrt
325×*-un-lft-identity
322×add-cube-cbrt
241×1-exp
232×rec-exp
133×add-cbrt-cube
87×associate-*r*
69×cbrt-undiv
56×div-inv
31×cbrt-unprod
18×associate-/r*
15×associate-/r/
13×pow1 associate-/l*
12×associate-*l*
6×unswap-sqr
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×associate-*l/ associate-*r/ difference-of-squares
1×clear-num frac-2neg flip3-- flip-- distribute-lft-out-- associate-/l/
Counts
4 → 1562
Calls
4 calls:
Slowest
368.0ms
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ l 1) (/ (* M (/ (/ D d) 2)) (/ 2 h))))) (* (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1 2)) (pow (/ d (cbrt l)) (/ 1 2))) (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))))
33.0ms
(/ (/ l 1) (/ (* M (/ (/ D d) 2)) (/ 2 h)))
28.0ms
(* M (/ (/ D d) 2))
26.0ms
(* M (/ (/ D d) 2))

series678.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
497.0ms
(* (- 1 (/ (* M (/ (/ D d) 2)) (/ (/ l 1) (/ (* M (/ (/ D d) 2)) (/ 2 h))))) (* (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1 2)) (pow (/ d (cbrt l)) (/ 1 2))) (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))))
111.0ms
(/ (/ l 1) (/ (* M (/ (/ D d) 2)) (/ 2 h)))
37.0ms
(* M (/ (/ D d) 2))
32.0ms
(* M (/ (/ D d) 2))

simplify5.8s

Counts
1574 → 1574

prune38.2s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 6.8b

regimes2.4s

Accuracy

-10.5% (3.5b remaining)

Error of 11.3b against oracle of 7.8b and baseline of 11.0b

bsearch28.0ms

end0.0ms

sample16.1s

Algorithm
intervals
Results
10.7s39203×body80nan
3.6s12813×body80valid