Details

Time bar (total: 1.5m)

sample840.0ms

Algorithm
intervals
Results
579.0ms1347×body80nan
165.0ms403×body80valid

simplify5.2s

Counts
1 → 1
Iterations
IterNodes
49507
31091
2188
155
022

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.6b

localize83.0ms

Local error

Found 4 expressions with local error:

7.0b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
12.6b
(pow (/ d h) (/ 1 2))
13.3b
(pow (/ d l) (/ 1 2))
14.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite107.0ms

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:
38.0ms
(* (* (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))
53.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series641.0ms

Counts
4 → 12
Calls
4 calls:
365.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
90.0ms
(pow (/ d h) (/ 1 2))
77.0ms
(pow (/ d l) (/ 1 2))
110.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify11.4s

Counts
234 → 234
Iterations
IterNodes
24293
11343
0461

prune4.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 14.3b

localize93.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (* M D) (* 2 d))
7.0b
(* (* (* (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))))
13.3b
(pow (/ d l) (/ 1 2))
14.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite813.0ms

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))
724.0ms
(* (* (* (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))))
8.0ms
(pow (/ d l) (/ 1 2))
52.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series575.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (* M D) (* 2 d))
364.0ms
(* (* (* (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))))
74.0ms
(pow (/ d l) (/ 1 2))
104.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify6.4s

Counts
231 → 231
Iterations
IterNodes
25362
11456
0491

prune5.3s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 12.1b

localize128.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (* M D) (* d 2))
7.0b
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))))
9.6b
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))
13.3b
(pow (/ d l) (/ 1 2))

rewrite2.9s

Algorithm
rewrite-expression-head
Rules
697×add-exp-log
515×add-cbrt-cube
463×prod-exp
448×cbrt-unprod
141×div-exp
138×cbrt-undiv
56×associate-*l/
37×times-frac
34×add-sqr-sqrt frac-times *-un-lft-identity add-cube-cbrt
32×pow1
30×sqrt-div
25×associate-*r*
20×pow-prod-down associate-*r/
13×pow-unpow unpow-prod-down
9×cbrt-prod
8×flip3-- flip--
6×prod-diff pow-exp
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×pow-to-exp
2×sub-neg associate-*l* *-commutative
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 325
Calls
4 calls:
11.0ms
(/ (* M D) (* d 2))
757.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))))
2.1s
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))
11.0ms
(pow (/ d l) (/ 1 2))

series642.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (* M D) (* d 2))
378.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))))
133.0ms
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))
85.0ms
(pow (/ d l) (/ 1 2))

simplify1.4s

Counts
337 → 337
Iterations
IterNodes
12331
0739

prune8.6s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 9.0b

localize146.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (* M D) (* d 2))
3.4b
(/ (* M D) (* d 2))
7.0b
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (pow (* (cbrt d) (cbrt d)) 1/2) (pow (/ (cbrt d) l) 1/2))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))))
9.6b
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))

rewrite2.9s

Algorithm
rewrite-expression-head
Rules
829×add-exp-log
572×prod-exp
536×add-cbrt-cube
459×cbrt-unprod
150×div-exp
142×cbrt-undiv
56×associate-*l/
38×pow1
34×frac-times
32×pow-exp
30×sqrt-div
25×associate-*r* pow-prod-down
20×add-sqr-sqrt *-un-lft-identity times-frac associate-*r/ add-cube-cbrt
16×pow-to-exp
9×cbrt-prod
8×flip3-- flip--
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×clear-num associate-/r* sub-neg frac-2neg associate-*l* *-commutative associate-/l*
Counts
4 → 338
Calls
4 calls:
24.0ms
(/ (* M D) (* d 2))
23.0ms
(/ (* M D) (* d 2))
775.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (pow (* (cbrt d) (cbrt d)) 1/2) (pow (/ (cbrt d) l) 1/2))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))))
2.0s
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))

series752.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (* M D) (* d 2))
34.0ms
(/ (* M D) (* d 2))
496.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (pow (* (cbrt d) (cbrt d)) 1/2) (pow (/ (cbrt d) l) 1/2))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))))
169.0ms
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))

simplify1.3s

Counts
350 → 350
Iterations
IterNodes
12317
0701

prune9.3s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 7.9b

regimes3.1s

Accuracy

0% (3.4b remaining)

Error of 10.9b against oracle of 7.5b and baseline of 10.9b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
240
140
030

end0.0ms

sample24.2s

Algorithm
intervals
Results
15.6s38235×body80nan
5.7s12653×body80valid