Details

Time bar (total: 45.7s)

sample435.0ms

Algorithm
intervals
Results
244.0ms1341×body80nan
73.0ms417×body80valid

simplify1.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
372035
done500035

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.4b

localize59.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ (* M D) (* 2.0 d))
9.2b
(pow (/ d l) (/ 1.0 2.0))
10.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.3b
(pow (/ d h) (/ 1.0 2.0))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
78×prod-exp
51×div-exp
46×times-frac
39×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
26×unpow-prod-down pow-unpow
24×pow-exp
14×cbrt-unprod
13×associate-*r*
9×cbrt-undiv
8×pow1
6×pow-to-exp div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l/
2×pow-pow sqr-pow
1×frac-times frac-2neg associate-*r/ associate-*l* pow-prod-down clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 167
Calls
4 calls:
14.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(pow (/ d l) (/ 1.0 2.0))
95.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
14.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (* M D) (* 2.0 d))
104.0ms
(pow (/ d l) (/ 1.0 2.0))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
80.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify691.0ms

Counts
179 → 179
Iterations

Useful iterations: done (684.0ms)

IterNodesCost
03922931
112522722
done50012416

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.0b

localize89.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
4.9b
(/ (* M D) (* 2.0 d))
9.2b
(pow (/ d l) (/ 1.0 2.0))
10.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite623.0ms

Algorithm
rewrite-expression-head
Rules
738×add-exp-log
487×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
46×add-cbrt-cube
28×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* pow-prod-down *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 274
Calls
4 calls:
486.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.0ms
(/ (* M D) (* 2.0 d))
19.0ms
(pow (/ d l) (/ 1.0 2.0))
75.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
46.0ms
(/ (* M D) (* 2.0 d))
81.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify846.0ms

Counts
286 → 286
Iterations

Useful iterations: done (815.0ms)

IterNodesCost
057411962
1185311051
done50019388

prune1.8s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 8.9b

localize101.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
4.9b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
9.2b
(pow (/ d l) (/ 1.0 2.0))

rewrite730.0ms

Algorithm
rewrite-expression-head
Rules
658×add-exp-log
450×prod-exp
206×pow-exp
141×div-exp
76×pow-to-exp
48×add-sqr-sqrt *-un-lft-identity
46×add-cube-cbrt
42×prod-diff
37×times-frac
34×add-cbrt-cube
23×distribute-rgt-in distribute-lft-in
15×cbrt-unprod
13×unpow-prod-down pow-unpow
9×pow1 div-inv
8×associate-*r*
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×sub-neg associate-*r/ associate-*l* pow-prod-down associate-*l/ *-commutative
1×flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 282
Calls
4 calls:
561.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
23.0ms
(/ (* M D) (* 2.0 d))
93.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
15.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
921.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
38.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
114.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify1.1s

Counts
294 → 294
Iterations

Useful iterations: done (1.1s)

IterNodesCost
063617159
1199715289
done500013012

prune1.6s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 7.4b

localize139.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
4.4b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
4.9b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

rewrite991.0ms

Algorithm
rewrite-expression-head
Rules
3060×add-exp-log
2393×prod-exp
1062×pow-exp
557×div-exp
423×pow-to-exp
57×add-cbrt-cube
42×prod-diff
36×add-sqr-sqrt *-un-lft-identity
34×add-cube-cbrt
27×cbrt-unprod
23×distribute-rgt-in distribute-lft-in
22×times-frac
11×pow1
10×cbrt-undiv
8×associate-*r* div-inv
4×expm1-log1p-u pow-prod-down associate-*l/ associate-/r* log1p-expm1-u add-log-exp
2×sub-neg frac-2neg associate-*r/ associate-*l* clear-num *-commutative associate-/l*
1×flip3-- flip-- associate-/l/ distribute-lft-out-- difference-of-squares
Counts
4 → 662
Calls
4 calls:
67.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
702.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
14.0ms
(/ (* M D) (* 2.0 d))
78.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

series3.8s

Counts
4 → 12
Calls
4 calls:
1.1s
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
1.5s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
57.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

simplify2.3s

Counts
674 → 674
Iterations

Useful iterations: done (2.2s)

IterNodesCost
089247526
1323941808
done500037883

prune1.7s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 7.2b

regimes2.3s

Accuracy

0% (6.2b remaining)

Error of 16.4b against oracle of 10.3b and baseline of 16.4b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03164
13864
done3864

end0.0ms

sample18.3s

Algorithm
intervals
Results
9.9s38038×body80nan
4.5s12698×body80valid