Details

Time bar (total: 1.1m)

sample518.0ms

Algorithm
intervals
Results
304.0ms1360×body80nan
102.0ms435×body80valid

simplify3.8s

Counts
1 → 1
Iterations
IterNodes
done5000
43968
3655
2170
154
022

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize89.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ (* M D) (* 2.0 d))
8.8b
(pow (/ d h) (/ 1.0 2.0))
13.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.2b
(pow (/ d l) (/ 1.0 2.0))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
78×prod-exp
51×div-exp
46×times-frac
39×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
37×add-cbrt-cube
26×pow-unpow unpow-prod-down
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 clear-num associate-/r* frac-2neg associate-*l* pow-prod-down associate-*r/ *-commutative associate-/l*
Counts
4 → 167
Calls
4 calls:
19.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(pow (/ d h) (/ 1.0 2.0))
82.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (* M D) (* 2.0 d))
115.0ms
(pow (/ d h) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
93.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify2.6s

Counts
179 → 179
Iterations
IterNodes
done5001
23992
11172
0392

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.4b

localize149.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.0b
(/ (* M D) (* 2.0 d))
8.8b
(pow (/ d h) (/ 1.0 2.0))
13.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite426.0ms

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 *-un-lft-identity times-frac add-cube-cbrt
20×cbrt-unprod
16×associate-*r*
13×pow-unpow unpow-prod-down
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-*l/ associate-*r/
2×sub-neg associate-*l* pow-prod-down *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 274
Calls
4 calls:
285.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
19.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(pow (/ d h) (/ 1.0 2.0))
87.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.4s

Counts
4 → 12
Calls
4 calls:
925.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
50.0ms
(/ (* M D) (* 2.0 d))
115.0ms
(pow (/ d h) (/ 1.0 2.0))
1.3s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.2s

Counts
286 → 286
Iterations
IterNodes
done5000
11619
0569

prune2.2s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 8.1b

localize289.0ms

Local error

Found 4 expressions with local error:

3.4b
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
4.7b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.0b
(/ (* M D) (* 2.0 d))
13.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite895.0ms

Algorithm
rewrite-expression-head
Rules
6975×add-exp-log
5249×prod-exp
2617×pow-exp
1629×div-exp
789×pow-to-exp
232×rec-exp 1-exp
55×add-cbrt-cube
27×cbrt-unprod
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×pow1 times-frac
16×associate-*r*
13×pow-unpow
9×cbrt-undiv
6×pow-pow prod-diff
5×distribute-rgt-in distribute-lft-in pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l/ associate-*r/ div-inv
2×sub-neg associate-*l* *-commutative
1×pow2 frac-times clear-num associate-/r* unpow-prod-down frac-2neg pow-plus flip3-- pow-sqr pow-prod-up flip-- associate-/l* sqr-pow
Counts
4 → 1230
Calls
4 calls:
23.0ms
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
539.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
19.0ms
(/ (* M D) (* 2.0 d))
78.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.6s

Counts
4 → 12
Calls
4 calls:
190.0ms
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
1.3s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
48.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify8.3s

Counts
1242 → 1242
Iterations
IterNodes
done5000
13622
01446

prune2.4s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 7.2b

localize278.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))
5.0b
(/ (* M D) (* 2.0 d))
5.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
7.3b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
7226×add-exp-log
5420×prod-exp
2642×pow-exp
1687×div-exp
794×pow-to-exp
248×rec-exp 1-exp
75×add-cbrt-cube
40×cbrt-unprod
19×associate-*r*
16×pow1
15×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×cbrt-undiv
10×times-frac
7×pow-prod-down associate-*l/
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* associate-*r/ *-commutative
2×sub-neg div-inv
1×frac-times clear-num associate-/r* frac-2neg flip3-- un-div-inv flip-- associate-/l*
Counts
4 → 1266
Calls
4 calls:
647.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))
24.0ms
(/ (* M D) (* 2.0 d))
72.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
186.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

series3.5s

Counts
4 → 12
Calls
4 calls:
1.3s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))
34.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
1.1s
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

simplify7.0s

Counts
1278 → 1278
Iterations
IterNodes
done5000
13214
01469

prune1.9s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 6.6b

regimes2.6s

Accuracy

-2% (7.6b remaining)

Error of 16.1b against oracle of 8.5b and baseline of 16.0b

bsearch956.0ms

Steps
ItersRangePoint
9
3.004520635708275e-80
5.217467663454771e-73
8.074891761185047e-74
9
-44468768.542654045
-1.060772524819629
-89.70047366523089

simplify26.0ms

Iterations
IterNodes
done75
175
058

end0.0ms

sample16.8s

Algorithm
intervals
Results
9.6s38365×body80nan
4.5s12777×body80valid