Details

Time bar (total: 53.0s)

sample480.0ms

Algorithm
intervals
Results
261.0ms1360×body80nan
119.0ms435×body80valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5001
3710
2174
154
022

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize74.0ms

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))

rewrite99.0ms

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×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 → 159
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
11.0ms
(pow (/ d h) (/ 1.0 2.0))
57.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
9.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ (* M D) (* 2.0 d))
65.0ms
(pow (/ d h) (/ 1.0 2.0))
876.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
88.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify1.3s

Counts
171 → 171
Iterations
IterNodes
done5001
11242
0384

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.2b

localize134.0ms

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))

rewrite371.0ms

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×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×cbrt-unprod
16×associate-*r*
13×pow-unpow unpow-prod-down
9×pow1 cbrt-undiv
4×div-inv add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in 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 → 260
Calls
4 calls:
250.0ms
(* (* (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))))
15.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(pow (/ d h) (/ 1.0 2.0))
65.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.0s

Counts
4 → 12
Calls
4 calls:
841.0ms
(* (* (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))))
36.0ms
(/ (* M D) (* 2.0 d))
90.0ms
(pow (/ d h) (/ 1.0 2.0))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.8s

Counts
272 → 272
Iterations
IterNodes
done5001
11804
0546

prune1.8s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 7.8b

localize238.0ms

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))

rewrite931.0ms

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
19×add-sqr-sqrt pow1 *-un-lft-identity times-frac add-cube-cbrt
16×associate-*r*
13×pow-unpow
9×cbrt-undiv
6×pow-pow
5×pow-prod-down
4×add-log-exp
3×associate-*l/ associate-*r/ div-inv
2×distribute-rgt-in sub-neg distribute-lft-in 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 → 1216
Calls
4 calls:
32.0ms
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
571.0ms
(* (* (* (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))))
9.0ms
(/ (* M D) (* 2.0 d))
67.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.9s

Counts
4 → 12
Calls
4 calls:
153.0ms
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
1.6s
(* (* (* (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))))
54.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify3.6s

Counts
1228 → 1228
Iterations
IterNodes
done5000
01423

prune2.3s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 7.1b

localize218.0ms

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))

rewrite1.1s

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
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×cbrt-undiv
10×times-frac
7×pow-prod-down associate-*l/
4×add-log-exp
3×associate-*l* associate-*r/ *-commutative
2×distribute-rgt-in sub-neg distribute-lft-in div-inv
1×frac-times clear-num associate-/r* frac-2neg flip3-- un-div-inv flip-- associate-/l*
Counts
4 → 1252
Calls
4 calls:
532.0ms
(* (* (* (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))))
14.0ms
(/ (* M D) (* 2.0 d))
44.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
166.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

series3.6s

Counts
4 → 12
Calls
4 calls:
1.4s
(* (* (* (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))))
54.0ms
(/ (* 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))

simplify3.5s

Counts
1264 → 1264
Iterations
IterNodes
done5000
01443

prune1.8s

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 6.7b

regimes3.0s

Accuracy

0.4% (7.5b remaining)

Error of 15.9b against oracle of 8.4b and baseline of 15.9b

bsearch993.0ms

Steps
ItersRangePoint
9
5.8772502400840374e-154
1.2282338867542081e-144
1.8643807789334048e-151
9
-44468768.542654045
-1.060772524819629
-89.70047366523089

simplify54.0ms

Iterations
IterNodes
done62
162
045

end0.0ms

sample16.5s

Algorithm
intervals
Results
9.4s38365×body80nan
4.6s12777×body80valid