Details

Time bar (total: 52.9s)

sample546.0ms

Algorithm
intervals
Results
324.0ms1360×body80nan
109.0ms435×body80valid

simplify2.1s

Counts
1 → 1
Iterations
IterNodes
done5000
3720
2174
154
022

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize79.0ms

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))

rewrite113.0ms

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:
12.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(pow (/ d h) (/ 1.0 2.0))
69.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (* M D) (* 2.0 d))
81.0ms
(pow (/ d h) (/ 1.0 2.0))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
88.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify1.1s

Counts
179 → 179
Iterations
IterNodes
done5001
11251
0392

prune1.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.2b

localize125.0ms

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))

rewrite320.0ms

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:
217.0ms
(* (* (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))))
13.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(pow (/ d h) (/ 1.0 2.0))
64.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.1s

Counts
4 → 12
Calls
4 calls:
999.0ms
(* (* (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))))
52.0ms
(/ (* M D) (* 2.0 d))
101.0ms
(pow (/ d h) (/ 1.0 2.0))
953.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.7s

Counts
286 → 286
Iterations
IterNodes
done5000
11917
0569

prune2.1s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 7.9b

localize282.0ms

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))

rewrite927.0ms

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:
16.0ms
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
496.0ms
(* (* (* (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))
83.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.8s

Counts
4 → 12
Calls
4 calls:
170.0ms
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
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 l))))
36.0ms
(/ (* M D) (* 2.0 d))
1.2s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify3.5s

Counts
1242 → 1242
Iterations
IterNodes
done5000
01446

prune2.4s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 6.7b

localize214.0ms

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) (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
5.0b
(/ (* M D) (* 2.0 d))
8.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))))

rewrite939.0ms

Algorithm
rewrite-expression-head
Rules
6991×add-exp-log
5258×prod-exp
2622×pow-exp
1632×div-exp
790×pow-to-exp
232×rec-exp 1-exp
44×add-cbrt-cube
26×cbrt-unprod
18×add-sqr-sqrt
17×pow1
16×*-un-lft-identity add-cube-cbrt
13×pow-unpow
11×times-frac
10×associate-*l*
8×cbrt-undiv
7×unpow-prod-down
6×pow-pow prod-diff associate-*r/
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u associate-*r* pow-prod-down log1p-expm1-u add-log-exp
3×div-inv unswap-sqr sqr-pow
2×sub-neg *-commutative
1×pow2 frac-times clear-num associate-/r* frac-2neg pow-plus flip3-- associate-*l/ pow-sqr pow-prod-up flip-- associate-/l*
Counts
4 → 1232
Calls
4 calls:
16.0ms
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
555.0ms
(* (* (* (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) (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
18.0ms
(/ (* M D) (* 2.0 d))
98.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))))

series2.5s

Counts
4 → 12
Calls
4 calls:
166.0ms
(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
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) (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
43.0ms
(/ (* M D) (* 2.0 d))
873.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))))

simplify4.0s

Counts
1244 → 1244
Iterations
IterNodes
done5000
01439

prune2.4s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 4.7b

regimes2.8s

Accuracy

0% (4.8b remaining)

Error of 12.1b against oracle of 7.3b and baseline of 12.1b

bsearch0.0ms

simplify20.0ms

Iterations
IterNodes
done48
148
037

end0.0ms

sample16.9s

Algorithm
intervals
Results
10.7s38365×body80nan
3.5s12777×body80valid