Details

Time bar (total: 46.7s)

sample456.0ms

Algorithm
intervals
Results
239.0ms1105×body80nan
90.0ms397×body80valid

simplify799.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
372035
done500035

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize53.0ms

Local error

Found 4 expressions with local error:

5.9b
(/ (* M D) (* 2.0 d))
9.4b
(pow (/ d h) (/ 1.0 2.0))
11.9b
(pow (/ d l) (/ 1.0 2.0))
13.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite112.0ms

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:
10.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(pow (/ d h) (/ 1.0 2.0))
10.0ms
(pow (/ d l) (/ 1.0 2.0))
79.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.2s

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (* M D) (* 2.0 d))
75.0ms
(pow (/ d h) (/ 1.0 2.0))
94.0ms
(pow (/ d l) (/ 1.0 2.0))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify565.0ms

Counts
179 → 179
Iterations

Useful iterations: done (554.0ms)

IterNodesCost
03922931
112502722
done50002416

prune1.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.0b

localize81.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* (* (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))))
5.9b
(/ (* M D) (* 2.0 d))
11.9b
(pow (/ d l) (/ 1.0 2.0))
13.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite542.0ms

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:
389.0ms
(* (* (* (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))))
18.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(pow (/ d l) (/ 1.0 2.0))
84.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.2s

Counts
4 → 12
Calls
4 calls:
998.0ms
(* (* (* (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))))
45.0ms
(/ (* M D) (* 2.0 d))
101.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.0s

Counts
286 → 286
Iterations

Useful iterations: done (985.0ms)

IterNodesCost
057111962
1184511051
done50019388

prune1.7s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.6b

localize184.0ms

Local error

Found 4 expressions with local error:

2.2b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
5.4b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.9b
(/ (* M D) (* 2.0 d))
13.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite994.0ms

Algorithm
rewrite-expression-head
Rules
6965×add-exp-log
5245×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
232×rec-exp 1-exp
55×add-cbrt-cube
37×times-frac
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×cbrt-unprod
22×unpow-prod-down
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-prod cbrt-undiv
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-*r/
2×sub-neg associate-*l* *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 1243
Calls
4 calls:
14.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
644.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.0ms
(/ (* M D) (* 2.0 d))
44.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series3.0s

Counts
4 → 12
Calls
4 calls:
282.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
1.6s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
32.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.2s

Counts
1255 → 1255
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0151884703
done500073181

prune3.0s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 9.8b

localize158.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
5.9b
(/ (* M D) (* 2.0 d))
6.8b
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
7.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
6964×add-exp-log
5245×prod-exp
2612×pow-exp
1626×div-exp
788×pow-to-exp
232×rec-exp 1-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 associate-/r* pow-prod-down associate-*l/ log1p-expm1-u add-log-exp
2×clear-num sub-neg frac-2neg associate-*l* associate-*r/ *-commutative associate-/l*
1×flip3-- flip-- distribute-lft-out-- difference-of-squares associate-/l/
Counts
4 → 1242
Calls
4 calls:
656.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
16.0ms
(/ (* M D) (* 2.0 d))
52.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
49.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

series3.5s

Counts
4 → 12
Calls
4 calls:
1.3s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
43.0ms
(/ (* M D) (* 2.0 d))
1.1s
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

simplify1.1s

Counts
1254 → 1254
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0149391089
done500078562

prune2.4s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 9.0b

regimes2.6s

Accuracy

0% (6.9b remaining)

Error of 15.9b against oracle of 9.0b and baseline of 15.9b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
038203
149203
done49203

end0.0ms

sample17.1s

Algorithm
intervals
Results
10.5s38229×body80nan
3.1s12797×body80valid