Details

Time bar (total: 23.0s)

sample76.0ms

Algorithm
intervals
Results
43.0ms285×body80valid
12.0ms96×body80nan

simplify958.0ms

Counts
1 → 1
Iterations
IterNodes
done2071
42071
3592
295
138
017

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize26.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* M D) (* 2 d))
3.8b
(/ (* M D) (* 2 d))
5.7b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
10.3b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
368×add-cbrt-cube add-exp-log
190×prod-exp cbrt-unprod
114×cbrt-undiv div-exp
16×add-sqr-sqrt
13×associate-*r*
12×*-un-lft-identity times-frac add-cube-cbrt
10×pow1
5×frac-times associate-*l/
4×insert-posit16 add-log-exp
3×pow-prod-down associate-*r/ sqrt-prod div-inv
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l* unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip--
Counts
4 → 198
Calls
4 calls:
13.0ms
(/ (* M D) (* 2 d))
23.0ms
(/ (* M D) (* 2 d))
8.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
169.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

series345.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (* M D) (* 2 d))
34.0ms
(/ (* M D) (* 2 d))
175.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
98.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

simplify1.2s

Counts
210 → 210
Iterations
IterNodes
done2002
22002
1961
0321

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.2b

localize52.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (/ (* M D) 2) d)
3.8b
(/ (/ (* M D) 2) d)
5.1b
(* (* (* (/ (/ (* M D) 2) d) (cbrt h)) (* (/ (/ (* M D) 2) d) (cbrt h))) (/ (cbrt h) l))
5.7b
(sqrt (- 1 (* (* (* (/ (/ (* M D) 2) d) (cbrt h)) (* (/ (/ (* M D) 2) d) (cbrt h))) (/ (cbrt h) l))))

rewrite545.0ms

Algorithm
rewrite-expression-head
Rules
402×add-exp-log
296×add-cbrt-cube
204×prod-exp cbrt-unprod
136×cbrt-undiv div-exp
86×times-frac
56×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
23×pow1
22×associate-*r*
14×associate-/l*
13×pow-prod-down associate-*l/
11×div-inv
10×cbrt-prod
6×associate-/r*
5×frac-times
4×insert-posit16 add-log-exp
3×associate-*r/ sqrt-prod unswap-sqr
2×clear-num frac-2neg sqrt-div associate-/l/
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip--
Counts
4 → 265
Calls
4 calls:
10.0ms
(/ (/ (* M D) 2) d)
14.0ms
(/ (/ (* M D) 2) d)
504.0ms
(* (* (* (/ (/ (* M D) 2) d) (cbrt h)) (* (/ (/ (* M D) 2) d) (cbrt h))) (/ (cbrt h) l))
8.0ms
(sqrt (- 1 (* (* (* (/ (/ (* M D) 2) d) (cbrt h)) (* (/ (/ (* M D) 2) d) (cbrt h))) (/ (cbrt h) l))))

series446.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (/ (* M D) 2) d)
47.0ms
(/ (/ (* M D) 2) d)
132.0ms
(* (* (* (/ (/ (* M D) 2) d) (cbrt h)) (* (/ (/ (* M D) 2) d) (cbrt h))) (/ (cbrt h) l))
223.0ms
(sqrt (- 1 (* (* (* (/ (/ (* M D) 2) d) (cbrt h)) (* (/ (/ (* M D) 2) d) (cbrt h))) (/ (cbrt h) l))))

simplify1.1s

Counts
277 → 277
Iterations
IterNodes
done2013
22013
11194
0417

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.8b

localize43.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (* (* (cbrt h) (* (/ M 2) (/ D d))) (* (cbrt h) (* (/ M 2) (/ D d)))) (* (cbrt l) (cbrt l)))
5.7b
(sqrt (- 1 (* (/ (* (* (cbrt h) (* (/ M 2) (/ D d))) (* (cbrt h) (* (/ M 2) (/ D d)))) (* (cbrt l) (cbrt l))) (/ (cbrt h) (cbrt l)))))
6.3b
(* (/ M 2) (/ D d))
6.3b
(* (/ M 2) (/ D d))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
597×add-exp-log
403×add-cbrt-cube
333×prod-exp cbrt-unprod
178×cbrt-undiv div-exp
58×add-sqr-sqrt
45×times-frac
37×associate-*r/
33×*-un-lft-identity add-cube-cbrt
26×associate-*r* associate-*l*
19×frac-times
15×associate-/l/
13×associate-*l/
9×pow1
8×unswap-sqr
5×div-inv
4×insert-posit16 add-log-exp
3×sqrt-prod
2×sqrt-div pow-prod-down *-commutative
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-- pow1/2 flip-- associate-/l*
Counts
4 → 295
Calls
4 calls:
196.0ms
(/ (* (* (cbrt h) (* (/ M 2) (/ D d))) (* (cbrt h) (* (/ M 2) (/ D d)))) (* (cbrt l) (cbrt l)))
4.0ms
(sqrt (- 1 (* (/ (* (* (cbrt h) (* (/ M 2) (/ D d))) (* (cbrt h) (* (/ M 2) (/ D d)))) (* (cbrt l) (cbrt l))) (/ (cbrt h) (cbrt l)))))
13.0ms
(* (/ M 2) (/ D d))
18.0ms
(* (/ M 2) (/ D d))

series757.0ms

Counts
4 → 12
Calls
4 calls:
274.0ms
(/ (* (* (cbrt h) (* (/ M 2) (/ D d))) (* (cbrt h) (* (/ M 2) (/ D d)))) (* (cbrt l) (cbrt l)))
403.0ms
(sqrt (- 1 (* (/ (* (* (cbrt h) (* (/ M 2) (/ D d))) (* (cbrt h) (* (/ M 2) (/ D d)))) (* (cbrt l) (cbrt l))) (/ (cbrt h) (cbrt l)))))
42.0ms
(* (/ M 2) (/ D d))
37.0ms
(* (/ M 2) (/ D d))

simplify3.2s

Counts
307 → 307
Iterations
IterNodes
done2005
22005
11656
0470

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.8b

localize84.0ms

Local error

Found 4 expressions with local error:

6.4b
(/ M (/ d D))
6.4b
(/ M (/ d D))
6.4b
(/ M (/ d D))
6.4b
(/ M (/ d D))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
300×times-frac
172×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
52×associate-/r*
24×add-cbrt-cube add-exp-log
20×div-inv
12×cbrt-undiv div-exp associate-/l*
4×pow1 clear-num frac-2neg associate-/r/ insert-posit16 add-log-exp
Counts
4 → 284
Calls
4 calls:
9.0ms
(/ M (/ d D))
6.0ms
(/ M (/ d D))
9.0ms
(/ M (/ d D))
9.0ms
(/ M (/ d D))

series106.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ M (/ d D))
25.0ms
(/ M (/ d D))
30.0ms
(/ M (/ d D))
23.0ms
(/ M (/ d D))

simplify1.1s

Counts
296 → 296
Iterations
IterNodes
done2002
32002
21002
1368
0151

prune3.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.8b

regimes1.6s

Accuracy

-3.5% (2.3b remaining)

Error of 9.6b against oracle of 7.3b and baseline of 9.5b

bsearch3.0ms

simplify17.0ms

Iterations
IterNodes
done53
153
040

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.9s9270×body80valid
499.0ms3051×body80nan