Details

Time bar (total: 44.3s)

sample631.0ms

Algorithm
intervals
Results
394.0ms1183×body80nan
138.0ms412×body80valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done2006
42006
31271
2198
158
022

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.9b

localize43.0ms

Local error

Found 4 expressions with local error:

13.6b
(sqrt (/ d l))
13.6b
(sqrt (/ d l))
14.8b
(sqrt (/ d h))
14.8b
(sqrt (/ d h))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
52×sqrt-prod
44×add-sqr-sqrt
40×times-frac
32×*-un-lft-identity add-cube-cbrt
8×pow1 rem-sqrt-square
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube pow1/2 sqrt-div add-exp-log insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
4 → 112
Calls
4 calls:
5.0ms
(sqrt (/ d l))
5.0ms
(sqrt (/ d l))
5.0ms
(sqrt (/ d h))
5.0ms
(sqrt (/ d h))

series275.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(sqrt (/ d l))
68.0ms
(sqrt (/ d l))
64.0ms
(sqrt (/ d h))
81.0ms
(sqrt (/ d h))

simplify1.0s

Counts
124 → 124
Iterations
IterNodes
done2003
32003
2660
1255
0143

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 23.2b

localize74.0ms

Local error

Found 4 expressions with local error:

12.2b
(* (* (* (/ M (* 2 d)) D) (* (/ M (* 2 d)) D)) (/ h l))
13.6b
(sqrt (/ d l))
14.8b
(sqrt (/ d h))
14.8b
(sqrt (/ d h))

rewrite372.0ms

Algorithm
rewrite-expression-head
Rules
217×add-cbrt-cube add-exp-log
130×prod-exp cbrt-unprod
49×cbrt-undiv div-exp
44×add-sqr-sqrt
40×times-frac
39×sqrt-prod
32×*-un-lft-identity add-cube-cbrt
25×pow1
13×associate-*r* pow-prod-down associate-*l/
6×rem-sqrt-square
5×frac-times
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×sqrt-pow1 pow1/2 sqrt-div associate-*r/
2×unswap-sqr
1×associate-*l* *-commutative
Counts
4 → 191
Calls
4 calls:
360.0ms
(* (* (* (/ M (* 2 d)) D) (* (/ M (* 2 d)) D)) (/ h l))
2.0ms
(sqrt (/ d l))
2.0ms
(sqrt (/ d h))
2.0ms
(sqrt (/ d h))

series366.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(* (* (* (/ M (* 2 d)) D) (* (/ M (* 2 d)) D)) (/ h l))
79.0ms
(sqrt (/ d l))
81.0ms
(sqrt (/ d h))
80.0ms
(sqrt (/ d h))

simplify1.1s

Counts
203 → 203
Iterations
IterNodes
done2001
22001
1913
0352

prune1.8s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 18.9b

localize98.0ms

Local error

Found 4 expressions with local error:

7.3b
(fma (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (* (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l))) (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
13.6b
(sqrt (/ d l))
14.8b
(sqrt (/ d h))
14.8b
(sqrt (/ d h))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
39×sqrt-prod
34×add-sqr-sqrt
30×times-frac
25×*-un-lft-identity add-cube-cbrt
7×pow1
6×rem-sqrt-square
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2 sqrt-div div-inv
1×fma-udef
Counts
4 → 95
Calls
4 calls:
0.0ms
(fma (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (* (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l))) (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
2.0ms
(sqrt (/ d l))
2.0ms
(sqrt (/ d h))
2.0ms
(sqrt (/ d h))

series2.1s

Counts
4 → 12
Calls
4 calls:
1.8s
(fma (* (sqrt (/ d l)) (sqrt (/ d h))) (* -1/2 (* (* (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l))) (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
87.0ms
(sqrt (/ d l))
80.0ms
(sqrt (/ d h))
65.0ms
(sqrt (/ d h))

simplify1.2s

Counts
107 → 107
Iterations
IterNodes
done2000
32000
21073
1344
0176

prune1.3s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 15.6b

localize124.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (/ M d) (/ D 2))
7.3b
(fma (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* -1/2 (* (* (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l))) (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
14.8b
(sqrt (/ d h))
14.8b
(sqrt (/ d h))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
42×times-frac
32×*-un-lft-identity add-cube-cbrt
26×sqrt-prod
16×add-cbrt-cube add-exp-log
13×associate-*r* associate-*l*
8×pow1
4×expm1-log1p-u cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp unswap-sqr
2×sqrt-pow1 pow1/2 sqrt-div
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative fma-udef
Counts
4 → 120
Calls
4 calls:
27.0ms
(* (/ M d) (/ D 2))
0.0ms
(fma (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* -1/2 (* (* (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l))) (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
5.0ms
(sqrt (/ d h))
5.0ms
(sqrt (/ d h))

series2.6s

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (/ M d) (/ D 2))
2.4s
(fma (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* -1/2 (* (* (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l))) (* (* (/ M d) (/ D 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
81.0ms
(sqrt (/ d h))
62.0ms
(sqrt (/ d h))

simplify1.2s

Counts
132 → 132
Iterations
IterNodes
done2001
22001
1708
0276

prune1.7s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 15.6b

regimes3.0s

Accuracy

0% (2.3b remaining)

Error of 16.6b against oracle of 14.3b and baseline of 16.6b

bsearch0.0ms

simplify16.0ms

Iterations
IterNodes
done51
151
040

end0.0ms

sample22.0s

Algorithm
intervals
Results
14.9s39086×body80nan
4.8s12717×body80valid